What Density Functional Theory could do for Quantum Information

NASA Astrophysics Data System (ADS)

Mattsson, Ann

2015-03-01

The Hohenberg-Kohn theorem of Density Functional Theory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT's utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantum mechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

ODE/IM correspondence and the Argyres-Douglas theory

NASA Astrophysics Data System (ADS)

Ito, Katsushi; Shu, Hongfei

2017-08-01

We study the quantum spectral curve of the Argyres-Douglas theories in the Nekrasov-Sahashvili limit of the Omega-background. Using the ODE/IM correspondence we investigate the quantum integrable model corresponding to the quantum spectral curve. We show that the models for the A 2 N -type theories are non-unitary coset models ( A 1)1 × ( A 1) L /( A 1) L+1 at the fractional level L=2/2N+1-2 , which appear in the study of the 4d/2d correspondence of N = 2 superconformal field theories. Based on the WKB analysis, we clarify the relation between the Y-functions and the quantum periods and study the exact Bohr-Sommerfeld quantization condition for the quantum periods. We also discuss the quantum spectral curves for the D and E type theories.

Density-functional theory simulation of large quantum dots

NASA Astrophysics Data System (ADS)

Jiang, Hong; Baranger, Harold U.; Yang, Weitao

2003-10-01

Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. Here an efficient method for the simulation of quantum dots using density-function theory is developed; it includes the particle-in-the-box representation of the Kohn-Sham orbitals, an efficient conjugate-gradient method to directly minimize the total energy, a Fourier convolution approach for the calculation of the Hartree potential, and a simplified multigrid technique to accelerate the convergence. We test the methodology in a two-dimensional model system and show that numerical studies of large quantum dots with several hundred electrons become computationally affordable. In the noninteracting limit, the classical dynamics of the system we study can be continuously varied from integrable to fully chaotic. The qualitative difference in the noninteracting classical dynamics has an effect on the quantum properties of the interacting system: integrable classical dynamics leads to higher-spin states and a broader distribution of spacing between Coulomb blockade peaks.

Probability and Quantum Paradigms: the Interplay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kracklauer, A. F.

Since the introduction of Born's interpretation of quantum wave functions as yielding the probability density of presence, Quantum Theory and Probability have lived in a troubled symbiosis. Problems arise with this interpretation because quantum probabilities exhibit features alien to usual probabilities, namely non Boolean structure and non positive-definite phase space probability densities. This has inspired research into both elaborate formulations of Probability Theory and alternate interpretations for wave functions. Herein the latter tactic is taken and a suggested variant interpretation of wave functions based on photo detection physics proposed, and some empirical consequences are considered. Although incomplete in a fewmore » details, this variant is appealing in its reliance on well tested concepts and technology.« less

Probability and Quantum Paradigms: the Interplay

NASA Astrophysics Data System (ADS)

Kracklauer, A. F.

2007-12-01

Since the introduction of Born's interpretation of quantum wave functions as yielding the probability density of presence, Quantum Theory and Probability have lived in a troubled symbiosis. Problems arise with this interpretation because quantum probabilities exhibit features alien to usual probabilities, namely non Boolean structure and non positive-definite phase space probability densities. This has inspired research into both elaborate formulations of Probability Theory and alternate interpretations for wave functions. Herein the latter tactic is taken and a suggested variant interpretation of wave functions based on photo detection physics proposed, and some empirical consequences are considered. Although incomplete in a few details, this variant is appealing in its reliance on well tested concepts and technology.

The Future of Theoretical Physics and Cosmology

NASA Astrophysics Data System (ADS)

Gibbons, G. W.; Shellard, E. P. S.; Rankin, S. J.

2009-08-01

Preface; List of contributors; 1. Introduction; Part I. Popular Symposium: 2. Our complex cosmos and its future Martin J. Rees; 3. Theories of everything and Hawking's wave function of the Universe James B. Hartle; 4. The problem of space-time singularities: implications for quantum gravity? Roger Penrose; 5. Warping spacetime Kip Thorne; 6. 60 years in a nutshell Stephen W. Hawking; Part II. Spacetime Singularities: 7. Cosmological perturbations and singularities George F. R. Ellis; 8. The quantum physics of chronology protection Matt Visser; 9. Energy dominance and the Hawking-Ellis vacuum conservation theorem Brandon Carter; 10. On the instability of extra space dimensions Roger Penrose; Part III. Black Holes: 11. Black hole uniqueness and the inner horizon stability problem Werner Israel; 12. Black holes in the real universe and their prospects as probes of relativistic gravity Martin J. Rees; 13. Primordial black holes Bernard Carr; 14. Black hole pair creation Simon F. Ross; 15. Black holes as accelerators Steven Giddings; Part IV. Hawking Radiation: 16. Black holes and string theory Malcolm Perry; 17. M theory and black hole quantum mechanics Joe Polchinski; 18. Playing with black strings Gary Horowitz; 19. Twenty years of debate with Stephen Leonard Susskind; Part V. Quantum Gravity: 20. Euclidean quantum gravity: the view from 2002 Gary Gibbons; 21. Zeta functions, anomalies and stable branes Ian Moss; 22. Some reflections on the status of conventional quantum theory when applied to quantum gravity Chris Isham; 23. Quantum geometry and its ramifications Abhay Ashtekar; 24. Topology change in quantum gravity Fay Dowker; Part VI. M Theory and Beyond: 25. The past and future of string theory Edward Witten; 26. String theory David Gross; 27. A brief description of string theory Michael Green; 28. The story of M Paul Townsend; 29. Gauged supergravity and holographic field theory Nick Warner; 30. 57 varieties in a NUTshell Chris Pope; Part VII. de Sitter Space: 31. Adventures in de Sitter space Raphael Bousso; 32. de Sitter space in non-critical string theory Andrew Strominger; 33. Supergravity, M theory and cosmology Renata Kallosh; Part VIII. Quantum Cosmology: 34. The state of the universe James B. Hartle; 35. Quantum cosmology Don Page; 36. Quantum cosmology and eternal inflation A. Vilenkin; 37. Probability in the deterministic theory known as quantum mechanics Bryce de Witt; 38. The interpretation of quantum cosmology and the problem of time J. Halliwell; 39. What local supersymmetry can do for quantum cosmology Peter D'Eath; Part IX. Cosmology: 40. Inflation and cosmological perturbations Alan Guth; 41. The future of cosmology: observational and computational prospects Paul Shellard; 42. The ekpyrotic universe and its cyclic extension Neil Turok; 43. Inflationary theory versus the ekpyrotic/cyclic scenario Andrei Linde; 44. Brane (new) worlds Pierre Binetruy; 45. Publications of Stephen Hawking; Index.

Dannie Heineman Prize for Mathematical Physics Prize Lecture: Correlation Functions in Integrable Models II: The Role of Quantum Affine Symmetry

NASA Astrophysics Data System (ADS)

Jimbo, Michio

2013-03-01

Since the beginning of 1980s, hidden infinite dimensional symmetries have emerged as the origin of integrability: first in soliton theory and then in conformal field theory. Quest for symmetries in quantum integrable models has led to the discovery of quantum groups. On one hand this opened up rapid mathematical developments in representation theory, combinatorics and other fields. On the other hand it has advanced understanding of correlation functions of lattice models, leading to multiple integral formulas in integrable spin chains. We shall review these developments which continue up to the present time.

Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations

NASA Astrophysics Data System (ADS)

He, Wei

2015-02-01

The Gauge/Bethe correspondence relates Omega-deformed N = 2 supersymmetric gauge theories to some quantum integrable models, in simple cases the integrable models can be treated as solvable quantum mechanics models. For SU(2) gauge theory with an adjoint matter, or with 4 fundamental matters, the potential of corresponding quantum model is the elliptic function. If the mass of matter takes special value then the potential is an elliptic solution of KdV hierarchy. We show that the deformed prepotential of gauge theory can be obtained from the average densities of conserved charges of the classical KdV solution, the UV gauge coupling dependence is assembled into the Eisenstein series. The gauge theory with adjoint mass is taken as the example.

Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory

NASA Astrophysics Data System (ADS)

Maroun, Michael Anthony

This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.

Quantum optical effective-medium theory and transformation quantum optics for metamaterials

NASA Astrophysics Data System (ADS)

Wubs, Martijn; Amooghorban, Ehsan; Zhang, Jingjing; Mortensen, N. Asger

2016-09-01

While typically designed to manipulate classical light, metamaterials have many potential applications for quantum optics as well. We argue why a quantum optical effective-medium theory is needed. We present such a theory for layered metamaterials that is valid for light propagation in all spatial directions, thereby generalizing earlier work for one-dimensional propagation. In contrast to classical effective-medium theory there is an additional effective parameter that describes quantum noise. Our results for metamaterials are based on a rather general Lagrangian theory for the quantum electrodynamics of media with both loss and gain. In the second part of this paper, we present a new application of transformation optics whereby local spontaneous-emission rates of quantum emitters can be designed. This follows from an analysis how electromagnetic Green functions trans- form under coordinate transformations. Spontaneous-emission rates can be either enhanced or suppressed using invisibility cloaks or gradient index lenses. Furthermore, the anisotropic material profile of the cloak enables the directional control of spontaneous emission.

Advanced capabilities for materials modelling with Quantum ESPRESSO

NASA Astrophysics Data System (ADS)

Giannozzi, P.; Andreussi, O.; Brumme, T.; Bunau, O.; Buongiorno Nardelli, M.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Cococcioni, M.; Colonna, N.; Carnimeo, I.; Dal Corso, A.; de Gironcoli, S.; Delugas, P.; DiStasio, R. A., Jr.; Ferretti, A.; Floris, A.; Fratesi, G.; Fugallo, G.; Gebauer, R.; Gerstmann, U.; Giustino, F.; Gorni, T.; Jia, J.; Kawamura, M.; Ko, H.-Y.; Kokalj, A.; Küçükbenli, E.; Lazzeri, M.; Marsili, M.; Marzari, N.; Mauri, F.; Nguyen, N. L.; Nguyen, H.-V.; Otero-de-la-Roza, A.; Paulatto, L.; Poncé, S.; Rocca, D.; Sabatini, R.; Santra, B.; Schlipf, M.; Seitsonen, A. P.; Smogunov, A.; Timrov, I.; Thonhauser, T.; Umari, P.; Vast, N.; Wu, X.; Baroni, S.

2017-11-01

Quantum EXPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches. Quantum EXPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.

Advanced capabilities for materials modelling with Quantum ESPRESSO.

PubMed

Giannozzi, P; Andreussi, O; Brumme, T; Bunau, O; Buongiorno Nardelli, M; Calandra, M; Car, R; Cavazzoni, C; Ceresoli, D; Cococcioni, M; Colonna, N; Carnimeo, I; Dal Corso, A; de Gironcoli, S; Delugas, P; DiStasio, R A; Ferretti, A; Floris, A; Fratesi, G; Fugallo, G; Gebauer, R; Gerstmann, U; Giustino, F; Gorni, T; Jia, J; Kawamura, M; Ko, H-Y; Kokalj, A; Küçükbenli, E; Lazzeri, M; Marsili, M; Marzari, N; Mauri, F; Nguyen, N L; Nguyen, H-V; Otero-de-la-Roza, A; Paulatto, L; Poncé, S; Rocca, D; Sabatini, R; Santra, B; Schlipf, M; Seitsonen, A P; Smogunov, A; Timrov, I; Thonhauser, T; Umari, P; Vast, N; Wu, X; Baroni, S

2017-10-24

Quantum EXPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches. Quantum EXPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.

Advanced capabilities for materials modelling with Quantum ESPRESSO.

PubMed

Andreussi, Oliviero; Brumme, Thomas; Bunau, Oana; Buongiorno Nardelli, Marco; Calandra, Matteo; Car, Roberto; Cavazzoni, Carlo; Ceresoli, Davide; Cococcioni, Matteo; Colonna, Nicola; Carnimeo, Ivan; Dal Corso, Andrea; de Gironcoli, Stefano; Delugas, Pietro; DiStasio, Robert; Ferretti, Andrea; Floris, Andrea; Fratesi, Guido; Fugallo, Giorgia; Gebauer, Ralph; Gerstmann, Uwe; Giustino, Feliciano; Gorni, Tommaso; Jia, Junteng; Kawamura, Mitsuaki; Ko, Hsin-Yu; Kokalj, Anton; Küçükbenli, Emine; Lazzeri, Michele; Marsili, Margherita; Marzari, Nicola; Mauri, Francesco; Nguyen, Ngoc Linh; Nguyen, Huy-Viet; Otero-de-la-Roza, Alberto; Paulatto, Lorenzo; Poncé, Samuel; Giannozzi, Paolo; Rocca, Dario; Sabatini, Riccardo; Santra, Biswajit; Schlipf, Martin; Seitsonen, Ari Paavo; Smogunov, Alexander; Timrov, Iurii; Thonhauser, Timo; Umari, Paolo; Vast, Nathalie; Wu, Xifan; Baroni, Stefano

2017-09-27

Quantum ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudo-potential and projector-augmented-wave approaches. Quantum ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement theirs ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software. © 2017 IOP Publishing Ltd.

Tales from the prehistory of Quantum Gravity. Léon Rosenfeld's earliest contributions

NASA Astrophysics Data System (ADS)

Peruzzi, Giulio; Rocci, Alessio

2018-05-01

The main purpose of this paper is to analyse the earliest work of Léon Rosenfeld, one of the pioneers in the search of Quantum Gravity, the supposed theory unifying quantum theory and general relativity. We describe how and why Rosenfeld tried to face this problem in 1927, analysing the role of his mentors: Oskar Klein, Louis de Broglie and Théophile De Donder. Rosenfeld asked himself how quantum mechanics should concretely modify general relativity. In the context of a five-dimensional theory, Rosenfeld tried to construct a unifying framework for the gravitational and electromagnetic interaction and wave mechanics. Using a sort of "general relativistic quantum mechanics" Rosenfeld introduced a wave equation on a curved background. He investigated the metric created by what he called `quantum phenomena', represented by wave functions. Rosenfeld integrated Einstein equations in the weak field limit, with wave functions as source of the gravitational field. The author performed a sort of semi-classical approximation obtaining at the first order the Reissner-Nordström metric. We analyse how Rosenfeld's work is part of the history of Quantum Mechanics, because in his investigation Rosenfeld was guided by Bohr's correspondence principle. Finally we briefly discuss how his contribution is connected with the task of finding out which metric can be generated by a quantum field, a problem that quantum field theory on curved backgrounds will start to address 35 years later.

Tales from the prehistory of Quantum Gravity - Léon Rosenfeld's earliest contributions

NASA Astrophysics Data System (ADS)

Peruzzi, Giulio; Rocci, Alessio

2018-04-01

The main purpose of this paper is to analyse the earliest work of Léon Rosenfeld, one of the pioneers in the search of Quantum Gravity, the supposed theory unifying quantum theory and general relativity. We describe how and why Rosenfeld tried to face this problem in 1927, analysing the role of his mentors: Oskar Klein, Louis de Broglie and Théophile De Donder. Rosenfeld asked himself how quantum mechanics should concretely modify general relativity. In the context of a five-dimensional theory, Rosenfeld tried to construct a unifying framework for the gravitational and electromagnetic interaction and wave mechanics. Using a sort of "general relativistic quantum mechanics" Rosenfeld introduced a wave equation on a curved background. He investigated the metric created by what he called `quantum phenomena', represented by wave functions. Rosenfeld integrated Einstein equations in the weak field limit, with wave functions as source of the gravitational field. The author performed a sort of semi-classical approximation obtaining at the first order the Reissner-Nordström metric. We analyse how Rosenfeld's work is part of the history of Quantum Mechanics, because in his investigation Rosenfeld was guided by Bohr's correspondence principle. Finally we briefly discuss how his contribution is connected with the task of finding out which metric can be generated by a quantum field, a problem that quantum field theory on curved backgrounds will start to address 35 years later.

Quantum mechanics over sets

NASA Astrophysics Data System (ADS)

Ellerman, David

2014-03-01

In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantum mechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.

Thermal quantum time-correlation functions from classical-like dynamics

NASA Astrophysics Data System (ADS)

Hele, Timothy J. H.

2017-07-01

Thermal quantum time-correlation functions are of fundamental importance in quantum dynamics, allowing experimentally measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact quantum statistics and approximate quantum dynamics modelled with classical-like trajectories. Here, we review recent progress in the field with the development of methods including centroid molecular dynamics , ring polymer molecular dynamics (RPMD) and thermostatted RPMD (TRPMD). We show how these methods have recently been obtained from 'Matsubara dynamics', a form of semiclassical dynamics which conserves the quantum Boltzmann distribution. We also apply the Matsubara formalism to reaction rate theory, rederiving t → 0+ quantum transition-state theory (QTST) and showing that Matsubara-TST, like RPMD-TST, is equivalent to QTST. We end by surveying areas for future progress.

Here and now: the intersection of computational science, quantum-mechanical simulations, and materials science

NASA Astrophysics Data System (ADS)

Marzari, Nicola

The last 30 years have seen the steady and exhilarating development of powerful quantum-simulation engines for extended systems, dedicated to the solution of the Kohn-Sham equations of density-functional theory, often augmented by density-functional perturbation theory, many-body perturbation theory, time-dependent density-functional theory, dynamical mean-field theory, and quantum Monte Carlo. Their implementation on massively parallel architectures, now leveraging also GPUs and accelerators, has started a massive effort in the prediction from first principles of many or of complex materials properties, leading the way to the exascale through the combination of HPC (high-performance computing) and HTC (high-throughput computing). Challenges and opportunities abound: complementing hardware and software investments and design; developing the materials' informatics infrastructure needed to encode knowledge into complex protocols and workflows of calculations; managing and curating data; resisting the complacency that we have already reached the predictive accuracy needed for materials design, or a robust level of verification of the different quantum engines. In this talk I will provide an overview of these challenges, with the ultimate prize being the computational understanding, prediction, and design of properties and performance for novel or complex materials and devices.

Performance of the density matrix functional theory in the quantum theory of atoms in molecules.

PubMed

García-Revilla, Marco; Francisco, E; Costales, A; Martín Pendás, A

2012-02-02

The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.

Can quantum transition state theory be defined as an exact t = 0+ limit?

NASA Astrophysics Data System (ADS)

Jang, Seogjoo; Voth, Gregory A.

2016-02-01

The definition of the classical transition state theory (TST) as a t → 0+ limit of the flux-side time correlation function relies on the assumption that simultaneous measurement of population and flux is a well defined physical process. However, the noncommutativity of the two measurements in quantum mechanics makes the extension of such a concept to the quantum regime impossible. For this reason, quantum TST (QTST) has been generally accepted as any kind of quantum rate theory reproducing the TST in the classical limit, and there has been a broad consensus that no unique QTST retaining all the properties of TST can be defined. Contrary to this widely held view, Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)] recently suggested that a true QTST can be defined as the exact t → 0+ limit of a certain kind of quantum flux-side time correlation function and that it is equivalent to the ring polymer molecular dynamics (RPMD) TST. This work seeks to question and clarify certain assumptions underlying these suggestions and their implications. First, the time correlation function used by HA as a starting expression is not related to the kinetic rate constant by virtue of linear response theory, which is the first important step in relating a t = 0+ limit to a physically measurable rate. Second, a theoretical analysis calls into question a key step in HA's proof which appears not to rely on an exact quantum mechanical identity. The correction of this makes the true t = 0+ limit of HA's QTST different from the RPMD-TST rate expression, but rather equal to the well-known path integral quantum transition state theory rate expression for the case of centroid dividing surface. An alternative quantum rate expression is then formulated starting from the linear response theory and by applying a recently developed formalism of real time dynamics of imaginary time path integrals [S. Jang, A. V. Sinitskiy, and G. A. Voth, J. Chem. Phys. 140, 154103 (2014)]. It is shown that the t → 0+ limit of the new rate expression vanishes in the exact quantum limit.

Quantum and classical behavior in interacting bosonic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hertzberg, Mark P.

It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories, especially on time scales longer than the dynamical relaxation time. Recently there have been claims that the quantum theory deviates spectacularly from the classical theory on this time scale, even if the occupancy numbers are extremely large. Furthermore, it is claimed that the quantum theory quickly thermalizes while the classical theory does not. The evidence for these claims comes from noticing a spectacular differencemore » in the time evolution of expectation values of quantum operators compared to the classical micro-state evolution. If true, this would have dramatic consequences for many important phenomena, including laboratory studies of interacting BECs, dark matter axions, preheating after inflation, etc. In this work we critically examine these claims. We show that in fact the classical theory can describe the quantum behavior in the high occupancy regime, even when interactions are large. The connection is that the expectation values of quantum operators in a single quantum micro-state are approximated by a corresponding classical ensemble average over many classical micro-states. Furthermore, by the ergodic theorem, a classical ensemble average of local fields with statistical translation invariance is the spatial average of a single micro-state. So the correlation functions of the quantum and classical field theories of a single micro-state approximately agree at high occupancy, even in interacting systems. Furthermore, both quantum and classical field theories can thermalize, when appropriate coarse graining is introduced, with the classical case requiring a cutoff on low occupancy UV modes. We discuss applications of our results.« less

Continuous Time in Consistent Histories

NASA Astrophysics Data System (ADS)

Savvidou, Konstantina

1999-12-01

We discuss the case of histories labelled by a continuous time parameter in the History Projection Operator consistent-histories quantum theory. We describe how the appropriate representation of the history algebra may be chosen by requiring the existence of projection operators that represent propositions about time averages of the energy. We define the action operator for the consistent histories formalism, as the quantum analogue of the classical action functional, for the simple harmonic oscillator case. We show that the action operator is the generator of two types of time transformations that may be related to the two laws of time-evolution of the standard quantum theory: the `state-vector reduction' and the unitary time-evolution. We construct the corresponding classical histories and demonstrate the relevance with the quantum histories; we demonstrate how the requirement of the temporal logic structure of the theory is sufficient for the definition of classical histories. Furthermore, we show the relation of the action operator to the decoherence functional which describes the dynamics of the system. Finally, the discussion is extended to give a preliminary account of quantum field theory in this approach to the consistent histories formalism.

Generalized uncertainty principles and quantum field theory

NASA Astrophysics Data System (ADS)

Husain, Viqar; Kothawala, Dawood; Seahra, Sanjeev S.

2013-01-01

Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator [x^,p^]=if(p^). We apply this deformed quantization to free scalar field theory for f±=1±βp2. The resulting quantum field theories have a rich fine scale structure. For small wavelength modes, the Green’s function for f+ exhibits a remarkable transition from Lorentz to Galilean invariance, whereas for f- such modes effectively do not propagate. For both cases Lorentz invariance is recovered at long wavelengths.

RSV-free formulation of quantum mondemolition theory

NASA Astrophysics Data System (ADS)

Lynch, Robert

1982-10-01

The entire validity of the “quantum nondemolition” (QND) concept has been called into question because of its deep reliance on “reduction of the state vector” (RSV) in the detailed development of the theory. In this letter QND theory is reformulated without use of RSV, except as found in the overall interpretation of the wave function.

Quantum power functional theory for many-body dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmidt, Matthias, E-mail: Matthias.Schmidt@uni-bayreuth.de

2015-11-07

We construct a one-body variational theory for the time evolution of nonrelativistic quantum many-body systems. The position- and time-dependent one-body density, particle current, and time derivative of the current act as three variational fields. The generating (power rate) functional is minimized by the true current time derivative. The corresponding Euler-Lagrange equation, together with the continuity equation for the density, forms a closed set of one-body equations of motion. Space- and time-nonlocal one-body forces are generated by the superadiabatic contribution to the functional. The theory applies to many-electron systems.

Origin of chaos near three-dimensional quantum vortices: A general Bohmian theory

NASA Astrophysics Data System (ADS)

Tzemos, Athanasios C.; Efthymiopoulos, Christos; Contopoulos, George

2018-04-01

We provide a general theory for the structure of the quantum flow near three-dimensional (3D) nodal lines, i.e., one-dimensional loci where the 3D wave function becomes equal to zero. In suitably defined coordinates (comoving with the nodal line) the generic structure of the flow implies the formation of 3D quantum vortices. We show that such vortices are accompanied by nearby invariant lines of the comoving quantum flow, called X lines, which are normally hyperbolic. Furthermore, the stable and unstable manifolds of the X lines produce chaotic scatterings of nearby quantum (Bohmian) trajectories, thus inducing an intricate form of the quantum current in the neighborhood of each 3D quantum vortex. Generic formulas describing the structure around 3D quantum vortices are provided, applicable to an arbitrary choice of 3D wave function. We also give specific numerical examples as well as a discussion of the physical consequences of chaos near 3D quantum vortices.

Origin of chaos near three-dimensional quantum vortices: A general Bohmian theory.

PubMed

Tzemos, Athanasios C; Efthymiopoulos, Christos; Contopoulos, George

2018-04-01

We provide a general theory for the structure of the quantum flow near three-dimensional (3D) nodal lines, i.e., one-dimensional loci where the 3D wave function becomes equal to zero. In suitably defined coordinates (comoving with the nodal line) the generic structure of the flow implies the formation of 3D quantum vortices. We show that such vortices are accompanied by nearby invariant lines of the comoving quantum flow, called X lines, which are normally hyperbolic. Furthermore, the stable and unstable manifolds of the X lines produce chaotic scatterings of nearby quantum (Bohmian) trajectories, thus inducing an intricate form of the quantum current in the neighborhood of each 3D quantum vortex. Generic formulas describing the structure around 3D quantum vortices are provided, applicable to an arbitrary choice of 3D wave function. We also give specific numerical examples as well as a discussion of the physical consequences of chaos near 3D quantum vortices.

A Safari Through Density Functional Theory

NASA Astrophysics Data System (ADS)

Dreizler, Reiner M.; Lüdde, Cora S.

Density functional theory is widely used to treat quantum many body problems in many areas of physics and related fields. A brief survey of this method covering foundations, functionals and applications is presented here.

A quantum Rosetta Stone for the information paradox

NASA Astrophysics Data System (ADS)

Pando Zayas, Leopoldo A.

2014-11-01

The black hole information loss paradox epitomizes the contradictions between general relativity and quantum field theory. The AdS/conformal field theory (CFT) correspondence provides an implicit answer for the information loss paradox in black hole physics by equating a gravity theory with an explicitly unitary field theory. Gravitational collapse in asymptotically AdS spacetimes is generically turbulent. Given that the mechanism to read out the information about correlations functions in the field theory side is plagued by deterministic classical chaos, we argue that quantum chaos might provide the true Rosetta Stone for answering the information paradox in the context of the AdS/CFT correspondence.

ADHM and the 4d quantum Hall effect

NASA Astrophysics Data System (ADS)

Barns-Graham, Alec; Dorey, Nick; Lohitsiri, Nakarin; Tong, David; Turner, Carl

2018-04-01

Yang-Mills instantons are solitonic particles in d = 4 + 1 dimensional gauge theories. We construct and analyse the quantum Hall states that arise when these particles are restricted to the lowest Landau level. We describe the ground state wavefunctions for both Abelian and non-Abelian quantum Hall states. Although our model is purely bosonic, we show that the excitations of this 4d quantum Hall state are governed by the Nekrasov partition function of a certain five dimensional supersymmetric gauge theory with Chern-Simons term. The partition function can also be interpreted as a variant of the Hilbert series of the instanton moduli space, counting holomorphic sections rather than holomorphic functions. It is known that the Hilbert series of the instanton moduli space can be rewritten using mirror symmetry of 3d gauge theories in terms of Coulomb branch variables. We generalise this approach to include the effect of a five dimensional Chern-Simons term. We demonstrate that the resulting Coulomb branch formula coincides with the corresponding Higgs branch Molien integral which, in turn, reproduces the standard formula for the Nekrasov partition function.

Power loss of a single electron charge distribution confined in a quantum plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mehramiz, A.; Department of Physics, Faculty of Science, I. K. Int'l University, Qazvin 34149-16818; Mahmoodi, J.

2011-05-15

The dielectric tensor for a quantum plasma is derived by using a linearized quantum hydrodynamic theory. The wave functions for a nanostructure bound system have been investigated. Finally, the power loss for an oscillating charge distribution of a mixed state will be calculated, using the dielectric function formalism.

Functional renormalization group analysis of tensorial group field theories on Rd

NASA Astrophysics Data System (ADS)

Geloun, Joseph Ben; Martini, Riccardo; Oriti, Daniele

2016-07-01

Rank-d tensorial group field theories are quantum field theories (QFTs) defined on a group manifold G×d , which represent a nonlocal generalization of standard QFT and a candidate formalism for quantum gravity, since, when endowed with appropriate data, they can be interpreted as defining a field theoretic description of the fundamental building blocks of quantum spacetime. Their renormalization analysis is crucial both for establishing their consistency as quantum field theories and for studying the emergence of continuum spacetime and geometry from them. In this paper, we study the renormalization group flow of two simple classes of tensorial group field theories (TGFTs), defined for the group G =R for arbitrary rank, both without and with gauge invariance conditions, by means of functional renormalization group techniques. The issue of IR divergences is tackled by the definition of a proper thermodynamic limit for TGFTs. We map the phase diagram of such models, in a simple truncation, and identify both UV and IR fixed points of the RG flow. Encouragingly, for all the models we study, we find evidence for the existence of a phase transition of condensation type.

Disciplines, models, and computers: the path to computational quantum chemistry.

PubMed

Lenhard, Johannes

2014-12-01

Many disciplines and scientific fields have undergone a computational turn in the past several decades. This paper analyzes this sort of turn by investigating the case of computational quantum chemistry. The main claim is that the transformation from quantum to computational quantum chemistry involved changes in three dimensions. First, on the side of instrumentation, small computers and a networked infrastructure took over the lead from centralized mainframe architecture. Second, a new conception of computational modeling became feasible and assumed a crucial role. And third, the field of computa- tional quantum chemistry became organized in a market-like fashion and this market is much bigger than the number of quantum theory experts. These claims will be substantiated by an investigation of the so-called density functional theory (DFT), the arguably pivotal theory in the turn to computational quantum chemistry around 1990.

A Systematic Approach for Computing Zero-Point Energy, Quantum Partition Function, and Tunneling Effect Based on Kleinert's Variational Perturbation Theory.

PubMed

Wong, Kin-Yiu; Gao, Jiali

2008-09-09

In this paper, we describe an automated integration-free path-integral (AIF-PI) method, based on Kleinert's variational perturbation (KP) theory, to treat internuclear quantum-statistical effects in molecular systems. We have developed an analytical method to obtain the centroid potential as a function of the variational parameter in the KP theory, which avoids numerical difficulties in path-integral Monte Carlo or molecular dynamics simulations, especially at the limit of zero-temperature. Consequently, the variational calculations using the KP theory can be efficiently carried out beyond the first order, i.e., the Giachetti-Tognetti-Feynman-Kleinert variational approach, for realistic chemical applications. By making use of the approximation of independent instantaneous normal modes (INM), the AIF-PI method can readily be applied to many-body systems. Previously, we have shown that in the INM approximation, the AIF-PI method is accurate for computing the quantum partition function of a water molecule (3 degrees of freedom) and the quantum correction factor for the collinear H(3) reaction rate (2 degrees of freedom). In this work, the accuracy and properties of the KP theory are further investigated by using the first three order perturbations on an asymmetric double-well potential, the bond vibrations of H(2), HF, and HCl represented by the Morse potential, and a proton-transfer barrier modeled by the Eckart potential. The zero-point energy, quantum partition function, and tunneling factor for these systems have been determined and are found to be in excellent agreement with the exact quantum results. Using our new analytical results at the zero-temperature limit, we show that the minimum value of the computed centroid potential in the KP theory is in excellent agreement with the ground state energy (zero-point energy) and the position of the centroid potential minimum is the expectation value of particle position in wave mechanics. The fast convergent property of the KP theory is further examined in comparison with results from the traditional Rayleigh-Ritz variational approach and Rayleigh-Schrödinger perturbation theory in wave mechanics. The present method can be used for thermodynamic and quantum dynamic calculations, including to systematically determine the exact value of zero-point energy and to study kinetic isotope effects for chemical reactions in solution and in enzymes.

Localization in quantum field theory

NASA Astrophysics Data System (ADS)

Balachandran, A. P.

In non-relativistic quantum mechanics, Born’s principle of localization is as follows: For a single particle, if a wave function ψK vanishes outside a spatial region K, it is said to be localized in K. In particular, if a spatial region K‧ is disjoint from K, a wave function ψK‧ localized in K‧ is orthogonal to ψK. Such a principle of localization does not exist compatibly with relativity and causality in quantum field theory (QFT) (Newton and Wigner) or interacting point particles (Currie, Jordan and Sudarshan). It is replaced by symplectic localization of observables as shown by Brunetti, Guido and Longo, Schroer and others. This localization gives a simple derivation of the spin-statistics theorem and the Unruh effect, and shows how to construct quantum fields for anyons and for massless particles with “continuous” spin. This review outlines the basic principles underlying symplectic localization and shows or mentions its deep implications. In particular, it has the potential to affect relativistic quantum information theory and black hole physics.

Measurements and mathematical formalism of quantum mechanics

NASA Astrophysics Data System (ADS)

Slavnov, D. A.

2007-03-01

A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantum mechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.

Path Integrals for Electronic Densities, Reactivity Indices, and Localization Functions in Quantum Systems

PubMed Central

Putz, Mihai V.

2009-01-01

The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems. PMID:20087467

Path integrals for electronic densities, reactivity indices, and localization functions in quantum systems.

PubMed

Putz, Mihai V

2009-11-10

The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.

Quantum Effects on the Capacitance of Graphene-Based Electrodes

DOE PAGES

Zhan, Cheng; Neal, Justin; Wu, Jianzhong; ...

2015-09-08

We recently measured quantum capacitance for electric double layers (EDL) at electrolyte/graphene interfaces. However, the importance of quantum capacitance in realistic carbon electrodes is not clear. Toward understanding that from a theoretical perspective, here we studied the quantum capacitance and total capacitance of graphene electrodes as a function of the number of graphene layers. The quantum capacitance was obtained from electronic density functional theory based on fixed band approximation with an implicit solvation model, while the EDL capacitances were from classical density functional theory. We found that quantum capacitance plays a dominant role in total capacitance of the single-layer graphenemore » both in aqueous and ionic-liquid electrolytes but the contribution decreases as the number of graphene layers increases. Moreover, the total integral capacitance roughly levels off and is dominated by the EDL capacitance beyond about four graphene layers. Finally, because many porous carbons have nanopores with stacked graphene layers at the surface, this research provides a good estimate of the effect of quantum capacitance on their electrochemical performance.« less

Chemical accuracy from quantum Monte Carlo for the benzene dimer.

PubMed

Azadi, Sam; Cohen, R E

2015-09-14

We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is -2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.

Quantum properties of supersymmetric theories regularized by higher covariant derivatives

NASA Astrophysics Data System (ADS)

Stepanyantz, Konstantin

2018-02-01

We investigate quantum corrections in \\mathscr{N} = 1 non-Abelian supersymmetric gauge theories, regularized by higher covariant derivatives. In particular, by the help of the Slavnov-Taylor identities we prove that the vertices with two ghost legs and one leg of the quantum gauge superfield are finite in all orders. This non-renormalization theorem is confirmed by an explicit one-loop calculation. By the help of this theorem we rewrite the exact NSVZ β-function in the form of the relation between the β-function and the anomalous dimensions of the matter superfields, of the quantum gauge superfield, and of the Faddeev-Popov ghosts. Such a relation has simple qualitative interpretation and allows suggesting a prescription producing the NSVZ scheme in all loops for the theories regularized by higher derivatives. This prescription is verified by the explicit three-loop calculation for the terms quartic in the Yukawa couplings.

Quantum corrections to the generalized Proca theory via a matter field

NASA Astrophysics Data System (ADS)

Amado, André; Haghani, Zahra; Mohammadi, Azadeh; Shahidi, Shahab

2017-09-01

We study the quantum corrections to the generalized Proca theory via matter loops. We consider two types of interactions, linear and nonlinear in the vector field. Calculating the one-loop correction to the vector field propagator, three- and four-point functions, we show that the non-linear interactions are harmless, although they renormalize the theory. The linear matter-vector field interactions introduce ghost degrees of freedom to the generalized Proca theory. Treating the theory as an effective theory, we calculate the energy scale up to which the theory remains healthy.

Quantum Theory of Orbital Magnetization and Its Generalization to Interacting Systems

NASA Astrophysics Data System (ADS)

Shi, Junren; Vignale, G.; Xiao, Di; Niu, Qian

2007-11-01

Based on standard perturbation theory, we present a full quantum derivation of the formula for the orbital magnetization in periodic systems. The derivation is generally valid for insulators with or without a Chern number, for metals at zero or finite temperatures, and at weak as well as strong magnetic fields. The formula is shown to be valid in the presence of electron-electron interaction, provided the one-electron energies and wave functions are calculated self-consistently within the framework of the exact current and spin-density functional theory.

Nonadiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density-Functional Theory

NASA Astrophysics Data System (ADS)

Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole

2018-04-01

We simulate the dynamics of a single-electron source, modeled as a quantum dot with on-site Coulomb interaction and tunnel coupling to an adjacent lead in time-dependent density-functional theory. Based on this system, we develop a time-nonlocal exchange-correlation potential by exploiting analogies with quantum-transport theory. The time nonlocality manifests itself in a dynamical potential step. We explicitly link the time evolution of the dynamical step to physical relaxation timescales of the electron dynamics. Finally, we discuss prospects for simulations of larger mesoscopic systems.

Nonadiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density-Functional Theory.

PubMed

Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole

2018-04-13

We simulate the dynamics of a single-electron source, modeled as a quantum dot with on-site Coulomb interaction and tunnel coupling to an adjacent lead in time-dependent density-functional theory. Based on this system, we develop a time-nonlocal exchange-correlation potential by exploiting analogies with quantum-transport theory. The time nonlocality manifests itself in a dynamical potential step. We explicitly link the time evolution of the dynamical step to physical relaxation timescales of the electron dynamics. Finally, we discuss prospects for simulations of larger mesoscopic systems.

Quantum spectral curve of the N=6 supersymmetric Chern-Simons theory.

PubMed

Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto

2014-07-11

Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N=6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.

Theory of melting at high pressures: Amending density functional theory with quantum Monte Carlo

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shulenburger, L.; Desjarlais, M. P.; Mattsson, T. R.

We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing Density Functional Theory (DFT) and quantum Monte Carlo (QMC) treatments of the system. The method is applied to address the longstanding discrepancy between density functional theory (DFT) calculations and diamond anvil cell (DAC) experiments on the melting curve of xenon, a noble gas solid where van der Waals binding is challenging for traditional DFT methods. The calculations show excellent agreement with data below 20 GPa and that the high-pressure melt curve is well described by a Lindemann behavior up to at least 80 GPa, amore » finding in stark contrast to DAC data.« less

Theory of melting at high pressures: Amending density functional theory with quantum Monte Carlo

DOE PAGES

Shulenburger, L.; Desjarlais, M. P.; Mattsson, T. R.

2014-10-01

We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing Density Functional Theory (DFT) and quantum Monte Carlo (QMC) treatments of the system. The method is applied to address the longstanding discrepancy between density functional theory (DFT) calculations and diamond anvil cell (DAC) experiments on the melting curve of xenon, a noble gas solid where van der Waals binding is challenging for traditional DFT methods. The calculations show excellent agreement with data below 20 GPa and that the high-pressure melt curve is well described by a Lindemann behavior up to at least 80 GPa, amore » finding in stark contrast to DAC data.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azadi, Sam, E-mail: s.azadi@ucl.ac.uk; Cohen, R. E.

We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimalmore » VMC and DMC binding energies of −2.3(4) and −2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is −2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.« less

On Replacing "Quantum Thinking" with Counterfactual Reasoning

NASA Astrophysics Data System (ADS)

Narens, Louis

The probability theory used in quantum mechanics is currently being employed by psychologists to model the impact of context on decision. Its event space consists of closed subspaces of a Hilbert space, and its probability function sometimes violate the law of the finite additivity of probabilities. Results from the quantum mechanics literature indicate that such a "Hilbert space probability theory" cannot be extended in a useful way to standard, finitely additive, probability theory by the addition of new events with specific probabilities. This chapter presents a new kind of probability theory that shares many fundamental algebraic characteristics with Hilbert space probability theory but does extend to standard probability theory by adjoining new events with specific probabilities. The new probability theory arises from considerations about how psychological experiments are related through counterfactual reasoning.

A new way of visualising quantum fields

NASA Astrophysics Data System (ADS)

Linde, Helmut

2018-05-01

Quantum field theory (QFT) is the basis of some of the most fundamental theories in modern physics, but it is not an easy subject to learn. In the present article we intend to pave the way from quantum mechanics to QFT for students at early graduate or advanced undergraduate level. More specifically, we propose a new way of visualising the wave function Ψ of a linear chain of interacting quantum harmonic oscillators, which can be seen as a model for a simple one-dimensional bosonic quantum field. The main idea is to draw randomly chosen classical states of the chain superimposed upon each other and use a grey scale to represent the value of Ψ at the corresponding coordinates of the quantised system. Our goal is to establish a better intuitive understanding of the mathematical objects underlying quantum field theories and solid state physics.

Completeness of the Coulomb Wave Functions in Quantum Mechanics

ERIC Educational Resources Information Center

Mukunda, N.

1978-01-01

Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)

Old Wine in New Bottles: Quantum Theory in Historical Perspective.

ERIC Educational Resources Information Center

Bent, Henry A.

1984-01-01

Discusses similarities between chemistry and three central concepts of quantum physics: (1) stationary states; (2) wave functions; and (3) complementarity. Based on these and other similarities, it is indicated that quantum physics is a chemical physics. (JN)

Stochastic Gravity: Theory and Applications.

PubMed

Hu, Bei Lok; Verdaguer, Enric

2004-01-01

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operatorvalued) stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole (enclosed in a box). We derive a fluctuation-dissipation relation between the fluctuations in the radiation and the dissipative dynamics of metric fluctuations.

Plasmonic resonances of nanoparticles from large-scale quantum mechanical simulations

NASA Astrophysics Data System (ADS)

Zhang, Xu; Xiang, Hongping; Zhang, Mingliang; Lu, Gang

2017-09-01

Plasmonic resonance of metallic nanoparticles results from coherent motion of its conduction electrons, driven by incident light. For the nanoparticles less than 10 nm in diameter, localized surface plasmonic resonances become sensitive to the quantum nature of the conduction electrons. Unfortunately, quantum mechanical simulations based on time-dependent Kohn-Sham density functional theory are computationally too expensive to tackle metal particles larger than 2 nm. Herein, we introduce the recently developed time-dependent orbital-free density functional theory (TD-OFDFT) approach which enables large-scale quantum mechanical simulations of plasmonic responses of metallic nanostructures. Using TD-OFDFT, we have performed quantum mechanical simulations to understand size-dependent plasmonic response of Na nanoparticles and plasmonic responses in Na nanoparticle dimers and trimers. An outlook of future development of the TD-OFDFT method is also presented.

Density Functional Theory Calculations of the Quantum Capacitance of Graphene Oxide as a Supercapacitor Electrode.

PubMed

Song, Ce; Wang, Jinyan; Meng, Zhaoliang; Hu, Fangyuan; Jian, Xigao

2018-03-31

Graphene oxide has become an attractive electrode-material candidate for supercapacitors thanks to its higher specific capacitance compared to graphene. The quantum capacitance makes relative contributions to the specific capacitance, which is considered as the major limitation of graphene electrodes, while the quantum capacitance of graphene oxide is rarely concerned. This study explores the quantum capacitance of graphene oxide, which bears epoxy and hydroxyl groups on its basal plane, by employing density functional theory (DFT) calculations. The results demonstrate that the total density of states near the Fermi level is significantly enhanced by introducing oxygen-containing groups, which is beneficial for the improvement of the quantum capacitance. Moreover, the quantum capacitances of the graphene oxide with different concentrations of these two oxygen-containing groups are compared, revealing that more epoxy and hydroxyl groups result in a higher quantum capacitance. Notably, the hydroxyl concentration has a considerable effect on the capacitive behavior. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Space and time in the quantum universe.

NASA Astrophysics Data System (ADS)

Smolin, L.

This paper is devoted to the problem of constructing a quantum theory that could describe a closed system - a quantum cosmology. The author argues that this problem is an aspect of a much older problem - that of how to eliminate from the physical theories "ideal elements", which are elements of the mathematical structure whose interpretation requires the existence of things outside the dynamical system described by the theory. This discussion is aimed at uncovering criteria that a theory of quantum cosmology must satisfy, if it is to give physically sensible predictions. The author proposes three such criteria and shows that conventional quantum cosmology can only satisfy them, if there is an intrinsic time coordinate on the phase space of the theory. It is shown that approaches based on correlations in the wave function, that do not use an inner product, cannot satisfy these criteria. As example, the author discusses the problem of quantizing a class of relational dynamical models invented by Barbour and Bertotti. The dynamical structure of these theories is closely analogous to general relativity, and the problem of their measurement theory is also similar. It is concluded that these theories can only be sensibly quantized if they contain an intrinsic time.

Connection between optimal control theory and adiabatic-passage techniques in quantum systems

NASA Astrophysics Data System (ADS)

Assémat, E.; Sugny, D.

2012-08-01

This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from Pontryagin's maximum principle. In a three-level quantum system, we show that the stimulated Raman adiabatic passage technique can be associated to a peculiar Hamiltonian singularity. One deduces that the adiabatic pulse is solution of the optimal control problem only for a specific cost functional. This analysis is extended to the case of a four-level quantum system.

Multicomponent Density Functional Theory: Impact of Nuclear Quantum Effects on Proton Affinities and Geometries.

PubMed

Brorsen, Kurt R; Yang, Yang; Hammes-Schiffer, Sharon

2017-08-03

Nuclear quantum effects such as zero point energy play a critical role in computational chemistry and often are included as energetic corrections following geometry optimizations. The nuclear-electronic orbital (NEO) multicomponent density functional theory (DFT) method treats select nuclei, typically protons, quantum mechanically on the same level as the electrons. Electron-proton correlation is highly significant, and inadequate treatments lead to highly overlocalized nuclear densities. A recently developed electron-proton correlation functional, epc17, has been shown to provide accurate nuclear densities for molecular systems. Herein, the NEO-DFT/epc17 method is used to compute the proton affinities for a set of molecules and to examine the role of nuclear quantum effects on the equilibrium geometry of FHF - . The agreement of the computed results with experimental and benchmark values demonstrates the promise of this approach for including nuclear quantum effects in calculations of proton affinities, pK a 's, optimized geometries, and reaction paths.

Sum rules for zeros and intersections of Bessel functions from quantum mechanical perturbation theory

NASA Astrophysics Data System (ADS)

Pedersen, Thomas Garm

2018-07-01

Bessel functions play an important role for quantum states in spherical and cylindrical geometries. In cases of perfect confinement, the energy of Schrödinger and massless Dirac fermions is determined by the zeros and intersections of Bessel functions, respectively. In an external electric field, standard perturbation theory therefore expresses the polarizability as a sum over these zeros or intersections. Both non-relativistic and relativistic polarizabilities can be calculated analytically, however. Hence, by equating analytical expressions to perturbation expansions, several sum rules for the zeros and intersections of Bessel functions emerge.

Multipoint Green's functions in 1 + 1 dimensional integrable quantum field theories

DOE PAGES

Babujian, H. M.; Karowski, M.; Tsvelik, A. M.

2017-02-14

We calculate the multipoint Green functions in 1+1 dimensional integrable quantum field theories. We use the crossing formula for general models and calculate the 3 and 4 point functions taking in to account only the lower nontrivial intermediate states contributions. Then we apply the general results to the examples of the scaling Z 2 Ising model, sinh-Gordon model and Z 3 scaling Potts model. We demonstrate this calculations explicitly. The results can be applied to physical phenomena as for example to the Raman scattering.

Expanding the Bethe/Gauge dictionary

NASA Astrophysics Data System (ADS)

Bullimore, Mathew; Kim, Hee-Cheol; Lukowski, Tomasz

2017-11-01

We expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d N = (2, 2) supersymmetric gauge theories to include aspects of the algebraic Bethe ansatz. We construct the wave functions of off-shell Bethe states as orbifold defects in the A-twisted supersymmetric gauge theory and study their correlation functions. We also present an alternative description of off-shell Bethe states as boundary conditions in an effective N = 4 supersymmetric quantum mechanics. Finally, we interpret spin chain R-matrices as correlation functions of Janus interfaces for mass parameters in the supersymmetric quantum mechanics.

Asymptotic behavior of Nambu-Bethe-Salpeter wave functions for multiparticles in quantum field theories

NASA Astrophysics Data System (ADS)

Aoki, Sinya; Ishii, Noriyoshi; Doi, Takumi; Ikeda, Yoichi; Inoue, Takashi

2013-07-01

We derive asymptotic behaviors of the Nambu-Bethe-Salpeter (NBS) wave function at large space separations for systems with more than two particles in quantum field theories. To deal with n particles in the center-of-mass frame coherently, we introduce the Jacobi coordinates of n particles and then combine their 3(n-1) coordinates into the one spherical coordinate in D=3(n-1) dimensions. We parametrize the on-shell T matrix for n scalar particles at low energy using the unitarity constraint of the S matrix. We then express asymptotic behaviors of the NBS wave function for n particles at low energy in terms of parameters of the T matrix and show that the NBS wave function carries information of the T matrix such as phase shifts and mixing angles of the n-particle system in its own asymptotic behavior, so that the NBS wave function can be considered as the scattering wave of n particles in quantum mechanics. This property is one of the essential ingredients of the HAL QCD scheme to define “potential” from the NBS wave function in quantum field theories such as QCD. Our results, together with an extension to systems with spin 1/2 particles, justify the HAL QCD’s definition of potentials for three or more nucleons (or baryons) in terms of the NBS wave functions.

Quantum critical dynamics for a prototype class of insulating antiferromagnets

NASA Astrophysics Data System (ADS)

Wu, Jianda; Yang, Wang; Wu, Congjun; Si, Qimiao

2018-06-01

Quantum criticality is a fundamental organizing principle for studying strongly correlated systems. Nevertheless, understanding quantum critical dynamics at nonzero temperatures is a major challenge of condensed-matter physics due to the intricate interplay between quantum and thermal fluctuations. The recent experiments with the quantum spin dimer material TlCuCl3 provide an unprecedented opportunity to test the theories of quantum criticality. We investigate the nonzero-temperature quantum critical spin dynamics by employing an effective O (N ) field theory. The on-shell mass and the damping rate of quantum critical spin excitations as functions of temperature are calculated based on the renormalized coupling strength and are in excellent agreement with experiment observations. Their T lnT dependence is predicted to be dominant at very low temperatures, which will be tested in future experiments. Our work provides confidence that quantum criticality as a theoretical framework, which is being considered in so many different contexts of condensed-matter physics and beyond, is indeed grounded in materials and experiments accurately. It is also expected to motivate further experimental investigations on the applicability of the field theory to related quantum critical systems.

Aspects of perturbation theory in quantum mechanics: The BenderWuMATHEMATICA® package

NASA Astrophysics Data System (ADS)

Sulejmanpasic, Tin; Ünsal, Mithat

2018-07-01

We discuss a general setup which allows the study of the perturbation theory of an arbitrary, locally harmonic 1D quantum mechanical potential as well as its multi-variable (many-body) generalization. The latter may form a prototype for regularized quantum field theory. We first generalize the method of Bender-Wu,and derive exact recursion relations which allow the determination of the perturbative wave-function and energy corrections to an arbitrary order, at least in principle. For 1D systems, we implement these equations in an easy to use MATHEMATICA® package we call BenderWu. Our package enables quick home-computer computation of high orders of perturbation theory (about 100 orders in 10-30 s, and 250 orders in 1-2 h) and enables practical study of a large class of problems in Quantum Mechanics. We have two hopes concerning the BenderWu package. One is that due to resurgence, large amount of non-perturbative information, such as non-perturbative energies and wave-functions (e.g. WKB wave functions), can in principle be extracted from the perturbative data. We also hope that the package may be used as a teaching tool, providing an effective bridge between perturbation theory and non-perturbative physics in textbooks. Finally, we show that for the multi-variable case, the recursion relation acquires a geometric character, and has a structure which allows parallelization to computer clusters.

Maass Forms and Quantum Modular Forms

NASA Astrophysics Data System (ADS)

Rolen, Larry

This thesis describes several new results in the theory of harmonic Maass forms and related objects. Maass forms have recently led to a flood of applications throughout number theory and combinatorics in recent years, especially following their development by the work of Bruinier and Funke the modern understanding Ramanujan's mock theta functions due to Zwegers. The first of three main theorems discussed in this thesis concerns the integrality properties of singular moduli. These are well-known to be algebraic integers, and they play a beautiful role in complex multiplication and explicit class field theory for imaginary quadratic fields. One can also study "singular moduli" for special non-holomorphic functions, which are algebraic but are not necessarily algebraic integers. Here we will explain the phenomenon of integrality properties and provide a sharp bound on denominators of symmetric functions in singular moduli. The second main theme of the thesis concerns Zagier's recent definition of a quantum modular form. Since their definition in 2010 by Zagier, quantum modular forms have been connected to numerous different topics such as strongly unimodal sequences, ranks, cranks, and asymptotics for mock theta functions. Motivated by Zagier's example of the quantum modularity of Kontsevich's "strange" function F(q), we revisit work of Andrews, Jimenez-Urroz, and Ono to construct a natural vector-valued quantum modular form whose components. The final chapter of this thesis is devoted to a study of asymptotics of mock theta functions near roots of unity. In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function, and he offered some alleged examples. The theory of mock theta functions has been brought to fruition using the framework of harmonic Maass forms, thanks to Zwegers. Despite this understanding, little attention has been given to Ramanujan's original definition. Here we prove that Ramanujan's examples do indeed satisfy his original definition.

The Strange (Hi)story of Particles and Waves

NASA Astrophysics Data System (ADS)

Zeh, H. Dieter

2016-03-01

This is an attempt of a non-technical but conceptually consistent presentation of quantum theory in a historical context. While the first part is written for a general readership, Section 5 may appear a bit provocative to some quantum physicists. I argue that the single-particle wave functions of quantum mechanics have to be correctly interpreted as field modes that are "occupied once" (i.e. first excited states of the corresponding quantum oscillators in the case of boson fields). Multiple excitations lead to apparent many-particle wave functions, while the quantum states proper are defined by wave function(al)s on the "configuration" space of fundamental fields, or on another, as yet elusive, fundamental local basis.

Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory.

PubMed

Marsalek, Ondrej; Markland, Thomas E

2016-02-07

Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost.

Symmetric polynomials in information theory: Entropy and subentropy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jozsa, Richard; Mitchison, Graeme

2015-06-15

Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the probabilities and reveal a series of remarkable properties. Derivatives of all orders are shown to satisfy a complete monotonicity property. H and Q themselves become multivariate Bernstein functions and we derive the density functions of their Levy-Khintchine representations. We also show that H and Q are Pick functions in each symmetric polynomial variable separately. Furthermore, we see that H and the intrinsically quantum informational quantitymore » Q become surprisingly closely related in functional form, suggesting a special significance for the symmetric polynomials in quantum information theory. Using the symmetric polynomials, we also derive a series of further properties of H and Q.« less

Physics of lateral triple quantum-dot molecules with controlled electron numbers.

PubMed

Hsieh, Chang-Yu; Shim, Yun-Pil; Korkusinski, Marek; Hawrylak, Pawel

2012-11-01

We review the recent progress in theory and experiments with lateral triple quantum dots with controlled electron numbers down to one electron in each dot. The theory covers electronic and spin properties as a function of topology, number of electrons, gate voltage and external magnetic field. The orbital Hund's rules and Nagaoka ferromagnetism, magnetic frustration and chirality, interplay of quantum interference and electron-electron interactions and geometrical phases are described and related to charging and transport spectroscopy. Fabrication techniques and recent experiments are covered, as well as potential applications of triple quantum-dot molecule in coherent control, spin manipulation and quantum computation.

Introduction to Classical Density Functional Theory by a Computational Experiment

ERIC Educational Resources Information Center

Jeanmairet, Guillaume; Levy, Nicolas; Levesque, Maximilien; Borgis, Daniel

2014-01-01

We propose an in silico experiment to introduce the classical density functional theory (cDFT). Density functional theories, whether quantum or classical, rely on abstract concepts that are nonintuitive; however, they are at the heart of powerful tools and active fields of research in both physics and chemistry. They led to the 1998 Nobel Prize in…

TRIQS: A toolbox for research on interacting quantum systems

NASA Astrophysics Data System (ADS)

Parcollet, Olivier; Ferrero, Michel; Ayral, Thomas; Hafermann, Hartmut; Krivenko, Igor; Messio, Laura; Seth, Priyanka

2015-11-01

We present the TRIQS library, a Toolbox for Research on Interacting Quantum Systems. It is an open-source, computational physics library providing a framework for the quick development of applications in the field of many-body quantum physics, and in particular, strongly-correlated electronic systems. It supplies components to develop codes in a modern, concise and efficient way: e.g. Green's function containers, a generic Monte Carlo class, and simple interfaces to HDF5. TRIQS is a C++/Python library that can be used from either language. It is distributed under the GNU General Public License (GPLv3). State-of-the-art applications based on the library, such as modern quantum many-body solvers and interfaces between density-functional-theory codes and dynamical mean-field theory (DMFT) codes are distributed along with it.

Quantum statistical mechanics of dense partially ionized hydrogen.

NASA Technical Reports Server (NTRS)

Dewitt, H. E.; Rogers, F. J.

1972-01-01

The theory of dense hydrogenic plasmas beginning with the two component quantum grand partition function is reviewed. It is shown that ionization equilibrium and molecular dissociation equilibrium can be treated in the same manner with proper consideration of all two-body states. A quantum perturbation expansion is used to give an accurate calculation of the equation of state of the gas for any degree of dissociation and ionization. In this theory, the effective interaction between any two charges is the dynamic screened potential obtained from the plasma dielectric function. We make the static approximation; and we carry out detailed numerical calculations with the bound and scattering states of the Debye potential, using the Beth-Uhlenbeck form of the quantum second virial coefficient. We compare our results with calculations from the Saha equation.

Quantum Stress: Density Functional Theory Formulation and Physical Manifestation

NASA Astrophysics Data System (ADS)

Hu, Hao; Liu, Feng

2012-02-01

The concept of ``quantum stress (QS)'' is introduced and formulated within density functional theory (DFT), to underlie extrinsic electronic effects on the stress state of solids and thin films in the absence of lattice strain. An explicit expression of QS (σ^Q) is derived in relation to the deformation potential of electronic states (ξ) and the variation of electron density (δn), σ^Q=ξ(δn), as a quantum analog of classical Hook's law. Two distinct QS manifestations are demonstrated quantitatively by DFT calculations: (1) in the form of bulk stress induced by charge carriers; and (2) in the form of surface stress induced by quantum confinement. QS has broad implications in physical phenomena and technological applications that are based on coupling of electronic structure with lattice strain.

Infinities in Quantum Field Theory and in Classical Computing: Renormalization Program

NASA Astrophysics Data System (ADS)

Manin, Yuri I.

Introduction. The main observable quantities in Quantum Field Theory, correlation functions, are expressed by the celebrated Feynman path integrals. A mathematical definition of them involving a measure and actual integration is still lacking. Instead, it is replaced by a series of ad hoc but highly efficient and suggestive heuristic formulas such as perturbation formalism. The latter interprets such an integral as a formal series of finite-dimensional but divergent integrals, indexed by Feynman graphs, the list of which is determined by the Lagrangian of the theory. Renormalization is a prescription that allows one to systematically "subtract infinities" from these divergent terms producing an asymptotic series for quantum correlation functions. On the other hand, graphs treated as "flowcharts", also form a combinatorial skeleton of the abstract computation theory. Partial recursive functions that according to Church's thesis exhaust the universe of (semi)computable maps are generally not everywhere defined due to potentially infinite searches and loops. In this paper I argue that such infinities can be addressed in the same way as Feynman divergences. More details can be found in [9,10].

False vacuum decay in quantum mechanics and four dimensional scalar field theory

NASA Astrophysics Data System (ADS)

Bezuglov, Maxim

2018-04-01

When the Higgs boson was discovered in 2012 it was realized that electroweak vacuum may suffer a possible metastability on the Planck scale and can eventually decay. To understand this problem it is important to have reliable predictions for the vacuum decay rate within the framework of quantum field theory. For now, it can only be done at one loop level, which is apparently is not enough. The aim of this work is to develop a technique for the calculation of two and higher order radiative corrections to the false vacuum decay rate in the framework of four dimensional scalar quantum field theory and then apply it to the case of the Standard Model. To achieve this goal, we first start from the case of d=1 dimensional QFT i.e. quantum mechanics. We show that for some potentials two and three loop corrections can be very important and must be taken into account. Next, we use quantum mechanical example as a template for the general d=4 dimensional theory. In it we are concentrating on the calculations of bounce solution and corresponding Green function in so called thin wall approximation. The obtained Green function is then used as a main ingredient for the calculation of two loop radiative corrections to the false vacuum decay rate.

Quantum entanglement of identical particles by standard information-theoretic notions

PubMed Central

Lo Franco, Rosario; Compagno, Giuseppe

2016-01-01

Quantum entanglement of identical particles is essential in quantum information theory. Yet, its correct determination remains an open issue hindering the general understanding and exploitation of many-particle systems. Operator-based methods have been developed that attempt to overcome the issue. Here we introduce a state-based method which, as second quantization, does not label identical particles and presents conceptual and technical advances compared to the previous ones. It establishes the quantitative role played by arbitrary wave function overlaps, local measurements and particle nature (bosons or fermions) in assessing entanglement by notions commonly used in quantum information theory for distinguishable particles, like partial trace. Our approach furthermore shows that bringing identical particles into the same spatial location functions as an entangling gate, providing fundamental theoretical support to recent experimental observations with ultracold atoms. These results pave the way to set and interpret experiments for utilizing quantum correlations in realistic scenarios where overlap of particles can count, as in Bose-Einstein condensates, quantum dots and biological molecular aggregates. PMID:26857475

Spectral functions of strongly correlated extended systems via an exact quantum embedding

NASA Astrophysics Data System (ADS)

Booth, George H.; Chan, Garnet Kin-Lic

2015-04-01

Density matrix embedding theory (DMET) [Phys. Rev. Lett. 109, 186404 (2012), 10.1103/PhysRevLett.109.186404], introduced an approach to quantum cluster embedding methods whereby the mapping of strongly correlated bulk problems to an impurity with finite set of bath states was rigorously formulated to exactly reproduce the entanglement of the ground state. The formalism provided similar physics to dynamical mean-field theory at a tiny fraction of the cost but was inherently limited by the construction of a bath designed to reproduce ground-state, static properties. Here, we generalize the concept of quantum embedding to dynamic properties and demonstrate accurate bulk spectral functions at similarly small computational cost. The proposed spectral DMET utilizes the Schmidt decomposition of a response vector, mapping the bulk dynamic correlation functions to that of a quantum impurity cluster coupled to a set of frequency-dependent bath states. The resultant spectral functions are obtained on the real-frequency axis, without bath discretization error, and allows for the construction of arbitrary dynamic correlation functions. We demonstrate the method on the one- (1D) and two-dimensional (2D) Hubbard model, where we obtain zero temperature and thermodynamic limit spectral functions, and show the trivial extension to two-particle Green's functions. This advance therefore extends the scope and applicability of DMET in condensed-matter problems as a computationally tractable route to correlated spectral functions of extended systems and provides a competitive alternative to dynamical mean-field theory for dynamic quantities.

Some thoughts about consciousness: from a quantum mechanics perspective.

PubMed

Gargiulo, Gerald J

2013-08-01

The article explores some of the basic findings of quantum physics and information theory and their possible usefulness in offering new vistas for understanding psychoanalysis and the patient-analyst interchange. Technical terms are explained and placed in context, and examples of applying quantum models to clinical experience are offered. Given the complexity of the findings of quantum mechanics and information theory, the article aims only to introduce some of the major concepts from these disciplines. Within this framework the article also briefly addresses the question of mind as well as the problematic of reducing the experience of consciousness to neurological brain functioning.

Polarization momentum transfer collision: Faxen-Holtzmark theory and quantum dynamic shielding.

PubMed

Ki, Dae-Han; Jung, Young-Dae

2013-04-21

The influence of the quantum dynamic shielding on the polarization momentum transport collision is investigated by using the Faxen-Holtzmark theory in strongly coupled Coulomb systems. The electron-atom polarization momentum transport cross section is derived as a function of the collision energy, de Broglie wavelength, Debye length, thermal energy, and atomic quantum states. It is found that the dynamic shielding enhances the scattering phase shift as well as the polarization momentum transport cross section. The variation of quantum effect on the momentum transport collision due to the change of thermal energy and de Broglie wavelength is also discussed.

Dannie Heineman Prize for Mathematical Physics: Applying mathematical techniques to solve important problems in quantum theory

NASA Astrophysics Data System (ADS)

Bender, Carl

2017-01-01

The theory of complex variables is extremely useful because it helps to explain the mathematical behavior of functions of a real variable. Complex variable theory also provides insight into the nature of physical theories. For example, it provides a simple and beautiful picture of quantization and it explains the underlying reason for the divergence of perturbation theory. By using complex-variable methods one can generalize conventional Hermitian quantum theories into the complex domain. The result is a new class of parity-time-symmetric (PT-symmetric) theories whose remarkable physical properties have been studied and verified in many recent laboratory experiments.

Nonperturbative light-front Hamiltonian methods

NASA Astrophysics Data System (ADS)

Hiller, J. R.

2016-09-01

We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, ϕ4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

Potential Functions and the Characterization of Economics-Based Information

NASA Astrophysics Data System (ADS)

Haven, Emmanuel

2015-10-01

The formulation of quantum mechanics as a diffusion process by Nelson (Phys Rev 150:1079-1085, 1966) provides for an interesting approach on how we may transit from classical mechanics into quantum mechanics. Besides the presence of the real potential function, another type of potential function (often denoted as `quantum potential') forms an intrinsic part of this theory. In this paper we attempt to show how both types of potential functions can have a use in a resolutely macroscopic context like financial asset pricing. We are particularly interested in uncovering how the `quantum potential' can add to the economics-based relevant information which is already supplied by the real potential function.

Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems

NASA Technical Reports Server (NTRS)

Isar, Aurelian

1995-01-01

The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.

Zirconia and its allotropes; A Quantum Monte Carlo study

NASA Astrophysics Data System (ADS)

Jokisaari, Andrea; Benali, Anouar; Shin, Hyeondeok; Luo, Ye; Lopez Bezanilla, Alejandro; Ratcliff, Laura; Littlewood, Peter; Heinonen, Olle

With a high strength and stability at elevated temperatures, Zirconia (zirconium dioxide) is one of the best corrosion-resistant and refractive materials used in metallurgy, and is used in structural ceramics, catalytic converters, oxygen sensors, nuclear industry, and in chemically passivating surfaces. The wide range of applications of ZrO2 has motivated a large number of electronic structures studies of its known allotropes (monoclinic, tetragonal and cubic). Density Functional Theory has been successful at reproducing some of the fundamental properties of some of the allotropes, but these results remain dependent on the specific combination of exchange-correlation functional and type of pseudopotentials, making any type of structural prediction or defect analysis uncertain. Quantum Monte Carlo (QMC) is a many-body quantum theory solving explicitly the electronic correlations, allowing reproducing and predicting materials properties with a limited number of controlled approximations. In this study, we use QMC to revisit the energetic stability of Zirconia's allotropes and compare our results with those obtained from density functional theory.

Multicomponent Time-Dependent Density Functional Theory: Proton and Electron Excitation Energies.

PubMed

Yang, Yang; Culpitt, Tanner; Hammes-Schiffer, Sharon

2018-04-05

The quantum mechanical treatment of both electrons and protons in the calculation of excited state properties is critical for describing nonadiabatic processes such as photoinduced proton-coupled electron transfer. Multicomponent density functional theory enables the consistent quantum mechanical treatment of more than one type of particle and has been implemented previously for studying ground state molecular properties within the nuclear-electronic orbital (NEO) framework, where all electrons and specified protons are treated quantum mechanically. To enable the study of excited state molecular properties, herein the linear response multicomponent time-dependent density functional theory (TDDFT) is derived and implemented within the NEO framework. Initial applications to FHF - and HCN illustrate that NEO-TDDFT provides accurate proton and electron excitation energies within a single calculation. As its computational cost is similar to that of conventional electronic TDDFT, the NEO-TDDFT approach is promising for diverse applications, particularly nonadiabatic proton transfer reactions, which may exhibit mixed electron-proton vibronic excitations.

Serenity: A subsystem quantum chemistry program.

PubMed

Unsleber, Jan P; Dresselhaus, Thomas; Klahr, Kevin; Schnieders, David; Böckers, Michael; Barton, Dennis; Neugebauer, Johannes

2018-05-15

We present the new quantum chemistry program Serenity. It implements a wide variety of functionalities with a focus on subsystem methodology. The modular code structure in combination with publicly available external tools and particular design concepts ensures extensibility and robustness with a focus on the needs of a subsystem program. Several important features of the program are exemplified with sample calculations with subsystem density-functional theory, potential reconstruction techniques, a projection-based embedding approach and combinations thereof with geometry optimization, semi-numerical frequency calculations and linear-response time-dependent density-functional theory. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

Framing anomaly in the effective theory of the fractional quantum Hall effect.

PubMed

Gromov, Andrey; Cho, Gil Young; You, Yizhi; Abanov, Alexander G; Fradkin, Eduardo

2015-01-09

We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.

Quantum dissipation theory and applications to quantum transport and quantum measurement in mesoscopic systems

NASA Astrophysics Data System (ADS)

Cui, Ping

The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO) systems, and its closely related solvation mode transformation of system-bath coupling Hamiltonian in general. The exact QDT of DBO systems is also used to clarify the validity of conventional QDT formulations that involve Markovian approximation. In Chapter 3, we develop three nonequivalent but all complete second-order QDT (CS-QDT) formulations. Two of them are of the conventional prescriptions in terms of time-local dissipation and memory kernel, respectively. The third one is called the correlated driving-dissipation equations of motion (CODDE). This novel CS-QDT combines the merits of the former two for its advantages in both the application and numerical implementation aspects. Also highlighted is the importance of correlated driving-dissipation effects on the dynamics of the reduced system. In Chapter 4, we construct an exact QDT formalism via the calculus on path integrals. The new theory aims at the efficient evaluation of non-Markovian dissipation beyond the weak system-bath interaction regime in the presence of time-dependent external field. By adopting exponential-like expansions for bath correlation function, hierarchical equations of motion formalism and continued fraction Liouville-space Green's function formalism are established. The latter will soon be used together with the Dyson equation technique for an efficient evaluation of non-perturbative reduced density matrix dynamics. The interplay between system-bath interaction strength, non-Markovian property, and the required level of hierarchy is also studied with the aid of simple spin-boson systems, together with the three proposed schemes to truncate the infinite hierarchy. In Chapter 5, we develop a nonperturbative theory of electron transfer (ET) in Debye solvents. The resulting exact and analytical rate expression is constructed on the basis of the aforementioned continued fraction Liouville-space Green's function formalism, together with the Dyson equation technique. Not only does it recover the celebrated Marcus' inversion and Kramers' turnover behaviors, the new theory also shows some distinct quantum solvation effects that can alter the ET mechanism. Moreover, the present theory predicts further for the ET reaction thermodynamics, such as equilibrium Gibbs free-energy and entropy, some interesting solvent-dependent features that are calling for experimental verification. In Chapter 6, we discuss the constructed QDTs, in terms of their unified mathematical structure that supports a linear dynamics space, and thus facilitates their applications to various physical problems. The involving details are exemplified with the CODDE form of QDT. As the linear space is concerned, we identify the Schrodinger versus Heisenberg picture and the forward versus backward propagation of the reduced, dissipative Liouville dynamics. For applications we discuss the reduced linear response theory and the optimal control problems, in which the correlated effects of non-Markovian dissipation and field driving are shown to be important. In Chapter 7, we turn to quantum transport, i.e., electric current through molecular or mesoscopic systems under finite applied voltage. By viewing the nonequilibrium transport setup as a quantum open system, we develop a reduced-density-matrix approach to quantum transport. The resulting current is explicitly expressed in terms of the molecular reduced density matrix by tracing out the degrees of freedom of the electrodes at finite bias and temperature. We propose a conditional quantum master equation theory, which is an extension of the conventional (or unconditional) QDT by tracing out the well-defined bath subsets individually, instead of the entire bath degrees of freedom. Both the current and the noise spectrum can be conveniently analyzed in terms of the conditional reduced density matrix dynamics. By far, the QDT (including the conditional one) has only been exploited in second-order form. A self-consistent Born approximation for the system-electrode coupling is further proposed to recover all existing nonlinear current-voltage behaviors including the nonequilibrium Kondo effect. Transport theory based on the exact QDT formalism will be developed in future. In Chapter 8, we study the quantum measurement of a qubit with a quantum-point-contact detector. On the basis of a unified quantum master equation (a form of QDT), we study the measurement-induced relaxation and dephasing of the qubit. Our treatment pays particular attention on the detailed-balance relation, which is a consequence of properly accounting for the energy exchange between the qubit and detector during the measurement process. We also derive a conditional quantum master equation for quantum measurement in general, and study the readout characteristics of the qubit measurement. Our theory is applicable to the quantum measurement at arbitrary voltage and temperature. A number of remarkable new features are found and highlighted in concern with their possible relevance to future experiments. In Chapter 9, we discuss the further development of QDT, aiming at an efficient evaluation of many-electron systems. This will be carried out by reducing the many-particle (Fermion or Boson) QDT to a single-particle one by exploring, e.g. the Wick's contraction theorem. It also results in a time-dependent density functional theory (TDDFT) for transport through complex large-scale (e.g. molecules) systems. Primary results of the TDDFT-QDT are reported. In Chapter 10, we summary the thesis, and comment and remark on the future work on both the theoretical and application aspects of QDT.

Time-Dependent Density Functional Theory for Open Systems and Its Applications.

PubMed

Chen, Shuguang; Kwok, YanHo; Chen, GuanHua

2018-02-20

Photovoltaic devices, electrochemical cells, catalysis processes, light emitting diodes, scanning tunneling microscopes, molecular electronics, and related devices have one thing in common: open quantum systems where energy and matter are not conserved. Traditionally quantum chemistry is confined to isolated and closed systems, while quantum dissipation theory studies open quantum systems. The key quantity in quantum dissipation theory is the reduced system density matrix. As the reduced system density matrix is an O(M! × M!) matrix, where M is the number of the particles of the system of interest, quantum dissipation theory can only be employed to simulate systems of a few particles or degrees of freedom. It is thus important to combine quantum chemistry and quantum dissipation theory so that realistic open quantum systems can be simulated from first-principles. We have developed a first-principles method to simulate the dynamics of open electronic systems, the time-dependent density functional theory for open systems (TDDFT-OS). Instead of the reduced system density matrix, the key quantity is the reduced single-electron density matrix, which is an N × N matrix where N is the number of the atomic bases of the system of interest. As the dimension of the key quantity is drastically reduced, the TDDFT-OS can thus be used to simulate the dynamics of realistic open electronic systems and efficient numerical algorithms have been developed. As an application, we apply the method to study how quantum interference develops in a molecular transistor in time domain. We include electron-phonon interaction in our simulation and show that quantum interference in the given system is robust against nuclear vibration not only in the steady state but also in the transient dynamics. As another application, by combining TDDFT-OS with Ehrenfest dynamics, we study current-induced dissociation of water molecules under scanning tunneling microscopy and follow its time dependent dynamics. Given the rapid development in ultrafast experiments with atomic resolution in recent years, time dependent simulation of open electronic systems will be useful to gain insight and understanding of such experiments. This Account will mainly focus on the practical aspects of the TDDFT-OS method, describing the numerical implementation and demonstrating the method with applications.

Entanglement entropy between real and virtual particles in ϕ4 quantum field theory

NASA Astrophysics Data System (ADS)

Ardenghi, Juan Sebastián

2015-04-01

The aim of this work is to compute the entanglement entropy of real and virtual particles by rewriting the generating functional of ϕ4 theory as a mean value between states and observables defined through the correlation functions. Then the von Neumann definition of entropy can be applied to these quantum states and in particular, for the partial traces taken over the internal or external degrees of freedom. This procedure can be done for each order in the perturbation expansion showing that the entanglement entropy for real and virtual particles behaves as ln (m0). In particular, entanglement entropy is computed at first order for the correlation function of two external points showing that mutual information is identical to the external entropy and that conditional entropies are negative for all the domain of m0. In turn, from the definition of the quantum states, it is possible to obtain general relations between total traces between different quantum states of a ϕr theory. Finally, discussion about the possibility of taking partial traces over external degrees of freedom is considered, which implies the introduction of some observables that measure space-time points where an interaction occurs.

Ab initio quantum chemistry: methodology and applications.

PubMed

Friesner, Richard A

2005-05-10

This Perspective provides an overview of state-of-the-art ab initio quantum chemical methodology and applications. The methods that are discussed include coupled cluster theory, localized second-order Moller-Plesset perturbation theory, multireference perturbation approaches, and density functional theory. The accuracy of each approach for key chemical properties is summarized, and the computational performance is analyzed, emphasizing significant advances in algorithms and implementation over the past decade. Incorporation of a condensed-phase environment by means of mixed quantum mechanical/molecular mechanics or self-consistent reaction field techniques, is presented. A wide range of illustrative applications, focusing on materials science and biology, are discussed briefly.

Reality, Contextuality, and Probability in Quantum Theory and Beyond

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

This chapter explores the relationships among reality, contextuality, and probability, especially in quantum theory and, brie y and by extension, in other fields where these concepts, in their quantum-like versions, may play key roles. The chapter contends, following Derrida's argument, that while no meaning or event could be determined apart from its context, no context ultimately permits saturation, that is, could ever be determined with certainty. Any such determination is ultimately provisional. However, because of its mathematical-experimental character, physics allows one, in classical physics and relativity, to disregard the role of the context of observation in describing the physical systems considered, and in quantum mechanics, where the context of observation cannot be so disregarded, to determine such a context sufficiently. While, however, classical physics or relativity and quantum mechanics can do so sufficiently for their disciplinary functioning and practice, they cannot do so entirely. Moreover, a given concept of this functioning, especially as concerns what is considered its proper functioning, still depends on a broader contextual field that defies saturation or guaranteed determination.

Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marsalek, Ondrej; Markland, Thomas E., E-mail: tmarkland@stanford.edu

Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding asmore » a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost.« less

Quantum-kinetic theory of photocurrent generation via direct and phonon-mediated optical transitions

NASA Astrophysics Data System (ADS)

Aeberhard, U.

2011-07-01

A quantum kinetic theory of direct and phonon-mediated indirect optical transitions is developed within the framework of the nonequilibrium Green’s function formalism. After validation against the standard Fermi golden rule approach in the bulk case, it is used in the simulation of photocurrent generation in ultrathin crystalline silicon p-i-n junction devices.

Quantum Liouville theory and BTZ black hole entropy

NASA Astrophysics Data System (ADS)

Chen, Yujun

In this thesis I give an explicit conformal field theory description of (2+1)-dimensional BTZ black hole entropy. In the boundary Liouville field theory I investigate the reducible Verma modules in the elliptic sector, which correspond to certain irreducible representations of the quantum algebra Uq(sl2) ⊙ Uq̂(sl2). I show that there are states that decouple from these reducible Verma modules in a similar fashion to the decoupling of null states in minimal models. Because of the nonstandard form of the Ward identity for the two-point correlation functions in quantum Liouville field theory, these decoupling states have positive-definite norms. The unitary representations built on these decoupling states give the Bekenstein-Hawking entropy of the BTZ black hole.

General theory for calculating disorder-averaged Green's function correlators within the coherent potential approximation

NASA Astrophysics Data System (ADS)

Zhou, Chenyi; Guo, Hong

2017-01-01

We report a diagrammatic method to solve the general problem of calculating configurationally averaged Green's function correlators that appear in quantum transport theory for nanostructures containing disorder. The theory treats both equilibrium and nonequilibrium quantum statistics on an equal footing. Since random impurity scattering is a problem that cannot be solved exactly in a perturbative approach, we combine our diagrammatic method with the coherent potential approximation (CPA) so that a reliable closed-form solution can be obtained. Our theory not only ensures the internal consistency of the diagrams derived at different levels of the correlators but also satisfies a set of Ward-like identities that corroborate the conserving consistency of transport calculations within the formalism. The theory is applied to calculate the quantum transport properties such as average ac conductance and transmission moments of a disordered tight-binding model, and results are numerically verified to high precision by comparing to the exact solutions obtained from enumerating all possible disorder configurations. Our formalism can be employed to predict transport properties of a wide variety of physical systems where disorder scattering is important.

Solving quantum optimal control problems using Clebsch variables and Lin constraints

NASA Astrophysics Data System (ADS)

Delgado-Téllez, M.; Ibort, A.; Rodríguez de la Peña, T.

2018-01-01

Clebsch variables (and Lin constraints) are applied to the study of a class of optimal control problems for affine-controlled quantum systems. The optimal control problem will be modelled with controls defined on an auxiliary space where the dynamical group of the system acts freely. The reciprocity between both theories: the classical theory defined by the objective functional and the quantum system, is established by using a suitable version of Lagrange’s multipliers theorem and a geometrical interpretation of the constraints of the system as defining a subspace of horizontal curves in an associated bundle. It is shown how the solutions of the variational problem defined by the objective functional determine solutions of the quantum problem. Then a new way of obtaining explicit solutions for a family of optimal control problems for affine-controlled quantum systems (finite or infinite dimensional) is obtained. One of its main advantages, is the the use of Clebsch variables allows to compute such solutions from solutions of invariant problems that can often be computed explicitly. This procedure can be presented as an algorithm that can be applied to a large class of systems. Finally, some simple examples, spin control, a simple quantum Hamiltonian with an ‘Elroy beanie’ type classical model and a controlled one-dimensional quantum harmonic oscillator, illustrating the main features of the theory, will be discussed.

Statistical Mechanics and Applications in Condensed Matter

NASA Astrophysics Data System (ADS)

Di Castro, Carlo; Raimondi, Roberto

2015-08-01

Preface; 1. Thermodynamics: a brief overview; 2. Kinetics; 3. From Boltzmann to Gibbs; 4. More ensembles; 5. The thermodynamic limit and its thermodynamic stability; 6. Density matrix and quantum statistical mechanics; 7. The quantum gases; 8. Mean-field theories and critical phenomena; 9. Second quantization and Hartree-Fock approximation; 10. Linear response and fluctuation-dissipation theorem in quantum systems: equilibrium and small deviations; 11. Brownian motion and transport in disordered systems; 12. Fermi liquids; 13. The Landau theory of the second order phase transitions; 14. The Landau-Wilson model for critical phenomena; 15. Superfluidity and superconductivity; 16. The scaling theory; 17. The renormalization group approach; 18. Thermal Green functions; 19. The microscopic foundations of Fermi liquids; 20. The Luttinger liquid; 21. Quantum interference effects in disordered electron systems; Appendix A. The central limit theorem; Appendix B. Some useful properties of the Euler Gamma function; Appendix C. Proof of the second theorem of Yang and Lee; Appendix D. The most probable distribution for the quantum gases; Appendix E. Fermi-Dirac and Bose-Einstein integrals; Appendix F. The Fermi gas in a uniform magnetic field: Landau diamagnetism; Appendix G. Ising and gas-lattice models; Appendix H. Sum over discrete Matsubara frequencies; Appendix I. Hydrodynamics of the two-fluid model of superfluidity; Appendix J. The Cooper problem in the theory of superconductivity; Appendix K. Superconductive fluctuations phenomena; Appendix L. Diagrammatic aspects of the exact solution of the Tomonaga Luttinger model; Appendix M. Details on the theory of the disordered Fermi liquid; References; Author index; Index.

Generalized effective-mass theory of subsurface scanning tunneling microscopy: Application to cleaved quantum dots

NASA Astrophysics Data System (ADS)

Roy, M.; Maksym, P. A.; Bruls, D.; Offermans, P.; Koenraad, P. M.

2010-11-01

An effective-mass theory of subsurface scanning tunneling microscopy (STM) is developed. Subsurface structures such as quantum dots embedded into a semiconductor slab are considered. States localized around subsurface structures match on to a tail that decays into the vacuum above the surface. It is shown that the lateral variation in this tail may be found from a surface envelope function provided that the effects of the slab surfaces and the subsurface structure decouple approximately. The surface envelope function is given by a weighted integral of a bulk envelope function that satisfies boundary conditions appropriate to the slab. The weight function decays into the slab inversely with distance and this slow decay explains the subsurface sensitivity of STM. These results enable STM images to be computed simply and economically from the bulk envelope function. The method is used to compute wave-function images of cleaved quantum dots and the computed images agree very well with experiment.

Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases

NASA Astrophysics Data System (ADS)

Zhou, Chi-Chun; Dai, Wu-Sheng

2018-02-01

In statistical mechanics, for a system with a fixed number of particles, e.g. a finite-size system, strictly speaking, the thermodynamic quantity needs to be calculated in the canonical ensemble. Nevertheless, the calculation of the canonical partition function is difficult. In this paper, based on the mathematical theory of the symmetric function, we suggest a method for the calculation of the canonical partition function of ideal quantum gases, including ideal Bose, Fermi, and Gentile gases. Moreover, we express the canonical partition functions of interacting classical and quantum gases given by the classical and quantum cluster expansion methods in terms of the Bell polynomial in mathematics. The virial coefficients of ideal Bose, Fermi, and Gentile gases are calculated from the exact canonical partition function. The virial coefficients of interacting classical and quantum gases are calculated from the canonical partition function by using the expansion of the Bell polynomial, rather than calculated from the grand canonical potential.

Two-time quantum transport and quantum diffusion.

PubMed

Kleinert, P

2009-05-01

Based on the nonequilibrium Green's function technique, a unified theory is developed that covers quantum transport and quantum diffusion in bulk semiconductors on the same footing. This approach, which is applicable to transport via extended and localized states, extends previous semiphenomenological studies and puts them on a firm microscopic basis. The approach is sufficiently general and applies not only to well-studied quantum-transport problems, but also to models, in which the Hamiltonian does not commute with the dipole operator. It is shown that even for the unified treatment of quantum transport and quantum diffusion in homogeneous systems, all quasimomenta of the carrier distribution function are present and fulfill their specific function. Particular emphasis is put on the double-time nature of quantum kinetics. To demonstrate the existence of robust macroscopic transport effects that have a true double-time character, a phononless steady-state current is identified that appears only beyond the generalized Kadanoff-Baym ansatz.

Decoherence and thermalization of a pure quantum state in quantum field theory.

PubMed

Giraud, Alexandre; Serreau, Julien

2010-06-11

We study the real-time evolution of a self-interacting O(N) scalar field initially prepared in a pure, coherent quantum state. We present a complete solution of the nonequilibrium quantum dynamics from a 1/N expansion of the two-particle-irreducible effective action at next-to-leading order, which includes scattering and memory effects. We demonstrate that, restricting one's attention (or ability to measure) to a subset of the infinite hierarchy of correlation functions, one observes an effective loss of purity or coherence and, on longer time scales, thermalization. We point out that the physics of decoherence is well described by classical statistical field theory.

Quantum cybernetics and its test in “late choice” experiments

NASA Astrophysics Data System (ADS)

Grössing, Gerhard

1986-11-01

A relativistically invariant wave equation for the propagation of wave fronts S = const ( S being the action function) is derived on the basis of a cybernetic model of quantum systems involving “hidden variables”. This equation can be considered both as an expression of Huygens' principle and as a general continuity equation providing a close link between classical and quantum mechanics. Although the theory reproduces ordinary quantum mechanics, there are particular situations providing experimental predictions differing from those existing theories. Such predictions are made for so-called “late choice” experiments, which are modified versions of the familiar “delayed choice” experiments.

Magnetic expansion of Nekrasov theory: The SU(2) pure gauge theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

He Wei; Miao Yangang

It is recently claimed by Nekrasov and Shatashvili that the N=2 gauge theories in the {Omega} background with {epsilon}{sub 1}=({h_bar}/2{pi}), {epsilon}{sub 2}=0 are related to the quantization of certain algebraic integrable systems. We study the special case of SU(2) pure gauge theory; the corresponding integrable model is the A{sub 1} Toda model, which reduces to the sine-Gordon quantum mechanics problem. The quantum effects can be expressed as the WKB series written analytically in terms of hypergeometric functions. We obtain the magnetic and dyonic expansions of the Nekrasov theory by studying the property of hypergeometric functions in the magnetic and dyonicmore » regions on the moduli space. We also discuss the relation between the electric-magnetic duality of gauge theory and the action-action duality of the integrable system.« less

EPR & Klein Paradoxes in Complex Hamiltonian Dynamics and Krein Space Quantization

NASA Astrophysics Data System (ADS)

Payandeh, Farrin

2015-07-01

Negative energy states are applied in Krein space quantization approach to achieve a naturally renormalized theory. For example, this theory by taking the full set of Dirac solutions, could be able to remove the propagator Green function's divergences and automatically without any normal ordering, to vanish the expected value for vacuum state energy. However, since it is a purely mathematical theory, the results are under debate and some efforts are devoted to include more physics in the concept. Whereas Krein quantization is a pure mathematical approach, complex quantum Hamiltonian dynamics is based on strong foundations of Hamilton-Jacobi (H-J) equations and therefore on classical dynamics. Based on complex quantum Hamilton-Jacobi theory, complex spacetime is a natural consequence of including quantum effects in the relativistic mechanics, and is a bridge connecting the causality in special relativity and the non-locality in quantum mechanics, i.e. extending special relativity to the complex domain leads to relativistic quantum mechanics. So that, considering both relativistic and quantum effects, the Klein-Gordon equation could be derived as a special form of the Hamilton-Jacobi equation. Characterizing the complex time involved in an entangled energy state and writing the general form of energy considering quantum potential, two sets of positive and negative energies will be realized. The new states enable us to study the spacetime in a relativistic entangled “space-time” state leading to 12 extra wave functions than the four solutions of Dirac equation for a free particle. Arguing the entanglement of particle and antiparticle leads to a contradiction with experiments. So, in order to correct the results, along with a previous investigation [1], we realize particles and antiparticles as physical entities with positive energy instead of considering antiparticles with negative energy. As an application of modified descriptions for entangled (space-time) states, the original version of EPR paradox can be discussed and the correct answer can be verified based on the strong rooted complex quantum Hamilton-Jacobi theory [2-27] and as another example we can use the negative energy states, to remove the Klein's paradox without the need of any further explanations or justifications like backwardly moving electrons. Finally, comparing the two approaches, we can point out to the existence of a connection between quantum Hamiltonian dynamics, standard quantum field theory, and Krein space quantization [28-43].

Carl Hempel's Philosophy of Science: How to Avoid Epistemic Discontinuity and Pedagogical Pitfalls

ERIC Educational Resources Information Center

Vemulapalli, G. Krishna; Byerly, Henry C.

2004-01-01

Mathematical theories are essential for explanations in physics, chemistry and engineering. These theories often incorporate functions that are defined by the irrelation to other variables in the theory but not with reference to experimental observations. The wave function in quantum mechanics is perhaps one of the best known example of such…

Entropy functional and the holographic attractor mechanism

DOE PAGES

Cabo-Bizet, Alejandro; Kol, Uri; Pando Zayas, Leopoldo A.; ...

2018-05-01

We provide a field theory interpretation of the attractor mechanism for asymptotically AdS4 dyonic BPS black holes whose entropy is captured by the supersymmetric index of the twisted ABJM theory at Chern-Simons level one. We holographically compute the renormalized off-shell quantum effective action in the twisted ABJM theory as a function of the supersymmetric fermion masses and the arbitrary vacuum expectation values of the dimension one scalar bilinear operators and show that extremizing the effective action with respect to the vacuum expectation values of the dimension one scalar bilinears is equivalent to the attractor mechanism in the bulk. In fact,more » we show that the holographic quantum effective action coincides with the entropy functional and, therefore, its value at the extremum reproduces the black hole entropy.« less

Does perturbative quantum chromodynamics imply a Regge singularity above unity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bishari, M.

1982-07-15

It is investigated whether perturbative quantum chromodynamics can have some implications on Regge behavior of deep-inelastic structure functions. The possible indirect but important role of unitarity, in constraining the theory, is pointed out.

Efficient quantum algorithm for computing n-time correlation functions.

PubMed

Pedernales, J S; Di Candia, R; Egusquiza, I L; Casanova, J; Solano, E

2014-07-11

We propose a method for computing n-time correlation functions of arbitrary spinorial, fermionic, and bosonic operators, consisting of an efficient quantum algorithm that encodes these correlations in an initially added ancillary qubit for probe and control tasks. For spinorial and fermionic systems, the reconstruction of arbitrary n-time correlation functions requires the measurement of two ancilla observables, while for bosonic variables time derivatives of the same observables are needed. Finally, we provide examples applicable to different quantum platforms in the frame of the linear response theory.

Energy flow in non-equilibrium conformal field theory

NASA Astrophysics Data System (ADS)

Bernard, Denis; Doyon, Benjamin

2012-09-01

We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact. We prove that these systems converge towards steady states, and give a general description of such non-equilibrium steady states in terms of quantum field theory data. We compute the large deviation function, also called the full counting statistics, of energy transfer through the contact. These are universal and satisfy fluctuation relations. We provide a simple representation of these quantum fluctuations in terms of classical Poisson processes whose intensities are proportional to Boltzmann weights.

Recent Progress in Treating Protein-Ligand Interactions with Quantum-Mechanical Methods.

PubMed

Yilmazer, Nusret Duygu; Korth, Martin

2016-05-16

We review the first successes and failures of a "new wave" of quantum chemistry-based approaches to the treatment of protein/ligand interactions. These approaches share the use of "enhanced", dispersion (D), and/or hydrogen-bond (H) corrected density functional theory (DFT) or semi-empirical quantum mechanical (SQM) methods, in combination with ensemble weighting techniques of some form to capture entropic effects. Benchmark and model system calculations in comparison to high-level theoretical as well as experimental references have shown that both DFT-D (dispersion-corrected density functional theory) and SQM-DH (dispersion and hydrogen bond-corrected semi-empirical quantum mechanical) perform much more accurately than older DFT and SQM approaches and also standard docking methods. In addition, DFT-D might soon become and SQM-DH already is fast enough to compute a large number of binding modes of comparably large protein/ligand complexes, thus allowing for a more accurate assessment of entropic effects.

Disappearing Q operator

NASA Astrophysics Data System (ADS)

Jones, H. F.; Rivers, R. J.

2007-01-01

In the Schrödinger formulation of non-Hermitian quantum theories a positive-definite metric operator η≡e-Q must be introduced in order to ensure their probabilistic interpretation. This operator also gives an equivalent Hermitian theory, by means of a similarity transformation. If, however, quantum mechanics is formulated in terms of functional integrals, we show that the Q operator makes only a subliminal appearance and is not needed for the calculation of expectation values. Instead, the relation to the Hermitian theory is encoded via the external source j(t). These points are illustrated and amplified for two non-Hermitian quantum theories: the Swanson model, a non-Hermitian transform of the simple harmonic oscillator, and the wrong-sign quartic oscillator, which has been shown to be equivalent to a conventional asymmetric quartic oscillator.

Disappearing Q operator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jones, H. F.; Rivers, R. J.

In the Schroedinger formulation of non-Hermitian quantum theories a positive-definite metric operator {eta}{identical_to}e{sup -Q} must be introduced in order to ensure their probabilistic interpretation. This operator also gives an equivalent Hermitian theory, by means of a similarity transformation. If, however, quantum mechanics is formulated in terms of functional integrals, we show that the Q operator makes only a subliminal appearance and is not needed for the calculation of expectation values. Instead, the relation to the Hermitian theory is encoded via the external source j(t). These points are illustrated and amplified for two non-Hermitian quantum theories: the Swanson model, a non-Hermitianmore » transform of the simple harmonic oscillator, and the wrong-sign quartic oscillator, which has been shown to be equivalent to a conventional asymmetric quartic oscillator.« less

Quantum thermodynamics: a nonequilibrium Green's function approach.

PubMed

Esposito, Massimiliano; Ochoa, Maicol A; Galperin, Michael

2015-02-27

We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green's functions. The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit.

Emergent Geometry from Entropy and Causality

NASA Astrophysics Data System (ADS)

Engelhardt, Netta

In this thesis, we investigate the connections between the geometry of spacetime and aspects of quantum field theory such as entanglement entropy and causality. This work is motivated by the idea that spacetime geometry is an emergent phenomenon in quantum gravity, and that the physics responsible for this emergence is fundamental to quantum field theory. Part I of this thesis is focused on the interplay between spacetime and entropy, with a special emphasis on entropy due to entanglement. In general spacetimes, there exist locally-defined surfaces sensitive to the geometry that may act as local black hole boundaries or cosmological horizons; these surfaces, known as holographic screens, are argued to have a connection with the second law of thermodynamics. Holographic screens obey an area law, suggestive of an association with entropy; they are also distinguished surfaces from the perspective of the covariant entropy bound, a bound on the total entropy of a slice of the spacetime. This construction is shown to be quite general, and is formulated in both classical and perturbatively quantum theories of gravity. The remainder of Part I uses the Anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence to both expand and constrain the connection between entanglement entropy and geometry. The AdS/CFT correspondence posits an equivalence between string theory in the "bulk" with AdS boundary conditions and certain quantum field theories. In the limit where the string theory is simply classical General Relativity, the Ryu-Takayanagi and more generally, the Hubeny-Rangamani-Takayanagi (HRT) formulae provide a way of relating the geometry of surfaces to entanglement entropy. A first-order bulk quantum correction to HRT was derived by Faulkner, Lewkowycz and Maldacena. This formula is generalized to include perturbative quantum corrections in the bulk at any (finite) order. Hurdles to spacetime emergence from entanglement entropy as described by HRT and its quantum generalizations are discussed, both at the classical and perturbatively quantum limits. In particular, several No Go Theorems are proven, indicative of a conclusion that supplementary approaches or information may be necessary to recover the full spacetime geometry. Part II of this thesis involves the relation between geometry and causality, the property that information cannot travel faster than light. Requiring this of any quantum field theory results in constraints on string theory setups that are dual to quantum field theories via the AdS/CFT correspondence. At the level of perturbative quantum gravity, it is shown that causality in the field theory constraints the causal structure in the bulk. At the level of nonperturbative quantum string theory, we find that constraints on causal signals restrict the possible ways in which curvature singularities can be resolved in string theory. Finally, a new program of research is proposed for the construction of bulk geometry from the divergences of correlation functions in the dual field theory. This divergence structure is linked to the causal structure of the bulk and of the field theory.

Covalent functionalized black phosphorus quantum dots

NASA Astrophysics Data System (ADS)

Scotognella, Francesco; Kriegel, Ilka; Sassolini, Simone

2018-01-01

Black phosphorus (BP) nanostructures enable a new strategy to tune the electronic and optical properties of this atomically thin material. In this paper we show, via density functional theory calculations, the possibility to modify the optical properties of BP quantum dots via covalent functionalization. The quantum dot selected in this study has chemical formula P24H12 and has been covalent functionalized with one or more benzene rings or anthracene. The effect of functionalization is highlighted in the absorption spectra, where a red shift of the absorption is noticeable. The shift can be ascribed to an electron delocalization in the black phosphorus/organic molecule nanostructure.

Topological and Orthomodular Modeling of Context in Behavioral Science

NASA Astrophysics Data System (ADS)

Narens, Louis

2017-02-01

Two non-boolean methods are discussed for modeling context in behavioral data and theory. The first is based on intuitionistic logic, which is similar to classical logic except that not every event has a complement. Its probability theory is also similar to classical probability theory except that the definition of probability function needs to be generalized to unions of events instead of applying only to unions of disjoint events. The generalization is needed, because intuitionistic event spaces may not contain enough disjoint events for the classical definition to be effective. The second method develops a version of quantum logic for its underlying probability theory. It differs from Hilbert space logic used in quantum mechanics as a foundation for quantum probability theory in variety of ways. John von Neumann and others have commented about the lack of a relative frequency approach and a rational foundation for this probability theory. This article argues that its version of quantum probability theory does not have such issues. The method based on intuitionistic logic is useful for modeling cognitive interpretations that vary with context, for example, the mood of the decision maker, the context produced by the influence of other items in a choice experiment, etc. The method based on this article's quantum logic is useful for modeling probabilities across contexts, for example, how probabilities of events from different experiments are related.

Quantum to classical transition in quantum field theory

NASA Astrophysics Data System (ADS)

Lombardo, Fernando C.

1998-12-01

We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat space. We also use this formalism for arbitrary geometries to analyze the quantum to classical transition in quantum gravity. After summarizing the main results known for the quantum Brownian motion, we consider a self-interacting field theory in Minkowski spacetime. We compute a coarse grained effective action by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients for this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius. On the other hand, we study the classical limit for scalar-tensorial models in two dimensions. We consider different couplings between the dilaton and the scalar field. We discuss the Hawking radiation process and, from an exact evaluation of the influence functional, we study the conditions by which decoherence ensures the validity of the semiclassical approximation in cosmological metrics. Finally we consider four dimensional models with massive scalar fields, arbitrary coupled to the geometry. We compute the Einstein-Langevin equations in order to study the effect of the fluctuations induced by the quantum fields on the classical geometry.

Generalized Galilean transformations and the measurement problem in the entropic dynamics approach to quantum theory

NASA Astrophysics Data System (ADS)

Johnson, David T.

Quantum mechanics is an extremely successful and accurate physical theory, yet since its inception, it has been afflicted with numerous conceptual difficulties. The primary subject of this thesis is the theory of entropic quantum dynamics (EQD), which seeks to avoid these conceptual problems by interpreting quantum theory from an informational perspective. We begin by reviewing Cox's work in describing probability theory as a means of rationally and consistently quantifying uncertainties. We then discuss how probabilities can be updated according to either Bayes' theorem or the extended method of maximum entropy (ME). After that discussion, we review the work of Caticha and Giffin that shows that Bayes' theorem is a special case of ME. This important result demonstrates that the ME method is the general method for updating probabilities. We then review some motivating difficulties in quantum mechanics before discussing Caticha's work in deriving quantum theory from the approach of entropic dynamics, which concludes our review. After entropic dynamics is introduced, we develop the concepts of symmetries and transformations from an informational perspective. The primary result is the formulation of a symmetry condition that any transformation must satisfy in order to qualify as a symmetry in EQD. We then proceed to apply this condition to the extended Galilean transformation. This transformation is of interest as it exhibits features of both special and general relativity. The transformation yields a gravitational potential that arises from an equivalence of information. We conclude the thesis with a discussion of the measurement problem in quantum mechanics. We discuss the difficulties that arise in the standard quantum mechanical approach to measurement before developing our theory of entropic measurement. In entropic dynamics, position is the only observable. We show how a theory built on this one observable can account for the multitude of measurements present in quantum theory. Furthermore, we show that the Born rule need not be postulated, but can be derived in EQD. Finally, we show how the wave function can be updated by the ME method as the phase is constructed purely in terms of probabilities.

Full-band quantum simulation of electron devices with the pseudopotential method: Theory, implementation, and applications

NASA Astrophysics Data System (ADS)

Pala, M. G.; Esseni, D.

2018-03-01

This paper presents the theory, implementation, and application of a quantum transport modeling approach based on the nonequilibrium Green's function formalism and a full-band empirical pseudopotential Hamiltonian. We here propose to employ a hybrid real-space/plane-wave basis that results in a significant reduction of the computational complexity compared to a full plane-wave basis. To this purpose, we provide a theoretical formulation in the hybrid basis of the quantum confinement, the self-energies of the leads, and the coupling between the device and the leads. After discussing the theory and the implementation of the new simulation methodology, we report results for complete, self-consistent simulations of different electron devices, including a silicon Esaki diode, a thin-body silicon field effect transistor (FET), and a germanium tunnel FET. The simulated transistors have technologically relevant geometrical features with a semiconductor film thickness of about 4 nm and a channel length ranging from 10 to 17 nm. We believe that the newly proposed formalism may find applications also in transport models based on ab initio Hamiltonians, as those employed in density functional theory methods.

On mini-superspace limit of boundary three-point function in Liouville field theory

NASA Astrophysics Data System (ADS)

Apresyan, Elena; Sarkissian, Gor

2017-12-01

We study the mini-superspace semiclassical limit of the boundary three-point function in the Liouville field theory. We compute also matrix elements for the Morse potential quantum mechanics. An exact agreement between the former and the latter is found. We show that both of them are given by the generalized hypergeometric functions.

Polarized electron beams elastically scattered by atoms as a tool for testing fundamental predictions of quantum mechanics.

PubMed

Dapor, Maurizio

2018-03-29

Quantum information theory deals with quantum noise in order to protect physical quantum bits (qubits) from its effects. A single electron is an emblematic example of a qubit, and today it is possible to experimentally produce polarized ensembles of electrons. In this paper, the theory of the polarization of electron beams elastically scattered by atoms is briefly summarized. Then the POLARe program suite, a set of computer programs aimed at the calculation of the spin-polarization parameters of electron beams elastically interacting with atomic targets, is described. Selected results of the program concerning Ar, Kr, and Xe atoms are presented together with the comparison with experimental data about the Sherman function for low kinetic energy of the incident electrons (1.5eV-350eV). It is demonstrated that the quantum-relativistic theory of the polarization of electron beams elastically scattered by atoms is in good agreement with experimental data down to energies smaller than a few eV.

Schroedinger's immortal cat

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peres, A.

1988-01-01

The purpose of this paper is to review and clarify the quantum measurement problem. The latter originates in the ambivalent nature of the observer: Although the observer is not described by the Schroedinger equation, it should nevertheless be possible to quantize him and include him in the wave function if quantum theory is universally valid. The problem is to prove that no contradiction may arise in these two conflicting descriptions. The proof invokes the notion of irreversibility. The validity of the latter is questionable, because the standard rationale for classical irreversibility, namely mixing and coarse graining, does not apply tomore » quantum theory. There is no chaos in a closed, finite quantum system. However, when a system is large enough, it cannot be perfectly isolated from it environment, namely from external (or even internal) degrees of freedom which are not fully accounted for in the Hamiltonian of that system. As a consequence, the long-range evolution of such a quantum system is essentially unpredictable. It follows that the notion of irreversibility is a valid one in quantum theory and the measurement problem can be brought to a satisfactory solution.« less

Feynman propagator for spin foam quantum gravity.

PubMed

Oriti, Daniele

2005-03-25

We link the notion causality with the orientation of the spin foam 2-complex. We show that all current spin foam models are orientation independent. Using the technology of evolution kernels for quantum fields on Lie groups, we construct a generalized version of spin foam models, introducing an extra proper time variable. We prove that different ranges of integration for this variable lead to different classes of spin foam models: the usual ones, interpreted as the quantum gravity analogue of the Hadamard function of quantum field theory (QFT) or as inner products between quantum gravity states; and a new class of causal models, the quantum gravity analogue of the Feynman propagator in QFT, nontrivial function of the orientation data, and implying a notion of "timeless ordering".

Instantons and Large N

NASA Astrophysics Data System (ADS)

Mariño, Marcos

2015-09-01

Preface; Part I. Instantons: 1. Instantons in quantum mechanics; 2. Unstable vacua in quantum field theory; 3. Large order behavior and Borel summability; 4. Non-perturbative aspects of Yang-Mills theories; 5. Instantons and fermions; Part II. Large N: 6. Sigma models at large N; 7. The 1=N expansion in QCD; 8. Matrix models and matrix quantum mechanics at large N; 9. Large N QCD in two dimensions; 10. Instantons at large N; Appendix A. Harmonic analysis on S3; Appendix B. Heat kernel and zeta functions; Appendix C. Effective action for large N sigma models; References; Author index; Subject index.

Quantum dark soliton: Nonperturbative diffusion of phase and position

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dziarmaga, J.

2004-12-01

The dark soliton solution of the Gross-Pitaevskii equation in one dimension has two parameters that do not change the energy of the solution: the global phase of the condensate wave function and the position of the soliton. These degeneracies appear in the Bogoliubov theory as Bogoliubov modes with zero frequencies and zero norms. These 'zero modes' cannot be quantized as the usual Bogoliubov quasiparticle harmonic oscillators. They must be treated in a nonperturbative way. In this paper I develop a nonperturbative theory of zero modes. This theory provides a nonperturbative description of quantum phase diffusion and quantum diffusion of solitonmore » position. An initially well localized wave packet for soliton position is predicted to disperse beyond the width of the soliton.« less

Can time-dependent density functional theory predict intersystem crossing in organic chromophores? A case study on benzo(bis)-X-diazole based donor-acceptor-donor type molecules.

PubMed

Tam, Teck Lip Dexter; Lin, Ting Ting; Chua, Ming Hui

2017-06-21

Here we utilized new diagnostic tools in time-dependent density functional theory to explain the trend of intersystem crossing in benzo(bis)-X-diazole based donor-acceptor-donor type molecules. These molecules display a wide range of fluorescence quantum yields and triplet yields, making them excellent candidates for testing the validity of these diagnostic tools. We believe that these tools are cost-effective and can be applied to structurally similar organic chromophores to predict/explain the trends of intersystem crossing, and thus fluorescence quantum yields and triplet yields without the use of complex and expensive multireference configuration interaction or multireference pertubation theory methods.

Generalized non-equilibrium vertex correction method in coherent medium theory for quantum transport simulation of disordered nanoelectronics

NASA Astrophysics Data System (ADS)

Yan, Jiawei; Ke, Youqi

In realistic nanoelectronics, disordered impurities/defects are inevitable and play important roles in electron transport. However, due to the lack of effective quantum transport method, the important effects of disorders remain poorly understood. Here, we report a generalized non-equilibrium vertex correction (NVC) method with coherent potential approximation to treat the disorder effects in quantum transport simulation. With this generalized NVC method, any averaged product of two single-particle Green's functions can be obtained by solving a set of simple linear equations. As a result, the averaged non-equilibrium density matrix and various important transport properties, including averaged current, disordered induced current fluctuation and the averaged shot noise, can all be efficiently computed in a unified scheme. Moreover, a generalized form of conditionally averaged non-equilibrium Green's function is derived to incorporate with density functional theory to enable first-principles simulation. We prove the non-equilibrium coherent potential equals the non-equilibrium vertex correction. Our approach provides a unified, efficient and self-consistent method for simulating non-equilibrium quantum transport through disorder nanoelectronics. Shanghaitech start-up fund.

Kibble Zurek mechanism of topological defect formation in quantum field theory with matrix product states

NASA Astrophysics Data System (ADS)

Gillman, Edward; Rajantie, Arttu

2018-05-01

The Kibble Zurek mechanism in a relativistic ϕ4 scalar field theory in D =(1 +1 ) is studied using uniform matrix product states. The equal time two point function in momentum space G2(k ) is approximated as the system is driven through a quantum phase transition at a variety of different quench rates τQ. We focus on looking for signatures of topological defect formation in the system and demonstrate the consistency of the picture that the two point function G2(k ) displays two characteristic scales, the defect density n and the kink width dK. Consequently, G2(k ) provides a clear signature for the formation of defects and a well defined measure of the defect density in the system. These results provide a benchmark for the use of tensor networks as powerful nonperturbative nonequilibrium methods for relativistic quantum field theory, providing a promising technique for the future study of high energy physics and cosmology.

Quantum geometry of resurgent perturbative/nonperturbative relations

NASA Astrophysics Data System (ADS)

Basar, Gökçe; Dunne, Gerald V.; Ünsal, Mithat

2017-05-01

For a wide variety of quantum potentials, including the textbook `instanton' examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential. These are related to the Chebyshev potentials, which are in turn related to certain \\mathcal{N} = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and `special geometry'. These systems inherit a natural modular structure corresponding to Ramanujan's theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Our approach is very elementary, using basic classical geometry combined with all-orders WKB.

Quantum plasmonics: optical properties of a nanomatryushka.

PubMed

Kulkarni, Vikram; Prodan, Emil; Nordlander, Peter

2013-01-01

Quantum mechanical effects can significantly reduce the plasmon-induced field enhancements around nanoparticles. Here we present a quantum mechanical investigation of the plasmon resonances in a nanomatryushka, which is a concentric core-shell nanoparticle consisting of a solid metallic core encapsulated in a thin metallic shell. We compute the optical response using the time-dependent density functional theory and compare the results with predictions based on the classical electromagnetic theory. We find strong quantum mechanical effects for core-shell spacings below 5 Å, a regime where both the absorption cross section and the local field enhancements differ significantly from the classical predictions. We also show that the workfunction of the metal is a crucial parameter determining the onset and magnitude of quantum effects. For metals with lower workfunctions such as aluminum, the quantum effects are found to be significantly more pronounced than for a noble metal such as gold.

Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction.

PubMed

Budiyono, Agung; Rohrlich, Daniel

2017-11-03

Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic framework, allowing an unambiguous account of how one theory is the limit of the other. Here we derive non-relativistic quantum mechanics and classical statistical mechanics within a common framework. The common axioms include conservation of average energy and conservation of probability current. But two axioms distinguish quantum mechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global) random variable that generates physical correlations, and an "epistemic restriction" constrains allowed phase space distributions. The ontic extension and epistemic restriction, with strength on the order of Planck's constant, imply quantum entanglement and uncertainty relations. This framework suggests that the wave function is epistemic, yet it does not provide an ontic dynamics for individual systems.

Barrierless association of CF2 and dissociation of C2F4 by variational transition-state theory and system-specific quantum Rice–Ramsperger–Kassel theory

PubMed Central

Bao, Junwei Lucas; Zhang, Xin

2016-01-01

Bond dissociation is a fundamental chemical reaction, and the first principles modeling of the kinetics of dissociation reactions with a monotonically increasing potential energy along the dissociation coordinate presents a challenge not only for modern electronic structure methods but also for kinetics theory. In this work, we use multifaceted variable-reaction-coordinate variational transition-state theory (VRC-VTST) to compute the high-pressure limit dissociation rate constant of tetrafluoroethylene (C2F4), in which the potential energies are computed by direct dynamics with the M08-HX exchange correlation functional. To treat the pressure dependence of the unimolecular rate constants, we use the recently developed system-specific quantum Rice–Ramsperger–Kassel theory. The calculations are carried out by direct dynamics using an exchange correlation functional validated against calculations that go beyond coupled-cluster theory with single, double, and triple excitations. Our computed dissociation rate constants agree well with the recent experimental measurements. PMID:27834727

Barrierless association of CF2 and dissociation of C2F4 by variational transition-state theory and system-specific quantum Rice-Ramsperger-Kassel theory.

PubMed

Bao, Junwei Lucas; Zhang, Xin; Truhlar, Donald G

2016-11-29

Bond dissociation is a fundamental chemical reaction, and the first principles modeling of the kinetics of dissociation reactions with a monotonically increasing potential energy along the dissociation coordinate presents a challenge not only for modern electronic structure methods but also for kinetics theory. In this work, we use multifaceted variable-reaction-coordinate variational transition-state theory (VRC-VTST) to compute the high-pressure limit dissociation rate constant of tetrafluoroethylene (C 2 F 4 ), in which the potential energies are computed by direct dynamics with the M08-HX exchange correlation functional. To treat the pressure dependence of the unimolecular rate constants, we use the recently developed system-specific quantum Rice-Ramsperger-Kassel theory. The calculations are carried out by direct dynamics using an exchange correlation functional validated against calculations that go beyond coupled-cluster theory with single, double, and triple excitations. Our computed dissociation rate constants agree well with the recent experimental measurements.

Quantum game theory

NASA Astrophysics Data System (ADS)

Stohler, Michael Lehman

2002-01-01

Non-cooperative quantum games have received much attention recently. This thesis defines and divides current works into two major categories of gaming techniques with close attention paid to Nash equilibria, form and possibilities for the payoff functions, and the benefits of using a quantum strategy. In addition to comparing and contrasting these techniques, new applications and calculations are discussed. Finally, the techniques are expanded into 3 x 3 games which allows the study of non-transitive strategies in quantum games.

Going through a quantum phase

NASA Technical Reports Server (NTRS)

Shapiro, Jeffrey H.

1992-01-01

Phase measurements on a single-mode radiation field are examined from a system-theoretic viewpoint. Quantum estimation theory is used to establish the primacy of the Susskind-Glogower (SG) phase operator; its phase eigenkets generate the probability operator measure (POM) for maximum likelihood phase estimation. A commuting observables description for the SG-POM on a signal x apparatus state space is derived. It is analogous to the signal-band x image-band formulation for optical heterodyne detection. Because heterodyning realizes the annihilation operator POM, this analogy may help realize the SG-POM. The wave function representation associated with the SG POM is then used to prove the duality between the phase measurement and the number operator measurement, from which a number-phase uncertainty principle is obtained, via Fourier theory, without recourse to linearization. Fourier theory is also employed to establish the principle of number-ket causality, leading to a Paley-Wiener condition that must be satisfied by the phase-measurement probability density function (PDF) for a single-mode field in an arbitrary quantum state. Finally, a two-mode phase measurement is shown to afford phase-conjugate quantum communication at zero error probability with finite average photon number. Application of this construct to interferometric precision measurements is briefly discussed.

Transport spin dependent in nanostructures: Current and geometry effect of quantum dots in presence of spin-orbit interaction

NASA Astrophysics Data System (ADS)

Paredes-Gutiérrez, H.; Pérez-Merchancano, S. T.; Beltran-Rios, C. L.

2017-12-01

In this work, we study the quantum electron transport through a Quantum Dots Structure (QDs), with different geometries, embedded in a Quantum Well (QW). The behaviour of the current through the nanostructure (dot and well) is studied considering the orbital spin coupling of the electrons and the Rashba effect, by means of the second quantization theory and the standard model of Green’s functions. Our results show the behaviour of the current in the quantum system as a function of the electric field, presenting resonant states for specific values of both the external field and the spin polarization. Similarly, the behaviour of the current on the nanostructure changes when the geometry of the QD and the size of the same are modified as a function of the polarization of the electron spin and the potential of quantum confinement.

Combinatorial quantisation of the Euclidean torus universe

NASA Astrophysics Data System (ADS)

Meusburger, C.; Noui, K.

2010-12-01

We quantise the Euclidean torus universe via a combinatorial quantisation formalism based on its formulation as a Chern-Simons gauge theory and on the representation theory of the Drinfel'd double DSU(2). The resulting quantum algebra of observables is given by two commuting copies of the Heisenberg algebra, and the associated Hilbert space can be identified with the space of square integrable functions on the torus. We show that this Hilbert space carries a unitary representation of the modular group and discuss the role of modular invariance in the theory. We derive the classical limit of the theory and relate the quantum observables to the geometry of the torus universe.

Momentum constraints as integrability conditions for the Hamiltonian constraint in general relativity.

NASA Technical Reports Server (NTRS)

Moncrief, V.; Teitelboim, C.

1972-01-01

It is shown that if the Hamiltonian constraint of general relativity is imposed as a restriction on the Hamilton principal functional in the classical theory, or on the state functional in the quantum theory, then the momentum constraints are automatically satisfied. This result holds both for closed and open spaces and it means that the full content of the theory is summarized by a single functional equation of the Tomonaga-Schwinger type.

Spekkens’ toy model in all dimensions and its relationship with stabiliser quantum mechanics

NASA Astrophysics Data System (ADS)

Catani, Lorenzo; E Browne, Dan

2017-07-01

Spekkens’ toy model is a non-contextual hidden variable model with an epistemic restriction, a constraint on what an observer can know about reality. The aim of the model, developed for continuous and discrete prime degrees of freedom, is to advocate the epistemic view of quantum theory, where quantum states are states of incomplete knowledge about a deeper underlying reality. Many aspects of quantum mechanics and protocols from quantum information can be reproduced in the model. In spite of its significance, a number of aspects of Spekkens’ model remained incomplete. Formal rules for the update of states after measurement had not been written down, and the theory had only been constructed for prime-dimensional and infinite dimensional systems. In this work, we remedy this, by deriving measurement update rules and extending the framework to derive models in all dimensions, both prime and non-prime. Stabiliser quantum mechanics (SQM) is a sub-theory of quantum mechanics with restricted states, transformations and measurements. First derived for the purpose of constructing error correcting codes, it now plays a role in many areas of quantum information theory. Previously, it had been shown that Spekkens’ model was operationally equivalent to SQM in the case of odd prime dimensions. Here, exploiting known results on Wigner functions, we extend this to show that Spekkens’ model is equivalent to SQM in all odd dimensions, prime and non-prime. This equivalence provides new technical tools for the study of technically difficult compound-dimensional SQM.

Microscopic Modeling of Intersubband Optical Processes in Type II Semiconductor Quantum Wells: Linear Absorption

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Kolokolov, Kanstantin I.; Ning, Cun-Zheng

2003-01-01

Linear absorption spectra arising from intersubband transitions in semiconductor quantum well heterostructures are analyzed using quantum kinetic theory by treating correlations to the first order within Hartree-Fock approximation. The resulting intersubband semiconductor Bloch equations take into account extrinsic dephasing contributions, carrier-longitudinal optical phonon interaction and carrier-interface roughness interaction which is considered with Ando s theory. As input for resonance lineshape calculation, a spurious-states-free 8-band kp Hamiltonian is used, in conjunction with the envelop function approximation, to compute self-consistently the energy subband structure of electrons in type II InAs/AlSb single quantum well structures. We demonstrate the interplay of nonparabolicity and many-body effects in the mid-infrared frequency range for such heterostructures.

Connes' embedding problem and winning strategies for quantum XOR games

NASA Astrophysics Data System (ADS)

Harris, Samuel J.

2017-12-01

We consider quantum XOR games, defined in the work of Regev and Vidick [ACM Trans. Comput. Theory 7, 43 (2015)], from the perspective of unitary correlations defined in the work of Harris and Paulsen [Integr. Equations Oper. Theory 89, 125 (2017)]. We show that the winning bias of a quantum XOR game in the tensor product model (respectively, the commuting model) is equal to the norm of its associated linear functional on the unitary correlation set from the appropriate model. We show that Connes' embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to the commuting bias. In particular, the embedding problem is equivalent to determining whether every quantum XOR game G with a winning strategy in the commuting model also has a winning strategy in the approximate finite-dimensional model.

Loop Quantum Gravity.

PubMed

Rovelli, Carlo

2008-01-01

The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime , is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler's "spacetime foam" intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein-Hawking black-hole entropy. (v) Low-energy calculations, yielding n -point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.

Conformal field theory construction for non-Abelian hierarchy wave functions

NASA Astrophysics Data System (ADS)

Tournois, Yoran; Hermanns, Maria

2017-12-01

The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular non-Abelian ones. Here we analyze a class of non-Abelian fractional quantum Hall model states which are generalizations of the Abelian Haldane-Halperin hierarchy. We derive their topological properties and show that the quasiparticles obey non-Abelian fusion rules of type su (q)k . For a subset of these states we are able to derive the conformal field theory description that makes the topological properties—in particular braiding—of the state manifest. The model states we study provide explicit wave functions for a large variety of interesting topological orders, which may be relevant for certain fractional quantum Hall states observed in the first excited Landau level.

International Workshop on Condensed Matter Theories (14th), Held in Isola d’Elba, Italy on June 18-23, 1990

DTIC Science & Technology

1990-06-23

structure calculations and neutron stars, and as density functional tc-c!niques and lattice gauge field theory, can still come together, understand each...to quantum chromodynamics ( QCD ) and subnucleonic degrees of freedom. Particularly noteworthy were the talks of Krotscheck and Migdal. In the former...phenomena near phase transitions, and the two applications of known techniques to quantum lattice models. In the first case, Ciftan reported on an

Thermodynamics and proton activities of protic ionic liquids with quantum cluster equilibrium theory

NASA Astrophysics Data System (ADS)

Ingenmey, Johannes; von Domaros, Michael; Perlt, Eva; Verevkin, Sergey P.; Kirchner, Barbara

2018-05-01

We applied the binary Quantum Cluster Equilibrium (bQCE) method to a number of alkylammonium-based protic ionic liquids in order to predict boiling points, vaporization enthalpies, and proton activities. The theory combines statistical thermodynamics of van-der-Waals-type clusters with ab initio quantum chemistry and yields the partition functions (and associated thermodynamic potentials) of binary mixtures over a wide range of thermodynamic phase points. Unlike conventional cluster approaches that are limited to the prediction of thermodynamic properties, dissociation reactions can be effortlessly included into the bQCE formalism, giving access to ionicities, as well. The method is open to quantum chemical methods at any level of theory, but combination with low-cost composite density functional theory methods and the proposed systematic approach to generate cluster sets provides a computationally inexpensive and mostly parameter-free way to predict such properties at good-to-excellent accuracy. Boiling points can be predicted within an accuracy of 50 K, reaching excellent accuracy for ethylammonium nitrate. Vaporization enthalpies are predicted within an accuracy of 20 kJ mol-1 and can be systematically interpreted on a molecular level. We present the first theoretical approach to predict proton activities in protic ionic liquids, with results fitting well into the experimentally observed correlation. Furthermore, enthalpies of vaporization were measured experimentally for some alkylammonium nitrates and an excellent linear correlation with vaporization enthalpies of their respective parent amines is observed.

Nonadiabatic Molecular Dynamics and Orthogonality Constrained Density Functional Theory

NASA Astrophysics Data System (ADS)

Shushkov, Philip Georgiev

The exact quantum dynamics of realistic, multidimensional systems remains a formidable computational challenge. In many chemical processes, however, quantum effects such as tunneling, zero-point energy quantization, and nonadiabatic transitions play an important role. Therefore, approximate approaches that improve on the classical mechanical framework are of special practical interest. We propose a novel ring polymer surface hopping method for the calculation of chemical rate constants. The method blends two approaches, namely ring polymer molecular dynamics that accounts for tunneling and zero-point energy quantization, and surface hopping that incorporates nonadiabatic transitions. We test the method against exact quantum mechanical calculations for a one-dimensional, two-state model system. The method reproduces quite accurately the tunneling contribution to the rate and the distribution of reactants between the electronic states for this model system. Semiclassical instanton theory, an approach related to ring polymer molecular dynamics, accounts for tunneling by the use of periodic classical trajectories on the inverted potential energy surface. We study a model of electron transfer in solution, a chemical process where nonadiabatic events are prominent. By representing the tunneling electron with a ring polymer, we derive Marcus theory of electron transfer from semiclassical instanton theory after a careful analysis of the tunneling mode. We demonstrate that semiclassical instanton theory can recover the limit of Fermi's Golden Rule rate in a low-temperature, deep-tunneling regime. Mixed quantum-classical dynamics treats a few important degrees of freedom quantum mechanically, while classical mechanics describes affordably the rest of the system. But the interface of quantum and classical description is a challenging theoretical problem, especially for low-energy chemical processes. We therefore focus on the semiclassical limit of the coupled nuclear-electronic dynamics. We show that the time-dependent Schrodinger equation for the electrons employed in the widely used fewest switches surface hopping method is applicable only in the limit of nearly identical classical trajectories on the different potential energy surfaces. We propose a short-time decoupling algorithm that restricts the use of the Schrodinger equation only to the interaction regions. We test the short-time approximation on three model systems against exact quantum-mechanical calculations. The approximation improves the performance of the surface hopping approach. Nonadiabatic molecular dynamics simulations require the efficient and accurate computation of ground and excited state potential energy surfaces. Unlike the ground state calculations where standard methods exist, the computation of excited state properties is a challenging task. We employ time-independent density functional theory, in which the excited state energy is represented as a functional of the total density. We suggest an adiabatic-like approximation that simplifies the excited state exchange-correlation functional. We also derive a set of minimal conditions to impose exactly the orthogonality of the excited state Kohn-Sham determinant to the ground state determinant. This leads to an efficient, variational algorithm for the self-consistent optimization of the excited state energy. Finally, we assess the quality of the excitation energies obtained by the new method on a set of 28 organic molecules. The new approach provides results of similar accuracy to time-dependent density functional theory.

Particle-hole symmetry and composite fermions in fractional quantum Hall states

NASA Astrophysics Data System (ADS)

Nguyen, Dung Xuan; Golkar, Siavash; Roberts, Matthew M.; Son, Dam Thanh

2018-05-01

We study fractional quantum Hall states at filling fractions in the Jain sequences using the framework of composite Dirac fermions. Synthesizing previous work, we write an effective field theory consistent with all symmetry requirements, including Galilean invariance and particle-hole symmetry. Employing a Fermi-liquid description, we demonstrate the appearance of the Girvin-Macdonald-Platzman algebra and compute the dispersion relation of neutral excitations and various response functions. Our results satisfy requirements of particle-hole symmetry. We show that while the dispersion relation obtained from the modified random-phase approximation (MRPA) of the Halperin-Lee-Read (HLR) theory is particle-hole symmetric, correlation functions obtained from this scheme are not. The results of the Dirac theory are shown to be consistent with the Haldane bound on the projected structure factor, while those of the MPRA of the HLR theory violate it.

Dynamical conductivity at the dirty superconductor-metal quantum phase transition.

PubMed

Del Maestro, Adrian; Rosenow, Bernd; Hoyos, José A; Vojta, Thomas

2010-10-01

We study the transport properties of ultrathin disordered nanowires in the neighborhood of the superconductor-metal quantum phase transition. To this end we combine numerical calculations with analytical strong-disorder renormalization group results. The quantum critical conductivity at zero temperature diverges logarithmically as a function of frequency. In the metallic phase, it obeys activated scaling associated with an infinite-randomness quantum critical point. We extend the scaling theory to higher dimensions and discuss implications for experiments.

Density of Trap States and Auger-mediated Electron Trapping in CdTe Quantum-Dot Solids.

PubMed

Boehme, Simon C; Azpiroz, Jon Mikel; Aulin, Yaroslav V; Grozema, Ferdinand C; Vanmaekelbergh, Daniël; Siebbeles, Laurens D A; Infante, Ivan; Houtepen, Arjan J

2015-05-13

Charge trapping is an ubiquitous process in colloidal quantum-dot solids and a major limitation to the efficiency of quantum dot based devices such as solar cells, LEDs, and thermoelectrics. Although empirical approaches led to a reduction of trapping and thereby efficiency enhancements, the exact chemical nature of the trapping mechanism remains largely unidentified. In this study, we determine the density of trap states in CdTe quantum-dot solids both experimentally, using a combination of electrochemical control of the Fermi level with ultrafast transient absorption and time-resolved photoluminescence spectroscopy, and theoretically, via density functional theory calculations. We find a high density of very efficient electron traps centered ∼0.42 eV above the valence band. Electrochemical filling of these traps increases the electron lifetime and the photoluminescence quantum yield by more than an order of magnitude. The trapping rate constant for holes is an order of magnitude lower that for electrons. These observations can be explained by Auger-mediated electron trapping. From density functional theory calculations we infer that the traps are formed by dicoordinated Te atoms at the quantum dot surface. The combination of our unique experimental determination of the density of trap states with the theoretical modeling of the quantum dot surface allows us to identify the trapping mechanism and chemical reaction at play during charge trapping in these quantum dots.

Quantum mechanical/molecular mechanical/continuum style solvation model: time-dependent density functional theory.

PubMed

Thellamurege, Nandun M; Cui, Fengchao; Li, Hui

2013-08-28

A combined quantum mechanical/molecular mechanical/continuum (QM/MMpol/C) style method is developed for time-dependent density functional theory (TDDFT, including long-range corrected TDDFT) method, induced dipole polarizable force field, and induced surface charge continuum model. Induced dipoles and induced charges are included in the TDDFT equations to solve for the transition energies, relaxed density, and transition density. Analytic gradient is derived and implemented for geometry optimization and molecular dynamics simulation. QM/MMpol/C style DFT and TDDFT methods are used to study the hydrogen bonding of the photoactive yellow protein chromopore in ground state and excited state.

Scalable nuclear density functional theory with Sky3D

NASA Astrophysics Data System (ADS)

Afibuzzaman, Md; Schuetrumpf, Bastian; Aktulga, Hasan Metin

2018-02-01

In nuclear astrophysics, quantum simulations of large inhomogeneous dense systems as they appear in the crusts of neutron stars present big challenges. The number of particles in a simulation with periodic boundary conditions is strongly limited due to the immense computational cost of the quantum methods. In this paper, we describe techniques for an efficient and scalable parallel implementation of Sky3D, a nuclear density functional theory solver that operates on an equidistant grid. Presented techniques allow Sky3D to achieve good scaling and high performance on a large number of cores, as demonstrated through detailed performance analysis on a Cray XC40 supercomputer.

Random matrix theory of singular values of rectangular complex matrices I: Exact formula of one-body distribution function in fixed-trace ensemble

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adachi, Satoshi; Toda, Mikito; Kubotani, Hiroto

The fixed-trace ensemble of random complex matrices is the fundamental model that excellently describes the entanglement in the quantum states realized in a coupled system by its strongly chaotic dynamical evolution [see H. Kubotani, S. Adachi, M. Toda, Phys. Rev. Lett. 100 (2008) 240501]. The fixed-trace ensemble fully takes into account the conservation of probability for quantum states. The present paper derives for the first time the exact analytical formula of the one-body distribution function of singular values of random complex matrices in the fixed-trace ensemble. The distribution function of singular values (i.e. Schmidt eigenvalues) of a quantum state ismore » so important since it describes characteristics of the entanglement in the state. The derivation of the exact analytical formula utilizes two recent achievements in mathematics, which appeared in 1990s. The first is the Kaneko theory that extends the famous Selberg integral by inserting a hypergeometric type weight factor into the integrand to obtain an analytical formula for the extended integral. The second is the Petkovsek-Wilf-Zeilberger theory that calculates definite hypergeometric sums in a closed form.« less

Relativistic (SR-ZORA) quantum theory of atoms in molecules properties.

PubMed

Anderson, James S M; Rodríguez, Juan I; Ayers, Paul W; Götz, Andreas W

2017-01-15

The Quantum Theory of Atoms in Molecules (QTAIM) is used to elucidate the effects of relativity on chemical systems. To do this, molecules are studied using density-functional theory at both the nonrelativistic level and using the scalar relativistic zeroth-order regular approximation. Relativistic effects on the QTAIM properties and topology of the electron density can be significant for chemical systems with heavy atoms. It is important, therefore, to use the appropriate relativistic treatment of QTAIM (Anderson and Ayers, J. Phys. Chem. 2009, 115, 13001) when treating systems with heavy atoms. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Dynamics of a quantum spin liquid beyond integrability: The Kitaev-Heisenberg-Γ model in an augmented parton mean-field theory

NASA Astrophysics Data System (ADS)

Knolle, Johannes; Bhattacharjee, Subhro; Moessner, Roderich

2018-04-01

We present an augmented parton mean-field theory which (i) reproduces the exact ground state, spectrum, and dynamics of the quantum spin-liquid phase of Kitaev's honeycomb model, and (ii) is amenable to the inclusion of integrability breaking terms, allowing a perturbation theory from a controlled starting point. Thus, we exemplarily study dynamical spin correlations of the honeycomb Kitaev quantum spin liquid within the K -J -Γ model, which includes Heisenberg and symmetric-anisotropic (pseudodipolar) interactions. This allows us to trace changes of the correlations in the regime of slowly moving fluxes, where the theory captures the dominant deviations when integrability is lost. These include an asymmetric shift together with a broadening of the dominant peak in the response as a function of frequency, the generation of further-neighbor correlations and their structure in real and spin space, and a resulting loss of an approximate rotational symmetry of the structure factor in reciprocal space. We discuss the limitations of this approach and also view the neutron-scattering experiments on the putative proximate quantum spin-liquid material α -RuCl3 in the light of the results from this extended parton theory.

Asymptotic neutron scattering laws for anomalously diffusing quantum particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kneller, Gerald R.; Université d’Orléans, Chateau de la Source-Ave. du Parc Floral, 45067 Orléans; Synchrotron-SOLEIL, L’Orme de Merisiers, 91192 Gif-sur-Yvette

2016-07-28

The paper deals with a model-free approach to the analysis of quasielastic neutron scattering intensities from anomalously diffusing quantum particles. All quantities are inferred from the asymptotic form of their time-dependent mean square displacements which grow ∝t{sup α}, with 0 ≤ α < 2. Confined diffusion (α = 0) is here explicitly included. We discuss in particular the intermediate scattering function for long times and the Fourier spectrum of the velocity autocorrelation function for small frequencies. Quantum effects enter in both cases through the general symmetry properties of quantum time correlation functions. It is shown that the fractional diffusion constantmore » can be expressed by a Green-Kubo type relation involving the real part of the velocity autocorrelation function. The theory is exact in the diffusive regime and at moderate momentum transfers.« less

Higher-order stochastic differential equations and the positive Wigner function

NASA Astrophysics Data System (ADS)

Drummond, P. D.

2017-12-01

General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and γ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.

Schrödinger's immortal cat

NASA Astrophysics Data System (ADS)

Peres, Asher

1988-01-01

The purpose of this paper is to review and clarify the quantum “measurement problem.” The latter originates in the ambivalent nature of the “observer”: Although the observer is not described by the Schrödinger equation, it should nevertheless be possible to “quantize” him and include him in the wave function if quantum theory is universally valid. The problem is to prove that no contradiction may arise in these two conflicting descriptions. The proof invokes the notion of irreversibility. The validity of the latter is questionable, because the standard rationale for classical irreversibility, namely mixing and coarse graining, does not apply to quantum theory. There is no chaos in a closed, finite quantum system. However, when a system is large enough, it cannot be perfectly isolated from its “environment,” namely from external (or even internal) degrees of freedom which are not fully accounted for in the Hamiltonian of that system. As a consequence, the long-range evolution of such a quantum system is essentially unpredictable. It follows that the notion of irreversibility is a valid one in quantum theory and the “measurement problem” can be brought to a satisfactory solution.

Quantum entangled dark solitons formed by ultracold atoms in optical lattices.

PubMed

Mishmash, R V; Carr, L D

2009-10-02

Inspired by experiments on Bose-Einstein condensates in optical lattices, we study the quantum evolution of dark soliton initial conditions in the context of the Bose-Hubbard Hamiltonian. An extensive set of quantum measures is utilized in our analysis, including von Neumann and generalized quantum entropies, quantum depletion, and the pair correlation function. We find that quantum effects cause the soliton to fill in. Moreover, soliton-soliton collisions become inelastic, in strong contrast to the predictions of mean-field theory. These features show that the lifetime and collision properties of dark solitons in optical lattices provide clear signals of quantum effects.

Quantum geometry of resurgent perturbative/nonperturbative relations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Basar, Gokce; Dunne, Gerald V.; Unsal, Mithat

For a wide variety of quantum potentials, including the textbook ‘instanton’ examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential.more » These are related to the Chebyshev potentials, which are in turn related to certain N = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and ‘special geometry’. These systems inherit a natural modular structure corresponding to Ramanujan’s theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Lastly, our approach is very elementary, using basic classical geometry combined with all-orders WKB.« less

Quantum geometry of resurgent perturbative/nonperturbative relations

DOE PAGES

Basar, Gokce; Dunne, Gerald V.; Unsal, Mithat

2017-05-16

For a wide variety of quantum potentials, including the textbook ‘instanton’ examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential.more » These are related to the Chebyshev potentials, which are in turn related to certain N = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and ‘special geometry’. These systems inherit a natural modular structure corresponding to Ramanujan’s theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Lastly, our approach is very elementary, using basic classical geometry combined with all-orders WKB.« less

Ab initio theory of the N2V defect in diamond for quantum memory implementation

NASA Astrophysics Data System (ADS)

Udvarhelyi, Péter; Thiering, Gergő; Londero, Elisa; Gali, Adam

2017-10-01

The N2V defect in diamond is characterized by means of ab initio methods relying on density functional theory calculated parameters of a Hubbard model Hamiltonian. It is shown that this approach appropriately describes the energy levels of correlated excited states induced by this defect. By determining its critical magneto-optical parameters, we propose to realize a long-living quantum memory by N2V defect, i.e., H 3 color center in diamond.

Matrix thermalization

NASA Astrophysics Data System (ADS)

Craps, Ben; Evnin, Oleg; Nguyen, Kévin

2017-02-01

Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.

Generalized formula for electron emission taking account of the polaron effect

NASA Astrophysics Data System (ADS)

Barengolts, Yu A.; Beril, S. I.; Barengolts, S. A.

2018-01-01

A generalized formula is derived for the electron emission current as a function of temperature, field, and electron work function in a metal-dielectric system that takes account of the quantum nature of the image forces. In deriving the formula, the Fermi-Dirac distribution for electrons in a metal and the quantum potential of the image obtained in the context of electron polaron theory are used.

Quantum Dynamics and a Semiclassical Description of the Photon.

ERIC Educational Resources Information Center

Henderson, Giles

1980-01-01

Uses computer graphics and nonstationary, superposition wave functions to reveal the dynamic quantum trajectories of several molecular and electronic transitions. These methods are then coupled with classical electromagnetic theory to provide a conceptually clear picture of the emission process and emitted radiation localized in time and space.…

Assessment of the electronic structure and properties of trichothecene toxins using density functional theory

USDA-ARS?s Scientific Manuscript database

A comprehensive quantum chemical study was carried out on 34 type A and type B trichothecenes, including selected derivatives and biosynthetic precursors of deoxynivalenol, nivalenol, and T-2 toxin. Quantum parameters, Natural Bond Orbital (NBO) analysis, and molecular properties were calculated on ...

Force-field functor theory: classical force-fields which reproduce equilibrium quantum distributions

PubMed Central

Babbush, Ryan; Parkhill, John; Aspuru-Guzik, Alán

2013-01-01

Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory. PMID:24790954

Dynamical conductivity at the dirty superconductor-metal quantum phase transition

NASA Astrophysics Data System (ADS)

Hoyos, J. A.; Del Maestro, Adrian; Rosenow, Bernd; Vojta, Thomas

2011-03-01

We study the transport properties of ultrathin disordered nanowires in the neighborhood of the superconductor-metal quantum phase transition. To this end we combine numerical calculations with analytical strong-disorder renormalization group results. The quantum critical conductivity at zero temperature diverges logarithmically as a function of frequency. In the metallic phase, it obeys activated scaling associated with an infinite-randomness quantum critical point. We extend the scaling theory to higher dimensions and discuss implications for experiments. Financial support: Fapesp, CNPq, NSF, and Research Corporation.

Kohn-Sham approach to quantum electrodynamical density-functional theory: Exact time-dependent effective potentials in real space.

PubMed

Flick, Johannes; Ruggenthaler, Michael; Appel, Heiko; Rubio, Angel

2015-12-15

The density-functional approach to quantum electrodynamics extends traditional density-functional theory and opens the possibility to describe electron-photon interactions in terms of effective Kohn-Sham potentials. In this work, we numerically construct the exact electron-photon Kohn-Sham potentials for a prototype system that consists of a trapped electron coupled to a quantized electromagnetic mode in an optical high-Q cavity. Although the effective current that acts on the photons is known explicitly, the exact effective potential that describes the forces exerted by the photons on the electrons is obtained from a fixed-point inversion scheme. This procedure allows us to uncover important beyond-mean-field features of the effective potential that mark the breakdown of classical light-matter interactions. We observe peak and step structures in the effective potentials, which can be attributed solely to the quantum nature of light; i.e., they are real-space signatures of the photons. Our findings show how the ubiquitous dipole interaction with a classical electromagnetic field has to be modified in real space to take the quantum nature of the electromagnetic field fully into account.

Is quantum theory a form of statistical mechanics?

NASA Astrophysics Data System (ADS)

Adler, S. L.

2007-05-01

We give a review of the basic themes of my recent book: Adler S L 2004 Quantum Theory as an Emergent Phenomenon (Cambridge: Cambridge University Press). We first give motivations for considering the possibility that quantum mechanics is not exact, but is instead an accurate asymptotic approximation to a deeper level theory. For this deeper level, we propose a non-commutative generalization of classical mechanics, that we call "trace dynamics", and we give a brief survey of how it works, considering for simplicity only the bosonic case. We then discuss the statistical mechanics of trace dynamics and give our argument that with suitable approximations, the Ward identities for trace dynamics imply that ensemble averages in the canonical ensemble correspond to Wightman functions in quantum field theory. Thus, quantum theory emerges as the statistical thermodynamics of trace dynamics. Finally, we argue that Brownian motion corrections to this thermodynamics lead to stochastic corrections to the Schrödinger equation, of the type that have been much studied in the "continuous spontaneous localization" model of objective state vector reduction. In appendices to the talk, we give details of the existence of a conserved operator in trace dynamics that encodes the structure of the canonical algebra, of the derivation of the Ward identities, and of the proof that the stochastically-modified Schrödinger equation leads to state vector reduction with Born rule probabilities.

A Holoinformational Model of the Physical Observer

NASA Astrophysics Data System (ADS)

di Biase, Francisco

2013-09-01

The author proposes a holoinformational view of the observer based, on the holonomic theory of brain/mind function and quantum brain dynamics developed by Karl Pribram, Sir John Eccles, R.L. Amoroso, Hameroff, Jibu and Yasue, and in the quantumholographic and holomovement theory of David Bohm. This conceptual framework is integrated with nonlocal information properties of the Quantum Field Theory of Umesawa, with the concept of negentropy, order, and organization developed by Shannon, Wiener, Szilard and Brillouin, and to the theories of self-organization and complexity of Prigogine, Atlan, Jantsch and Kauffman. Wheeler's "it from bit" concept of a participatory universe, and the developments of the physics of information made by Zureck and others with the concepts of statistical entropy and algorithmic entropy, related to the number of bits being processed in the mind of the observer are also considered. This new synthesis gives a self-organizing quantum nonlocal informational basis for a new model of awareness in a participatory universe. In this synthesis, awareness is conceived as meaningful quantum nonlocal information interconnecting the brain and the cosmos, by a holoinformational unified field (integrating nonlocal holistic (quantum) and local (Newtonian). We propose that the cosmology of the physical observer is this unified nonlocal quantum-holographic cosmos manifesting itself through awareness, interconnected in a participatory holistic and indivisible way the human mind-brain to all levels of the self-organizing holographic anthropic multiverse.

Renormalizable Quantum Field Theories in the Large -n Limit

NASA Astrophysics Data System (ADS)

Guruswamy, Sathya

1995-01-01

In this thesis, we study two examples of renormalizable quantum field theories in the large-N limit. Chapter one is a general introduction describing physical motivations for studying such theories. In chapter two, we describe the large-N method in field theory and discuss the pioneering work of 't Hooft in large-N two-dimensional Quantum Chromodynamics (QCD). In chapter three we study a spherically symmetric approximation to four-dimensional QCD ('spherical QCD'). We recast spherical QCD into a bilocal (constrained) theory of hadrons which in the large-N limit is equivalent to large-N spherical QCD for all energy scales. The linear approximation to this theory gives an eigenvalue equation which is the analogue of the well-known 't Hooft's integral equation in two dimensions. This eigenvalue equation is a scale invariant one and therefore leads to divergences in the theory. We give a non-perturbative renormalization prescription to cure this and obtain a beta function which shows that large-N spherical QCD is asymptotically free. In chapter four, we review the essentials of conformal field theories in two and higher dimensions, particularly in the context of critical phenomena. In chapter five, we study the O(N) non-linear sigma model on three-dimensional curved spaces in the large-N limit and show that there is a non-trivial ultraviolet stable critical point at which it becomes conformally invariant. We study this model at this critical point on examples of spaces of constant curvature and compute the mass gap in the theory, the free energy density (which turns out to be a universal function of the information contained in the geometry of the manifold) and the two-point correlation functions. The results we get give an indication that this model is an example of a three-dimensional analogue of a rational conformal field theory. A conclusion with a brief summary and remarks follows at the end.

More on Weinberg's no-go theorem in quantum gravity

NASA Astrophysics Data System (ADS)

Nagahama, Munehiro; Oda, Ichiro

2018-05-01

We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the G L (4 ) symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.

Quantum learning of classical stochastic processes: The completely positive realization problem

NASA Astrophysics Data System (ADS)

Monràs, Alex; Winter, Andreas

2016-01-01

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651-664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print arXiv:1303.3771(2013)].

Anatomy of quantum critical wave functions in dissipative impurity problems

NASA Astrophysics Data System (ADS)

Blunden-Codd, Zach; Bera, Soumya; Bruognolo, Benedikt; Linden, Nils-Oliver; Chin, Alex W.; von Delft, Jan; Nazir, Ahsan; Florens, Serge

2017-02-01

Quantum phase transitions reflect singular changes taking place in a many-body ground state; however, computing and analyzing large-scale critical wave functions constitutes a formidable challenge. Physical insights into the sub-Ohmic spin-boson model are provided by the coherent-state expansion (CSE), which represents the wave function by a linear combination of classically displaced configurations. We find that the distribution of low-energy displacements displays an emergent symmetry in the absence of spontaneous symmetry breaking while experiencing strong fluctuations of the order parameter near the quantum critical point. Quantum criticality provides two strong fingerprints in critical low-energy modes: an algebraic decay of the average displacement and a constant universal average squeezing amplitude. These observations, confirmed by extensive variational matrix-product-state (VMPS) simulations and field theory arguments, offer precious clues into the microscopics of critical many-body states in quantum impurity models.

Conformal and Nearly Conformal Theories at Large N

NASA Astrophysics Data System (ADS)

Tarnoplskiy, Grigory M.

In this thesis we present new results in conformal and nearly conformal field theories in various dimensions. In chapter two, we study different properties of the conformal Quantum Electrodynamics (QED) in continuous dimension d. At first we study conformal QED using large Nf methods, where Nf is the number of massless fermions. We compute its sphere free energy as a function of d, ignoring the terms of order 1/Nf and higher. For finite Nf we use the epsilon-expansion. Next we use a large Nf diagrammatic approach to calculate the leading corrections to CT, the coefficient of the two-point function of the stress-energy tensor, and CJ, the coefficient of the two-point function of the global symmetry current. We present explicit formulae as a function of d and check them versus the expectations in 2 and 4 - epsilon dimensions. In chapter three, we discuss vacuum stability in 1 + 1 dimensional conformal field theories with external background fields. We show that the vacuum decay rate is given by a non-local two-form. This two-form is a boundary term that must be added to the effective in/out Lagrangian. The two-form is expressed in terms of a Riemann-Hilbert decomposition for background gauge fields, and is given by its novel "functional'' version in the gravitational case. In chapter four, we explore Tensor models. Such models possess the large N limit dominated by the melon diagrams. The quantum mechanics of a real anti-commuting rank-3 tensor has a large N limit similar to the Sachdev-Ye-Kitaev (SYK) model. We also discuss the quantum mechanics of a complex 3-index anti-commuting tensor and argue that it is equivalent in the large N limit to a version of SYK model with complex fermions. Finally, we discuss models of a commuting tensor in dimension d. We study the spectrum of the large N quantum field theory of bosonic rank-3 tensors using the Schwinger-Dyson equations. We compare some of these results with the 4 - epsilon expansion, finding perfect agreement. We also study the spectra of bosonic theories of rank q - 1 tensors with φq interactions.

Siewert solutions of transcendental equations, generalized Lambert functions and physical applications

NASA Astrophysics Data System (ADS)

Barsan, Victor

2018-05-01

Several classes of transcendental equations, mainly eigenvalue equations associated to non-relativistic quantum mechanical problems, are analyzed. Siewert's systematic approach of such equations is discussed from the perspective of the new results recently obtained in the theory of generalized Lambert functions and of algebraic approximations of various special or elementary functions. Combining exact and approximate analytical methods, quite precise analytical outputs are obtained for apparently untractable problems. The results can be applied in quantum and classical mechanics, magnetism, elasticity, solar energy conversion, etc.

Single-hidden-layer feed-forward quantum neural network based on Grover learning.

PubMed

Liu, Cheng-Yi; Chen, Chein; Chang, Ching-Ter; Shih, Lun-Min

2013-09-01

In this paper, a novel single-hidden-layer feed-forward quantum neural network model is proposed based on some concepts and principles in the quantum theory. By combining the quantum mechanism with the feed-forward neural network, we defined quantum hidden neurons and connected quantum weights, and used them as the fundamental information processing unit in a single-hidden-layer feed-forward neural network. The quantum neurons make a wide range of nonlinear functions serve as the activation functions in the hidden layer of the network, and the Grover searching algorithm outstands the optimal parameter setting iteratively and thus makes very efficient neural network learning possible. The quantum neuron and weights, along with a Grover searching algorithm based learning, result in a novel and efficient neural network characteristic of reduced network, high efficient training and prospect application in future. Some simulations are taken to investigate the performance of the proposed quantum network and the result show that it can achieve accurate learning. Copyright © 2013 Elsevier Ltd. All rights reserved.

Quantum dot properties in the multiband envelope-function approximation using boundary conditions based upon first-principles quantum calculations

NASA Astrophysics Data System (ADS)

Flory, Curt A.; Musgrave, Charles B.; Zhang, Zhiyong

2008-05-01

A number of physical processes involving quantum dots depend critically upon the “evanescent” electron eigenstate wave function that extends outside of the material surface into the surrounding region. These processes include electron tunneling through quantum dots, as well as interactions between multiple quantum dot structures. In order to unambiguously determine these evanescent fields, appropriate boundary conditions have been developed to connect the electronic solutions interior to the semiconductor quantum dot to exterior vacuum solutions. In standard envelope function theory, the interior wave function consists of products of band edge and envelope functions, and both must be considered when matching to the external solution. While the envelope functions satisfy tractable equations, the band edge functions are generally not known. In this work, symmetry arguments in the spherically symmetric approximation are used in conjunction with the known qualitative behavior of bonding and antibonding orbitals to catalog the behavior of the band edge functions at the unit cell boundary. This physical approximation allows consolidation of the influence of the band edge functions to two simple surface parameters that are incorporated into the boundary conditions and are straightforwardly computed by using numerical first-principles quantum techniques. These new boundary conditions are employed to analyze an isolated spherically symmetric semiconductor quantum dot in vacuum within the analytical model of Sercel and Vahala [Phys. Rev. Lett. 65, 239 (1990); Phys. Rev. B 42, 3690 (1990)]. Results are obtained for quantum dots made of GaAs and InP, which are compared with ab initio calculations that have appeared in the literature.

Functional Integration

NASA Astrophysics Data System (ADS)

Cartier, Pierre; DeWitt-Morette, Cecile

2006-11-01

Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

Functional Integration

NASA Astrophysics Data System (ADS)

Cartier, Pierre; DeWitt-Morette, Cecile

2010-06-01

Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

BV Quantization of the Rozansky-Witten Model

NASA Astrophysics Data System (ADS)

Chan, Kwokwai; Leung, Naichung Conan; Li, Qin

2017-10-01

We investigate the perturbative aspects of Rozansky-Witten's 3d {σ}-model (Rozansky and Witten in Sel Math 3(3):401-458, 1997) using Costello's approach to the Batalin-Vilkovisky (BV) formalism (Costello in Renormalization and effective field theory, American Mathematical Society, Providence, 2011). We show that the BV quantization (in Costello's sense) of the model, which produces a perturbative quantum field theory, can be obtained via the configuration space method of regularization due to Kontsevich (First European congress of mathematics, Paris, 1992) and Axelrod-Singer (J Differ Geom 39(1):173-213, 1994). We also study the factorization algebra structure of quantum observables following Costello-Gwilliam (Factorization algebras in quantum field theory, Cambridge University Press, Cambridge 2017). In particular, we show that the cohomology of local quantum observables on a genus g handle body is given by {H^*(X, (\\wedge^*T_X)^{⊗ g})} (where X is the target manifold), and we prove that the partition function reproduces the Rozansky-Witten invariants.

Quantum mechanical force field for hydrogen fluoride with explicit electronic polarization.

PubMed

Mazack, Michael J M; Gao, Jiali

2014-05-28

The explicit polarization (X-Pol) theory is a fragment-based quantum chemical method that explicitly models the internal electronic polarization and intermolecular interactions of a chemical system. X-Pol theory provides a framework to construct a quantum mechanical force field, which we have extended to liquid hydrogen fluoride (HF) in this work. The parameterization, called XPHF, is built upon the same formalism introduced for the XP3P model of liquid water, which is based on the polarized molecular orbital (PMO) semiempirical quantum chemistry method and the dipole-preserving polarization consistent point charge model. We introduce a fluorine parameter set for PMO, and find good agreement for various gas-phase results of small HF clusters compared to experiments and ab initio calculations at the M06-2X/MG3S level of theory. In addition, the XPHF model shows reasonable agreement with experiments for a variety of structural and thermodynamic properties in the liquid state, including radial distribution functions, interaction energies, diffusion coefficients, and densities at various state points.

Nonlinear responses of chiral fluids from kinetic theory

NASA Astrophysics Data System (ADS)

Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun

2018-01-01

The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.

Consistent resolution of some relativistic quantum paradoxes

NASA Astrophysics Data System (ADS)

Griffiths, Robert B.

2002-12-01

A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the paradoxes of spherical wave packet collapse, Bohm's formulation of the Einstein-Podolsky-Rosen paradox, and Hardy's paradox. It is argued that wave function collapse is not needed for introducing probabilities into relativistic quantum mechanics, and in any case should never be thought of as a physical process. Alternative approaches to stochastic time dependence can be used to construct a physical picture of the measurement process that is less misleading than collapse models. In particular, one can employ a coarse-grained but fully quantum-mechanical description in which particles move along trajectories, with behavior under Lorentz transformations the same as in classical relativistic physics, and detectors are triggered by particles reaching them along such trajectories. States entangled between spacelike separate regions are also legitimate quantum descriptions, and can be consistently handled by the formalism presented here. The paradoxes in question arise because of using modes of reasoning which, while correct for classical physics, are inconsistent with the mathematical structure of quantum theory, and are resolved (or tamed) by using a proper quantum analysis. In particular, there is no need to invoke, nor any evidence for, mysterious long-range superluminal influences, and thus no incompatibility, at least from this source, between relativity theory and quantum mechanics.

Bohmian mechanics without wave function ontology

NASA Astrophysics Data System (ADS)

Solé, Albert

2013-11-01

In this paper, I critically assess different interpretations of Bohmian mechanics that are not committed to an ontology based on the wave function being an actual physical object that inhabits configuration space. More specifically, my aim is to explore the connection between the denial of configuration space realism and another interpretive debate that is specific to Bohmian mechanics: the quantum potential versus guidance approaches. Whereas defenders of the quantum potential approach to the theory claim that Bohmian mechanics is better formulated as quasi-Newtonian, via the postulation of forces proportional to acceleration; advocates of the guidance approach defend the notion that the theory is essentially first-order and incorporates some concepts akin to those of Aristotelian physics. Here I analyze whether the desideratum of an interpretation of Bohmian mechanics that is both explanatorily adequate and not committed to configuration space realism favors one of these two approaches to the theory over the other. Contrary to some recent claims in the literature, I argue that the quasi-Newtonian approach based on the idea of a quantum potential does not come out the winner.

[Carl Friedrich von Weizsäcker and the interpretations of quantum theory].

PubMed

Stöckler, Manfred

2014-01-01

What are 'interpretations' of quantum theory? What are the differences between Carl Friedrich von Weizsäkcker's approach and contemporary views? The various interpretations of quantum mechanics give diverse answers to questions concerning the relation between measuring process and standard time development, the embedding of quantum objects in space ('wave-particle-dualism'), and the reference of state vectors. Does the wave function describe states in the real world or does it refer to our knowledge about nature? First, some relevant conceptions in Weizsäcker's book The Structure of Physics (Der Aufbau der Physik, 1985) are introduced. In a second step I point out why his approach is not any longer present in contemporary debates. One reason is that Weizsäcker is mainly affected by classical philosophy (Platon, Aristoteles, Kant). He could not esteem the philosophy of science that was developed in the spirit of logical empiricism. So he lost interest in disputes with Anglo-Saxon philosophy of quantum mechanics. Especially his interpretation of probability and his analysis of the collapse of the state function as change in knowledge differ from contemporary standard views. In recent years, however, epistemic interpretations of quantum mechanics are proposed that share some of Weizsäcker's intuitions.

Local renormalization group functions from quantum renormalization group and holographic bulk locality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakayama, Yu

Here, the bulk locality in the constructive holographic renormalization group requires miraculous cancellations among various local renormalization group functions. The cancellation is not only from the properties of the spectrum but from more detailed aspects of operator product expansions in relation to conformal anomaly. It is remarkable that one-loop computation of the universal local renormalization group functions in the weakly coupled limit of the N = 4 super Yang-Mills theory fulfils the necessary condition for the cancellation in the strongly coupled limit in its SL(2, Z) duality invariant form. From the consistency between the quantum renormalization group and the holographicmore » renormalization group, we determine some unexplored local renormalization group functions (e.g. diffusive term in the beta function for the gauge coupling constant) in the strongly coupled limit of the planar N = 4 super Yang-Mills theory.« less

Non-perturbative background field calculations

NASA Astrophysics Data System (ADS)

Stephens, C. R.

1988-01-01

New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation—perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation.

Quantum critical singularities in two-dimensional metallic XY ferromagnets

NASA Astrophysics Data System (ADS)

Varma, Chandra M.; Gannon, W. J.; Aronson, M. C.; Rodriguez-Rivera, J. A.; Qiu, Y.

2018-02-01

An important problem in contemporary physics concerns quantum-critical fluctuations in metals. A scaling function for the momentum, frequency, temperature, and magnetic field dependence of the correlation function near a 2D-ferromagnetic quantum-critical point (QCP) is constructed, and its singularities are determined by comparing to the recent calculations of the correlation functions of the dissipative quantum XY model (DQXY). The calculations are motivated by the measured properties of the metallic compound YFe2Al10 , which is a realization of the DQXY model in 2D. The frequency, temperature, and magnetic field dependence of the scaling function as well as the singularities measured in the experiments are given by the theory without adjustable exponents. The same model is applicable to the superconductor-insulator transitions, classes of metallic AFM-QCPs, and as fluctuations of the loop-current ordered state in hole-doped cuprates. The results presented here lend credence to the solution found for the 2D-DQXY model and its applications in understanding quantum-critical properties of diverse systems.

Intrinsic retrieval efficiency for quantum memories: A three-dimensional theory of light interaction with an atomic ensemble

NASA Astrophysics Data System (ADS)

Gujarati, Tanvi P.; Wu, Yukai; Duan, Luming

2018-03-01

Duan-Lukin-Cirac-Zoller quantum repeater protocol, which was proposed to realize long distance quantum communication, requires usage of quantum memories. Atomic ensembles interacting with optical beams based on off-resonant Raman scattering serve as convenient on-demand quantum memories. Here, a complete free space, three-dimensional theory of the associated read and write process for this quantum memory is worked out with the aim of understanding intrinsic retrieval efficiency. We develop a formalism to calculate the transverse mode structure for the signal and the idler photons and use the formalism to study the intrinsic retrieval efficiency under various configurations. The effects of atomic density fluctuations and atomic motion are incorporated by numerically simulating this system for a range of realistic experimental parameters. We obtain results that describe the variation in the intrinsic retrieval efficiency as a function of the memory storage time for skewed beam configuration at a finite temperature, which provides valuable information for optimization of the retrieval efficiency in experiments.

The Holst spin foam model via cubulations

NASA Astrophysics Data System (ADS)

Baratin, Aristide; Flori, Cecilia; Thiemann, Thomas

2012-10-01

Spin foam models are an attempt at a covariant or path integral formulation of canonical loop quantum gravity. The construction of such models usually relies on the Plebanski formulation of general relativity as a constrained BF theory and is based on the discretization of the action on a simplicial triangulation, which may be viewed as an ultraviolet regulator. The triangulation dependence can be removed by means of group field theory techniques, which allows one to sum over all triangulations. The main tasks for these models are the correct quantum implementation of the Plebanski constraints, the existence of a semiclassical sector implementing additional ‘Regge-like’ constraints arising from simplicial triangulations and the definition of the physical inner product of loop quantum gravity via group field theory. Here we propose a new approach to tackle these issues stemming directly from the Holst action for general relativity, which is also a proper starting point for canonical loop quantum gravity. The discretization is performed by means of a ‘cubulation’ of the manifold rather than a triangulation. We give a direct interpretation of the resulting spin foam model as a generating functional for the n-point functions on the physical Hilbert space at finite regulator. This paper focuses on ideas and tasks to be performed before the model can be taken seriously. However, our analysis reveals some interesting features of this model: firstly, the structure of its amplitudes differs from the standard spin foam models. Secondly, the tetrad n-point functions admit a ‘Wick-like’ structure. Thirdly, the restriction to simple representations does not automatically occur—unless one makes use of the time gauge, just as in the classical theory.

Hamiltonian lattice field theory: Computer calculations using variational methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zako, Robert L.

1991-12-03

I develop a variational method for systematic numerical computation of physical quantities -- bound state energies and scattering amplitudes -- in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. I present an algorithm for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. I also show how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato`s generalizations of Temple`s formula. The algorithm could bemore » adapted to systems such as atoms and molecules. I show how to compute Green`s functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green`s functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. I discuss the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, I do not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. I apply the method to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. I describe a computer implementation of the method and present numerical results for simple quantum mechanical systems.« less

Corner entanglement as a probe of quantum criticality

NASA Astrophysics Data System (ADS)

Witczak-Krempa, William; Bueno, Pablo; Myers, Robert C.

The entanglement entropy in many gapless quantum systems in 2+1D receives a contribution from corners in the entangling surface. It is characterized by a universal function a (θ) that depends non-trivially on the corner opening angle θ. Focusing on a large family of quantum critical theories with emergent Lorentz invariance (CFTs), we argue that the smooth limit a (θ ~ π) is entirely determined by the energy-density or stress tensor 2-point function coefficient. This explains recent results obtained via cutting edge simulations on the quantum critical Ising, XY and Heisenberg models. We also show how to extract the full thermal entropy of the quantum critical system using corner entanglement of the groundstate alone. ** Bueno, Myers, WK, Phys. Rev. Lett. (2015) Work supported by Perimeter Institute and NSERC.

Transition operators in acoustic-wave diffraction theory. I - General theory. II - Short-wavelength behavior, dominant singularities of Zk0 and Zk0 exp -1

NASA Technical Reports Server (NTRS)

Hahne, G. E.

1991-01-01

A formal theory of the scattering of time-harmonic acoustic scalar waves from impenetrable, immobile obstacles is established. The time-independent formal scattering theory of nonrelativistic quantum mechanics, in particular the theory of the complete Green's function and the transition (T) operator, provides the model. The quantum-mechanical approach is modified to allow the treatment of acoustic-wave scattering with imposed boundary conditions of impedance type on the surface (delta-Omega) of an impenetrable obstacle. With k0 as the free-space wavenumber of the signal, a simplified expression is obtained for the k0-dependent T operator for a general case of homogeneous impedance boundary conditions for the acoustic wave on delta-Omega. All the nonelementary operators entering the expression for the T operator are formally simple rational algebraic functions of a certain invertible linear radiation impedance operator which maps any sufficiently well-behaved complex-valued function on delta-Omega into another such function on delta-Omega. In the subsequent study, the short-wavelength and the long-wavelength behavior of the radiation impedance operator and its inverse (the 'radiation admittance' operator) as two-point kernels on a smooth delta-Omega are studied for pairs of points that are close together.

Phosphorene quantum dot-fullerene nanocomposites for solar energy conversion: An unexplored inorganic-organic nanohybrid with novel photovoltaic properties

NASA Astrophysics Data System (ADS)

Rajbanshi, Biplab; Kar, Moumita; Sarkar, Pallavi; Sarkar, Pranab

2017-10-01

Using the self-consistent charge density-functional based tight-binding (SCC-DFTB) method, coupled with time-dependent density functional theory (TDDFT) calculations, for the first time we explore the possibility of use of phosphorene quantum dots in solar energy harvesting devices. The phosphorene quantum dots-fullerene (PQDs-PCBA) nanocomposites show type-II band alignment indicating spatial separation of charge carriers. The TDDFT calculations also show that the PQD-fullerene nanocomposites seem to be exciting material for future generation solar energy harvester, with extremely fast charge transfer and very poor recombination rate.

Development of multicomponent hybrid density functional theory with polarizable continuum model for the analysis of nuclear quantum effect and solvent effect on NMR chemical shift.

PubMed

Kanematsu, Yusuke; Tachikawa, Masanori

2014-04-28

We have developed the multicomponent hybrid density functional theory [MC_(HF+DFT)] method with polarizable continuum model (PCM) for the analysis of molecular properties including both nuclear quantum effect and solvent effect. The chemical shifts and H/D isotope shifts of the picolinic acid N-oxide (PANO) molecule in chloroform and acetonitrile solvents are applied by B3LYP electron exchange-correlation functional for our MC_(HF+DFT) method with PCM (MC_B3LYP/PCM). Our MC_B3LYP/PCM results for PANO are in reasonable agreement with the corresponding experimental chemical shifts and isotope shifts. We further investigated the applicability of our method for acetylacetone in several solvents.

Fine Structure of Dark Energy and New Physics

DOE PAGES

Jejjala, Vishnu; Kavic, Michael; Minic, Djordje

2007-01-01

Following our recent work on the cosmological constant problem, in this letter we make a specific proposal regarding the fine structure (i.e., the spectrum) of dark energy. The proposal is motivated by a deep analogy between the blackbody radiation problem, which led to the development of quantum theory, and the cosmological constant problem, for which we have recently argued calls for a conceptual extension of the quantum theory. We argue that the fine structure of dark energy is governed by a Wien distribution, indicating its dual quantum and classical nature. We discuss observational consequences of such a picture of darkmore » energy and constrain the distribution function.« less

Sampling Molecular Conformers in Solution with Quantum Mechanical Accuracy at a Nearly Molecular-Mechanics Cost.

PubMed

Rosa, Marta; Micciarelli, Marco; Laio, Alessandro; Baroni, Stefano

2016-09-13

We introduce a method to evaluate the relative populations of different conformers of molecular species in solution, aiming at quantum mechanical accuracy, while keeping the computational cost at a nearly molecular-mechanics level. This goal is achieved by combining long classical molecular-dynamics simulations to sample the free-energy landscape of the system, advanced clustering techniques to identify the most relevant conformers, and thermodynamic perturbation theory to correct the resulting populations, using quantum-mechanical energies from density functional theory. A quantitative criterion for assessing the accuracy thus achieved is proposed. The resulting methodology is demonstrated in the specific case of cyanin (cyanidin-3-glucoside) in water solution.

A new look at the position operator in quantum theory

NASA Astrophysics Data System (ADS)

Lev, F. M.

2015-01-01

The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory by analogy with classical electrodynamics. As a consequence, an inevitable effect in standard theory is the wave packet spreading (WPS) of the photon coordinate wave function in directions perpendicular to the photon momentum. This leads to the following paradoxes: if the major part of photons emitted by stars are in wave packet states (what is the most probable scenario) then we should see not separate stars but only an almost continuous background from all stars; no anisotropy of the CMB radiation should be observable; data on gamma-ray bursts, signals from directional radio antennas (in particular, in experiments on Shapiro delay) and signals from pulsars show no signs of WPS. In addition, a problem arises why there are no signs of WPS for protons in the LHC ring. We argue that the above postulate is based neither on strong theoretical arguments nor on experimental data and propose a new consistent definition of the position operator. Then WPS in directions perpendicular to the particle momentum is absent and the paradoxes are resolved. Different components of the new position operator do not commute with each other and, as a consequence, there is no wave function in coordinate representation. Implications of the results for entanglement, quantum locality and the problem of time in quantum theory are discussed.

Quantum market games: implementing tactics via measurements

NASA Astrophysics Data System (ADS)

Pakula, I.; Piotrowski, E. W.; Sladkowski, J.

2006-02-01

A major development in applying quantum mechanical formalism to various fields has been made during the last few years. Quantum counterparts of Game Theory, Economy, as well as diverse approaches to Quantum Information Theory have been found and currently are being explored. Using connections between Quantum Game Theory and Quantum Computations, an application of the universality of a measurement based computation in Quantum Market Theory is presented.

Beable-guided quantum theories: Generalizing quantum probability laws

NASA Astrophysics Data System (ADS)

Kent, Adrian

2013-02-01

Beable-guided quantum theories (BGQT) are generalizations of quantum theory, inspired by Bell's concept of beables. They modify the quantum probabilities for some specified set of fundamental events, histories, or other elements of quasiclassical reality by probability laws that depend on the realized configuration of beables. For example, they may define an additional probability weight factor for a beable configuration, independent of the quantum dynamics. Beable-guided quantum theories can be fitted to observational data to provide foils against which to compare explanations based on standard quantum theory. For example, a BGQT could, in principle, characterize the effects attributed to dark energy or dark matter, or any other deviation from the predictions of standard quantum dynamics, without introducing extra fields or a cosmological constant. The complexity of the beable-guided theory would then parametrize how far we are from a standard quantum explanation. Less conservatively, we give reasons for taking suitably simple beable-guided quantum theories as serious phenomenological theories in their own right. Among these are the possibility that cosmological models defined by BGQT might in fact fit the empirical data better than any standard quantum explanation, and the fact that BGQT suggest potentially interesting nonstandard ways of coupling quantum matter to gravity.

Kirchhoff's rule for quantum wires

NASA Astrophysics Data System (ADS)

Kostrykin, V.; Schrader, R.

1999-01-01

We formulate and discuss one-particle quantum scattering theory on an arbitrary finite graph with n open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general boundary conditions at the vertices. This results in a scattering theory with n channels. The corresponding on-shell S-matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy E>0 is given explicitly in terms of the boundary conditions and the lengths of the internal lines. It is shown to be unitary, which may be viewed as the quantum version of Kirchhoff's law. We exhibit covariance and symmetry properties. It is symmetric if the boundary conditions are real. Also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low-energy behaviour of one theory gives the high-energy behaviour of the transformed theory. Finally, we provide a composition rule by which the on-shell S-matrix of a graph is factorizable in terms of the S-matrices of its subgraphs. All proofs use only known facts from the theory of self-adjoint extensions, standard linear algebra, complex function theory and elementary arguments from the theory of Hermitian symplectic forms.

Controlled Quantum Packets

NASA Technical Reports Server (NTRS)

DeMartino, Salvatore; DeSiena, Silvio

1996-01-01

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

Nuclear quantum effects in electronically adiabatic quantum time correlation functions: Application to the absorption spectrum of a hydrated electron

NASA Astrophysics Data System (ADS)

Turi, László; Hantal, György; Rossky, Peter J.; Borgis, Daniel

2009-07-01

A general formalism for introducing nuclear quantum effects in the expression of the quantum time correlation function of an operator in a multilevel electronic system is presented in the adiabatic limit. The final formula includes the nuclear quantum time correlation functions of the operator matrix elements, of the energy gap, and their cross terms. These quantities can be inferred and evaluated from their classical analogs obtained by mixed quantum-classical molecular dynamics simulations. The formalism is applied to the absorption spectrum of a hydrated electron, expressed in terms of the time correlation function of the dipole operator in the ground electronic state. We find that both static and dynamic nuclear quantum effects distinctly influence the shape of the absorption spectrum, especially its high energy tail related to transitions to delocalized electron states. Their inclusion does improve significantly the agreement between theory and experiment for both the low and high frequency edges of the spectrum. It does not appear sufficient, however, to resolve persistent deviations in the slow Lorentzian-like decay part of the spectrum in the intermediate 2-3 eV region.

Transformation Theory, Accelerating Frames, and Two Simple Problems

ERIC Educational Resources Information Center

Schmid, G. Bruno

1977-01-01

Presents an operator which transforms quantum functions to solve problems of the stationary state wave functions for a particle and the motion and spreading of a Gaussian wave packet in uniform gravitational fields. (SL)

Hall viscosity of hierarchical quantum Hall states

NASA Astrophysics Data System (ADS)

Fremling, M.; Hansson, T. H.; Suorsa, J.

2014-03-01

Using methods based on conformal field theory, we construct model wave functions on a torus with arbitrary flat metric for all chiral states in the abelian quantum Hall hierarchy. These functions have no variational parameters, and they transform under the modular group in the same way as the multicomponent generalizations of the Laughlin wave functions. Assuming the absence of Berry phases upon adiabatic variations of the modular parameter τ, we calculate the quantum Hall viscosity and find it to be in agreement with the formula, given by Read, which relates the viscosity to the average orbital spin of the electrons. For the filling factor ν =2/5 Jain state, which is at the second level in the hierarchy, we compare our model wave function with the numerically obtained ground state of the Coulomb interaction Hamiltonian in the lowest Landau level, and find very good agreement in a large region of the complex τ plane. For the same example, we also numerically compute the Hall viscosity and find good agreement with the analytical result for both the model wave function and the numerically obtained Coulomb wave function. We argue that this supports the notion of a generalized plasma analogy that would ensure that wave functions obtained using the conformal field theory methods do not acquire Berry phases upon adiabatic evolution.

Quantum Field Theory in (0 + 1) Dimensions

ERIC Educational Resources Information Center

Boozer, A. D.

2007-01-01

We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…

Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baldsiefen, Tim; Cangi, Attila; Eich, F. G.

Here, we derive an intrinsically temperature-dependent approximation to the correlation grand potential for many-electron systems in thermodynamical equilibrium in the context of finite-temperature reduced-density-matrix-functional theory (FT-RDMFT). We demonstrate its accuracy by calculating the magnetic phase diagram of the homogeneous electron gas. We compare it to known limits from highly accurate quantum Monte Carlo calculations as well as to phase diagrams obtained within existing exchange-correlation approximations from density functional theory and zero-temperature RDMFT.

Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas

DOE PAGES

Baldsiefen, Tim; Cangi, Attila; Eich, F. G.; ...

2017-12-18

Here, we derive an intrinsically temperature-dependent approximation to the correlation grand potential for many-electron systems in thermodynamical equilibrium in the context of finite-temperature reduced-density-matrix-functional theory (FT-RDMFT). We demonstrate its accuracy by calculating the magnetic phase diagram of the homogeneous electron gas. We compare it to known limits from highly accurate quantum Monte Carlo calculations as well as to phase diagrams obtained within existing exchange-correlation approximations from density functional theory and zero-temperature RDMFT.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fromm, Andrea; Bonitz, Michael; Dufty, James

The idea of treating quantum systems by semiclassical representations using effective quantum potentials (forces) has been successfully applied in equilibrium by many authors, see e.g. [D. Bohm, Phys. Rev. 85 (1986) 166 and 180; D.K. Ferry, J.R. Zhou, Phys. Rev. B 48 (1993) 7944; A.V. Filinov, M. Bonitz, W. Ebeling, J. Phys. A 36 (2003) 5957 and references cited therein]. Here, this idea is extended to nonequilibrium quantum systems in an external field. A gauge-invariant quantum kinetic theory for weakly inhomogeneous charged particle systems in a strong electromagnetic field is developed within the framework of nonequilibrium Green's functions. The equationmore » for the spectral density is simplified by introducing a classical (local) form for the kinetics. Nonlocal quantum effects are accounted for in this way by replacing the bare external confinement potential with an effective quantum potential. The equation for this effective potential is identified and solved for weak inhomogeneity in the collisionless limit. The resulting nonequilibrium spectral function is used to determine the density of states and the modification of the Born collision operator in the kinetic equation for the Wigner function due to quantum confinement effects.« less

Gaussian Hypothesis Testing and Quantum Illumination.

PubMed

Wilde, Mark M; Tomamichel, Marco; Lloyd, Seth; Berta, Mario

2017-09-22

Quantum hypothesis testing is one of the most basic tasks in quantum information theory and has fundamental links with quantum communication and estimation theory. In this paper, we establish a formula that characterizes the decay rate of the minimal type-II error probability in a quantum hypothesis test of two Gaussian states given a fixed constraint on the type-I error probability. This formula is a direct function of the mean vectors and covariance matrices of the quantum Gaussian states in question. We give an application to quantum illumination, which is the task of determining whether there is a low-reflectivity object embedded in a target region with a bright thermal-noise bath. For the asymmetric-error setting, we find that a quantum illumination transmitter can achieve an error probability exponent stronger than a coherent-state transmitter of the same mean photon number, and furthermore, that it requires far fewer trials to do so. This occurs when the background thermal noise is either low or bright, which means that a quantum advantage is even easier to witness than in the symmetric-error setting because it occurs for a larger range of parameters. Going forward from here, we expect our formula to have applications in settings well beyond those considered in this paper, especially to quantum communication tasks involving quantum Gaussian channels.

Feynman perturbation expansion for the price of coupon bond options and swaptions in quantum finance. I. Theory

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

2007-01-01

European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coupon bond option is included it makes the field theory nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed form approximation for the price of coupon bond option. A special case of the approximate bond option is shown to yield the industry standard one-factor HJM formula with exponential volatility.

Feynman perturbation expansion for the price of coupon bond options and swaptions in quantum finance. I. Theory.

PubMed

Baaquie, Belal E

2007-01-01

European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coupon bond option is included it makes the field theory nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed form approximation for the price of coupon bond option. A special case of the approximate bond option is shown to yield the industry standard one-factor HJM formula with exponential volatility.

Conceptual Foundations of Quantum Mechanics:. the Role of Evidence Theory, Quantum Sets, and Modal Logic

NASA Astrophysics Data System (ADS)

Resconi, Germano; Klir, George J.; Pessa, Eliano

Recognizing that syntactic and semantic structures of classical logic are not sufficient to understand the meaning of quantum phenomena, we propose in this paper a new interpretation of quantum mechanics based on evidence theory. The connection between these two theories is obtained through a new language, quantum set theory, built on a suggestion by J. Bell. Further, we give a modal logic interpretation of quantum mechanics and quantum set theory by using Kripke's semantics of modal logic based on the concept of possible worlds. This is grounded on previous work of a number of researchers (Resconi, Klir, Harmanec) who showed how to represent evidence theory and other uncertainty theories in terms of modal logic. Moreover, we also propose a reformulation of the many-worlds interpretation of quantum mechanics in terms of Kripke's semantics. We thus show how three different theories — quantum mechanics, evidence theory, and modal logic — are interrelated. This opens, on one hand, the way to new applications of quantum mechanics within domains different from the traditional ones, and, on the other hand, the possibility of building new generalizations of quantum mechanics itself.

Multicomponent density functional theory embedding formulation.

PubMed

Culpitt, Tanner; Brorsen, Kurt R; Pak, Michael V; Hammes-Schiffer, Sharon

2016-07-28

Multicomponent density functional theory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density is separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF(-) molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.

Multicomponent density functional theory embedding formulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Culpitt, Tanner; Brorsen, Kurt R.; Pak, Michael V.

Multicomponent density functional theory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density ismore » separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF{sup −} molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.« less

Recent developments in LIBXC - A comprehensive library of functionals for density functional theory

NASA Astrophysics Data System (ADS)

Lehtola, Susi; Steigemann, Conrad; Oliveira, Micael J. T.; Marques, Miguel A. L.

2018-01-01

LIBXC is a library of exchange-correlation functionals for density-functional theory. We are concerned with semi-local functionals (or the semi-local part of hybrid functionals), namely local-density approximations, generalized-gradient approximations, and meta-generalized-gradient approximations. Currently we include around 400 functionals for the exchange, correlation, and the kinetic energy, spanning more than 50 years of research. Moreover, LIBXC is by now used by more than 20 codes, not only from the atomic, molecular, and solid-state physics, but also from the quantum chemistry communities.

General theory of feedback control of a nuclear spin ensemble in quantum dots

NASA Astrophysics Data System (ADS)

Yang, Wen; Sham, L. J.

2013-12-01

We present a microscopic theory of the nonequilibrium nuclear spin dynamics driven by the electron and/or hole under continuous-wave pumping in a quantum dot. We show the correlated dynamics of the nuclear spin ensemble and the electron and/or hole under optical excitation as a quantum feedback loop and investigate the dynamics of the many nuclear spins as a nonlinear collective motion. This gives rise to three observable effects: (i) hysteresis, (ii) locking (avoidance) of the pump absorption strength to (from) the natural resonance, and (iii) suppression (amplification) of the fluctuation of weakly polarized nuclear spins, leading to prolonged (shortened) electron-spin coherence time. A single nonlinear feedback function is constructed which determines the different outcomes of the three effects listed above depending on the feedback being negative or positive. The general theory also helps to put in perspective the wide range of existing theories on the problem of a single electron spin in a nuclear spin bath.

The problems in quantum foundations in the light of gauge theories

NASA Astrophysics Data System (ADS)

Ne'Eman, Yuval

1986-04-01

We review the issues of nonseparability and seemingly acausal propagation of information in EPR, as displayed by experiments and the failure of Bell's inequalities. We show that global effects are in the very nature of the geometric structure of modern physical theories, occurring even at the classical level. The Aharonov-Bohm effect, magnetic monopoles, instantons, etc. result from the topology and homotopy features of the fiber bundle manifolds of gauge theories. The conservation of probabilities, a supposedly highly quantum effect, is also achieved through global geometry equations. The EPR observables all fit in such geometries, and space-time is a truncated representation and is not the correct arena for their understanding. Relativistic quantum field theory represents the global action of the measurement operators as the zero-momentum (and therefore spatially infinitely spread) limit of their wave functions (form factors). We also analyze the collapse of the state vector as a case of spontaneous symmetry breakdown in the apparatus-observed state interaction.

String theory, gauge theory and quantum gravity. Proceedings. Trieste Spring School and Workshop on String Theory, Gauge Theory and Quantum Gravity, Trieste (Italy), 11 - 22 Apr 1994.

NASA Astrophysics Data System (ADS)

1995-04-01

The following topics were dealt with: string theory, gauge theory, quantum gravity, quantum geometry, black hole physics and information loss, second quantisation of the Wilson loop, 2D Yang-Mills theory, topological field theories, equivariant cohomology, superstring theory and fermion masses, supergravity, topological gravity, waves in string cosmology, superstring theories, 4D space-time.

Loop Quantum Cosmology.

PubMed

Bojowald, Martin

2008-01-01

Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time. Supplementary material is available for this article at 10.12942/lrr-2008-4.

Shape dependence of two-cylinder Rényi entropies for free bosons on a lattice

NASA Astrophysics Data System (ADS)

Chojnacki, Leilee; Cook, Caleb Q.; Dalidovich, Denis; Hayward Sierens, Lauren E.; Lantagne-Hurtubise, Étienne; Melko, Roger G.; Vlaar, Tiffany J.

2016-10-01

Universal scaling terms occurring in Rényi entanglement entropies have the potential to bring new understanding to quantum critical points in free and interacting systems. Quantitative comparisons between analytical continuum theories and numerical calculations on lattice models play a crucial role in advancing such studies. In this paper, we exactly calculate the universal two-cylinder shape dependence of entanglement entropies for free bosons on finite-size square lattices, and compare to approximate functions derived in the continuum using several different Ansätze. Although none of these Ansätze are exact in the thermodynamic limit, we find that numerical fits are in good agreement with continuum functions derived using the anti-de Sitter/conformal field theory correspondence, an extensive mutual information model, and a quantum Lifshitz model. We use fits of our lattice data to these functions to calculate universal scalars defined in the thin-cylinder limit, and compare to values previously obtained for the free boson field theory in the continuum.

Quantum Structure of Space and Time

NASA Astrophysics Data System (ADS)

Duff, M. J.; Isham, C. J.

2012-07-01

Foreword Abdus Salam; Preface; List of participants; Part I. Quantum Gravity, Fields and Topology: 1. Some remarks on gravity and quantum mechanics Roger Penrose; 2. An experimental test of quantum gravity Don N. Page and C. D. Geilker; 3. Quantum mechanical origin of the sandwich theorem in classical gravitation theory Claudio Teitelboim; 4. θ-States induced by the diffeomorphism group in canonically quantized gravity C. J. Isham; 5. Strong coupling quantum gravity: an introduction Martin Pilati; 6. Quantizing fourth order gravity theories S. M. Christensen; 7. Green's functions, states and renormalisation M. R. Brown and A. C. Ottewill; 8. Introduction to quantum regge calculus Martin Roček and Ruth Williams; 9. Spontaneous symmetry breaking in curved space-time D. J. Toms; 10. Spontaneous symmetry breaking near a black hole M. S. Fawcett and B. F. Whiting; 11. Yang-Mills vacua in a general three-space G. Kunstatter; 12. Fermion fractionization in physics R. Jackiw; Part II. Supergravity: 13. The new minimal formulation of N=1 supergravity and its tensor calculus M. F. Sohnius and P. C. West; 14. A new deteriorated energy-momentum tensor M. J. Duff and P. K. Townsend; 15. Off-shell N=2 and N=4 supergravity in five dimensions P. Howe; 16. Supergravity in high dimensions P. van Niewenhuizen; 17. Building linearised extended supergravities J. G. Taylor; 18. (Super)gravity in the complex angular momentum plane M. T. Grisaru; 19. The multiplet structure of solitons in the O(2) supergravity theory G. W. Gibbons; 20. Ultra-violet properties of supersymmetric gauge theory S. Ferrara; 21. Extended supercurrents and the ultra-violet finiteness of N=4 supersymmetric Yang-Mills theories K. S. Stelle; 22. Duality rotations B. Zumino; Part III. Cosmology and the Early Universe: 23. Energy, stability and cosmological constant S. Deser; 24. Phase transitions in the early universe T. W. B. Kibble; 25. Complete cosmological theories L. P. Grishchuk and Ya. B. Zeldovich; 26. The cosmological constant and the weak anthropic principle S. W. Hawking.

Understanding photon sideband statistics and correlation for determining phonon coherence

NASA Astrophysics Data System (ADS)

Ding, Ding; Yin, Xiaobo; Li, Baowen

2018-01-01

Generating and detecting coherent high-frequency heat-carrying phonons have been topics of great interest in recent years. Although there have been successful attempts in generating and observing coherent phonons, rigorous techniques to characterize and detect phonon coherence in a crystalline material have been lagging compared to what has been achieved for photons. One main challenge is a lack of detailed understanding of how detection signals for phonons can be related to coherence. The quantum theory of photoelectric detection has greatly advanced the ability to characterize photon coherence in the past century, and a similar theory for phonon detection is necessary. Here, we reexamine the optical sideband fluorescence technique that has been used to detect high-frequency phonons in materials with optically active defects. We propose a quantum theory of phonon detection using the sideband technique and found that there are distinct differences in sideband counting statistics between thermal and coherent phonons. We further propose a second-order correlation function unique to sideband signals that allows for a rigorous distinction between thermal and coherent phonons. Our theory is relevant to a correlation measurement with nontrivial response functions at the quantum level and can potentially bridge the gap of experimentally determining phonon coherence to be on par with that of photons.

Derivation of the cut-off length from the quantum quadratic enhancement of a mass in vacuum energy constant Lambda

NASA Astrophysics Data System (ADS)

Fukushima, Kimichika; Sato, Hikaru

2018-04-01

Ultraviolet self-interaction energies in field theory sometimes contain meaningful physical quantities. The self-energies in such as classical electrodynamics are usually subtracted from the rest mass. For the consistent treatment of energies as sources of curvature in the Einstein field equations, this study includes these subtracted self-energies into vacuum energy expressed by the constant Lambda (used in such as Lambda-CDM). In this study, the self-energies in electrodynamics and macroscopic classical Einstein field equations are examined, using the formalisms with the ultraviolet cut-off scheme. One of the cut-off formalisms is the field theory in terms of the step-function-type basis functions, developed by the present authors. The other is a continuum theory of a fundamental particle with the same cut-off length. Based on the effectiveness of the continuum theory with the cut-off length shown in the examination, the dominant self-energy is the quadratic term of the Higgs field at a quantum level (classical self-energies are reduced to logarithmic forms by quantum corrections). The cut-off length is then determined to reproduce today's tiny value of Lambda for vacuum energy. Additionally, a field with nonperiodic vanishing boundary conditions is treated, showing that the field has no zero-point energy.

Application of Percolation Theory to Complex Interconnected Networks in Advanced Functional Composites

NASA Astrophysics Data System (ADS)

Hing, P.

2011-11-01

Percolation theory deals with the behaviour of connected clusters in a system. Originally developed for studying the flow of liquid in a porous body, the percolation theory has been extended to quantum computation and communication, entanglement percolation in quantum networks, cosmology, chaotic situations, properties of disordered solids, pandemics, petroleum industry, finance, control of traffic and so on. In this paper, the application of various models of the percolation theory to predict and explain the properties of a specially developed family of dense sintered and highly refractory Al2O3-W composites for potential application in high intensity discharge light sources such as high pressure sodium lamps and ceramic metal halide lamps are presented and discussed. The low cost, core-shell concept can be extended to develop functional composite materials with unusual dielectric, electrical, magnetic, superconducting, and piezoelectric properties starting from a classical insulator. The core shell concept can also be applied to develop catalysts with high specific surface areas with minimal amount of expensive platinium, palladium or rare earth nano structured materials for light harvesting, replicating natural photosynthesis, in synthetic zeolite composites for the cracking and separation of crude oil. There is also possibility of developing micron and nanosize Faraday cages for quantum devices, nano electronics and spintronics. The possibilities are limitless.

The pursuit of locality in quantum mechanics

NASA Astrophysics Data System (ADS)

Hodkin, Malcolm

The rampant success of quantum theory is the result of applications of the 'new' quantum mechanics of Schrodinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum Electro-dynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9), and Quantum Chromodynamics (1973-); in fact, this success of 'the' quantum theory has depended on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously accurate calculational tools there has been no sensible explanation of all that is going on. It is even argued that such an understanding is nothing to do with physics. A long-standing and famous illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935). Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency. This project encompasses a detailed, critical survey of the tangled history of Position within quantum theories. The first step is to show that, contrary to appearances, canonical quantum mechanics has only a vague notion of locality. After analysing a number of previous attempts at a 'relativistic quantum mechanics', two lines of thought are considered in detail. The first is the work of Wan and students, which is shown to be no real improvement on the iisu.al 'nonrelativistic' theory. The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface in space-time. There remain considerable difficulties in the way of producing a consistent scheme here. To keep things nicely stirred up, the author then proposes his own approach - an adaptation of Feynman's QED propagators. This new approach is distinguished from Feynman's since the propagator or Green's function is not obtained by Feynman's rule. The type of equation solved is also different: instead of an initial-value problem, a solution that obeys a time-symmetric causality criterion is found for an inhomogeneous partial differential equation with homogeneous boundary conditions. To make the consideration of locality more precise, some results of Fourier transform theory are presented in a form that is directly applicable. Somewhat away from the main thrust of the thesis, there is also an attempt to explain, the manner in which quantum effects disappear as the number of particles increases in such things as experimental realisations of the EPR and de Broglie thought experiments.

Can we Predict Quantum Yields Using Excited State Density Functional Theory for New Families of Fluorescent Dyes?

NASA Astrophysics Data System (ADS)

Kohn, Alexander W.; Lin, Zhou; Shepherd, James J.; Van Voorhis, Troy

2016-06-01

For a fluorescent dye, the quantum yield characterizes the efficiency of energy transfer from the absorbed light to the emitted fluorescence. In the screening among potential families of dyes, those with higher quantum yields are expected to have more advantages. From the perspective of theoreticians, an efficient prediction of the quantum yield using a universal excited state electronic structure theory is in demand but still challenging. The most representative examples for such excited state theory include time-dependent density functional theory (TDDFT) and restricted open-shell Kohn-Sham (ROKS). In the present study, we explore the possibility of predicting the quantum yields for conventional and new families of organic dyes using a combination of TDDFT and ROKS. We focus on radiative (kr) and nonradiative (knr) rates for the decay of the first singlet excited state (S_1) into the ground state (S_0) in accordance with Kasha's rule. M. Kasha, Discuss. Faraday Soc., 9, 14 (1950). For each dye compound, kr is calculated with the S_1-S_0 energy gap and transition dipole moment obtained using ROKS and TDDFT respectively at the relaxed S_1 geometry. Our predicted kr agrees well with the experimental value, so long as the order of energy levels is correctly predicted. Evaluation of knr is less straightforward as multiple processes are involved. Our study focuses on the S_1-T_1 intersystem crossing (ISC) and the S_1-S_0 internal conversion (IC): we investigate the properties that allow us to model the knr value using a Marcus-like expression, such as the Stokes shift, the reorganization energy, and the S_1-T_1 and S_1-S_0 energy gaps. Taking these factors into consideration, we compare our results with those obtained using the actual Marcus theory and provide explanation for discrepancy. T. Kowalczyk, T. Tsuchimochi, L. Top, P.-T. Chen, and T. Van Voorhis, J. Chem. Phys., 138, 164101 (2013). M. Kasha, Discuss. Faraday Soc., 9, 14 (1950).

The future (and past) of quantum theory after the Higgs boson: a quantum-informational viewpoint.

PubMed

Plotnitsky, Arkady

2016-05-28

Taking as its point of departure the discovery of the Higgs boson, this article considers quantum theory, including quantum field theory, which predicted the Higgs boson, through the combined perspective of quantum information theory and the idea of technology, while also adopting anon-realistinterpretation, in 'the spirit of Copenhagen', of quantum theory and quantum phenomena themselves. The article argues that the 'events' in question in fundamental physics, such as the discovery of the Higgs boson (a particularly complex and dramatic, but not essentially different, case), are made possible by the joint workings of three technologies: experimental technology, mathematical technology and, more recently, digital computer technology. The article will consider the role of and the relationships among these technologies, focusing on experimental and mathematical technologies, in quantum mechanics (QM), quantum field theory (QFT) and finite-dimensional quantum theory, with which quantum information theory has been primarily concerned thus far. It will do so, in part, by reassessing the history of quantum theory, beginning with Heisenberg's discovery of QM, in quantum-informational and technological terms. This history, the article argues, is defined by the discoveries of increasingly complex configurations of observed phenomena and the emergence of the increasingly complex mathematical formalism accounting for these phenomena, culminating in the standard model of elementary-particle physics, defining the current state of QFT. © 2016 The Author(s).

No extension of quantum theory can have improved predictive power.

PubMed

Colbeck, Roger; Renner, Renato

2011-08-02

According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory that removes this indeterminism, as suspected by Einstein, Podolsky and Rosen. Although this has been shown to be impossible, existing results do not imply that the current theory is maximally informative. Here we ask the more general question of whether any improved predictions can be achieved by any extension of quantum theory. Under the assumption that measurements can be chosen freely, we answer this question in the negative: no extension of quantum theory can give more information about the outcomes of future measurements than quantum theory itself. Our result has significance for the foundations of quantum mechanics, as well as applications to tasks that exploit the inherent randomness in quantum theory, such as quantum cryptography.

No extension of quantum theory can have improved predictive power

PubMed Central

Colbeck, Roger; Renner, Renato

2011-01-01

According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory that removes this indeterminism, as suspected by Einstein, Podolsky and Rosen. Although this has been shown to be impossible, existing results do not imply that the current theory is maximally informative. Here we ask the more general question of whether any improved predictions can be achieved by any extension of quantum theory. Under the assumption that measurements can be chosen freely, we answer this question in the negative: no extension of quantum theory can give more information about the outcomes of future measurements than quantum theory itself. Our result has significance for the foundations of quantum mechanics, as well as applications to tasks that exploit the inherent randomness in quantum theory, such as quantum cryptography. PMID:21811240

Many-Body Theory of Proton-Generated Point Defects for Losses of Electron Energy and Photons in Quantum Wells

NASA Astrophysics Data System (ADS)

Huang, Danhong; Iurov, Andrii; Gao, Fei; Gumbs, Godfrey; Cardimona, D. A.

2018-02-01

The effects of point defects on the loss of either energies of ballistic electron beams or incident photons are studied by using a many-body theory in a multi-quantum-well system. This theory includes the defect-induced vertex correction to a bare polarization function of electrons within the ladder approximation, and the intralayer and interlayer screening of defect-electron interactions is also taken into account in the random-phase approximation. The numerical results of defect effects on both energy-loss and optical-absorption spectra are presented and analyzed for various defect densities, numbers of quantum wells, and wave vectors. The diffusion-reaction equation is employed for calculating distributions of point defects in a layered structure. For completeness, the production rate for Frenkel-pair defects and their initial concentration are obtained based on atomic-level molecular-dynamics simulations. By combining the defect-effect, diffusion-reaction, and molecular-dynamics models with an available space-weather-forecast model, it will be possible in the future to enable specific designing for electronic and optoelectronic quantum devices that will be operated in space with radiation-hardening protection and, therefore, effectively extend the lifetime of these satellite onboard electronic and optoelectronic devices. Specifically, this theory can lead to a better characterization of quantum-well photodetectors not only for high quantum efficiency and low dark current density but also for radiation tolerance or mitigating the effects of the radiation.

Book Review:

NASA Astrophysics Data System (ADS)

Folacci, Antoine; Jensen, Bruce

2003-12-01

Thanks to its impressive success in the second half of the 20th century, both in high-energy physics and in critical phenomena, quantum field theory has enjoyed an abundant literature. We therefore greet yet another book on this subject with caution: what can a monograph on quantum field theory bring now that is new, either conceptually or pedagogically? But when it is written by a physicist such as Bryce DeWitt, who has made his own contribution to the collection of field theory books with The Global Approach to Quantum Field Theory, all suspicion is naturally abandoned. One knows in advance that this book can only lead to a genuine enrichment of the literature. DeWitt has made a formidable contribution to various areas of physics: general relativity, the interpretation of quantum mechanics, and most of all the quantization of non-Abelian gauge theories and quantum gravity. In addition, his pedagogical publications, especially the Les Houches schools of 1963 and 1983 [1, 2], have had a great impact on quantum field theory. All this makes the reader keen to pick up his new work and a deeper reading confirms the reviewer's initial enthusiasm. We must begin by alerting the potential readers of this book that it cannot be compared to any other book in the field (unless of course we are talking about references [1] and [2], of which the book under review is an extension and reworking). This uniqueness applies to both the scientific content and the way the ideas are presented. A quick description of this book and a brief explanation of its title should convince the reader of the book's unique quality. For DeWitt, a central concept of field theory is that of `space of histories'. For a field varphii defined on a given spacetime M, the set of all varphii(x) for all x in all charts of M defines its history. It is the space Phi of all possible histories (dynamically allowed or not) of the fields defined on M which is called the `space of histories' by DeWitt. If only bosonic fields are considered, the space of histories is an infinite-dimensional manifold and if fermionic fields are also present, it must be viewed as an infinite-dimensional supermanifold [3]. The fields can then be regarded as coordinates on these structures, and the geometrical notions of differentiation, metric, connections, measure, as well as the geodesics which can be defined on it, are of fundamental importance in the development of the formalism of quantum field theory. This is the so-called global approach to quantum field theory where time does not play any particular role, and quantization is then naturally realized covariantly using tools such as the Peierls bracket (a covariant generalization of Poisson bracket), the Schwinger variational principle and Feynman sums over histories. However, it should be noted that the boycott of canonical methods by DeWitt is not total: when he judges they genuinely illuminate the physics of a problem, he does not hesitate to descend from the global point of view and to use them. In a few words, we have in fact described the research program initiated by DeWitt forty years ago, which has progressively evolved in order to take into account the latest development of gauge theories. While the Les Houches Lectures of 1963 [1] were mainly concentrated on the formal structure and the quantization of Yang--Mills and gravitational fields, the present book also deals with more general gauge theories including those with open gauge algebras and structure functions, and therefore supergravity theories. More precisely, the book, more than a thousand pages in length, consists of eight parts and is completed by six appendices where certain technical aspects are singled out. An enormous variety of topics is covered, including the invariance transformations of the action functional, the Batalin--Vilkovisky formalism, Green's functions, the Peierls bracket, conservation laws, the theory of measurement, the Everett (or many worlds) interpretation of quantum mechanics, decoherence, the Schwinger variational principle and Feynman functional integrals, the heat kernel, aspects of quantization for linear systems in stationary and non-stationary backgrounds, the S-matrix, the background field method, the effective action and the Vilkovisky--DeWitt formalism, the quantization of gauge theories without ghosts, anomalies, black holes and Hawking radiation, renormalization, and more. It should be noted that DeWitt's book is rather difficult to read because of its great breadth. From the start he is faithful to his own view of field theory by developing a powerful formalism which permits him to discuss broad general features common to all field theories. He demands a considerable effort from the reader to penetrate his formalism, and a reading of Appendix~A which presents the basics of super-analysis is a prerequisite. To keep the reader on course, DeWitt offers a series of exercises on applications of global formalism in Part 8, nearly 200 pages worth. The exercises are to be worked in parallel with reading the text, starting from the beginning. It should be noted that these exercises previously appeared in references [1], [2] and [3], but here they have been worked out in some detail by the author. Before concluding, some criticisms. DeWitt has anticipated some criticism himself in the Preface, where he warns the reader that `this book is in no sense a reference book on quantum field theory and its application to particle physics. The selection of topics is idiosyncratic.' But the reviewers should add a few more remarks: (1) There are very few references. Of course, this is because the work is largely original. Even where the work of other researchers is presented, it has mostly been transformed by the DeWittian point of view. (2) There are very few diagrams, which sometimes hinders the exposition. In summary, in our opinion, this is one of the best books dealing with quantum field theory existing today. It will be of great interest for graduate and postgraduate students as well as workers in the domains of quantum field theory in flat and in curved spacetime and string theories. But we believe that the reader must have previously studied standard textbooks on quantum field theory and general relativity. Even with this preparation, it is by no means an easy book to read. However, the reward is to be able to share the deep and unique vision of the quantum theory of fields and its formalism by one of its greatest expositors. References [1] DeWitt B S 1965 Dynamical Theory of Groups and Fields (Les Houches Lectures 1963) (New York: Gordon and Breach) [2] DeWitt B S 1984 Relativity, Groups and Topology II (Les Houches Lectures 1983) ed R Stora and B S DeWitt (Amsterdam: North-Holland) [3] DeWitt B S 1994 Supermanifolds (Cambridge: Cambridge University Press)

Emergent geometric description for a topological phase transition in the Kitaev superconductor model

NASA Astrophysics Data System (ADS)

Kim, Ki-Seok; Park, Miok; Cho, Jaeyoon; Park, Chanyong

2017-10-01

Resorting to Wilsonian renormalization group (RG) transformations, we propose an emergent geometric description for a topological phase transition in the Kitaev superconductor model. An effective field theory consists of an emergent bulk action with an extra dimension, an ultraviolet (UV) boundary condition for an initial value of a coupling function, and an infrared (IR) effective action with a fully renormalized coupling function. The bulk action describes the evolution of the coupling function along the direction of the extra dimension, where the extra dimension is identified with an RG scale and the resulting equation of motion is nothing but a β function. In particular, the IR effective field theory turns out to be consistent with a Callan-Symanzik equation which takes into account both the bulk and IR boundary contributions. This derived Callan-Symanzik equation gives rise to a metric structure. Based on this emergent metric tensor, we uncover the equivalence of the entanglement entropy between the emergent geometric description and the quantum field theory in the vicinity of the quantum critical point.

Properties of resonance wave functions.

NASA Technical Reports Server (NTRS)

More, R. M.; Gerjuoy, E.

1973-01-01

Construction and study of resonance wave functions corresponding to poles of the Green's function for several illustrative models of theoretical interest. Resonance wave functions obtained from the Siegert and Kapur-Peierls definitions of the resonance energies are compared. The comparison especially clarifies the meaning of the normalization constant of the resonance wave functions. It is shown that the wave functions may be considered renormalized in a sense analogous to that of quantum field theory. However, this renormalization is entirely automatic, and the theory has neither ad hoc procedures nor infinite quantities.

Quantum Metric of Classic Physics

NASA Astrophysics Data System (ADS)

Machusky, Eugene

2017-09-01

By methods of differential geometry and number theory the following has been established: All fundamental physical constants are the medians of quasi-harmonic functions of relative space and relative time. Basic quantum units are, in fact, the gradients of normal distribution of standing waves between the points of pulsating spherical spiral, which are determined only by functional bonds of transcendental numbers PI and E. Analytically obtained values of rotational speed, translational velocity, vibrational speed, background temperature and molar mass give the possibility to evaluate all basic quantum units with practically unlimited accuracy. Metric of quantum physics really is two-dimensional image of motion of waves in three-dimensional space. Standard physical model is correct, but SI metric system is insufficiently exact at submillimeter distances.

Density functional theory and an experimentally-designed energy functional of electron density.

PubMed

Miranda, David A; Bueno, Paulo R

2016-09-21

We herein demonstrate that capacitance spectroscopy (CS) experimentally allows access to the energy associated with the quantum mechanical ground state of many-electron systems. Priorly, electrochemical capacitance, C [small mu, Greek, macron] [ρ], was previously understood from conceptual and computational density functional theory (DFT) calculations. Thus, we herein propose a quantum mechanical experiment-based variational method for electron charging processes based on an experimentally-designed functional of the ground state electron density. In this methodology, the electron state density, ρ, and an energy functional of the electron density, E [small mu, Greek, macron] [ρ], can be obtained from CS data. CS allows the derivative of the electrochemical potential with respect to the electron density, (δ[small mu, Greek, macron][ρ]/δρ), to be obtained as a unique functional of the energetically minimised system, i.e., β/C [small mu, Greek, macron] [ρ], where β is a constant (associated with the size of the system) and C [small mu, Greek, macron] [ρ] is an experimentally observable quantity. Thus the ground state energy (at a given fixed external potential) can be obtained simply as E [small mu, Greek, macron] [ρ], from the experimental measurement of C [small mu, Greek, macron] [ρ]. An experimental data-set was interpreted to demonstrate the potential of this quantum mechanical experiment-based variational principle.

A Parameter-Free Semilocal Exchange Energy Functional for Two-Dimensional Quantum Systems.

PubMed

Patra, Abhilash; Jana, Subrata; Samal, Prasanjit

2018-04-05

The method of constructing semilocal density functional for exchange in two dimensions using one of the premier approaches, i.e., density matrix expansion, is revisited, and an accurate functional is constructed. The form of the functional is quite simple and includes no adjustable semiempirical parameters. In it, the kinetic energy dependent momentum is used to compensate nonlocal effects of the system. The functional is then examined by considering the very well-known semiconductor quantum dot systems. And despite its very simple form, the results obtained for quantum dots containing a higher number of electrons agrees pretty well with that of the standard exact exchange theory. Some of the desired properties relevant for the two-dimensional exchange functional and the lower bound associated with it are also discussed. It is observed that the above parameter-free semilocal exchange functional satisfies most of the discussed conditions.

Peculiarities of the momentum distribution functions of strongly correlated charged fermions

NASA Astrophysics Data System (ADS)

Larkin, A. S.; Filinov, V. S.; Fortov, V. E.

2018-01-01

New numerical version of the Wigner approach to quantum thermodynamics of strongly coupled systems of particles has been developed for extreme conditions, when analytical approximations based on different kinds of perturbation theories cannot be applied. An explicit analytical expression of the Wigner function has been obtained in linear and harmonic approximations. Fermi statistical effects are accounted for by effective pair pseudopotential depending on coordinates, momenta and degeneracy parameter of particles and taking into account Pauli blocking of fermions. A new quantum Monte-Carlo method for calculations of average values of arbitrary quantum operators has been developed. Calculations of the momentum distribution functions and the pair correlation functions of degenerate ideal Fermi gas have been carried out for testing the developed approach. Comparison of the obtained momentum distribution functions of strongly correlated Coulomb systems with the Maxwell-Boltzmann and the Fermi distributions shows the significant influence of interparticle interaction both at small momenta and in high energy quantum ‘tails’.

Energetics and Dynamics of GaAs Epitaxial Growth via Quantum Wave Packet Studies

NASA Technical Reports Server (NTRS)

Dzegilenko, Fedor N.; Saini, Subhash (Technical Monitor)

1998-01-01

The dynamics of As(sub 2) molecule incorporation into the flat Ga-terminated GaAs(100) surface is studied computationally. The time-dependent Schrodinger equation is solved on a two-dimensional potential energy surface obtained using density functional theory calculations. The probabilities of trapping and subsequent dissociation of the molecular As(sub 2) bond are calculated as a function of beam translational energy and vibrational quantum number of As(sub 2).

Book Review:

NASA Astrophysics Data System (ADS)

Das, Ashok

2007-01-01

It is not usual for someone to write a book on someone else's Ph.D. thesis, but then Feynman was not a usual physicist. He was without doubt one of the most original physicists of the twentieth century, who has strongly influenced the developments in quantum field theory through his many ingenious contributions. Path integral approach to quantum theories is one such contribution which pervades almost all areas of physics. What is astonishing is that he developed this idea as a graduate student for his Ph.D. thesis which has been printed, for the first time, in the present book along with two other related articles. The early developments in quantum theory, by Heisenberg and Schrödinger, were based on the Hamiltonian formulation, where one starts with the Hamiltonian description of a classical system and then promotes the classical observables to noncommuting quantum operators. However, Dirac had already stressed in an article in 1932 (this article is also reproduced in the present book) that the Lagrangian is more fundamental than the Hamiltonian, at least from the point of view of relativistic invariance and he wondered how the Lagrangian may enter into the quantum description. He had developed this idea through his 'transformation matrix' theory and had even hinted on how the action of the classical theory may enter such a description. However, although the brief paper by Dirac contained the basic essential ideas, it did not fully develop the idea of a Lagrangian description in detail in the functional language. Feynman, on the other hand, was interested in the electromagnetic interactions of the electron from a completely different point of view rooted in a theory involving action-at-a-distance. His theory (along with John Wheeler) did not have a Hamiltonian description and, in order to quantize such a theory, he needed an alternative formulation of quantum mechanics. When the article by Dirac was brought to his attention, he immediately realized what he was looking for and developed fully what is known today as the path integral approach to quantum theories. Although his main motivation was in the study of theories involving the concept of action-at-a-distance, as he emphasizes in his thesis, his formulation of quantum theories applies to any theory in general. The thesis develops quite systematically and in detail all the concepts of functionals necessary for this formulation. The motivation and the physical insights are described in the brilliant 'Feynman' style. It is incredible that even at that young age, the signs of his legendary teaching style were evident in his presentation of the material in the thesis. The path integral approach is now something that every graduate student in theoretical physics is supposed to know. There are several books on the subject, even one by Feynman himself (and Hibbs). Nonetheless, the thesis provides a very good background for the way these ideas came about. The two companion articles, although available in print, also gives a complete picture of the development of this line of thinking. The helpful introductory remarks by the editor also puts things in the proper historical perspective. This book would be very helpful to anyone interested in the development of modern ideas in physics.

A model of adaptive decision-making from representation of information environment by quantum fields.

PubMed

Bagarello, F; Haven, E; Khrennikov, A

2017-11-13

We present the mathematical model of decision-making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioural and geopolitical factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are a purely informational nature. The QFT model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism. We demonstrate the quantum-like interference effect in DM, which is exhibited as a violation of the formula of total probability, and hence the classical Bayesian inference scheme.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).

A model of adaptive decision-making from representation of information environment by quantum fields

NASA Astrophysics Data System (ADS)

Bagarello, F.; Haven, E.; Khrennikov, A.

2017-10-01

We present the mathematical model of decision-making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioural and geopolitical factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are a purely informational nature. The QFT model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism. We demonstrate the quantum-like interference effect in DM, which is exhibited as a violation of the formula of total probability, and hence the classical Bayesian inference scheme. This article is part of the themed issue `Second quantum revolution: foundational questions'.

Spiers Memorial Lecture. Quantum chemistry: the first seventy years.

PubMed

McWeeny, Roy

2007-01-01

Present-day theoretical chemistry is rooted in Quantum Mechanics. The aim of the opening lecture is to trace the evolution of Quantum Chemistry from the Heitler-London paper of 1927 up to the end of the last century, emphasizing concepts rather than calculations. The importance of symmetry concepts became evident in the early years: one thinks of the necessary anti-symmetry of the wave function under electron permutations, the Pauli principle, the aufbau scheme, and the classification of spectroscopic states. But for chemists perhaps the key concept is embodied in the Hellmann-Feynman theorem, which provides a pictorial interpretation of chemical bonding in terms of classical electrostatic forces exerted on the nuclei by the electron distribution. Much of the lecture is concerned with various electron distribution functions--the electron density, the current density, the spin density, and other 'property densities'--and with their use in interpreting both molecular structure and molecular properties. Other topics touched upon include Response theory and propagators; Chemical groups in molecules and the group function approach; Atoms in molecules and Bader's theory; Electron correlation and the 'pair function'. Finally, some long-standing controversies, in particular the EPR paradox, are re-examined in the context of molecular dissociation. By admitting the concept of symmetry breaking, along with the use of the von Neumann-Dirac statistical ensemble, orthodox quantum mechanics can lead to a convincing picture of the dissociation mechanism.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Opanchuk, B.; Drummond, P. D.

2013-04-01

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such as quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.

Creativity and Quantum Physics: a New World View Unifying Current Theories of Creativity and Pointing Toward New Research Methodologies.

NASA Astrophysics Data System (ADS)

McCarthy, Kimberly Ann

1990-01-01

Divisions in definitions of creativity have centered primarily on the working definition of discontinuity and the inclusion of intrinsic features such as unconscious processing and intrinsic motivation and reinforcement. These differences generally result from Cohen's two world views underlying theories of creativity: Organismic, oriented toward holism; or mechanistic, oriented toward cause-effect reductionism. The quantum world view is proposed which theoretically and empirically unifies organismic and mechanistic elements of creativity. Based on Goswami's Idealistic Interpretation of quantum physics, the quantum view postulates the mind -brain as consisting of both classical and quantum structures and functions. The quantum domain accesses the transcendent order through coherent superpositions (a state of potentialities), while the classical domain performs the function of measuring apparatus through amplifying and recording the result of the collapse of the pure mental state. A theoretical experiment, based on the 1980 Marcel study of conscious and unconscious word-sense disambiguation, is conducted which compares the predictions of the quantum model with those of the 1975 Posner and Snyder Facilitation and Inhibition model. Each model agrees that while conscious access to information is limited, unconscious access is unlimited. However, each model differently defines the connection between these states: The Posner model postulates a central processing mechanism while the quantum model postulates a self-referential consciousness. Consequently, the two models predict differently. The strength of the quantum model lies in its ability to distinguish between classical and quantum definitions of discontinuity, as well as clarifying the function of consciousness, without added assumptions or ad-hoc analysis: Consciousness is an essential, valid feature of quantum mechanisms independent of the field of cognitive psychology. According to the quantum model, through a cycle of conscious and unconscious processing, various contexts are accessed, specifically, coherent superposition states and the removal of the subject-object dichotomy in unconscious processing. Coupled with a high tolerance for ambiguity, the individual has access not only to an increased quantity of information, but is exposed to this information in the absence of a self-referential or biased context, the result of which is an increase in creative behavior.

Square-integrable solutions to a family of nonlinear schrödinger equations from nonlinear quantum theory

NASA Astrophysics Data System (ADS)

Teismann, Holger

2005-10-01

We consider nonlinear Schrödinger equations which have been proposed as fundamental equations of nonlinear quantum theories. The equations are singular in that the wave function ψ appears in the denominator of rational expressions. To avoid the problem of zeros of ψ it is natural to make the ansatz ψ = e ν. This ansatz, however, conflicts with the—physically motivated—requirement that the solutions ψ be square integrable. We show that this conflict can be resolved by considering an unusual function space whose definition involves the derivative ∇ ν of ν. This function space turns out to be dense subset of L2 and the equations can be solved in the L2-sense (as desired) by first solving an evolutionary system for ∇ ν and then transforming back to ψ.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azadi, Sam, E-mail: s.azadi@ucl.ac.uk; Cohen, R. E.; Department of Earth- and Environmental Sciences, Ludwig Maximilians Universität, Munich 80333

We studied the low-pressure (0–10 GPa) phase diagram of crystalline benzene using quantum Monte Carlo and density functional theory (DFT) methods. We performed diffusion quantum Monte Carlo (DMC) calculations to obtain accurate static phase diagrams as benchmarks for modern van der Waals density functionals. Using density functional perturbation theory, we computed the phonon contributions to the free energies. Our DFT enthalpy-pressure phase diagrams indicate that the Pbca and P2{sub 1}/c structures are the most stable phases within the studied pressure range. The DMC Gibbs free-energy calculations predict that the room temperature Pbca to P2{sub 1}/c phase transition occurs at 2.1(1)more » GPa. This prediction is consistent with available experimental results at room temperature. Our DMC calculations give 50.6 ± 0.5 kJ/mol for crystalline benzene lattice energy.« less

Logarithmic corrections to entropy of magnetically charged AdS4 black holes

NASA Astrophysics Data System (ADS)

Jeon, Imtak; Lal, Shailesh

2017-11-01

Logarithmic terms are quantum corrections to black hole entropy determined completely from classical data, thus providing a strong check for candidate theories of quantum gravity purely from physics in the infrared. We compute these terms in the entropy associated to the horizon of a magnetically charged extremal black hole in AdS4×S7 using the quantum entropy function and discuss the possibility of matching against recently derived microscopic expressions.

Generalized Causal Quantum Theories

NASA Astrophysics Data System (ADS)

Parmeggiani, Claudio

2007-12-01

We shall show that is always possible to construct causal Quantum Theories fully equivalent (as predictive tools) to acausal, standard Quantum Theory, relativistic or not relativistic; we re-obtain, as a particular case, the usual Quantum Bohmian Theory. Then we consider the measurement process, in causal theories, and we conclude that the state of affairs is not really improved, with respect to standard theories.

Local U(2,2) symmetry in relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Finster, Felix

1998-12-01

Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2,2) gauge transformations acting on the spinor index of the wave functions. This local U(2,2) symmetry allows a unified description of electrodynamics and general relativity as a classical gauge theory.

Quantum learning of classical stochastic processes: The completely positive realization problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Monràs, Alex; Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543; Winter, Andreas

2016-01-15

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece inmore » the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print http://arxiv.org/abs/1303.3771 (2013)].« less

Phase space theory of evaporation in neon clusters: the role of quantum effects.

PubMed

Calvo, F; Parneix, P

2009-12-31

Unimolecular evaporation of neon clusters containing between 14 and 148 atoms is theoretically investigated in the framework of phase space theory. Quantum effects are incorporated in the vibrational densities of states, which include both zero-point and anharmonic contributions, and in the possible tunneling through the centrifugal barrier. The evaporation rates, kinetic energy released, and product angular momentum are calculated as a function of excess energy or temperature in the parent cluster and compared to the classical results. Quantum fluctuations are found to generally increase both the kinetic energy released and the angular momentum of the product, but the effects on the rate constants depend nontrivially on the excess energy. These results are interpreted as due to the very few vibrational states available in the product cluster when described quantum mechanically. Because delocalization also leads to much narrower thermal energy distributions, the variations of evaporation observables as a function of canonical temperature appear much less marked than in the microcanonical ensemble. While quantum effects tend to smooth the caloric curve in the product cluster, the melting phase change clearly keeps a signature on these observables. The microcanonical temperature extracted from fitting the kinetic energy released distribution using an improved Arrhenius form further suggests a backbending in the quantum Ne(13) cluster that is absent in the classical system. Finally, in contrast to delocalization effects, quantum tunneling through the centrifugal barrier does not play any appreciable role on the evaporation kinetics of these rather heavy clusters.

String Theory, the Crisis in Particle Physics and the Ascent of Metaphoric Arguments

NASA Astrophysics Data System (ADS)

Schroer, Bert

This essay presents a critical evaluation of the concepts of string theory and its impact on particle physics. The point of departure is a historical review of four decades of string theory within the broader context of six decades of failed attempts at an autonomous S matrix approach to particle theory. The central message, contained in Secs. 5 and 6, is that string theory is not what its name suggests, namely a theory of objects in space-time whose localization is string-instead of pointlike. Contrary to popular opinion, the oscillators corresponding to the Fourier models of a quantum-mechanical string do not become embedded in space-time and neither does the "range space" of a chiral conformal QFT acquire the interpretation of stringlike-localized quantum matter. Rather, string theory represents a solution to a problem which enjoyed some popularity in the 1960s: find a principle which, similar to the SO(4,2) group in the case of the hydrogen spectrum, determines an infinite component wave function with a (realistic) mass/spin spectrum. Instead of the group theory used in the old failed attempts, it creates this mass/spin spectrum by combining an internal oscillator quantum mechanics with a pointlike-localized quantum-field-theoretic object, i.e. the mass/spin tower "sits" over one point and does not arise from a wiggling string in space-time. The widespread acceptance of a theory whose interpretation has been based on metaphoric reasoning had a corroding influence on particle theory, a point which will be illustrated in the last section with some remarks of a more sociological nature. These remarks also lend additional support to observations on connections between the discourse in particle physics and the present Zeitgeist of the post-Cold War period that are made in the introduction.

Free Quantum Field Theory from Quantum Cellular Automata

NASA Astrophysics Data System (ADS)

Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro

2015-10-01

After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).

Quantum theory of multiscale coarse-graining.

PubMed

Han, Yining; Jin, Jaehyeok; Wagner, Jacob W; Voth, Gregory A

2018-03-14

Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. This approach provides an interesting physical picture for coarse-graining in quantum Boltzmann statistical mechanics in which the consistency with the quantum particle delocalization is obviously manifest, and it opens up an avenue for using path integral centroid-based effective classical force fields in a coarse-graining methodology.

Higher-Order Interference in Extensions of Quantum Theory

NASA Astrophysics Data System (ADS)

Lee, Ciarán M.; Selby, John H.

2017-01-01

Quantum interference, manifest in the two slit experiment, lies at the heart of several quantum computational speed-ups and provides a striking example of a quantum phenomenon with no classical counterpart. An intriguing feature of quantum interference arises in a variant of the standard two slit experiment, in which there are three, rather than two, slits. The interference pattern in this set-up can be written in terms of the two and one slit patterns obtained by blocking one, or more, of the slits. This is in stark contrast with the standard two slit experiment, where the interference pattern cannot be written as a sum of the one slit patterns. This was first noted by Rafael Sorkin, who raised the question of why quantum theory only exhibits irreducible interference in the two slit experiment. One approach to this problem is to compare the predictions of quantum theory to those of operationally-defined `foil' theories, in the hope of determining whether theories that do exhibit higher-order interference suffer from pathological—or at least undesirable—features. In this paper two proposed extensions of quantum theory are considered: the theory of Density Cubes proposed by Dakić, Paterek and Brukner, which has been shown to exhibit irreducible interference in the three slit set-up, and the Quartic Quantum Theory of Życzkowski. The theory of Density Cubes will be shown to provide an advantage over quantum theory in a certain computational task and to posses a well-defined mechanism which leads to the emergence of quantum theory—analogous to the emergence of classical physics from quantum theory via decoherence. Despite this, the axioms used to define Density Cubes will be shown to be insufficient to uniquely characterise the theory. In comparison, Quartic Quantum Theory is a well-defined theory and we demonstrate that it exhibits irreducible interference to all orders. This feature of Życzkowski's theory is argued not to be a genuine phenomenon, but to arise from an ambiguity in the current definition of higher-order interference in operationally-defined theories. Thus, to begin to understand why quantum theory is limited to a certain kind of interference, a new definition of higher-order interference is needed that is applicable to, and makes good operational sense in, arbitrary operationally-defined theories.

Action and entanglement in gravity and field theory.

PubMed

Neiman, Yasha

2013-12-27

In nongravitational quantum field theory, the entanglement entropy across a surface depends on the short-distance regularization. Quantum gravity should not require such regularization, and it has been conjectured that the entanglement entropy there is always given by the black hole entropy formula evaluated on the entangling surface. We show that these statements have precise classical counterparts at the level of the action. Specifically, we point out that the action can have a nonadditive imaginary part. In gravity, the latter is fixed by the black hole entropy formula, while in nongravitating theories it is arbitrary. From these classical facts, the entanglement entropy conjecture follows by heuristically applying the relation between actions and wave functions.

Using conceptual metaphor and functional grammar to explore how language used in physics affects student learning

NASA Astrophysics Data System (ADS)

Brookes, David T.; Etkina, Eugenia

2007-06-01

This paper introduces a theory about the role of language in learning physics. The theory is developed in the context of physics students and physicists talking and writing about the subject of quantum mechanics. We found that physicists’ language encodes different varieties of analogical models through the use of grammar and conceptual metaphor. We hypothesize that students categorize concepts into ontological categories based on the grammatical structure of physicists’ language. We also hypothesize that students overextend and misapply conceptual metaphors in physicists’ speech and writing. Using our theory, we will show how, in some cases, we can explain student difficulties in quantum mechanics as difficulties with language.

Quantum transitions through cosmological singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bramberger, Sebastian F.; Lehners, Jean-Luc; Hertog, Thomas

2017-07-01

In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddlemore » points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.« less

Quantum transitions through cosmological singularities

NASA Astrophysics Data System (ADS)

Bramberger, Sebastian F.; Hertog, Thomas; Lehners, Jean-Luc; Vreys, Yannick

2017-07-01

In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.

El control de las concentraciones empresariales en el sector electrico

NASA Astrophysics Data System (ADS)

Montoya Pardo, Milton Fernando

The rampant success of quantum theory is the result of applications of the 'new' quantum mechanics of Schrodinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum Electro-dynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9), and Quantum Chromodynamics (1973-); in fact, this success of 'the' quantum theory has depended on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously accurate calculational tools there has been no sensible explanation of all that is going on. It is even argued that such an understanding is nothing to do with physics. A long-standing and famous illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935). Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency. This project encompasses a detailed, critical survey of the tangled history of Position within quantum theories. The first step is to show that, contrary to appearances, canonical quantum mechanics has only a vague notion of locality. After analysing a number of previous attempts at a 'relativistic quantum mechanics', two lines of thought are considered in detail. The first is the work of Wan and students, which is shown to be no real improvement on the iisu.al 'nonrelativistic' theory. The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface in space-time. There remain considerable difficulties in the way of producing a consistent scheme here. To keep things nicely stirred up, the author then proposes his own approach - an adaptation of Feynman's QED propagators. This new approach is distinguished from Feynman's since the propagator or Green's function is not obtained by Feynman's rule. The type of equation solved is also different: instead of an initial-value problem, a solution that obeys a time-symmetric causality criterion is found for an inhomogeneous partial differential equation with homogeneous boundary conditions. To make the consideration of locality more precise, some results of Fourier transform theory are presented in a form that is directly applicable. Somewhat away from the main thrust of the thesis, there is also an attempt to explain, the manner in which quantum effects disappear as the number of particles increases in such things as experimental realisations of the EPR and de Broglie thought experiments.

Tectonica activa y geodinamica en el norte de centroamerica

NASA Astrophysics Data System (ADS)

Alvarez Gomez, Jose Antonio

The rampant success of quantum theory is the result of applications of the 'new' quantum mechanics of Schrodinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum Electro-dynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9), and Quantum Chromodynamics (1973-); in fact, this success of 'the' quantum theory has depended on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously accurate calculational tools there has been no sensible explanation of all that is going on. It is even argued that such an understanding is nothing to do with physics. A long-standing and famous illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935). Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency. This project encompasses a detailed, critical survey of the tangled history of Position within quantum theories. The first step is to show that, contrary to appearances, canonical quantum mechanics has only a vague notion of locality. After analysing a number of previous attempts at a 'relativistic quantum mechanics', two lines of thought are considered in detail. The first is the work of Wan and students, which is shown to be no real improvement on the iisu.al 'nonrelativistic' theory. The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface in space-time. There remain considerable difficulties in the way of producing a consistent scheme here. To keep things nicely stirred up, the author then proposes his own approach - an adaptation of Feynman's QED propagators. This new approach is distinguished from Feynman's since the propagator or Green's function is not obtained by Feynman's rule. The type of equation solved is also different: instead of an initial-value problem, a solution that obeys a time-symmetric causality criterion is found for an inhomogeneous partial differential equation with homogeneous boundary conditions. To make the consideration of locality more precise, some results of Fourier transform theory are presented in a form that is directly applicable. Somewhat away from the main thrust of the thesis, there is also an attempt to explain, the manner in which quantum effects disappear as the number of particles increases in such things as experimental realisations of the EPR and de Broglie thought experiments.

Estabilidad de ciertas ondas solitarias sometidas a perturbaciones estocasticas

NASA Astrophysics Data System (ADS)

Rodriguez Plaza, Maria Jesus

The rampant success of quantum theory is the result of applications of the 'new' quantum mechanics of Schrodinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum Electro-dynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9), and Quantum Chromodynamics (1973-); in fact, this success of 'the' quantum theory has depended on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously accurate calculational tools there has been no sensible explanation of all that is going on. It is even argued that such an understanding is nothing to do with physics. A long-standing and famous illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935). Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency. This project encompasses a detailed, critical survey of the tangled history of Position within quantum theories. The first step is to show that, contrary to appearances, canonical quantum mechanics has only a vague notion of locality. After analysing a number of previous attempts at a 'relativistic quantum mechanics', two lines of thought are considered in detail. The first is the work of Wan and students, which is shown to be no real improvement on the iisu.al 'nonrelativistic' theory. The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface in space-time. There remain considerable difficulties in the way of producing a consistent scheme here. To keep things nicely stirred up, the author then proposes his own approach - an adaptation of Feynman's QED propagators. This new approach is distinguished from Feynman's since the propagator or Green's function is not obtained by Feynman's rule. The type of equation solved is also different: instead of an initial-value problem, a solution that obeys a time-symmetric causality criterion is found for an inhomogeneous partial differential equation with homogeneous boundary conditions. To make the consideration of locality more precise, some results of Fourier transform theory are presented in a form that is directly applicable. Somewhat away from the main thrust of the thesis, there is also an attempt to explain, the manner in which quantum effects disappear as the number of particles increases in such things as experimental realisations of the EPR and de Broglie thought experiments.

Teoria de chovitz de segundo orden aplicada a la busqueda de proyecciones cartograficas de minima deformacion

NASA Astrophysics Data System (ADS)

Malpica Velasco, Jose Antonio

The rampant success of quantum theory is the result of applications of the 'new' quantum mechanics of Schrodinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum Electro-dynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9), and Quantum Chromodynamics (1973-); in fact, this success of 'the' quantum theory has depended on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously accurate calculational tools there has been no sensible explanation of all that is going on. It is even argued that such an understanding is nothing to do with physics. A long-standing and famous illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935). Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency. This project encompasses a detailed, critical survey of the tangled history of Position within quantum theories. The first step is to show that, contrary to appearances, canonical quantum mechanics has only a vague notion of locality. After analysing a number of previous attempts at a 'relativistic quantum mechanics', two lines of thought are considered in detail. The first is the work of Wan and students, which is shown to be no real improvement on the iisu.al 'nonrelativistic' theory. The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface in space-time. There remain considerable difficulties in the way of producing a consistent scheme here. To keep things nicely stirred up, the author then proposes his own approach - an adaptation of Feynman's QED propagators. This new approach is distinguished from Feynman's since the propagator or Green's function is not obtained by Feynman's rule. The type of equation solved is also different: instead of an initial-value problem, a solution that obeys a time-symmetric causality criterion is found for an inhomogeneous partial differential equation with homogeneous boundary conditions. To make the consideration of locality more precise, some results of Fourier transform theory are presented in a form that is directly applicable. Somewhat away from the main thrust of the thesis, there is also an attempt to explain, the manner in which quantum effects disappear as the number of particles increases in such things as experimental realisations of the EPR and de Broglie thought experiments.

Analisis espectroscopico de estrellas variables Delta Scuti

NASA Astrophysics Data System (ADS)

Solano Marquez, Enrique

The rampant success of quantum theory is the result of applications of the 'new' quantum mechanics of Schrodinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum Electro-dynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9), and Quantum Chromodynamics (1973-); in fact, this success of 'the' quantum theory has depended on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously accurate calculational tools there has been no sensible explanation of all that is going on. It is even argued that such an understanding is nothing to do with physics. A long-standing and famous illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935). Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency. This project encompasses a detailed, critical survey of the tangled history of Position within quantum theories. The first step is to show that, contrary to appearances, canonical quantum mechanics has only a vague notion of locality. After analysing a number of previous attempts at a 'relativistic quantum mechanics', two lines of thought are considered in detail. The first is the work of Wan and students, which is shown to be no real improvement on the iisu.al 'nonrelativistic' theory. The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface in space-time. There remain considerable difficulties in the way of producing a consistent scheme here. To keep things nicely stirred up, the author then proposes his own approach - an adaptation of Feynman's QED propagators. This new approach is distinguished from Feynman's since the propagator or Green's function is not obtained by Feynman's rule. The type of equation solved is also different: instead of an initial-value problem, a solution that obeys a time-symmetric causality criterion is found for an inhomogeneous partial differential equation with homogeneous boundary conditions. To make the consideration of locality more precise, some results of Fourier transform theory are presented in a form that is directly applicable. Somewhat away from the main thrust of the thesis, there is also an attempt to explain, the manner in which quantum effects disappear as the number of particles increases in such things as experimental realisations of the EPR and de Broglie thought experiments.

Inversion gravimetrica 3D por tecnicas de evolucion: Aplicacion a la Isla de Fuerteventura

NASA Astrophysics Data System (ADS)

Gonzalez Montesinos, Fuensanta

The rampant success of quantum theory is the result of applications of the 'new' quantum mechanics of Schrodinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum Electro-dynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9), and Quantum Chromodynamics (1973-); in fact, this success of 'the' quantum theory has depended on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously accurate calculational tools there has been no sensible explanation of all that is going on. It is even argued that such an understanding is nothing to do with physics. A long-standing and famous illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935). Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency. This project encompasses a detailed, critical survey of the tangled history of Position within quantum theories. The first step is to show that, contrary to appearances, canonical quantum mechanics has only a vague notion of locality. After analysing a number of previous attempts at a 'relativistic quantum mechanics', two lines of thought are considered in detail. The first is the work of Wan and students, which is shown to be no real improvement on the iisu.al 'nonrelativistic' theory. The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface in space-time. There remain considerable difficulties in the way of producing a consistent scheme here. To keep things nicely stirred up, the author then proposes his own approach - an adaptation of Feynman's QED propagators. This new approach is distinguished from Feynman's since the propagator or Green's function is not obtained by Feynman's rule. The type of equation solved is also different: instead of an initial-value problem, a solution that obeys a time-symmetric causality criterion is found for an inhomogeneous partial differential equation with homogeneous boundary conditions. To make the consideration of locality more precise, some results of Fourier transform theory are presented in a form that is directly applicable. Somewhat away from the main thrust of the thesis, there is also an attempt to explain, the manner in which quantum effects disappear as the number of particles increases in such things as experimental realisations of the EPR and de Broglie thought experiments.

Evolution tectonothermale du massif Hercynien des Rehamna (zone centre-mesetienne, Maroc)

NASA Astrophysics Data System (ADS)

Aghzer, Abdel Mouhsine

The rampant success of quantum theory is the result of applications of the 'new' quantum mechanics of Schrodinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum Electro-dynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9), and Quantum Chromodynamics (1973-); in fact, this success of 'the' quantum theory has depended on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously accurate calculational tools there has been no sensible explanation of all that is going on. It is even argued that such an understanding is nothing to do with physics. A long-standing and famous illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935). Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency. This project encompasses a detailed, critical survey of the tangled history of Position within quantum theories. The first step is to show that, contrary to appearances, canonical quantum mechanics has only a vague notion of locality. After analysing a number of previous attempts at a 'relativistic quantum mechanics', two lines of thought are considered in detail. The first is the work of Wan and students, which is shown to be no real improvement on the iisu.al 'nonrelativistic' theory. The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface in space-time. There remain considerable difficulties in the way of producing a consistent scheme here. To keep things nicely stirred up, the author then proposes his own approach - an adaptation of Feynman's QED propagators. This new approach is distinguished from Feynman's since the propagator or Green's function is not obtained by Feynman's rule. The type of equation solved is also different: instead of an initial-value problem, a solution that obeys a time-symmetric causality criterion is found for an inhomogeneous partial differential equation with homogeneous boundary conditions. To make the consideration of locality more precise, some results of Fourier transform theory are presented in a form that is directly applicable. Somewhat away from the main thrust of the thesis, there is also an attempt to explain, the manner in which quantum effects disappear as the number of particles increases in such things as experimental realisations of the EPR and de Broglie thought experiments.

Comportamiento mecanico de la interfase de subduccion durante el ciclo sismico: Estudio mediante la geodesia espacial en el norte de Chile

NASA Astrophysics Data System (ADS)

Bejar Pizarro, Marta

The rampant success of quantum theory is the result of applications of the 'new' quantum mechanics of Schrodinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum Electro-dynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9), and Quantum Chromodynamics (1973-); in fact, this success of 'the' quantum theory has depended on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously accurate calculational tools there has been no sensible explanation of all that is going on. It is even argued that such an understanding is nothing to do with physics. A long-standing and famous illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935). Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency. This project encompasses a detailed, critical survey of the tangled history of Position within quantum theories. The first step is to show that, contrary to appearances, canonical quantum mechanics has only a vague notion of locality. After analysing a number of previous attempts at a 'relativistic quantum mechanics', two lines of thought are considered in detail. The first is the work of Wan and students, which is shown to be no real improvement on the iisu.al 'nonrelativistic' theory. The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface in space-time. There remain considerable difficulties in the way of producing a consistent scheme here. To keep things nicely stirred up, the author then proposes his own approach - an adaptation of Feynman's QED propagators. This new approach is distinguished from Feynman's since the propagator or Green's function is not obtained by Feynman's rule. The type of equation solved is also different: instead of an initial-value problem, a solution that obeys a time-symmetric causality criterion is found for an inhomogeneous partial differential equation with homogeneous boundary conditions. To make the consideration of locality more precise, some results of Fourier transform theory are presented in a form that is directly applicable. Somewhat away from the main thrust of the thesis, there is also an attempt to explain, the manner in which quantum effects disappear as the number of particles increases in such things as experimental realisations of the EPR and de Broglie thought experiments.

Sintesis y caracterizacion microestructural de aluminas obtenidas a partir de un precursor no convencional

NASA Astrophysics Data System (ADS)

Fillali, Laila

The rampant success of quantum theory is the result of applications of the 'new' quantum mechanics of Schrodinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum Electro-dynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9), and Quantum Chromodynamics (1973-); in fact, this success of 'the' quantum theory has depended on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously accurate calculational tools there has been no sensible explanation of all that is going on. It is even argued that such an understanding is nothing to do with physics. A long-standing and famous illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935). Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency. This project encompasses a detailed, critical survey of the tangled history of Position within quantum theories. The first step is to show that, contrary to appearances, canonical quantum mechanics has only a vague notion of locality. After analysing a number of previous attempts at a 'relativistic quantum mechanics', two lines of thought are considered in detail. The first is the work of Wan and students, which is shown to be no real improvement on the iisu.al 'nonrelativistic' theory. The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface in space-time. There remain considerable difficulties in the way of producing a consistent scheme here. To keep things nicely stirred up, the author then proposes his own approach - an adaptation of Feynman's QED propagators. This new approach is distinguished from Feynman's since the propagator or Green's function is not obtained by Feynman's rule. The type of equation solved is also different: instead of an initial-value problem, a solution that obeys a time-symmetric causality criterion is found for an inhomogeneous partial differential equation with homogeneous boundary conditions. To make the consideration of locality more precise, some results of Fourier transform theory are presented in a form that is directly applicable. Somewhat away from the main thrust of the thesis, there is also an attempt to explain, the manner in which quantum effects disappear as the number of particles increases in such things as experimental realisations of the EPR and de Broglie thought experiments.

Holonomy, quantum mechanics and the signal-tuned Gabor approach to the striate cortex

NASA Astrophysics Data System (ADS)

Torreão, José R. A.

2016-02-01

It has been suggested that an appeal to holographic and quantum properties will be ultimately required for the understanding of higher brain functions. On the other hand, successful quantum-like approaches to cognitive and behavioral processes bear witness to the usefulness of quantum prescriptions as applied to the analysis of complex non-quantum systems. Here, we show that the signal-tuned Gabor approach for modeling cortical neurons, although not based on quantum assumptions, also admits a quantum-like interpretation. Recently, the equation of motion for the signal-tuned complex cell response has been derived and proven equivalent to the Schrödinger equation for a dissipative quantum system whose solutions come under two guises: as plane-wave and Airy-packet responses. By interpreting the squared magnitude of the plane-wave solution as a probability density, in accordance with the quantum mechanics prescription, we arrive at a Poisson spiking probability — a common model of neuronal response — while spike propagation can be described by the Airy-packet solution. The signal-tuned approach is also proven consistent with holonomic brain theories, as it is based on Gabor functions which provide a holographic representation of the cell’s input, in the sense that any restricted subset of these functions still allows stimulus reconstruction.

Relativity, Symmetry, and the Structure of Quantum Theory, Volume 2; Point form relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Klink, William H.; Schweiger, Wolfgang

2018-03-01

This book covers relativistic quantum theory from the point of view of a particle theory, based on the irreducible representations of the Poincaré group, the group that expresses the symmetry of Einstein relativity. There are several ways of formulating such a theory; this book develops what is called relativistic point form quantum mechanics, which, unlike quantum field theory, deals with a fixed number of particles in a relativistically invariant way. A chapter is devoted to applications of point form quantum mechanics to nuclear physics.

Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation.

PubMed

Sels, Dries; Brosens, Fons

2013-10-01

The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation.

Trade-off between quantum capacitance and thermodynamic stability of defected graphene: an implication for supercapacitor electrodes

NASA Astrophysics Data System (ADS)

Srivastava, Anurag; SanthiBhushan, Boddepalli

2018-03-01

Defects are inevitable most of the times either at the synthesis, handling or processing stage of graphene, causes significant deviation of properties. The present work discusses the influence of vacancy defects on the quantum capacitance as well as thermodynamic stability of graphene, and the nitrogen doping pattern needs to be followed to attain a trade-off between these two. Density Functional Theory (DFT) calculations have been performed to analyze various vacancy defects and different possible nitrogen doping patterns at the vacancy site of graphene, with an implication for supercapacitor electrodes. The results signify that vacancy defect improves the quantum capacitance of graphene at the cost of thermodynamic stability, while the nitrogen functionalization at the vacancy improves thermodynamic stability and quantum capacitance both. It has been observed that functionalizing all the dangling carbons at the defect site with nitrogen is the key to attain high thermodynamic stability as well as quantum capacitance. Furthermore, the results signify the suitability of these functionalized graphenes for anode electrode of high energy density asymmetric supercapacitors.

Effective field theories for topological insulators by functional bosonization

NASA Astrophysics Data System (ADS)

Chan, AtMa; Hughes, Taylor L.; Ryu, Shinsei; Fradkin, Eduardo

2013-02-01

Effective field theories that describe the dynamics of a conserved U(1) current in terms of “hydrodynamic” degrees of freedom of topological phases in condensed matter are discussed in general dimension D=d+1 using the functional bosonization technique. For noninteracting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant [more specifically, they are topological insulators in the complex symmetry classes (class A and AIII), and in the “primary series” of topological insulators, in the eight real symmetry classes], we derive the BF-type topological field theories supplemented with the Chern-Simons (when D is odd) or the θ (when D is even) terms. For topological insulators characterized by a Z2 topological invariant (the first and second descendants of the primary series), their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative “fractional” topological insulators and their possible effective field theories, and use them to determine the physical properties of these nontrivial quantum phases.

Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum.

PubMed

Fradkin, Eduardo; Moore, Joel E

2006-08-04

The entanglement entropy of a pure quantum state of a bipartite system A union or logical sumB is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. In one dimension, the entanglement of critical ground states diverges logarithmically in the subsystem size, with a universal coefficient that for conformally invariant critical points is related to the central charge of the conformal field theory. We find that the entanglement entropy of a standard class of z=2 conformal quantum critical points in two spatial dimensions, in addition to a nonuniversal "area law" contribution linear in the size of the AB boundary, generically has a universal logarithmically divergent correction, which is completely determined by the geometry of the partition and by the central charge of the field theory that describes the critical wave function.

Non-Fermi-liquid superconductivity: Eliashberg approach versus the renormalization group

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Huajia; Raghu, Srinivas; Torroba, Gonzalo

Here, we address the problem of superconductivity for non-Fermi liquids using two commonly adopted, yet apparently distinct, methods: (1) the renormalization group (RG) and (2) Eliashberg theory. The extent to which both methods yield consistent solutions for the low-energy behavior of quantum metals has remained unclear. We show that the perturbative RG beta function for the 4-Fermi coupling can be explicitly derived from the linearized Eliashberg equations, under the assumption that quantum corrections are approximately local across energy scales. We apply our analysis to the test case of phonon-mediated superconductivity and show the consistency of both the Eliashberg and RGmore » treatments. We next study superconductivity near a class of quantum critical points and find a transition between superconductivity and a “naked” metallic quantum critical point with finite, critical BCS couplings. We speculate on the applications of our theory to the phenomenology of unconventional metals.« less

Non-Fermi-liquid superconductivity: Eliashberg approach versus the renormalization group

DOE PAGES

Wang, Huajia; Raghu, Srinivas; Torroba, Gonzalo

2017-04-15

Here, we address the problem of superconductivity for non-Fermi liquids using two commonly adopted, yet apparently distinct, methods: (1) the renormalization group (RG) and (2) Eliashberg theory. The extent to which both methods yield consistent solutions for the low-energy behavior of quantum metals has remained unclear. We show that the perturbative RG beta function for the 4-Fermi coupling can be explicitly derived from the linearized Eliashberg equations, under the assumption that quantum corrections are approximately local across energy scales. We apply our analysis to the test case of phonon-mediated superconductivity and show the consistency of both the Eliashberg and RGmore » treatments. We next study superconductivity near a class of quantum critical points and find a transition between superconductivity and a “naked” metallic quantum critical point with finite, critical BCS couplings. We speculate on the applications of our theory to the phenomenology of unconventional metals.« less

Ferromagnetic quantum critical point avoided by the appearance of another magnetic phase in LaCrGe 3 under pressure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Taufour, Valentin; Kaluarachchi, Udhara S.; Khasanov, Rustem

2016-07-13

Here, the temperature-pressure phase diagram of the ferromagnet LaCrGe 3 is determined for the first time from a combination of magnetization, muon-spin-rotation, and electrical resistivity measurements. The ferromagnetic phase is suppressed near 2.1 GPa, but quantum criticality is avoided by the appearance of a magnetic phase, likely modulated, AFMQ. Our density functional theory total energy calculations suggest a near degeneracy of antiferromagnetic states with small magnetic wave vectors Q allowing for the potential of an ordering wave vector evolving from Q=0 to finite Q, as expected from the most recent theories on ferromagnetic quantum criticality. Our findings show that LaCrGemore » 3 is a very simple example to study this scenario of avoided ferromagnetic quantum criticality and will inspire further study on this material and other itinerant ferromagnets.« less

"Genetically Engineered" Nanoelectronics

NASA Technical Reports Server (NTRS)

Klimeck, Gerhard; Salazar-Lazaro, Carlos H.; Stoica, Adrian; Cwik, Thomas

2000-01-01

The quantum mechanical functionality of nanoelectronic devices such as resonant tunneling diodes (RTDs), quantum well infrared-photodetectors (QWIPs), quantum well lasers, and heterostructure field effect transistors (HFETs) is enabled by material variations on an atomic scale. The design and optimization of such devices requires a fundamental understanding of electron transport in such dimensions. The Nanoelectronic Modeling Tool (NEMO) is a general-purpose quantum device design and analysis tool based on a fundamental non-equilibrium electron transport theory. NEW was combined with a parallelized genetic algorithm package (PGAPACK) to evolve structural and material parameters to match a desired set of experimental data. A numerical experiment that evolves structural variations such as layer widths and doping concentrations is performed to analyze an experimental current voltage characteristic. The genetic algorithm is found to drive the NEMO simulation parameters close to the experimentally prescribed layer thicknesses and doping profiles. With such a quantitative agreement between theory and experiment design synthesis can be performed.

Quantum ring-polymer contraction method: Including nuclear quantum effects at no additional computational cost in comparison to ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

John, Christopher; Spura, Thomas; Habershon, Scott; Kühne, Thomas D.

2016-04-01

We present a simple and accurate computational method which facilitates ab initio path-integral molecular dynamics simulations, where the quantum-mechanical nature of the nuclei is explicitly taken into account, at essentially no additional computational cost in comparison to the corresponding calculation using classical nuclei. The predictive power of the proposed quantum ring-polymer contraction method is demonstrated by computing various static and dynamic properties of liquid water at ambient conditions using density functional theory. This development will enable routine inclusion of nuclear quantum effects in ab initio molecular dynamics simulations of condensed-phase systems.

The Contradiction Between the Measurement Theory of Quantum Mechanics and the Theory that the Velocity of Any Particle Can Not be Larger than the Velocity of Light

NASA Technical Reports Server (NTRS)

Shen, Y.; Shen, Z. J.; Shen, G. T.; Yang, B. C.

1996-01-01

By the measurement theory of quantum mechanics and the method of Fourier transform,we proved that the wave function psi(x,y,z,t)= (8/((2(pi)(2L(exp (1/2)))(exp 3))(Phi(L,t,x)Phi(L,t,y)Phi(L,t,z)). According to the theory that the velocity of any particle can not be larger than the velocity of light and the Born interpretation, when absolute value of delta greater than (ct+ L),Phi(L,t,delta) = 0. But according to the calculation, we proved that for some delta, even if absolute value of delta is greater than (ct+L), Phi(L,t,delta) is not equal to 0.

Loop Quantum Gravity and the Meaning of Diffeomorphism Invariance

NASA Astrophysics Data System (ADS)

Rovelli, Carlo; Gaul, Marcus

This series of lectures gives an introduction to the non-perturbative and background-independent formulation for a quantum theory of gravitation which is called loop quantum gravity . The Hilbert space of kinematical quantum states is constructed and a complete basis of spin network states is introduced. Afterwards an application of the formalism is provided by the spectral analysis of the area operator, which is the quantum analogue of the classical area function. This leads to one of the key results of loop quantum gravity obtained in the last few years: the derivation of the discreteness of the geometry and the computation of the quanta of area. Special importance is attached to the role played by the diffeomorphism group in order to clarify the notion of observability in general relativity - a concept far from being trivial. Finally an outlock onto a possible dynamical extension of the theory is given, leading to a "sum over histories" approach, namely a so-called spin foam model . Throughout the whole lecture great significance is attached to conceptual and interpretational issues.

Exact solution of matricial Φ23 quantum field theory

NASA Astrophysics Data System (ADS)

Grosse, Harald; Sako, Akifumi; Wulkenhaar, Raimar

2017-12-01

We apply a recently developed method to exactly solve the Φ3 matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and Schwinger-Dyson equations lead in a special large- N limit to integral equations that we solve exactly for all correlation functions. The solved model arises from noncommutative field theory in a special limit of strong deformation parameter. The limit defines ordinary 2D Schwinger functions which, however, do not satisfy reflection positivity.

Quantum mechanics: The Bayesian theory generalized to the space of Hermitian matrices

NASA Astrophysics Data System (ADS)

Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco

2016-10-01

We consider the problem of gambling on a quantum experiment and enforce rational behavior by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield the Bayesian theory generalized to the space of Hermitian matrices. This very theory is quantum mechanics: in fact, we derive all its four postulates from the generalized Bayesian theory. This implies that quantum mechanics is self-consistent. It also leads us to reinterpret the main operations in quantum mechanics as probability rules: Bayes' rule (measurement), marginalization (partial tracing), independence (tensor product). To say it with a slogan, we obtain that quantum mechanics is the Bayesian theory in the complex numbers.

Quantum-like behavior without quantum physics I : Kinematics of neural-like systems.

PubMed

Selesnick, S A; Rawling, J P; Piccinini, Gualtiero

2017-09-01

Recently there has been much interest in the possible quantum-like behavior of the human brain in such functions as cognition, the mental lexicon, memory, etc., producing a vast literature. These studies are both empirical and theoretical, the tenets of the theory in question being mainly, and apparently inevitably, those of quantum physics itself, for lack of other arenas in which quantum-like properties are presumed to obtain. However, attempts to explain this behavior on the basis of actual quantum physics going on at the atomic or molecular level within some element of brain or neuronal anatomy (other than the ordinary quantum physics that underlies everything), do not seem to survive much scrutiny. Moreover, it has been found empirically that the usual physics-like Hilbert space model seems not to apply in detail to human cognition in the large. In this paper we lay the groundwork for a theory that might explain the provenance of quantum-like behavior in complex systems whose internal structure is essentially hidden or inaccessible. The approach is via the logic obeyed by these systems which is similar to, but not identical with, the logic obeyed by actual quantum systems. The results reveal certain effects in such systems which, though quantum-like, are not identical to the kinds of quantum effects found in physics. These effects increase with the size of the system.

The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory

NASA Astrophysics Data System (ADS)

Frey, Kimberly

The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum mathematics in a sense which parallels the foundational role of classical set theory in classical mathematics. One immediate application of the quantum set theory we develop is to provide a foundation on which to construct quantum natural numbers, which are the quantum analog of the classical counting numbers. It turns out that in a special class of models, there exists a 1-1 correspondence between the quantum natural numbers and bounded observables in quantum theory whose eigenvalues are (ordinary) natural numbers. This 1-1 correspondence is remarkably satisfying, and not only gives us great confidence in our quantum set theory, but indicates the naturalness of such models for quantum theory itself. We go on to develop a Peano-like arithmetic for these new "numbers," as well as consider some of its consequences. Finally, we conclude by summarizing our results, and discussing directions for future work.

Quantum Sets and Clifford Algebras

NASA Astrophysics Data System (ADS)

Finkelstein, David

1982-06-01

The mathematical language presently used for quantum physics is a high-level language. As a lowest-level or basic language I construct a quantum set theory in three stages: (1) Classical set theory, formulated as a Clifford algebra of “ S numbers” generated by a single monadic operation, “bracing,” Br = {…}. (2) Indefinite set theory, a modification of set theory dealing with the modal logical concept of possibility. (3) Quantum set theory. The quantum set is constructed from the null set by the familiar quantum techniques of tensor product and antisymmetrization. There are both a Clifford and a Grassmann algebra with sets as basis elements. Rank and cardinality operators are analogous to Schroedinger coordinates of the theory, in that they are multiplication or “ Q-type” operators. “ P-type” operators analogous to Schroedinger momenta, in that they transform the Q-type quantities, are bracing (Br), Clifford multiplication by a set X, and the creator of X, represented by Grassmann multiplication c( X) by the set X. Br and its adjoint Br* form a Bose-Einstein canonical pair, and c( X) and its adjoint c( X)* form a Fermi-Dirac or anticanonical pair. Many coefficient number systems can be employed in this quantization. I use the integers for a discrete quantum theory, with the usual complex quantum theory as limit. Quantum set theory may be applied to a quantum time space and a quantum automaton.

Natural occupation numbers in two-electron quantum rings.

PubMed

Tognetti, Vincent; Loos, Pierre-François

2016-02-07

Natural orbitals (NOs) are central constituents for evaluating correlation energies through efficient approximations. Here, we report the closed-form expression of the NOs of two-electron quantum rings, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory. We also show that the natural occupation numbers for these two-electron paradigms are in general non-vanishing and follow the same power law decay as atomic and molecular two-electron systems.

Corrigendum: First principles calculation of field emission from nanostructures using time-dependent density functional theory: A simplified approach

NASA Astrophysics Data System (ADS)

Tawfik, Sherif A.; El-Sheikh, S. M.; Salem, N. M.

2016-09-01

Recently we have become aware that the description of the quantum wave functions in Sec. 2.1 is incorrect. In the published version of the paper, we have stated that the states are expanded in terms of plane waves. However, the correct description of the quantum states in the context of the real space implementation (using the Octopus code) is that states are represented by discrete points in a real space grid.

Natural occupation numbers in two-electron quantum rings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tognetti, Vincent, E-mail: vincent.tognetti@univ-rouen.fr; Loos, Pierre-François

2016-02-07

Natural orbitals (NOs) are central constituents for evaluating correlation energies through efficient approximations. Here, we report the closed-form expression of the NOs of two-electron quantum rings, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory. We also show that the natural occupation numbers for these two-electron paradigms are in general non-vanishing and follow the same power law decay as atomic and molecular two-electron systems.

Quantum algorithms for quantum field theories.

PubMed

Jordan, Stephen P; Lee, Keith S M; Preskill, John

2012-06-01

Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.

Reliable but Timesaving: In Search of an Efficient Quantum-chemical Method for the Description of Functional Fullerenes.

PubMed

Reis, H; Rasulev, B; Papadopoulos, M G; Leszczynski, J

2015-01-01

Fullerene and its derivatives are currently one of the most intensively investigated species in the area of nanomedicine and nanochemistry. Various unique properties of fullerenes are responsible for their wide range applications in industry, biology and medicine. A large pool of functionalized C60 and C70 fullerenes is investigated theoretically at different levels of quantum-mechanical theory. The semiempirial PM6 method, density functional theory with the B3LYP functional, and correlated ab initio MP2 method are employed to compute the optimized structures, and an array of properties for the considered species. In addition to the calculations for isolated molecules, the results of solution calculations are also reported at the DFT level, using the polarizable continuum model (PCM). Ionization potentials (IPs) and electron affinities (EAs) are computed by means of Koopmans' theorem as well as with the more accurate but computationally expensive ΔSCF method. Both procedures yield comparable values, while comparison of IPs and EAs computed with different quantum-mechanical methods shows surprisingly large differences. Harmonic vibrational frequencies are computed at the PM6 and B3LYP levels of theory and compared with each other. A possible application of the frequencies as 3D descriptors in the EVA (EigenVAlues) method is shown. All the computed data are made available, and may be used to replace experimental data in routine applications where large amounts of data are required, e.g. in structure-activity relationship studies of the toxicity of fullerene derivatives.

Thermal density functional theory, ensemble density functional theory, and potential functional theory for warm dense matter

NASA Astrophysics Data System (ADS)

Pribram-Jones, Aurora

Warm dense matter (WDM) is a high energy phase between solids and plasmas, with characteristics of both. It is present in the centers of giant planets, within the earth's core, and on the path to ignition of inertial confinement fusion. The high temperatures and pressures of warm dense matter lead to complications in its simulation, as both classical and quantum effects must be included. One of the most successful simulation methods is density functional theory-molecular dynamics (DFT-MD). Despite great success in a diverse array of applications, DFT-MD remains computationally expensive and it neglects the explicit temperature dependence of electron-electron interactions known to exist within exact DFT. Finite-temperature density functional theory (FT DFT) is an extension of the wildly successful ground-state DFT formalism via thermal ensembles, broadening its quantum mechanical treatment of electrons to include systems at non-zero temperatures. Exact mathematical conditions have been used to predict the behavior of approximations in limiting conditions and to connect FT DFT to the ground-state theory. An introduction to FT DFT is given within the context of ensemble DFT and the larger field of DFT is discussed for context. Ensemble DFT is used to describe ensembles of ground-state and excited systems. Exact conditions in ensemble DFT and the performance of approximations depend on ensemble weights. Using an inversion method, exact Kohn-Sham ensemble potentials are found and compared to approximations. The symmetry eigenstate Hartree-exchange approximation is in good agreement with exact calculations because of its inclusion of an ensemble derivative discontinuity. Since ensemble weights in FT DFT are temperature-dependent Fermi weights, this insight may help develop approximations well-suited to both ground-state and FT DFT. A novel, highly efficient approach to free energy calculations, finite-temperature potential functional theory, is derived, which has the potential to transform the simulation of warm dense matter. As a semiclassical method, it connects the normally disparate regimes of cold condensed matter physics and hot plasma physics. This orbital-free approach captures the smooth classical density envelope and quantum density oscillations that are both crucial to accurate modeling of materials where temperature and pressure effects are influential.

Superconformal quantum field theory in curved spacetime

NASA Astrophysics Data System (ADS)

de Medeiros, Paul; Hollands, Stefan

2013-09-01

By conformally coupling vector and hyper multiplets in Minkowski space, we obtain a class of field theories with extended rigid conformal supersymmetry on any Lorentzian 4-manifold admitting twistor spinors. We construct the conformal symmetry superalgebras which describe classical symmetries of these theories and derive an appropriate BRST operator in curved spacetime. In the process, we elucidate the general framework of cohomological algebra which underpins the construction. We then consider the corresponding perturbative quantum field theories. In particular, we examine the conditions necessary for conformal supersymmetries to be preserved at the quantum level, i.e. when the BRST operator commutes with the perturbatively defined S-matrix, which ensures superconformal invariance of amplitudes. To this end, we prescribe a renormalization scheme for time-ordered products that enter the perturbative S-matrix and show that such products obey certain Ward identities in curved spacetime. These identities allow us to recast the problem in terms of the cohomology of the BRST operator. Through a careful analysis of this cohomology, and of the renormalization group in curved spacetime, we establish precise criteria which ensure that all conformal supersymmetries are preserved at the quantum level. As a by-product, we provide a rigorous proof that the beta-function for such theories is one-loop exact. We also briefly discuss the construction of chiral rings and the role of non-perturbative effects in curved spacetime.

Quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi4 model

NASA Astrophysics Data System (ADS)

Kwiatkowski, G.; Leble, S.

2014-03-01

Analytical form of quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi4 model is obtained through zeta function regularisation with account of all rest variables of a d-dimensional theory. Qualitative dependence of quantum corrections on parameters of the classical systems is also evaluated for a much broader class of potentials u(x) = b2f(bx) + C with b and C as arbitrary real constants.

Atomistic full-quantum transport model for zigzag graphene nanoribbon-based structures: Complex energy-band method

NASA Astrophysics Data System (ADS)

Chen, Chun-Nan; Luo, Win-Jet; Shyu, Feng-Lin; Chung, Hsien-Ching; Lin, Chiun-Yan; Wu, Jhao-Ying

2018-01-01

Using a non-equilibrium Green’s function framework in combination with the complex energy-band method, an atomistic full-quantum model for solving quantum transport problems for a zigzag-edge graphene nanoribbon (zGNR) structure is proposed. For transport calculations, the mathematical expressions from the theory for zGNR-based device structures are derived in detail. The transport properties of zGNR-based devices are calculated and studied in detail using the proposed method.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Opanchuk, B.; Drummond, P. D.

2013-04-15

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such asmore » quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.« less

Physics of Electronic Materials

NASA Astrophysics Data System (ADS)

Rammer, Jørgen

2017-03-01

1. Quantum mechanics; 2. Quantum tunneling; 3. Standard metal model; 4. Standard conductor model; 5. Electric circuit theory; 6. Quantum wells; 7. Particle in a periodic potential; 8. Bloch currents; 9. Crystalline solids; 10. Semiconductor doping; 11. Transistors; 12. Heterostructures; 13. Mesoscopic physics; 14. Arithmetic, logic and machines; Appendix A. Principles of quantum mechanics; Appendix B. Dirac's delta function; Appendix C. Fourier analysis; Appendix D. Classical mechanics; Appendix E. Wave function properties; Appendix F. Transfer matrix properties; Appendix G. Momentum; Appendix H. Confined particles; Appendix I. Spin and quantum statistics; Appendix J. Statistical mechanics; Appendix K. The Fermi-Dirac distribution; Appendix L. Thermal current fluctuations; Appendix M. Gaussian wave packets; Appendix N. Wave packet dynamics; Appendix O. Screening by symmetry method; Appendix P. Commutation and common eigenfunctions; Appendix Q. Interband coupling; Appendix R. Common crystal structures; Appendix S. Effective mass approximation; Appendix T. Integral doubling formula; Bibliography; Index.

Properties of field functionals and characterization of local functionals

NASA Astrophysics Data System (ADS)

Brouder, Christian; Dang, Nguyen Viet; Laurent-Gengoux, Camille; Rejzner, Kasia

2018-02-01

Functionals (i.e., functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the proper space of test functions (smooth functions) and of the relevant concept of differential (Bastiani differential) are discussed. The relation between the multiple derivatives of a functional and the corresponding distributions is described in detail. It is proved that, in a neighborhood of every test function, the support of a smooth functional is uniformly compactly supported and the order of the corresponding distribution is uniformly bounded. Relying on a recent work by Dabrowski, several spaces of functionals are furnished with a complete and nuclear topology. In view of physical applications, it is shown that most formal manipulations can be given a rigorous meaning. A new concept of local functionals is proposed and two characterizations of them are given: the first one uses the additivity (or Hammerstein) property, the second one is a variant of Peetre's theorem. Finally, the first step of a cohomological approach to quantum field theory is carried out by proving a global Poincaré lemma and defining multi-vector fields and graded functionals within our framework.

Quantum leadership: the implication for Iranian nursing leaders.

PubMed

Dargahi, Hossein

2013-07-13

Quantum organizations are referred where stakeholders know how to access the infinite potential of the quantum field. Viewing healthcare organizations from perspective of quantum theory suggest new approaches into management techniques for effective and efficient delivery of healthcare services. This research is aimed to determine the quantum skills, quantum leadership characteristics and functions of Tehran University of Medical Sciences hospitals' nursing administrators. A cross-sectional, descriptive and analytical study was conducted among 25 nursing administrators of Tehran University of Medical Sciences (TUMS) hospitals, Tehran, Iran. The research tool for data collection was a self-constructed questionnaire that measured the quantum skills, quantum leadership characteristics and functions of TUMS hospitals' nursing administrators. The validity of questionnaire was confirmed by 5 management science experts and its reliability was performed by using test-retest method yielded a Cronbach's alpha coefficient of 0.90. Data were collected and analyzed by SPSS software and t-test statistical methods. The results of this research showed that all respondents had desired quantum skills (75.71±5.98), quantum leadership characteristics (82.01±6.77), and quantum leadership functions (78.57±6.28) and total quantum leadership (78.76±4.50). Also, passing management training courses of the respondents was significantly correlated with their quantum leadership. Iranian healthcare organizations require quantum leadership that provides an important resource to advance Iranian nursing leadership to the organizational excellence. We hope Iranian hospitals' nursing leaders who have quantum skills potentially, present a highly developed sense of self and the ability to improve nursing care outcomes in these hospitals.

A Process Algebra Approach to Quantum Electrodynamics

NASA Astrophysics Data System (ADS)

Sulis, William

2017-12-01

The process algebra program is directed towards developing a realist model of quantum mechanics free of paradoxes, divergences and conceptual confusions. From this perspective, fundamental phenomena are viewed as emerging from primitive informational elements generated by processes. The process algebra has been shown to successfully reproduce scalar non-relativistic quantum mechanics (NRQM) without the usual paradoxes and dualities. NRQM appears as an effective theory which emerges under specific asymptotic limits. Space-time, scalar particle wave functions and the Born rule are all emergent in this framework. In this paper, the process algebra model is reviewed, extended to the relativistic setting, and then applied to the problem of electrodynamics. A semiclassical version is presented in which a Minkowski-like space-time emerges as well as a vector potential that is discrete and photon-like at small scales and near-continuous and wave-like at large scales. QED is viewed as an effective theory at small scales while Maxwell theory becomes an effective theory at large scales. The process algebra version of quantum electrodynamics is intuitive and realist, free from divergences and eliminates the distinction between particle, field and wave. Computations are carried out using the configuration space process covering map, although the connection to second quantization has not been fully explored.

Quantum Field Theory in Two Dimensions: Light-front Versus Space-like Solutions

NASA Astrophysics Data System (ADS)

Martinovic̆, L'ubomír

2017-07-01

A few non-perturbative topics of quantum field theory in D=1+1 are studied in both the conventional (SL) and light-front (LF) versions. First, we give a concise review of the recently proposed quantization of the two-dimensional massless LF fields. The LF version of bosonization follows in a simple and natural way including the bosonized form of the Thirring model. As a further application, we demonstrate the closeness of the 2D massless LF quantum fields to conformal field theory (CFT). We calculate several correlation functions including those between the components of the LF energy-momentum tensor and derive the LF version of the Virasoro algebra. Using the Euclidean time variable, we can immediately transform calculated quantities to the (anti)holomorphic form. The results found are in agreement with those from CFT. Finally, we show that the proposed framework provides us with the elements needed for an independent LF study of exactly solvable models. We compute the non-perturbative correlation functions from the exact operator solution of the LF Thirring model and compare it to the analogous results in the SL theory. While the vacuum effects are automatically taken into account in the LF case, the non-trivial vacuum structure has to be incorported by an explicit diagonalization of the SL Hamiltonians, to obtain the equivalently complete solution.

Reality, Causality, and Probability, from Quantum Mechanics to Quantum Field Theory

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2015-10-01

These three lectures consider the questions of reality, causality, and probability in quantum theory, from quantum mechanics to quantum field theory. They do so in part by exploring the ideas of the key founding figures of the theory, such N. Bohr, W. Heisenberg, E. Schrödinger, or P. A. M. Dirac. However, while my discussion of these figures aims to be faithful to their thinking and writings, and while these lectures are motivated by my belief in the helpfulness of their thinking for understanding and advancing quantum theory, this project is not driven by loyalty to their ideas. In part for that reason, these lectures also present different and even conflicting ways of thinking in quantum theory, such as that of Bohr or Heisenberg vs. that of Schrödinger. The lectures, most especially the third one, also consider new physical, mathematical, and philosophical complexities brought in by quantum field theory vis-à-vis quantum mechanics. I close by briefly addressing some of the implications of the argument presented here for the current state of fundamental physics.

Opening Talk: Opening Talk

NASA Astrophysics Data System (ADS)

Doebner, H.-D.

2008-02-01

Ladies and Gentlemen Dear Friends and Colleagues I welcome you at the 5th International Symposium `Quantum Theory and Symmetries, QTS5' in Valladolid as Chairman of the Conference Board of this biannual series. The aim of the series is to arrange an international meeting place for scientists working in theoretical and mathematical physics, in mathematics, in mathematical biology and chemistry and in other sciences for the presentation and discussion of recent developments in connection with quantum physics and chemistry, material science and related further fields, like life sciences and engineering, which are based on mathematical methods which can be applied to model and to understand microphysical and other systems through inherent symmetries in their widest sense. These systems include, e.g., foundations and extensions of quantum theory; quantum probability; quantum optics and quantum information; the description of nonrelativistic, finite dimensional and chaotic systems; quantum field theory, particle physics, string theory and quantum gravity. Symmetries in their widest sense describe properties of a system which could be modelled, e.g., through geometry, group theory, topology, algebras, differential geometry, noncommutative geometry, functional analysis and approximation methods; numerical evaluation techniques are necessary to connect such symmetries with experimental results. If you ask for a more detailed characterisation of this notion a hand waving indirect answer is: Collect titles and contents of the contributions of the proceedings of QTS4 and get a characterisation through semantic closure. Quantum theory and its Symmetries was and is a diversified and rapidly growing field. The number of and the types of systems with an internal symmetry and the corresponding mathematical models develop fast. This is reflected in the content of the five former international symposia of this series: The first symposium, QTS1-1999, was organized in Goslar (Germany) with 170 participants and 89 contributions in the proceedings; it was centred on the foundations and extensions of quantum theory, on quantisation methods and on q-algebras. In QTS2-2001 in Cracow (Poland) with 175 participants and 81 contributions; the main topics were applications of quantum mechanics, representations of algebras and group theoretical techniques in physics. In the symposium QTS3-2003 in Cincinnati (USA) with 145 participants and 92 contributions, quantum field theory, loop quantum gravity, string and brane theory was discussed. The focus in QTS4-2005 in Varna (Bulgaria) with 228 participant and 105 contributions, was on conformal field theory, quantum gravity, noncommutative geometry and quantum groups. Three proceedings volumes were published with World Scientific and one volume with Heron Press. The promising and interesting programme for QTS5-2007 in Valladolid (Spain) attracted more than 200 participants; the contributions will be published in a special issue of Journal of Physics A: Mathematical and Theoretical and a volume of Journal of Physics: Conference Series. This shows the wide scope of symmetry in connection with quantum physics and related sciences. In the background of the symposia series is the Conference Board with presently 13 members. The Board encourages scientists and Institutions to present detailed proposals for a QTS symposium; it agrees to one proposal and is prepared to assist in matters of organisation; the local organisers are responsible for the scientific programme and for the organisation, including the budget. The Board decided that the next symposium QTS6 will be held 2009 at the University of Kentucky in Lexington (USA); Alan Shapere is the chairman of the Local Organizing committee. In the name of all of you I express my appreciation and my thanks to the members of the Local Organizing Committee of QTS5, especially to Mariano del Olmo. The programme is outstanding; it covers recent and new developments in our field. The organization is very effective and complete. We have all the necessary condition for a successful and smooth meeting. Thank you again Mariano. H-D Doebner Chairman of the Conference Board of QTS5

Intersecting surface defects and instanton partition functions

NASA Astrophysics Data System (ADS)

Pan, Yiwen; Peelaers, Wolfger

2017-07-01

We analyze intersecting surface defects inserted in interacting four-dimensional N=2 supersymmetric quantum field theories. We employ the realization of a class of such systems as the infrared fixed points of renormalization group flows from larger theories, triggered by perturbed Seiberg-Witten monopole-like configurations, to compute their partition functions. These results are cast into the form of a partition function of 4d/2d/0d coupled systems. Our computations provide concrete expressions for the instanton partition function in the presence of intersecting defects and we study the corresponding ADHM model.

Quantum Critical Point revisited by the Dynamical Mean Field Theory

NASA Astrophysics Data System (ADS)

Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei

Dynamical mean field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. The QCP is characterized by a universal scaling form of the self energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low energy kink and the high energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high energy antiferromagnetic paramagnons. We use the frequency dependent four-point correlation function of spin operators to calculate the momentum dependent correction to the electron self energy. Our results reveal a substantial difference with the calculations based on the Spin-Fermion model which indicates that the frequency dependence of the the quasiparitcle-paramagnon vertices is an important factor. The authors are supported by Center for Computational Design of Functional Strongly Correlated Materials and Theoretical Spectroscopy under DOE Grant DE-FOA-0001276.

Electronic structure calculations of PbS quantum rods and tubes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pimachev, Artem; Dahnovsky, Yuri, E-mail: yurid@uwyo.edu

2014-01-28

We study absorption spectra, optical and HOMO-LUMO gaps, and the density of states for PbS quantum rods (QRs) and tubes (QTs). We find some similarities and also differences in QR and QT properties. For both QRs and QTs, the optical and HOMO-LUMO gaps reach the plateaus for small lengths. We find that tubes are as stable as rods. The optical spectra exhibit a peak that can be due to the electron-hole interaction or be a prototype of an S{sub e}–S{sub h} transition in the effective mass approximation. We also calculate the density of states by the density functional theory (DFT)more » and time-dependent density functional theory (TDDFT) methods. The TDDFT density of states function is shifted towards the red side by 0.5 eV indicating the strong e-h interaction.« less

On the 'principle of the quantumness', the quantumness of Relativity, and the computational grand-unification

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Ariano, Giacomo Mauro

2010-05-04

I will argue that the proposal of establishing operational foundations of Quantum Theory should have top-priority, and that the Lucien Hardy's program on Quantum Gravity should be paralleled by an analogous program on Quantum Field Theory (QFT), which needs to be reformulated, notwithstanding its experimental success. In this paper, after reviewing recently suggested operational 'principles of the quantumness', I address the problem on whether Quantum Theory and Special Relativity are unrelated theories, or instead, if the one implies the other. I show how Special Relativity can be indeed derived from causality of Quantum Theory, within the computational paradigm 'the universemore » is a huge quantum computer', reformulating QFT as a Quantum-Computational Field Theory (QCFT). In QCFT Special Relativity emerges from the fabric of the computational network, which also naturally embeds gauge invariance. In this scheme even the quantization rule and the Planck constant can in principle be derived as emergent from the underlying causal tapestry of space-time. In this way Quantum Theory remains the only theory operating the huge computer of the universe.Is the computational paradigm only a speculative tautology (theory as simulation of reality), or does it have a scientific value? The answer will come from Occam's razor, depending on the mathematical simplicity of QCFT. Here I will just start scratching the surface of QCFT, analyzing simple field theories, including Dirac's. The number of problems and unmotivated recipes that plague QFT strongly motivates us to undertake the QCFT project, since QCFT makes all such problems manifest, and forces a re-foundation of QFT.« less

Functional renormalization group and Kohn-Sham scheme in density functional theory

NASA Astrophysics Data System (ADS)

Liang, Haozhao; Niu, Yifei; Hatsuda, Tetsuo

2018-04-01

Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the φ4 theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.

Kinetic theory for strongly coupled Coulomb systems

NASA Astrophysics Data System (ADS)

Dufty, James; Wrighton, Jeffrey

2018-01-01

The calculation of dynamical properties for matter under extreme conditions is a challenging task. The popular Kubo-Greenwood model exploits elements from equilibrium density-functional theory (DFT) that allow a detailed treatment of electron correlations, but its origin is largely phenomenological; traditional kinetic theories have a more secure foundation but are limited to weak ion-electron interactions. The objective here is to show how a combination of the two evolves naturally from the short-time limit for the generator of the effective single-electron dynamics governing time correlation functions without such limitations. This provides a theoretical context for the current DFT-related approach, the Kubo-Greenwood model, while showing the nature of its corrections. The method is to calculate the short-time dynamics in the single-electron subspace for a given configuration of the ions. This differs from the usual kinetic theory approach in which an average over the ions is performed as well. In this way the effective ion-electron interaction includes strong Coulomb coupling and is shown to be determined from DFT. The correlation functions have the form of the random-phase approximation for an inhomogeneous system but with renormalized ion-electron and electron-electron potentials. The dynamic structure function, density response function, and electrical conductivity are calculated as examples. The static local field corrections in the dielectric function are identified in this way. The current analysis is limited to semiclassical electrons (quantum statistical potentials), so important quantum conditions are excluded. However, a quantization of the kinetic theory is identified for broader application while awaiting its detailed derivation.

USSR and Eastern Europe Scientific Abstracts, Electronics and Electrical Engineering, Number 27

DTIC Science & Technology

1977-02-10

input and output conditions. The power section of the circuit is modified to permit triacs and thyristors, respectively, to function. The purpose of the...electronic materials, components, and devices, on circuit theory, pulse techniques, electromagnetic wave propagation, radar, quantum electronic theory...Lasers, Masers, Holography, Quasi-Optical 20 Microelectronics and General Circuit Theory and Information 21 Radars and Radio Wavigati on 22

Quantum Chemical Simulation of the Interaction of Functional Groups in Polyurethanes with 3 d-Metal Ions During Their Extraction from Aqueous Solutions

NASA Astrophysics Data System (ADS)

Ksenofontov, M. A.; Bobkova, E. Yu.; Shundalau, M. B.; Ostrovskaya, L. E.; Vasil'eva, V. S.

2017-11-01

The interaction of the functional groups in the polyurethane foam adsorbent Penopurm® with the cations of some 3d-metals upon their extraction from aqueous solutions has been studied by atomic emission spectroscopy, UV/Vis and vibrational IR spectroscopy, and quantum chemical simulation using density functional theory. Penopurm® absorbs 3d-metal cations from aqueous solutions in the pH range 5-7. Some spectral criteria have been found indicating a predominant interaction of Ni2+ ions with various fragments of the polyurethane foam structure.

Interference of quantum market strategies

NASA Astrophysics Data System (ADS)

Piotrowski, Edward W.; Sładkowski, Jan; Syska, Jacek

2003-02-01

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper is devoted to the analysis of interference of quantum strategies in quantum market games.

Fast and accurate quantum molecular dynamics of dense plasmas across temperature regimes

DOE PAGES

Sjostrom, Travis; Daligault, Jerome

2014-10-10

Here, we develop and implement a new quantum molecular dynamics approximation that allows fast and accurate simulations of dense plasmas from cold to hot conditions. The method is based on a carefully designed orbital-free implementation of density functional theory. The results for hydrogen and aluminum are in very good agreement with Kohn-Sham (orbital-based) density functional theory and path integral Monte Carlo calculations for microscopic features such as the electron density as well as the equation of state. The present approach does not scale with temperature and hence extends to higher temperatures than is accessible in the Kohn-Sham method and lowermore » temperatures than is accessible by path integral Monte Carlo calculations, while being significantly less computationally expensive than either of those two methods.« less

Generation of Crystal-Structure Transverse Patterns via a Self-Frequency-Doubling Laser

PubMed Central

Yu, Haohai; Zhang, Huaijin; Wang, Yicheng; Wang, Zhengping; Wang, Jiyang; Petrov, V.

2013-01-01

Two-dimensional (2D) visible crystal-structure patterns analogous to the quantum harmonic oscillator (QHO) have been experimentally observed in the near- and far-fields of a self-frequency-doubling (SFD) microchip laser. Different with the fundamental modes, the localization of the SFD light is changed with the propagation. Calculation based on Hermite-Gaussian (HG) functions and second harmonic generation theory reproduces well the patterns both in the near- and far-field which correspond to the intensity distribution in coordinate and momentum spaces, respectively. Considering the analogy of wave functions of the transverse HG mode and 2D harmonic oscillator, we propose that the simple monolithic SFD lasers can be used for developing of new materials and devices and testing 2D quantum mechanical theories. PMID:23336067

Quantum transport of the single metallocene molecule

NASA Astrophysics Data System (ADS)

Yu, Jing-Xin; Chang, Jing; Wei, Rong-Kai; Liu, Xiu-Ying; Li, Xiao-Dong

2016-10-01

The Quantum transport of three single metallocene molecule is investigated by performing theoretical calculations using the non-equilibrium Green's function method combined with density functional theory. We find that the three metallocen molecules structure become stretched along the transport direction, the distance between two Cp rings longer than the other theory and experiment results. The lager conductance is found in nickelocene molecule, the main transmission channel is the electron coupling between molecule and the electrodes is through the Ni dxz and dyz orbitals and the s, dxz, dyz of gold. This is also confirmed by the highest occupied molecular orbital resonance at Fermi level. In addition, negative differential resistance effect is found in the ferrocene, cobaltocene molecules, this is also closely related with the evolution of the transmission spectrum under applied bias.

Generation of crystal-structure transverse patterns via a self-frequency-doubling laser.

PubMed

Yu, Haohai; Zhang, Huaijin; Wang, Yicheng; Wang, Zhengping; Wang, Jiyang; Petrov, V

2013-01-01

Two-dimensional (2D) visible crystal-structure patterns analogous to the quantum harmonic oscillator (QHO) have been experimentally observed in the near- and far-fields of a self-frequency-doubling (SFD) microchip laser. Different with the fundamental modes, the localization of the SFD light is changed with the propagation. Calculation based on Hermite-Gaussian (HG) functions and second harmonic generation theory reproduces well the patterns both in the near- and far-field which correspond to the intensity distribution in coordinate and momentum spaces, respectively. Considering the analogy of wave functions of the transverse HG mode and 2D harmonic oscillator, we propose that the simple monolithic SFD lasers can be used for developing of new materials and devices and testing 2D quantum mechanical theories.

Optimal and robust control of quantum state transfer by shaping the spectral phase of ultrafast laser pulses.

PubMed

Guo, Yu; Dong, Daoyi; Shu, Chuan-Cun

2018-04-04

Achieving fast and efficient quantum state transfer is a fundamental task in physics, chemistry and quantum information science. However, the successful implementation of the perfect quantum state transfer also requires robustness under practically inevitable perturbative defects. Here, we demonstrate how an optimal and robust quantum state transfer can be achieved by shaping the spectral phase of an ultrafast laser pulse in the framework of frequency domain quantum optimal control theory. Our numerical simulations of the single dibenzoterrylene molecule as well as in atomic rubidium show that optimal and robust quantum state transfer via spectral phase modulated laser pulses can be achieved by incorporating a filtering function of the frequency into the optimization algorithm, which in turn has potential applications for ultrafast robust control of photochemical reactions.

Quantum strain sensor with a topological insulator HgTe quantum dot

PubMed Central

Korkusinski, Marek; Hawrylak, Pawel

2014-01-01

We present a theory of electronic properties of HgTe quantum dot and propose a strain sensor based on a strain-driven transition from a HgTe quantum dot with inverted bandstructure and robust topologically protected quantum edge states to a normal state without edge states in the energy gap. The presence or absence of edge states leads to large on/off ratio of conductivity across the quantum dot, tunable by adjusting the number of conduction channels in the source-drain voltage window. The electronic properties of a HgTe quantum dot as a function of size and applied strain are described using eight-band Luttinger and Bir-Pikus Hamiltonians, with surface states identified with chirality of Luttinger spinors and obtained through extensive numerical diagonalization of the Hamiltonian. PMID:24811674

Condensed Matter Theories: Volume 25

NASA Astrophysics Data System (ADS)

Ludeña, Eduardo V.; Bishop, Raymond F.; Iza, Peter

2011-03-01

pt. A. Fermi and Bose fluids, exotic systems. Reemergence of the collective mode in [symbol]He and electron layers / H. M. Bohm ... [et al.]. Dissecting and testing collective and topological scenarios for the quantum critical point / J. W. Clark, V. A. Khodel and M. V. Zverev. Helium on nanopatterned surfaces at finite temperature / E. S. Hernandez ... [et al.]. Towards DFT calculations of metal clusters in quantum fluid matrices / S. A. Chin ... [et al.]. Acoustic band gap formation in metamaterials / D. P. Elford ... [et al.]. Dissipative processes in low density strongly interacting 2D electron systems / D. Neilson. Dynamical spatially resolved response function of finite 1-D nano plasmas / T. Raitza, H. Reinholz and G. Ropke. Renormalized bosons and fermions / K. A. Gernoth and M. L. Ristig. Light clusters in nuclear matter / G. Ropke -- pt. B. Quantum magnets, quantum dynamics and phase transitions. Magnetic ordering of antiferromagnets on a spatially anisotropic triangular lattice / R. F. Bishop ... [et al.]. Thermodynamic detection of quantum phase transitions / M. K. G. Kruse ... [et al.]. The SU(2) semi quantum systems dynamics and thermodynamics / C. M. Sarris and A. N. Proto -- pt. C. Physics of nanosystems and nanotechnology. Quasi-one dimensional fluids that exhibit higher dimensional behavior / S. M. Gatica ... [et al.]. Spectral properties of molecular oligomers. A non-Markovian quantum state diffusion approach / J. Roden, W. T. Strunz and A. Eisfeld. Quantum properties in transport through nanoscopic rings: Charge-spin separation and interference effects / K. Hallberg, J. Rincon and S. Ramasesha. Cooperative localization-delocalization in the high T[symbol] cuprates / J. Ranninger. Thermodynamically stable vortex states in superconducting nanowires / W. M. Wu, M. B. Sobnack and F. V. Kusmartsev.pt. D. Quantum information. Quantum information in optical lattices / A. M. Guzman and M. A. Duenas E. -- pt. E. Theory and applications of molecular dynamics and density functional theory. Exchange-correlation functionals from the identical-particle Ornstein-Zernike equation: Basic formulation and numerical algorithms / R. Cuevas-Saavedra and P. W. Ayers. Features and catalytic properties of RhCu: A review / S. Gonzalez, C. Sousa and F. Illas. Kinetic energy functionals: Exact ones from analytic model wave functions and approximate ones in orbital-free molecular dynamics / V. V. Karasiev ... [et al.]. Numerical analysis of hydrogen storage in carbon nanopores / C. Wexler ... [et al.] -- pt. F. Superconductivity. Generalized Bose-Einstein condensation in superconductivity / M. de Llano. Kohn anomaly energy in conventional superconductors equals twice the energy of the superconducting gap: How and why? / R. Chaudhury and M. P. Das. Collective excitations in superconductors and semiconductors in the presence of a condensed phase / Z. Koinov. Thermal expansion of ferromagnetic superconductors: Possible application to UGe[symbol] / N. Hatayama and R. Konno. Generalized superconducting gap in a Boson-Fermion model / T. A. Mamedov and M. de Llano. Influence of domain walls in the superconductor/ferromagnet proximity effect / E. J. Patino. Spin singlet and triplet superconductivity induced by correlated hopping interactions / L. A. Perez, J. S. Millan and C. Wang -- pt. G. Statistical mechanics, relativistic quantum mechanics. Boltzmann's ergodic hypothesis: A meeting place for two cultures / M. H. Lee. Electron-electron interaction in the non-relativistic limit / F. B. Malik.

Quantum theory for the dynamic structure factor in correlated two-component systems in nonequilibrium: Application to x-ray scattering.

PubMed

Vorberger, J; Chapman, D A

2018-01-01

We present a quantum theory for the dynamic structure factors in nonequilibrium, correlated, two-component systems such as plasmas or warm dense matter. The polarization function, which is needed as the input for the calculation of the structure factors, is calculated in nonequilibrium based on a perturbation expansion in the interaction strength. To make our theory applicable for x-ray scattering, a generalized Chihara decomposition for the total electron structure factor in nonequilibrium is derived. Examples are given and the influence of correlations and exchange on the structure and the x-ray-scattering spectrum are discussed for a model nonequilibrium distribution, as often encountered during laser heating of materials, as well as for two-temperature systems.

Quantum theory for the dynamic structure factor in correlated two-component systems in nonequilibrium: Application to x-ray scattering

NASA Astrophysics Data System (ADS)

Vorberger, J.; Chapman, D. A.

2018-01-01

We present a quantum theory for the dynamic structure factors in nonequilibrium, correlated, two-component systems such as plasmas or warm dense matter. The polarization function, which is needed as the input for the calculation of the structure factors, is calculated in nonequilibrium based on a perturbation expansion in the interaction strength. To make our theory applicable for x-ray scattering, a generalized Chihara decomposition for the total electron structure factor in nonequilibrium is derived. Examples are given and the influence of correlations and exchange on the structure and the x-ray-scattering spectrum are discussed for a model nonequilibrium distribution, as often encountered during laser heating of materials, as well as for two-temperature systems.

Controlling the sign problem in finite-density quantum field theory

NASA Astrophysics Data System (ADS)

Garron, Nicolas; Langfeld, Kurt

2017-07-01

Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analog. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the "telegraphic" approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close—if not identical—to the full answer in the strong sign-problem regime.

Density functional theory across chemistry, physics and biology.

PubMed

van Mourik, Tanja; Bühl, Michael; Gaigeot, Marie-Pierre

2014-03-13

The past decades have seen density functional theory (DFT) evolve from a rising star in computational quantum chemistry to one of its major players. This Theme Issue, which comes half a century after the publication of the Hohenberg-Kohn theorems that laid the foundations of modern DFT, reviews progress and challenges in present-day DFT research. Rather than trying to be comprehensive, this Theme Issue attempts to give a flavour of selected aspects of DFT.

Tribute to Julian Schwinger

NASA Astrophysics Data System (ADS)

Kohn, Walter

It is a melancholy privilege for me to take part in this symposium in honor of my venerated teacher, Julian Schwinger. All of us here know that his brilliant scientific insights and methodologies have l deep imprints across the entire spectrum of theoretical physics, both pure and applied. No doubt his most outstanding work was his monumental relativistically covariant renormalization theory of quantum electrodynamics; other areas which he substantially reshaped include quantum gauge theories, whose significance he was one of the first to realize; nuclear physics — beginning with his first papers written as a teenager and in which he offered perhaps the first comprehensive lecture course; the theory of waveguides, a powerful reformulation during World War II in terms of tensor Green's functions and variational principles; scattering theory; particle accelerators; and, very broadly, the structure of elementary particle theory…

An automated integration-free path-integral method based on Kleinert's variational perturbation theory

NASA Astrophysics Data System (ADS)

Wong, Kin-Yiu; Gao, Jiali

2007-12-01

Based on Kleinert's variational perturbation (KP) theory [Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 3rd ed. (World Scientific, Singapore, 2004)], we present an analytic path-integral approach for computing the effective centroid potential. The approach enables the KP theory to be applied to any realistic systems beyond the first-order perturbation (i.e., the original Feynman-Kleinert [Phys. Rev. A 34, 5080 (1986)] variational method). Accurate values are obtained for several systems in which exact quantum results are known. Furthermore, the computed kinetic isotope effects for a series of proton transfer reactions, in which the potential energy surfaces are evaluated by density-functional theory, are in good accordance with experiments. We hope that our method could be used by non-path-integral experts or experimentalists as a "black box" for any given system.

Large-N kinetic theory for highly occupied systems

NASA Astrophysics Data System (ADS)

Walz, R.; Boguslavski, K.; Berges, J.

2018-06-01

We consider an effective kinetic description for quantum many-body systems, which is not based on a weak-coupling or diluteness expansion. Instead, it employs an expansion in the number of field components N of the underlying scalar quantum field theory. Extending previous studies, we demonstrate that the large-N kinetic theory at next-to-leading order is able to describe important aspects of highly occupied systems, which are beyond standard perturbative kinetic approaches. We analyze the underlying quasiparticle dynamics by computing the effective scattering matrix elements analytically and solve numerically the large-N kinetic equation for a highly occupied system far from equilibrium. This allows us to compute the universal scaling form of the distribution function at an infrared nonthermal fixed point within a kinetic description, and we compare to existing lattice field theory simulation results.

Nature of isomerism of solid isothiourea salts, inhibitors of nitric oxide synthases, as studied by 1H-14N nuclear quadrupole double resonance, X-ray, and density functional theory/quantum theory of atoms in molecules.

PubMed

Latosińska, J N; Latosińska, M; Seliger, J; Žagar, V; Maurin, J K; Kazimierczuk, Z

2012-02-09

Isothioureas, inhibitors of nitric oxide synthases, have been studied experimentally in solid state by nuclear quadrupole double resonance (NQDR) and X-ray methods and theoretically by the quantum theory of atoms in molecules/density functional theory. Resonance frequencies on (14)N have been detected and assigned to particular nitrogen sites in each molecule. The crystal packings of (S)-3,4-dichlorobenzyl-N-methylisothiouronium chloride with the disordered chlorine positions in benzene ring and (S)-butyloisothiouronium bromide have been resolved in X-ray diffraction studies. (14)N NQDR spectra have been found good indicators of isomer type and strength of intra- or intermolecular N-H···X (X = Cl, Br) interactions. From among all salts studied, only for (S)-2,3,4,5,6-pentabromobenzylisothiouronium chloride are both nitrogen sites equivalent, which has been explained by the slow exchange. This unique structural feature can be a key factor in the high biological activity of (S)-2,3,4,5,6-pentabromobenzylisothiouronium salts.

Non-Hermitian photonics based on parity-time symmetry

NASA Astrophysics Data System (ADS)

Feng, Liang; El-Ganainy, Ramy; Ge, Li

2017-12-01

Nearly one century after the birth of quantum mechanics, parity-time symmetry is revolutionizing and extending quantum theories to include a unique family of non-Hermitian Hamiltonians. While conceptually striking, experimental demonstration of parity-time symmetry remains unexplored in quantum electronic systems. The flexibility of photonics allows for creating and superposing non-Hermitian eigenstates with ease using optical gain and loss, which makes it an ideal platform to explore various non-Hermitian quantum symmetry paradigms for novel device functionalities. Such explorations that employ classical photonic platforms not only deepen our understanding of fundamental quantum physics but also facilitate technological breakthroughs for photonic applications. Research into non-Hermitian photonics therefore advances and benefits both fields simultaneously.

Equivariant Verlinde Formula from Fivebranes and Vortices

NASA Astrophysics Data System (ADS)

Gukov, Sergei; Pei, Du

2017-10-01

We study complex Chern-Simons theory on a Seifert manifold M 3 by embedding it into string theory. We show that complex Chern-Simons theory on M 3 is equivalent to a topologically twisted supersymmetric theory and its partition function can be naturally regularized by turning on a mass parameter. We find that the dimensional reduction of this theory to 2d gives the low energy dynamics of vortices in four-dimensional gauge theory, the fact apparently overlooked in the vortex literature. We also generalize the relations between (1) the Verlinde algebra, (2) quantum cohomology of the Grassmannian, (3) Chern-Simons theory on {Σ× S^1} and (4) index of a spin c Dirac operator on the moduli space of flat connections to a new set of relations between (1) the "equivariant Verlinde algebra" for a complex group, (2) the equivariant quantum K-theory of the vortex moduli space, (3) complex Chern-Simons theory on {Σ × S^1} and (4) the equivariant index of a spin c Dirac operator on the moduli space of Higgs bundles.

Introduction to the Neutrosophic Quantum Theory

NASA Astrophysics Data System (ADS)

Smarandache, Florentin

2014-10-01

Neutrosophic Quantum Theory (NQT) is the study of the principle that certain physical quantities can assume neutrosophic values, instead of discrete values as in quantum theory. These quantities are thus neutrosophically quantized. A neutrosophic values (neutrosophic amount) is expressed by a set (mostly an interval) that approximates (or includes) a discrete value. An oscillator can lose or gain energy by some neutrosophic amount (we mean neither continuously nor discretely, but as a series of integral sets: S, 2S, 3S, ..., where S is a set). In the most general form, one has an ensemble of sets of sets, i.e. R1S1 ,R2S2 ,R3S3 , ..., where all Rn and Sn are sets that may vary in function of time and of other parameters. Several such sets may be equal, or may be reduced to points, or may be empty. {The multiplication of two sets A and B is classically defined as: AB ={ab, a??A and b??B}. And similarly a number n times a set A is defined as: nA ={na, a??A}.} The unit of neutrosophic energy is Hν , where H is a set (in particular an interval) that includes Planck constant h, and ν is the frequency. Therefore, an oscillator could change its energy by a neutrosophic number of quanta: Hν , 2H ν, 3H ν, etc. For example, when H is an interval [h1 ,h2 ] , with 0 <=h1 <=h2 , that contains Planck constant h, then one has: [h1 ν ,h2 ν ], [2h1 ν , 2h2 ν ], [3h1 ν , 3h2 ν ],..., as series of intervals of energy change of the oscillator. The most general form of the units of neutrosophic energy is Hnνn , where all Hn and νn are sets that similarly as above may vary in function of time and of other oscillator and environment parameters. Neutrosophic quantum theory combines classical mechanics and quantum mechanics.

Quantum theory of the generalised uncertainty principle

NASA Astrophysics Data System (ADS)

Bruneton, Jean-Philippe; Larena, Julien

2017-04-01

We extend significantly previous works on the Hilbert space representations of the generalized uncertainty principle (GUP) in 3 + 1 dimensions of the form [X_i,P_j] = i F_{ij} where F_{ij} = f({{P}}^2) δ _{ij} + g({{P}}^2) P_i P_j for any functions f. However, we restrict our study to the case of commuting X's. We focus in particular on the symmetries of the theory, and the minimal length that emerge in some cases. We first show that, at the algebraic level, there exists an unambiguous mapping between the GUP with a deformed quantum algebra and a quadratic Hamiltonian into a standard, Heisenberg algebra of operators and an aquadratic Hamiltonian, provided the boost sector of the symmetries is modified accordingly. The theory can also be mapped to a completely standard Quantum Mechanics with standard symmetries, but with momentum dependent position operators. Next, we investigate the Hilbert space representations of these algebraically equivalent models, and focus specifically on whether they exhibit a minimal length. We carry the functional analysis of the various operators involved, and show that the appearance of a minimal length critically depends on the relationship between the generators of translations and the physical momenta. In particular, because this relationship is preserved by the algebraic mapping presented in this paper, when a minimal length is present in the standard GUP, it is also present in the corresponding Aquadratic Hamiltonian formulation, despite the perfectly standard algebra of this model. In general, a minimal length requires bounded generators of translations, i.e. a specific kind of quantization of space, and this depends on the precise shape of the function f defined previously. This result provides an elegant and unambiguous classification of which universal quantum gravity corrections lead to the emergence of a minimal length.

Bell's Inequalities, Superquantum Correlations, and String Theory

DOE PAGES

Chang, Lay Nam; Lewis, Zachary; Minic, Djordje; ...

2011-01-01

We offermore » an interpretation of superquantum correlations in terms of a “doubly” quantum theory. We argue that string theory, viewed as a quantum theory with two deformation parameters, the string tension α ' , and the string coupling constant g s , is such a superquantum theory that transgresses the usual quantum violations of Bell's inequalities. We also discuss the ℏ → ∞ limit of quantum mechanics in this context. As a superquantum theory, string theory should display distinct experimentally observable supercorrelations of entangled stringy states.« less

Quantum Kramers model: Corrections to the linear response theory for continuous bath spectrum

NASA Astrophysics Data System (ADS)

Rips, Ilya

2017-01-01

Decay of the metastable state is analyzed within the quantum Kramers model in the weak-to-intermediate dissipation regime. The decay kinetics in this regime is determined by energy exchange between the unstable mode and the stable modes of thermal bath. In our previous paper [Phys. Rev. A 42, 4427 (1990), 10.1103/PhysRevA.42.4427], Grabert's perturbative approach to well dynamics in the case of the discrete bath [Phys. Rev. Lett. 61, 1683 (1988), 10.1103/PhysRevLett.61.1683] has been extended to account for the second order terms in the classical equations of motion (EOM) for the stable modes. Account of the secular terms reduces EOM for the stable modes to those of the forced oscillator with the time-dependent frequency (TDF oscillator). Analytic expression for the characteristic function of energy loss of the unstable mode has been derived in terms of the generating function of the transition probabilities for the quantum forced TDF oscillator. In this paper, the approach is further developed and applied to the case of the continuous frequency spectrum of the bath. The spectral density functions of the bath of stable modes are expressed in terms of the dissipative properties (the friction function) of the original bath. They simplify considerably for the one-dimensional systems, when the density of phonon states is constant. Explicit expressions for the fourth order corrections to the linear response theory result for the characteristic function of the energy loss and its cumulants are obtained for the particular case of the cubic potential with Ohmic (Markovian) dissipation. The range of validity of the perturbative approach in this case is determined (γ /ωb<0.26 ), which includes the turnover region. The dominant correction to the linear response theory result is associated with the "work function" and leads to reduction of the average energy loss and its dispersion. This reduction increases with the increasing dissipation strength (up to ˜10 % ) within the range of validity of the approach. We have also calculated corrections to the depopulation factor and the escape rate for the quantum and for the classical Kramers models. Results for the classical escape rate are in very good agreement with the numerical simulations for high barriers. The results can serve as an additional proof of the robustness and accuracy of the linear response theory.

Quantum Kramers model: Corrections to the linear response theory for continuous bath spectrum.

PubMed

Rips, Ilya

2017-01-01

Decay of the metastable state is analyzed within the quantum Kramers model in the weak-to-intermediate dissipation regime. The decay kinetics in this regime is determined by energy exchange between the unstable mode and the stable modes of thermal bath. In our previous paper [Phys. Rev. A 42, 4427 (1990)PLRAAN1050-294710.1103/PhysRevA.42.4427], Grabert's perturbative approach to well dynamics in the case of the discrete bath [Phys. Rev. Lett. 61, 1683 (1988)PRLTAO0031-900710.1103/PhysRevLett.61.1683] has been extended to account for the second order terms in the classical equations of motion (EOM) for the stable modes. Account of the secular terms reduces EOM for the stable modes to those of the forced oscillator with the time-dependent frequency (TDF oscillator). Analytic expression for the characteristic function of energy loss of the unstable mode has been derived in terms of the generating function of the transition probabilities for the quantum forced TDF oscillator. In this paper, the approach is further developed and applied to the case of the continuous frequency spectrum of the bath. The spectral density functions of the bath of stable modes are expressed in terms of the dissipative properties (the friction function) of the original bath. They simplify considerably for the one-dimensional systems, when the density of phonon states is constant. Explicit expressions for the fourth order corrections to the linear response theory result for the characteristic function of the energy loss and its cumulants are obtained for the particular case of the cubic potential with Ohmic (Markovian) dissipation. The range of validity of the perturbative approach in this case is determined (γ/ω_{b}<0.26), which includes the turnover region. The dominant correction to the linear response theory result is associated with the "work function" and leads to reduction of the average energy loss and its dispersion. This reduction increases with the increasing dissipation strength (up to ∼10%) within the range of validity of the approach. We have also calculated corrections to the depopulation factor and the escape rate for the quantum and for the classical Kramers models. Results for the classical escape rate are in very good agreement with the numerical simulations for high barriers. The results can serve as an additional proof of the robustness and accuracy of the linear response theory.

Dissipative time-dependent quantum transport theory.

PubMed

Zhang, Yu; Yam, Chi Yung; Chen, GuanHua

2013-04-28

A dissipative time-dependent quantum transport theory is developed to treat the transient current through molecular or nanoscopic devices in presence of electron-phonon interaction. The dissipation via phonon is taken into account by introducing a self-energy for the electron-phonon coupling in addition to the self-energy caused by the electrodes. Based on this, a numerical method is proposed. For practical implementation, the lowest order expansion is employed for the weak electron-phonon coupling case and the wide-band limit approximation is adopted for device and electrodes coupling. The corresponding hierarchical equation of motion is derived, which leads to an efficient and accurate time-dependent treatment of inelastic effect on transport for the weak electron-phonon interaction. The resulting method is applied to a one-level model system and a gold wire described by tight-binding model to demonstrate its validity and the importance of electron-phonon interaction for the quantum transport. As it is based on the effective single-electron model, the method can be readily extended to time-dependent density functional theory.

Use of the Lorentz-operator in relativistic quantum mechanics to guarentee a single-energy root

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ritchie, A B

1998-08-01

The Lorentz-operator form of relativistic quantum mechanics, with relativistic wave equation i{h_bar}{partial_derivative}{psi}/{partial_derivative}t=(mc{sup 2}{gamma}+e{Phi}){psi}, is implemented to guarantee a single-energy root. The Lorentz factor as modified by Pauli's ansatz is given by {gamma}={radical}1+[{rvec {sigma}}{center_dot}(i{h_bar}{rvec {del}}+(e/c){rvec A})]{sup 2}/m{sup 2}c{sup 2}, such that the theory is appropriate for electrons. Magnetic fine structure in the Lorentz relativistic wave equation emerges on the use of an appropriate operator form of the Lienard-Wiechert four- potential ({Phi},{rvec A}) from electromagnetic theory. Although computationally more intensive the advantage of the theory is the elimination of the negative-root of the energy and an interpretation of the wave function basedmore » on a one-particle, positive definite probability density like that of nonrelativistic quantum mechanics.« less

Matrix quantum mechanics on S1 /Z2

NASA Astrophysics Data System (ADS)

Betzios, P.; Gürsoy, U.; Papadoulaki, O.

2018-03-01

We study Matrix Quantum Mechanics on the Euclidean time orbifold S1 /Z2. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two dimensional non-critical string theory where the orbifold fixed points become cosmological singularities. We derive the MQM partition function both in the canonical and grand canonical ensemble in two different formulations and demonstrate agreement between them. We pinpoint the contribution of twisted states in both of these formulations either in terms of bi-local operators acting at the end-points of time or branch-cuts on the complex plane. We calculate, in the matrix model, the contribution of the twisted states to the torus level partition function explicitly and show that it precisely matches the world-sheet result, providing a non-trivial test of the proposed duality. Finally we discuss some interesting features of the partition function and the possibility of realising it as a τ-function of an integrable hierarchy.

Nonperturbative Quantum Physics from Low-Order Perturbation Theory.

PubMed

Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K

2015-10-02

The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.

Graphene quantum dots with visible light absorption of the carbon core: insights from single-particle spectroscopy and first principles based theory

NASA Astrophysics Data System (ADS)

Ghosh, Siddharth; Awasthi, Manohar; Ghosh, Moumita; Seibt, Michael; Niehaus, Thomas A.

2016-12-01

Luminescent carbon nanodots (CND) are a recent addition to the family of carbon nanostructures. Interestingly, a large group of CNDs are fluorescent in the visible spectrum and possess single dipole emitters with potential applications in super-resolution microscopy, quantum information science, and optoelectronics. There is a large diversity of CND’s size as well as a strong variability of edge topology and functional groups in real samples. This hampers a direct comparison of experimental and theoretical findings that is necessary to understand the unusual photophysics of these systems. Here, we derive atomistic models of finite sized (<2.5 nm) CNDs from high resolution transmission electron microscopy (HRTEM) which are studied using approximate time-dependent density functional theory. The atomistic models are found to be primarily two-dimensional (2D) and can hence be categorised as graphene quantum dots (GQD). The GQD model structures that are presented here show excitation energies in the visible spectrum matching previous single GQD level photoluminescence studies. We also present the effect of edge hydroxyl and carboxyl functional groups on the absorption spectrum. Overall, the study reveals the atomistic origin of CNDs photoluminescence in the visible range.

Multiconfiguration pair-density functional theory investigation of the electronic spectrum of MnO4-

NASA Astrophysics Data System (ADS)

Sharma, Prachi; Truhlar, Donald G.; Gagliardi, Laura

2018-03-01

The electronic spectrum of permanganate ions contains various highly multiconfigurational ligand-to-metal charge transfer states and is notorious for being one of the most challenging systems to be treated by quantum-chemical methods. Here we studied the lowest nine vertical excitation energies using restricted active space second-order perturbation theory (RASPT2) and multiconfiguration pair-density functional theory (MC-PDFT) to test and compare these two theories in computing such a challenging spectrum. The results are compared to literature data, including time-dependent density functional theory, completely renormalized equation-of-motion couple-cluster theory with single and double excitations, symmetry-adapted-cluster configuration interaction, and experimental spectra in the gas phase and solution. Our results show that MC-PDFT accurately predicts the spectrum at a significantly reduced cost as compared to RASPT2.

Multiconfiguration pair-density functional theory investigation of the electronic spectrum of MnO4.

PubMed

Sharma, Prachi; Truhlar, Donald G; Gagliardi, Laura

2018-03-28

The electronic spectrum of permanganate ions contains various highly multiconfigurational ligand-to-metal charge transfer states and is notorious for being one of the most challenging systems to be treated by quantum-chemical methods. Here we studied the lowest nine vertical excitation energies using restricted active space second-order perturbation theory (RASPT2) and multiconfiguration pair-density functional theory (MC-PDFT) to test and compare these two theories in computing such a challenging spectrum. The results are compared to literature data, including time-dependent density functional theory, completely renormalized equation-of-motion couple-cluster theory with single and double excitations, symmetry-adapted-cluster configuration interaction, and experimental spectra in the gas phase and solution. Our results show that MC-PDFT accurately predicts the spectrum at a significantly reduced cost as compared to RASPT2.

Quantum Chemical Studies of Actinides and Lanthanides: From Small Molecules to Nanoclusters

NASA Astrophysics Data System (ADS)

Vlaisavljevich, Bess

Research into actinides is of high interest because of their potential applications as an energy source and for the environmental implications therein. Global concern has arisen since the development of the actinide concept in the 1940s led to the industrial scale use of the commercial nuclear energy cycle and nuclear weapons production. Large quantities of waste have been generated from these processes inspiring efforts to address fundamental questions in actinide science. In this regard, the objective of this work is to use theory to provide insight and predictions into actinide chemistry, where experimental work is extremely challenging because of the intrinsic difficulties of the experiments themselves and the safety issues associated with this type of chemistry. This thesis is a collection of theoretical studies of actinide chemistry falling into three categories: quantum chemical and matrix isolation studies of small molecules, the electronic structure of organoactinide systems, and uranyl peroxide nanoclusters and other solid state actinide compounds. The work herein not only spans a wide range of systems size but also investigates a range of chemical problems. Various quantum chemical approaches have been employed. Wave function-based methods have been used to study the electronic structure of actinide containing molecules of small to middle-size. Among these methods, the complete active space self consistent field (CASSCF) approach with corrections from second-order perturbation theory (CASPT2), the generalized active space SCF (GASSCF) approach, and Moller-Plesset second-order perturbation theory (MP2) have been employed. Likewise, density functional theory (DFT) has been used along with analysis tools like bond energy decomposition, bond orders, and Bader's Atoms in Molecules. From these quantum chemical results, comparison with experimentally obtained structures and spectra are made.

Using the Chebychev expansion in quantum transport calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Popescu, Bogdan; Rahman, Hasan; Kleinekathöfer, Ulrich, E-mail: u.kleinekathoefer@jacobs-university.de

2015-04-21

Irradiation by laser pulses and a fluctuating surrounding liquid environment can, for example, lead to time-dependent effects in the transport through molecular junctions. From the theoretical point of view, time-dependent theories of quantum transport are still challenging. In one of these existing transport theories, the energy-dependent coupling between molecule and leads is decomposed into Lorentzian functions. This trick has successfully been combined with quantum master approaches, hierarchical formalisms, and non-equilibrium Green’s functions. The drawback of this approach is, however, its serious limitation to certain forms of the molecule-lead coupling and to higher temperatures. Tian and Chen [J. Chem. Phys. 137,more » 204114 (2012)] recently employed a Chebychev expansion to circumvent some of these latter problems. Here, we report on a similar approach also based on the Chebychev expansion but leading to a different set of coupled differential equations using the fact that a derivative of a zeroth-order Bessel function can again be given in terms of Bessel functions. Test calculations show the excellent numerical accuracy and stability of the presented formalism. The time span for which this Chebychev expansion scheme is valid without any restrictions on the form of the spectral density or temperature can be determined a priori.« less

Quantum cellular automata and free quantum field theory

NASA Astrophysics Data System (ADS)

D'Ariano, Giacomo Mauro; Perinotti, Paolo

2017-02-01

In a series of recent papers [1-4] it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.

2D Quantum Simulation of MOSFET Using the Non Equilibrium Green's Function Method

NASA Technical Reports Server (NTRS)

Svizhenko, Alexel; Anantram, M. P.; Govindan, T. R.; Yan, Jerry (Technical Monitor)

2000-01-01

The objectives this viewgraph presentation summarizes include: (1) the development of a quantum mechanical simulator for ultra short channel MOSFET simulation, including theory, physical approximations, and computer code; (2) explore physics that is not accessible by semiclassical methods; (3) benchmarking of semiclassical and classical methods; and (4) study other two-dimensional devices and molecular structure, from discretized Hamiltonian to tight-binding Hamiltonian.

Continuum modes of nonlocal field theories

NASA Astrophysics Data System (ADS)

Saravani, Mehdi

2018-04-01

We study a class of nonlocal Lorentzian quantum field theories, where the d’Alembertian operator \\Box is replaced by a non-analytic function of the d’Alembertian, f(\\Box) . This is inspired by the causal set program where such an evolution arises as the continuum limit of a wave equation on causal sets. The spectrum of these theories contains a continuum of massive excitations. This is perhaps the most important feature which leads to distinct/interesting phenomenology. In this paper, we study properties of the continuum massive modes in depth. We derive the path integral formulation of these theories. Meanwhile, this derivation introduces a dual picture in terms of local fields which clearly shows how continuum massive modes of the nonlocal field interact. As an example, we calculate the leading order modification to the Casimir force of a pair of parallel planes. The dual picture formulation opens the way for future developments in the study of nonlocal field theories using tools already available in local quantum field theories.

Estudio de reflectancia enfocado a la cartografia litologica de rocas igneas, efectos de distintos tipos de metamorfismo y analisis estructural en materiales precambricos, basado en datos espectrales de laboratorio e imagenes thematic mapper (Macizo Hesperico Central, Prov. de Caceres y Badajoz)

NASA Astrophysics Data System (ADS)

Plaza Garcia, Maria Asuncion

The rampant success of quantum theory is the result of applications of the 'new' quantum mechanics of Schrodinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum Electro-dynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9), and Quantum Chromodynamics (1973-); in fact, this success of 'the' quantum theory has depended on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously accurate calculational tools there has been no sensible explanation of all that is going on. It is even argued that such an understanding is nothing to do with physics. A long-standing and famous illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935). Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency. This project encompasses a detailed, critical survey of the tangled history of Position within quantum theories. The first step is to show that, contrary to appearances, canonical quantum mechanics has only a vague notion of locality. After analysing a number of previous attempts at a 'relativistic quantum mechanics', two lines of thought are considered in detail. The first is the work of Wan and students, which is shown to be no real improvement on the iisu.al 'nonrelativistic' theory. The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface in space-time. There remain considerable difficulties in the way of producing a consistent scheme here. To keep things nicely stirred up, the author then proposes his own approach - an adaptation of Feynman's QED propagators. This new approach is distinguished from Feynman's since the propagator or Green's function is not obtained by Feynman's rule. The type of equation solved is also different: instead of an initial-value problem, a solution that obeys a time-symmetric causality criterion is found for an inhomogeneous partial differential equation with homogeneous boundary conditions. To make the consideration of locality more precise, some results of Fourier transform theory are presented in a form that is directly applicable. Somewhat away from the main thrust of the thesis, there is also an attempt to explain, the manner in which quantum effects disappear as the number of particles increases in such things as experimental realisations of the EPR and de Broglie thought experiments.

Analytical methods for describing charged particle dynamics in general focusing lattices using generalized Courant-Snyder theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qin, Hong; Davidson, Ronald C.; Burby, Joshua W.

2014-04-08

The dynamics of charged particles in general linear focusing lattices with quadrupole, skew-quadrupole, dipole, and solenoidal components, as well as torsion of the fiducial orbit and variation of beam energy is parametrized using a generalized Courant-Snyder (CS) theory, which extends the original CS theory for one degree of freedom to higher dimensions. The envelope function is generalized into an envelope matrix, and the phase advance is generalized into a 4D symplectic rotation, or a Uð2Þ element. The 1D envelope equation, also known as the Ermakov-Milne-Pinney equation in quantum mechanics, is generalized to an envelope matrix equation in higher dimensions. Othermore » components of the original CS theory, such as the transfer matrix, Twiss functions, and CS invariant (also known as the Lewis invariant) all have their counterparts, with remarkably similar expressions, in the generalized theory. The gauge group structure of the generalized theory is analyzed. By fixing the gauge freedom with a desired symmetry, the generalized CS parametrization assumes the form of the modified Iwasawa decomposition, whose importance in phase space optics and phase space quantum mechanics has been recently realized. This gauge fixing also symmetrizes the generalized envelope equation and expresses the theory using only the generalized Twiss function β. The generalized phase advance completely determines the spectral and structural stability properties of a general focusing lattice. For structural stability, the generalized CS theory enables application of the Krein-Moser theory to greatly simplify the stability analysis. The generalized CS theory provides an effective tool to study coupled dynamics and to discover more optimized lattice designs in the larger parameter space of general focusing lattices.« less

Hacking the quantum revolution: 1925-1975

NASA Astrophysics Data System (ADS)

Schweber, Silvan S.

2015-01-01

I argue that the quantum revolution should be seen as an Ian Hacking type of scientific revolution: a profound, longue durée, multidisciplinary process of transforming our understanding of physical nature, with deep-rooted social components from the start. The "revolution" exhibits a characteristic style of reasoning - the hierarchization of physical nature - and developed and uses a specific language - quantum field theory (QFT). It is by virtue of that language that the quantum theory has achieved some of its deepest insights into the description of the dynamics of the physical world. However, the meaning of what a quantum field theory is and what it describes has deeply altered, and one now speaks of "effective" quantum field theories. Interpreting all present day quantum field theories as but "effective" field theories sheds additional light on Phillip Anderson's assertion that "More is different". This important element is addressed in the last part of the paper.

Solving the Quantum Many-Body Problem via Correlations Measured with a Momentum Microscope

NASA Astrophysics Data System (ADS)

Hodgman, S. S.; Khakimov, R. I.; Lewis-Swan, R. J.; Truscott, A. G.; Kheruntsyan, K. V.

2017-06-01

In quantum many-body theory, all physical observables are described in terms of correlation functions between particle creation or annihilation operators. Measurement of such correlation functions can therefore be regarded as an operational solution to the quantum many-body problem. Here, we demonstrate this paradigm by measuring multiparticle momentum correlations up to third order between ultracold helium atoms in an s -wave scattering halo of colliding Bose-Einstein condensates, using a quantum many-body momentum microscope. Our measurements allow us to extract a key building block of all higher-order correlations in this system—the pairing field amplitude. In addition, we demonstrate a record violation of the classical Cauchy-Schwarz inequality for correlated atom pairs and triples. Measuring multiparticle momentum correlations could provide new insights into effects such as unconventional superconductivity and many-body localization.

An information theory model for dissipation in open quantum systems

NASA Astrophysics Data System (ADS)

Rogers, David M.

2017-08-01

This work presents a general model for open quantum systems using an information game along the lines of Jaynes’ original work. It is shown how an energy based reweighting of propagators provides a novel moment generating function at each time point in the process. Derivatives of the generating function give moments of the time derivatives of observables. Aside from the mathematically helpful properties, the ansatz reproduces key physics of stochastic quantum processes. At high temperature, the average density matrix follows the Caldeira-Leggett equation. Its associated Langevin equation clearly demonstrates the emergence of dissipation and decoherence time scales, as well as an additional diffusion due to quantum confinement. A consistent interpretation of these results is that decoherence and wavefunction collapse during measurement are directly related to the degree of environmental noise, and thus occur because of subjective uncertainty of an observer.

Density-functional calculations of transport properties in the nondegenerate limit and the role of electron-electron scattering

DOE PAGES

Desjarlais, Michael P.; Scullard, Christian R.; Benedict, Lorin X.; ...

2017-03-13

We compute electrical and thermal conductivities of hydrogen plasmas in the non-degenerate regime using Kohn-Sham Density Functional Theory (DFT) and an application of the Kubo- Greenwood response formula, and demonstrate that for thermal conductivity, the mean-field treatment of the electron-electron (e-e) interaction therein is insufficient to reproduce the weak-coupling limit obtained by plasma kinetic theories. An explicit e-e scattering correction to the DFT is posited by appealing to Matthiessen's Rule and the results of our computations of conductivities with the quantum Lenard-Balescu (QLB) equation. Further motivation of our correction is provided by an argument arising from the Zubarev quantum kineticmore » theory approach. Significant emphasis is placed on our efforts to produce properly converged results for plasma transport using Kohn-Sham DFT, so that an accurate assessment of the importance and efficacy of our e-e scattering corrections to the thermal conductivity can be made.« less

The geometrical structure of quantum theory as a natural generalization of information geometry

NASA Astrophysics Data System (ADS)

Reginatto, Marcel

2015-01-01

Quantum mechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantum mechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantum mechanics is constructed using geometrical quantities. This suggests that quantum theory has its roots in information geometry.

Niels Bohr on the wave function and the classical/quantum divide

NASA Astrophysics Data System (ADS)

Zinkernagel, Henrik

2016-02-01

It is well known that Niels Bohr insisted on the necessity of classical concepts in the account of quantum phenomena. But there is little consensus concerning his reasons, and what he exactly meant by this. In this paper, I re-examine Bohr's interpretation of quantum mechanics, and argue that the necessity of the classical can be seen as part of his response to the measurement problem. More generally, I attempt to clarify Bohr's view on the classical/quantum divide, arguing that the relation between the two theories is that of mutual dependence. An important element in this clarification consists in distinguishing Bohr's idea of the wave function as symbolic from both a purely epistemic and an ontological interpretation. Together with new evidence concerning Bohr's conception of the wave function collapse, this sets his interpretation apart from both standard versions of the Copenhagen interpretation, and from some of the reconstructions of his view found in the literature. I conclude with a few remarks on how Bohr's ideas make much sense also when modern developments in quantum gravity and early universe cosmology are taken into account.

Nonthermal Quantum Channels as a Thermodynamical Resource.

PubMed

Navascués, Miguel; García-Pintos, Luis Pedro

2015-07-03

Quantum thermodynamics can be understood as a resource theory, whereby thermal states are free and the only allowed operations are unitary transformations commuting with the total Hamiltonian of the system. Previous literature on the subject has just focused on transformations between different state resources, overlooking the fact that quantum operations which do not commute with the total energy also constitute a potentially valuable resource. In this Letter, given a number of nonthermal quantum channels, we study the problem of how to integrate them in a thermal engine so as to distill a maximum amount of work. We find that, in the limit of asymptotically many uses of each channel, the distillable work is an additive function of the considered channels, computable for both finite dimensional quantum operations and bosonic channels. We apply our results to bound the amount of distillable work due to the natural nonthermal processes postulated in the Ghirardi-Rimini-Weber (GRW) collapse model. We find that, although GRW theory predicts the possibility of extracting work from the vacuum at no cost, the power which a collapse engine could, in principle, generate is extremely low.

Nonthermal Quantum Channels as a Thermodynamical Resource

NASA Astrophysics Data System (ADS)

Navascués, Miguel; García-Pintos, Luis Pedro

2015-07-01

Quantum thermodynamics can be understood as a resource theory, whereby thermal states are free and the only allowed operations are unitary transformations commuting with the total Hamiltonian of the system. Previous literature on the subject has just focused on transformations between different state resources, overlooking the fact that quantum operations which do not commute with the total energy also constitute a potentially valuable resource. In this Letter, given a number of nonthermal quantum channels, we study the problem of how to integrate them in a thermal engine so as to distill a maximum amount of work. We find that, in the limit of asymptotically many uses of each channel, the distillable work is an additive function of the considered channels, computable for both finite dimensional quantum operations and bosonic channels. We apply our results to bound the amount of distillable work due to the natural nonthermal processes postulated in the Ghirardi-Rimini-Weber (GRW) collapse model. We find that, although GRW theory predicts the possibility of extracting work from the vacuum at no cost, the power which a collapse engine could, in principle, generate is extremely low.

A quantum-classical theory with nonlinear and stochastic dynamics

NASA Astrophysics Data System (ADS)

Burić, N.; Popović, D. B.; Radonjić, M.; Prvanović, S.

2014-12-01

The method of constrained dynamical systems on the quantum-classical phase space is utilized to develop a theory of quantum-classical hybrid systems. Effects of the classical degrees of freedom on the quantum part are modeled using an appropriate constraint, and the interaction also includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement.

Theory of electronic and optical properties for different shapes of InAs/In0.52Al0.48As quantum wires

NASA Astrophysics Data System (ADS)

Bouazra, A.; Nasrallah, S. Abdi-Ben; Said, M.

2016-01-01

In this work, we propose an efficient method to investigate optical properties as well as their dependence on geometrical parameters in InAs/InAlAs quantum wires. The used method is based on the coordinate transformation and the finite difference method. It provides sufficient accuracy, stability and flexibility with respect to the size and shape of the quantum wire. The electron and hole energy levels as well as their corresponding wave functions are investigated for different shape of quantum wires. The optical transition energies, the emission wavelengths and the oscillator strengths are also studied.

Analog model for quantum gravity effects: phonons in random fluids.

PubMed

Krein, G; Menezes, G; Svaiter, N F

2010-09-24

We describe an analog model for quantum gravity effects in condensed matter physics. The situation discussed is that of phonons propagating in a fluid with a random velocity wave equation. We consider that there are random fluctuations in the reciprocal of the bulk modulus of the system and study free phonons in the presence of Gaussian colored noise with zero mean. We show that, in this model, after performing the random averages over the noise function a free conventional scalar quantum field theory describing free phonons becomes a self-interacting model.

Microscopic Theory and Simulation of Quantum-Well Intersubband Absorption

NASA Technical Reports Server (NTRS)

Li, Jianzhong; Ning, C. Z.

2004-01-01

We study the linear intersubband absorption spectra of a 15 nm InAs quantum well using the intersubband semiconductor Bloch equations with a three-subband model and a constant dephasing rate. We demonstrate the evolution of intersubband absorption spectral line shape as a function of temperature and electron density. Through a detailed examination of various contributions, such as the phase space filling effects, the Coulomb many-body effects and the non-parabolicity effect, we illuminate the underlying physics that shapes the spectra. Keywords: Intersubband transition, linear absorption, semiconductor heterostructure, InAs quantum well

Perturbative quantum field theory in the framework of the fermionic projector

NASA Astrophysics Data System (ADS)

Finster, Felix

2014-04-01

We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.

Quantum resource theories in the single-shot regime

NASA Astrophysics Data System (ADS)

Gour, Gilad

2017-06-01

One of the main goals of any resource theory such as entanglement, quantum thermodynamics, quantum coherence, and asymmetry, is to find necessary and sufficient conditions that determine whether one resource can be converted to another by the set of free operations. Here we find such conditions for a large class of quantum resource theories which we call affine resource theories. Affine resource theories include the resource theories of athermality, asymmetry, and coherence, but not entanglement. Remarkably, the necessary and sufficient conditions can be expressed as a family of inequalities between resource monotones (quantifiers) that are given in terms of the conditional min-entropy. The set of free operations is taken to be (1) the maximal set (i.e., consists of all resource nongenerating quantum channels) or (2) the self-dual set of free operations (i.e., consists of all resource nongenerating maps for which the dual map is also resource nongenerating). As an example, we apply our results to quantum thermodynamics with Gibbs preserving operations, and several other affine resource theories. Finally, we discuss the applications of these results to resource theories that are not affine and, along the way, provide the necessary and sufficient conditions that a quantum resource theory consists of a resource destroying map.

Quantum chemical methods for the investigation of photoinitiated processes in biological systems: theory and applications.

PubMed

Dreuw, Andreas

2006-11-13

With the advent of modern computers and advances in the development of efficient quantum chemical computer codes, the meaningful computation of large molecular systems at a quantum mechanical level became feasible. Recent experimental effort to understand photoinitiated processes in biological systems, for instance photosynthesis or vision, at a molecular level also triggered theoretical investigations in this field. In this Minireview, standard quantum chemical methods are presented that are applicable and recently used for the calculation of excited states of photoinitiated processes in biological molecular systems. These methods comprise configuration interaction singles, the complete active space self-consistent field method, and time-dependent density functional theory and its variants. Semiempirical approaches are also covered. Their basic theoretical concepts and mathematical equations are briefly outlined, and their properties and limitations are discussed. Recent successful applications of the methods to photoinitiated processes in biological systems are described and theoretical tools for the analysis of excited states are presented.

A quantum perturbative pair distribution for determining interatomic potentials from extended x-ray absorption spectroscopy

NASA Astrophysics Data System (ADS)

Piazza, F.

2002-11-01

In this paper we develop a technique for determining interatomic potentials in materials in the quantum regime from single-shell extended x-ray absorption spectroscopy (EXAFS) spectra. We introduce a pair distribution function, based on ordinary quantum time-independent perturbation theory. In the proposed scheme, the model potential parameters enter the distribution through a fourth-order Taylor expansion of the potential, and are directly refined in the fit of the model signal to the experimental spectrum. We discuss in general the validity of our theoretical framework, namely the quantum regime and perturbative treatment, and work out a simple tool for monitoring the sensitivity of our theory in determining lattice anharmonicities based on the statistical F-test. As an example, we apply our formalism to an EXAFS spectrum at the Ag K edge of AgI at T = 77 K. We determine the Ag-I potential parameters and find good agreement with previous studies.

Array of nanoparticles coupling with quantum-dot: Lattice plasmon quantum features

NASA Astrophysics Data System (ADS)

Salmanogli, Ahmad; Gecim, H. Selcuk

2018-06-01

In this study, we analyze the interaction of lattice plasmon with quantum-dot in order to mainly examine the quantum features of the lattice plasmon containing the photonic/plasmonic properties. Despite optical properties of the localized plasmon, the lattice plasmon severely depends on the array geometry, which may influence its quantum features such as uncertainty and the second-order correlation function. To investigate this interaction, we consider a closed system containing an array of the plasmonic nanoparticles and quantum-dot. We analyze this system with full quantum theory by which the array electric far field is quantized and the strength coupling of the quantum-dot array is analytically calculated. Moreover, the system's dynamics are evaluated and studied via the Heisenberg-Langevin equations to attain the system optical modes. We also analytically examine the Purcell factor, which shows the effect of the lattice plasmon on the quantum-dot spontaneous emission. Finally, the lattice plasmon uncertainty and its time evolution of the second-order correlation function at different spatial points are examined. These parameters are dramatically affected by the retarded field effect of the array nanoparticles. We found a severe quantum fluctuation at points where the lattice plasmon occurs, suggesting that the lattice plasmon photons are correlated.

Quantum Sheaf Cohomology on Grassmannians

NASA Astrophysics Data System (ADS)

Guo, Jirui; Lu, Zhentao; Sharpe, Eric

2017-05-01

In this paper we study the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2) deformation of the ordinary quantum cohomology ring, realized as the OPE ring in A/2-twisted theories. Quantum sheaf cohomology has previously been computed for abelian gauged linear sigma models (GLSMs); here, we study (0,2) deformations of nonabelian GLSMs, for which previous methods have been intractable. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. We also utilize recent advances in supersymmetric localization to compute A/2 correlation functions and check the general result in examples. In this paper we focus on physics derivations and examples; in a companion paper, we will provide a mathematically rigorous derivation of the classical sheaf cohomology ring.

Discrete symmetries and the propagator approach to coupled fermions in Quantum Field Theory. Generalities: The case of a single fermion-antifermion pair

NASA Astrophysics Data System (ADS)

Duret, Q.; Machet, B.

2010-10-01

Starting from Wigner's symmetry representation theorem, we give a general account of discrete symmetries (parity P, charge conjugation C, time-reversal T), focusing on fermions in Quantum Field Theory. We provide the rules of transformation of Weyl spinors, both at the classical level (grassmanian wave functions) and quantum level (operators). Making use of Wightman's definition of invariance, we outline ambiguities linked to the notion of classical fermionic Lagrangian. We then present the general constraints cast by these transformations and their products on the propagator of the simplest among coupled fermionic system, the one made with one fermion and its antifermion. Last, we put in correspondence the propagation of C eigenstates (Majorana fermions) and the criteria cast on their propagator by C and CP invariance.

Relativistic hydrodynamics from quantum field theory on the basis of the generalized Gibbs ensemble method

NASA Astrophysics Data System (ADS)

Hayata, Tomoya; Hidaka, Yoshimasa; Noumi, Toshifumi; Hongo, Masaru

2015-09-01

We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energy-momentum tensor and particle current into nondissipative and dissipative parts, and analyze their time evolution in detail. Performing the path-integral formulation of the local Gibbs distribution, we microscopically derive the generating functional for the nondissipative hydrodynamics. We also construct a basis to study dissipative corrections. In particular, we derive the first-order dissipative hydrodynamic equations without a choice of frame such as the Landau-Lifshitz or Eckart frame.

Quantum chemical calculations of Cr2O3/SnO2 using density functional theory method

NASA Astrophysics Data System (ADS)

Jawaher, K. Rackesh; Indirajith, R.; Krishnan, S.; Robert, R.; Das, S. Jerome

2018-03-01

Quantum chemical calculations have been employed to study the molecular effects produced by Cr2O3/SnO2 optimised structure. The theoretical parameters of the transparent conducting metal oxides were calculated using DFT / B3LYP / LANL2DZ method. The optimised bond parameters such as bond lengths, bond angles and dihedral angles were calculated using the same theory. The non-linear optical property of the title compound was calculated using first-order hyperpolarisability calculation. The calculated HOMO-LUMO analysis explains the charge transfer interaction between the molecule. In addition, MEP and Mulliken atomic charges were also calculated and analysed.

The transactional interpretation of quantum mechanics

NASA Astrophysics Data System (ADS)

Cramer, John G.

2001-06-01

The transactional interpretation of quantum mechanics [1] was originally published in 1986 and is now about 14 years old. It is an explicitly nonlocal and Lorentz invariant alternative to the Copenhagen interpretation. It interprets the formalism for a quantum interaction as describing a "handshake" between retarded waves (ψ) and advanced waves (ψ*) for each quantum event or "transaction" in which energy, momentum, angular momentum, and other conserved quantities are transferred. The transactional interpretation offers the advantages that (1) it is actually "visible" in the formalism of quantum mechanics, (2) it is economical, involving fewer independent assumptions than its rivals, (3) it is paradox-free, resolving all of the paradoxes of standard quantum theory including nonlocality and wave function collapse, (4) it does not give a privileged role to observers or measurements, and (5) it permits the visualization of quantum events. We will review the transactional interpretation and some of its applications to "quantum paradoxes."

Equilibrium properties of dense hydrogen isotope gases based on the theory of simple fluids.

PubMed

Kowalczyk, Piotr; MacElroy, J M D

2006-08-03

We present a new method for the prediction of the equilibrium properties of dense gases containing hydrogen isotopes. The proposed approach combines the Feynman-Hibbs effective potential method and a deconvolution scheme introduced by Weeks et al. The resulting equations of state and the chemical potentials as functions of pressure for each of the hydrogen isotope gases depend on a single set of Lennard-Jones parameters. In addition to its simplicity, the proposed method with optimized Lennard-Jones potential parameters accurately describes the equilibrium properties of hydrogen isotope fluids in the regime of moderate temperatures and pressures. The present approach should find applications in the nonlocal density functional theory of inhomogeneous quantum fluids and should also be of particular relevance to hydrogen (clean energy) storage and to the separation of quantum isotopes by novel nanomaterials.

Quantum critical point revisited by dynamical mean-field theory

NASA Astrophysics Data System (ADS)

Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei M.

2017-03-01

Dynamical mean-field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. The QCP is characterized by a universal scaling form of the self-energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low-energy kink and the high-energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high-energy antiferromagnetic paramagnons. We use the frequency-dependent four-point correlation function of spin operators to calculate the momentum-dependent correction to the electron self-energy. By comparing with the calculations based on the spin-fermion model, our results indicate the frequency dependence of the quasiparticle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.

Synthesis, crystal structure, vibrational spectra and theoretical calculations of quantum chemistry of a potential antimicrobial Meldrum's acid derivative

NASA Astrophysics Data System (ADS)

Campelo, M. J. M.; Freire, P. T. C.; Mendes Filho, J.; de Toledo, T. A.; Teixeira, A. M. R.; da Silva, L. E.; Bento, R. R. F.; Faria, J. L. B.; Pizani, P. S.; Gusmão, G. O. M.; Coutinho, H. D. M.; Oliveira, M. T. A.

2017-10-01

A new derivative of Meldrum's acid 5-((5-chloropyridin-2-ylamino)methylene)-2,2-dimethyl-1,3-dioxane-4,6-dione (CYMM) of molecular formula C12H11ClN2O4 was synthesized and structurally characterized using single crystal X-ray diffraction technique. The vibrational properties of the crystal were studied by Fourier Transform infrared (FT-IR), Fourier Transform Raman (FT-Raman) techniques and theoretical calculations of quantum chemistry using Density functional theory (DFT) and Density functional perturbation theory (DFPT). A comparison with experimental spectra allowed the assignment of all the normal modes. The descriptions of the normal modes were carried by means of potential energy distribution (PED). Additionally, analysis of the antimicrobial activity and antibiotic resistance modulatory activity was carried out to evaluate the antibacterial potential of the CYMM.

Quantum critical point revisited by dynamical mean-field theory

DOE PAGES

Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei M.

2017-03-31

Dynamical mean-field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. We characterize the QCP by a universal scaling form of the self-energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low-energy kink and the high-energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high-energy antiferromagnetic paramagnons. Here, we use the frequency-dependent four-point correlation function of spin operators to calculate the momentum-dependent correction to the electron self-energy. Furthermore, by comparing with the calculations basedmore » on the spin-fermion model, our results indicate the frequency dependence of the quasiparticle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.« less

Intersecting surface defects and instanton partition functions

DOE PAGES

Pan, Yiwen; Peelaers, Wolfger

2017-07-14

We analyze intersecting surface defects inserted in interacting four-dimensional N = 2 supersymmetric quantum field theories. We employ the realization of a class of such systems as the infrared xed points of renormalization group flows from larger theories, triggered by perturbed Seiberg-Witten monopole-like con gurations, to compute their partition functions. These results are cast into the form of a partition function of 4d/2d/0d coupled systems. In conclusion, our computations provide concrete expressions for the instanton partition function in the presence of intersecting defects and we study the corresponding ADHM model.

Intersecting surface defects and instanton partition functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Yiwen; Peelaers, Wolfger

We analyze intersecting surface defects inserted in interacting four-dimensional N = 2 supersymmetric quantum field theories. We employ the realization of a class of such systems as the infrared xed points of renormalization group flows from larger theories, triggered by perturbed Seiberg-Witten monopole-like con gurations, to compute their partition functions. These results are cast into the form of a partition function of 4d/2d/0d coupled systems. In conclusion, our computations provide concrete expressions for the instanton partition function in the presence of intersecting defects and we study the corresponding ADHM model.

Niels Bohr as philosopher of experiment: Does decoherence theory challenge Bohr's doctrine of classical concepts?

NASA Astrophysics Data System (ADS)

Camilleri, Kristian; Schlosshauer, Maximilian

2015-02-01

Niels Bohr's doctrine of the primacy of "classical concepts" is arguably his most criticized and misunderstood view. We present a new, careful historical analysis that makes clear that Bohr's doctrine was primarily an epistemological thesis, derived from his understanding of the functional role of experiment. A hitherto largely overlooked disagreement between Bohr and Heisenberg about the movability of the "cut" between measuring apparatus and observed quantum system supports the view that, for Bohr, such a cut did not originate in dynamical (ontological) considerations, but rather in functional (epistemological) considerations. As such, both the motivation and the target of Bohr's doctrine of classical concepts are of a fundamentally different nature than what is understood as the dynamical problem of the quantum-to-classical transition. Our analysis suggests that, contrary to claims often found in the literature, Bohr's doctrine is not, and cannot be, at odds with proposed solutions to the dynamical problem of the quantum-classical transition that were pursued by several of Bohr's followers and culminated in the development of decoherence theory.

Multiscale Electrodynamics/Time-Dependent Density Functional Theory Modeling of Coupled Plasmon/Molecule Excitations

NASA Astrophysics Data System (ADS)

Lopata, Kenneth; Smith, Holden

The coupled dynamics of molecular chromophores and plasmons at surface of metal nanostructures are important for a range of processes such as molecular sensing, light harvesting, and near-field photochemistry. Modeling these dynamics from first principles, however, is challenging, as the large system sizes precludes a purely quantum mechanical treatment. In this talk I will present an approach based on propagating the plasmonic currents and fields using electrodynamics (finite-difference time-domain) with each chromophore described using an isolated quantum sub-region embedded in the overall classical background. This approach can be readily parallelized over these quantum regions, which enables large multiscale simulations of tens or hundreds of dyes, each of which is described individually by real-time time-dependent density functional theory. Application to gold nanoparticles coated with malachite green and rhodamine 6G monolayers shows good agreement with experimentally measured coupling spectra, including the polariton peaks, as well as the plasmon and molecular depletions. This research was supported by the Louisiana Board of Regents Research Competitiveness Subprogram under Contract Number LEQSF(2014-17)-RD-A-0.

Quantum dynamics of hydrogen atoms on graphene. I. System-bath modeling.

PubMed

Bonfanti, Matteo; Jackson, Bret; Hughes, Keith H; Burghardt, Irene; Martinazzo, Rocco

2015-09-28

An accurate system-bath model to investigate the quantum dynamics of hydrogen atoms chemisorbed on graphene is presented. The system comprises a hydrogen atom and the carbon atom from graphene that forms the covalent bond, and it is described by a previously developed 4D potential energy surface based on density functional theory ab initio data. The bath describes the rest of the carbon lattice and is obtained from an empirical force field through inversion of a classical equilibrium correlation function describing the hydrogen motion. By construction, model building easily accommodates improvements coming from the use of higher level electronic structure theory for the system. Further, it is well suited to a determination of the system-environment coupling by means of ab initio molecular dynamics. This paper details the system-bath modeling and shows its application to the quantum dynamics of vibrational relaxation of a chemisorbed hydrogen atom, which is here investigated at T = 0 K with the help of the multi-configuration time-dependent Hartree method. Paper II deals with the sticking dynamics.

The geometrical structure of quantum theory as a natural generalization of information geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reginatto, Marcel

2015-01-13

Quantum mechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantum mechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantum mechanics is constructed usingmore » geometrical quantities. This suggests that quantum theory has its roots in information geometry.« less

Ordinary versus PT-symmetric Φ³ quantum field theory

DOE PAGES

Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele

2012-04-02

A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum fieldmore » theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.« less

Koopman-von Neumann formulation of classical Yang-Mills theories: I

NASA Astrophysics Data System (ADS)

Carta, P.; Gozzi, E.; Mauro, D.

2006-03-01

In this paper we present the Koopman-von Neumann (KvN) formulation of classical non-Abelian gauge field theories. In particular we shall explore the functional (or classical path integral) counterpart of the KvN method. In the quantum path integral quantization of Yang-Mills theories concepts like gauge-fixing and Faddeev-Popov determinant appear in a quite natural way. We will prove that these same objects are needed also in this classical path integral formulation for Yang-Mills theories. We shall also explore the classical path integral counterpart of the BFV formalism and build all the associated universal and gauge charges. These last are quite different from the analog quantum ones and we shall show the relation between the two. This paper lays the foundation of this formalism which, due to the many auxiliary fields present, is rather heavy. Applications to specific topics outlined in the paper will appear in later publications.

Fractional quantum Hall systems near nematicity: Bimetric theory, composite fermions, and Dirac brackets

NASA Astrophysics Data System (ADS)

Nguyen, Dung Xuan; Gromov, Andrey; Son, Dam Thanh

2018-05-01

We perform a detailed comparison of the Dirac composite fermion and the recently proposed bimetric theory for a quantum Hall Jain states near half filling. By tuning the composite Fermi liquid to the vicinity of a nematic phase transition, we find that the two theories are equivalent to each other. We verify that the single mode approximation for the response functions and the static structure factor becomes reliable near the phase transition. We show that the dispersion relation of the nematic mode near the phase transition can be obtained from the Dirac brackets between the components of the nematic order parameter. The dispersion is quadratic at low momenta and has a magnetoroton minimum at a finite momentum, which is not related to any nearby inhomogeneous phase.

Evidence for a first-order liquid-liquid transition in high-pressure hydrogen from ab initio simulations.

PubMed

Morales, Miguel A; Pierleoni, Carlo; Schwegler, Eric; Ceperley, D M

2010-07-20

Using quantum simulation techniques based on either density functional theory or quantum Monte Carlo, we find clear evidence of a first-order transition in liquid hydrogen, between a low conductivity molecular state and a high conductivity atomic state. Using the temperature dependence of the discontinuity in the electronic conductivity, we estimate the critical point of the transition at temperatures near 2,000 K and pressures near 120 GPa. Furthermore, we have determined the melting curve of molecular hydrogen up to pressures of 200 GPa, finding a reentrant melting line. The melting line crosses the metalization line at 700 K and 220 GPa using density functional energetics and at 550 K and 290 GPa using quantum Monte Carlo energetics.

Vibrational analysis and quantum chemical calculations of 2,2‧-bipyridine Zinc(II) halide complexes

NASA Astrophysics Data System (ADS)

Ozel, Aysen E.; Kecel, Serda; Akyuz, Sevim

2007-05-01

In this study the molecular structure and vibrational spectra of Zn(2,2'-bipyridine)X 2 (X = Cl and Br) complexes were studied in their ground states by computational vibrational study and scaled quantum mechanical (SQM) analysis. The geometry optimization, vibrational wavenumber and intensity calculations of free and coordinated 2,2'-bipyridine were carried out with the Gaussian03 program package by using Hartree-Fock (HF) and Density Functional Theory (DFT) with B3LYP functional and 6-31G (d,p) basis set. The total energy distributions (TED) of the vibrational modes were calculated by using Scaled Quantum Mechanical (SQM) analysis. Fundamentals were characterised by their total energy distributions. Coordination sensitive modes of 2,2'-bipyridine were determined.

Thermal isomerization of azobenzenes: on the performance of Eyring transition state theory.

PubMed

Rietze, Clemens; Titov, Evgenii; Lindner, Steven; Saalfrank, Peter

2017-08-09

The thermal [Formula: see text] (back-)isomerization of azobenzenes is a prototypical reaction occurring in molecular switches. It has been studied for decades, yet its kinetics is not fully understood. In this paper, quantum chemical calculations are performed to model the kinetics of an experimental benchmark system, where a modified azobenzene (AzoBiPyB) is embedded in a metal-organic framework (MOF). The molecule can be switched thermally from cis to trans, under solvent-free conditions. We critically test the validity of Eyring transition state theory for this reaction. As previously found for other azobenzenes (albeit in solution), good agreement between theory and experiment emerges for activation energies and activation free energies, already at a comparatively simple level of theory, B3LYP/6-31G * including dispersion corrections. However, theoretical Arrhenius prefactors and activation entropies are in qualitiative disagreement with experiment. Several factors are discussed that may have an influence on activation entropies, among them dynamical and geometric constraints (imposed by the MOF). For a simpler model-[Formula: see text] isomerization in azobenzene-a systematic test of quantum chemical methods from both density functional theory and wavefunction theory is carried out in the context of Eyring theory. Also, the effect of anharmonicities on activation entropies is discussed for this model system. Our work highlights capabilities and shortcomings of Eyring transition state theory and quantum chemical methods, when applied for the [Formula: see text] (back-)isomerization of azobenzenes under solvent-free conditions.

Thermal isomerization of azobenzenes: on the performance of Eyring transition state theory

NASA Astrophysics Data System (ADS)

Rietze, Clemens; Titov, Evgenii; Lindner, Steven; Saalfrank, Peter

2017-08-01

The thermal Z\\to E (back-)isomerization of azobenzenes is a prototypical reaction occurring in molecular switches. It has been studied for decades, yet its kinetics is not fully understood. In this paper, quantum chemical calculations are performed to model the kinetics of an experimental benchmark system, where a modified azobenzene (AzoBiPyB) is embedded in a metal-organic framework (MOF). The molecule can be switched thermally from cis to trans, under solvent-free conditions. We critically test the validity of Eyring transition state theory for this reaction. As previously found for other azobenzenes (albeit in solution), good agreement between theory and experiment emerges for activation energies and activation free energies, already at a comparatively simple level of theory, B3LYP/6-31G* including dispersion corrections. However, theoretical Arrhenius prefactors and activation entropies are in qualitiative disagreement with experiment. Several factors are discussed that may have an influence on activation entropies, among them dynamical and geometric constraints (imposed by the MOF). For a simpler model—Z\\to E isomerization in azobenzene—a systematic test of quantum chemical methods from both density functional theory and wavefunction theory is carried out in the context of Eyring theory. Also, the effect of anharmonicities on activation entropies is discussed for this model system. Our work highlights capabilities and shortcomings of Eyring transition state theory and quantum chemical methods, when applied for the Z\\to E (back-)isomerization of azobenzenes under solvent-free conditions.

Discrete sudden perturbation theory for inelastic scattering. I. Quantum and semiclassical treatment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cross, R.J.

1985-12-01

A double perturbation theory is constructed to treat rotationally and vibrationally inelastic scattering. It uses both the elastic scattering from the spherically averaged potential and the infinite-order sudden (IOS) approximation as the unperturbed solutions. First, a standard perturbation expansion is done to express the radial wave functions in terms of the elastic wave functions. The resulting coupled equations are transformed to the discrete-variable representation where the IOS equations are diagonal. Then, the IOS solutions are removed from the equations which are solved by an exponential perturbation approximation. The results for Ar+N/sub 2/ are very much more accurate than the IOSmore » and somewhat more accurate than a straight first-order exponential perturbation theory. The theory is then converted into a semiclassical, time-dependent form by using the WKB approximation. The result is an integral of the potential times a slowly oscillating factor over the classical trajectory. A method of interpolating the result is given so that the calculation is done at the average velocity for a given transition. With this procedure, the semiclassical version of the theory is more accurate than the quantum version and very much faster. Calculations on Ar+N/sub 2/ show the theory to be much more accurate than the infinite-order sudden (IOS) approximation and the exponential time-dependent perturbation theory.« less

Holographic description of a quantum black hole on a computer

NASA Astrophysics Data System (ADS)

Hanada, Masanori; Hyakutake, Yoshifumi; Ishiki, Goro; Nishimura, Jun

2014-05-01

Black holes have been predicted to radiate particles and eventually evaporate, which has led to the information loss paradox and implies that the fundamental laws of quantum mechanics may be violated. Superstring theory, a consistent theory of quantum gravity, provides a possible solution to the paradox if evaporating black holes can actually be described in terms of standard quantum mechanical systems, as conjectured from the theory. Here, we test this conjecture by calculating the mass of a black hole in the corresponding quantum mechanical system numerically. Our results agree well with the prediction from gravity theory, including the leading quantum gravity correction. Our ability to simulate black holes offers the potential to further explore the yet mysterious nature of quantum gravity through well-established quantum mechanics.

The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer

NASA Astrophysics Data System (ADS)

Garner, Andrew J. P.; Müller, Markus P.; Dahlsten, Oscar C. O.

2017-12-01

The patterns of fringes produced by an interferometer have long been important testbeds for our best contemporary theories of physics. Historically, interference has been used to contrast quantum mechanics with classical physics, but recently experiments have been performed that test quantum theory against even more exotic alternatives. A physically motivated family of theories are those where the state space of a two-level system is given by a sphere of arbitrary dimension. This includes classical bits, and real, complex and quaternionic quantum theory. In this paper, we consider relativity of simultaneity (i.e. that observers may disagree about the order of events at different locations) as applied to a two-armed interferometer, and show that this forbids most interference phenomena more complicated than those of complex quantum theory. If interference must depend on some relational property of the setting (such as path difference), then relativity of simultaneity will limit state spaces to standard complex quantum theory, or a subspace thereof. If this relational assumption is relaxed, we find one additional theory compatible with relativity of simultaneity: quaternionic quantum theory. Our results have consequences for current laboratory interference experiments: they have to be designed carefully to avoid rendering beyond-quantum effects invisible by relativity of simultaneity.

The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer.

PubMed

Garner, Andrew J P; Müller, Markus P; Dahlsten, Oscar C O

2017-12-01

The patterns of fringes produced by an interferometer have long been important testbeds for our best contemporary theories of physics. Historically, interference has been used to contrast quantum mechanics with classical physics, but recently experiments have been performed that test quantum theory against even more exotic alternatives. A physically motivated family of theories are those where the state space of a two-level system is given by a sphere of arbitrary dimension. This includes classical bits, and real, complex and quaternionic quantum theory. In this paper, we consider relativity of simultaneity (i.e. that observers may disagree about the order of events at different locations) as applied to a two-armed interferometer, and show that this forbids most interference phenomena more complicated than those of complex quantum theory. If interference must depend on some relational property of the setting (such as path difference), then relativity of simultaneity will limit state spaces to standard complex quantum theory, or a subspace thereof. If this relational assumption is relaxed, we find one additional theory compatible with relativity of simultaneity: quaternionic quantum theory. Our results have consequences for current laboratory interference experiments: they have to be designed carefully to avoid rendering beyond-quantum effects invisible by relativity of simultaneity.

The Place of Learning Quantum Theory in Physics Teacher Education: Motivational Elements Arising from the Context

ERIC Educational Resources Information Center

Körhasan, Nilüfer Didis

2015-01-01

Quantum theory is one of the most successful theories in physics. Because of its abstract, mathematical, and counter-intuitive nature, many students have problems learning the theory, just as teachers experience difficulty in teaching it. Pedagogical research on quantum theory has mainly focused on cognitive issues. However, affective issues about…

Quantum liquid droplets in a mixture of Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Cabrera, C. R.; Tanzi, L.; Sanz, J.; Naylor, B.; Thomas, P.; Cheiney, P.; Tarruell, L.

2018-01-01

Quantum droplets are small clusters of atoms self-bound by the balance of attractive and repulsive forces. Here, we report on the observation of droplets solely stabilized by contact interactions in a mixture of two Bose-Einstein condensates. We demonstrate that they are several orders of magnitude more dilute than liquid helium by directly measuring their size and density via in situ imaging. We show that the droplets are stablized against collapse by quantum fluctuations and that they require a minimum atom number to be stable. Below that number, quantum pressure drives a liquid-to-gas transition that we map out as a function of interaction strength. These ultradilute isotropic liquids remain weakly interacting and constitute an ideal platform to benchmark quantum many-body theories.

Gravitational decoherence, alternative quantum theories and semiclassical gravity

NASA Astrophysics Data System (ADS)

Hu, B. L.

2014-04-01

In this report we discuss three aspects: 1) Semiclassical gravity theory (SCG): 4 levels of theories describing the interaction of quantum matter with classical gravity. 2) Alternative Quantum Theories: Discerning those which are derivable from general relativity (GR) plus quantum field theory (QFT) from those which are not 3) Gravitational Decoherence: derivation of a master equation and examination of the assumptions which led to the claims of observational possibilities. We list three sets of corresponding problems worthy of pursuit: a) Newton-Schrödinger Equations in relation to SCG; b) Master equation of gravity-induced effects serving as discriminator of 2); and c) Role of gravity in macroscopic quantum phenomena.

Transition operators in electromagnetic-wave diffraction theory - General theory

NASA Technical Reports Server (NTRS)

Hahne, G. E.

1992-01-01

A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.

Mapping the current–current correlation function near a quantum critical point

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prodan, Emil, E-mail: prodan@yu.edu; Bellissard, Jean

2016-05-15

The current–current correlation function is a useful concept in the theory of electron transport in homogeneous solids. The finite-temperature conductivity tensor as well as Anderson’s localization length can be computed entirely from this correlation function. Based on the critical behavior of these two physical quantities near the plateau–insulator or plateau–plateau transitions in the integer quantum Hall effect, we derive an asymptotic formula for the current–current correlation function, which enables us to make several theoretical predictions about its generic behavior. For the disordered Hofstadter model, we employ numerical simulations to map the current–current correlation function, obtain its asymptotic form near amore » critical point and confirm the theoretical predictions.« less

Theory of a peristaltic pump for fermionic quantum fluids

NASA Astrophysics Data System (ADS)

Romeo, F.; Citro, R.

2018-05-01

Motivated by the recent developments in fermionic cold atoms and in nanostructured systems, we propose the model of a peristaltic quantum pump. Differently from the Thouless paradigm, a peristaltic pump is a quantum device that generates a particle flux as the effect of a sliding finite-size microlattice. A one-dimensional tight-binding Hamiltonian model of this quantum machine is formulated and analyzed within a lattice Green's function formalism on the Keldysh contour. The pump observables, as, e.g., the pumped particles per cycle, are studied as a function of the pumping frequency, the width of the pumping potential, the particles mean free path, and system temperature. The proposed analysis applies to arbitrary peristaltic potentials acting on fermionic quantum fluids confined to one dimension. These confinement conditions can be realized in nanostructured systems or, in a more controllable way, in cold atoms experiments. In view of the validation of the theoretical results, we describe the outcomes of the model considering a fermionic cold atoms system as a paradigmatic example.

Correlating electronic transport to atomic structures in self-assembled quantum wires.

PubMed

Qin, Shengyong; Kim, Tae-Hwan; Zhang, Yanning; Ouyang, Wenjie; Weitering, Hanno H; Shih, Chih-Kang; Baddorf, Arthur P; Wu, Ruqian; Li, An-Ping

2012-02-08

Quantum wires, as a smallest electronic conductor, are expected to be a fundamental component in all quantum architectures. The electronic conductance in quantum wires, however, is often dictated by structural instabilities and electron localization at the atomic scale. Here we report on the evolutions of electronic transport as a function of temperature and interwire coupling as the quantum wires of GdSi(2) are self-assembled on Si(100) wire-by-wire. The correlation between structure, electronic properties, and electronic transport are examined by combining nanotransport measurements, scanning tunneling microscopy, and density functional theory calculations. A metal-insulator transition is revealed in isolated nanowires, while a robust metallic state is obtained in wire bundles at low temperature. The atomic defects lead to electron localizations in isolated nanowire, and interwire coupling stabilizes the structure and promotes the metallic states in wire bundles. This illustrates how the conductance nature of a one-dimensional system can be dramatically modified by the environmental change on the atomic scale. © 2012 American Chemical Society

A signed particle formulation of non-relativistic quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sellier, Jean Michel, E-mail: jeanmichel.sellier@parallel.bas.bg

2015-09-15

A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schrödinger time-dependent wave-function. Its classical limit is discussedmore » and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the validity of the suggested approach.« less

"Lagrangian" for a Non-Lagrangian Field Theory with N=2 Supersymmetry.

PubMed

Gadde, Abhijit; Razamat, Shlomo S; Willett, Brian

2015-10-23

We suggest that at least some of the strongly coupled N=2 quantum field theories in 4D can have a nonconformal N=1 Lagrangian description flowing to them at low energies. In particular, we construct such a description for the N=2 rank one superconformal field theory with E(6) flavor symmetry, for which a Lagrangian description was previously unavailable. We utilize this description to compute several supersymmetric partition functions.

Gravitation and cosmology with York time

NASA Astrophysics Data System (ADS)

Roser, Philipp

Despite decades of inquiry an adequate theory of 'quantum gravity' has remained elusive, in part due to the absence of data that would guide the search and in part due to technical difficulties, prominently among them the 'problem of time'. The problem is a result of the attempt to quantise a classical theory with temporal reparameterisation and refoliation invariance such as general relativity. One way forward is therefore the breaking of this invariance via the identification of a preferred foliation of spacetime into parameterised spatial slices. In this thesis we argue that a foliation into slices of constant extrinsic curvature, parameterised by 'York time', is a viable contender. We argue that the role of York time in the initial-value problem of general relativity as well as a number of the parameter's other properties make it the most promising candidate for a physically preferred notion of time. A Hamiltonian theory describing gravity in the York-time picture may be derived from general relativity by 'Hamiltonian reduction', a procedure that eliminates certain degrees of freedom -- specifically the local scale and its rate of change -- in favour of an explicit time parameter and a functional expression for the associated Hamiltonian. In full generality this procedure is impossible to carry out since the equation that determines the Hamiltonian cannot be solved using known methods. However, it is possible to derive explicit Hamiltonian functions for cosmological scenarios (where matter and geometry is treated as spatially homogeneous). Using a perturbative expansion of the unsolvable equation enables us to derive a quantisable Hamiltonian for cosmological perturbations on such a homogeneous background. We analyse the (classical) theories derived in this manner and look at the York-time description of a number of cosmological processes. We then proceed to apply the canonical quantisation procedure to these systems and analyse the resulting quantum theories. We discuss a number of conceptual and technical points, such as the notion of volume eigen functions and the absence of a momentum representation as a result of the non-canonical commutator structure. While not problematic in a technical sense, the conceptual problems with canonical quantisation are particularly apparent when the procedure is applied in cosmological contexts. In the final part of this thesis we develop a new quantisation method based on configuration-space trajectories and a dynamical configuration-space Weyl geometry. There is no wave function in this type of quantum theory and so many of the conceptual issues do not arise. We outline the application of this quantisation procedure to gravity and discuss some technical points. The actual technical developments are however left for future work. We conclude by reviewing how the York-time Hamiltonian-reduced theory deals with the problem of time. We place it in the wider context of a search for a theory of quantum gravity and briefly discuss the future of physics if and when such a theory is found.

Wheeled Pro(p)file of Batalin-Vilkovisky Formalism

NASA Astrophysics Data System (ADS)

Merkulov, S. A.

2010-05-01

Using a technique of wheeled props we establish a correspondence between the homotopy theory of unimodular Lie 1-bialgebras and the famous Batalin-Vilkovisky formalism. Solutions of the so-called quantum master equation satisfying certain boundary conditions are proven to be in 1-1 correspondence with representations of a wheeled dg prop which, on the one hand, is isomorphic to the cobar construction of the prop of unimodular Lie 1-bialgebras and, on the other hand, is quasi-isomorphic to the dg wheeled prop of unimodular Poisson structures. These results allow us to apply properadic methods for computing formulae for a homotopy transfer of a unimodular Lie 1-bialgebra structure on an arbitrary complex to the associated quantum master function on its cohomology. It is proven that in the category of quantum BV manifolds associated with the homotopy theory of unimodular Lie 1-bialgebras quasi-isomorphisms are equivalence relations. It is shown that Losev-Mnev’s BF theory for unimodular Lie algebras can be naturally extended to the case of unimodular Lie 1-bialgebras (and, eventually, to the case of unimodular Poisson structures). Using a finite-dimensional version of the Batalin-Vilkovisky quantization formalism it is rigorously proven that the Feynman integrals computing the effective action of this new BF theory describe precisely homotopy transfer formulae obtained within the wheeled properadic approach to the quantum master equation. Quantum corrections (which are present in our BF model to all orders of the Planck constant) correspond precisely to what are often called “higher Massey products” in the homological algebra.

Asymptotic quantum elastic generalized Lorenz Mie theory

NASA Astrophysics Data System (ADS)

Gouesbet, G.

2006-10-01

The (electromagnetic) generalized Lorenz-Mie theory describes the interaction between an electromagnetic arbitrary shaped beam and a homogeneous sphere. It is a generalization of the Lorenz-Mie theory which deals with the simpler case of a plane-wave illumination. In a recent paper, we established that, if we restrict ourselves to the study of cross-sections, both for elastic and inelastic scatterings, a macroscopic sphere in Lorenz-Mie theory is formally equivalent to a quantum-like radial potential. To generalize this result, a prerequisite is to possess an asymptotic quantum generalized Lorenz-Mie theory expressing cross-sections in the case of a quantum radial potential interacting with a sub-class of quantum arbitrary wave-packets. Such a theory, restricted however to elastic scattering, is presented in this paper.

An Alternative to the Gauge Theoretic Setting

NASA Astrophysics Data System (ADS)

Schroer, Bert

2011-10-01

The standard formulation of quantum gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic quantum theoretical access in the spirit of Wigner's representation theory shows that there is a fundamental clash between the pointlike localization of zero mass (vector, tensor) potentials and the Hilbert space (positivity, unitarity) structure of QT. The quantization approach has no other way than to stay with pointlike localization and sacrifice the Hilbert space whereas the approach built on the intrinsic quantum concept of modular localization keeps the Hilbert space and trades the conflict creating pointlike generation with the tightest consistent localization: semiinfinite spacelike string localization. Whereas these potentials in the presence of interactions stay quite close to associated pointlike field strengths, the interacting matter fields to which they are coupled bear the brunt of the nonlocal aspect in that they are string-generated in a way which cannot be undone by any differentiation. The new stringlike approach to gauge theory also revives the idea of a Schwinger-Higgs screening mechanism as a deeper and less metaphoric description of the Higgs spontaneous symmetry breaking and its accompanying tale about "God's particle" and its mass generation for all the other particles.

Asymptotic Time Decay in Quantum Physics: a Selective Review and Some New Results

NASA Astrophysics Data System (ADS)

Marchetti, Domingos H. U.; Wreszinski, Walter F.

2013-05-01

Decay of various quantities (return or survival probability, correlation functions) in time are the basis of a multitude of important and interesting phenomena in quantum physics, ranging from spectral properties, resonances, return and approach to equilibrium, to dynamical stability properties and irreversibility and the "arrow of time" in [Asymptotic Time Decay in Quantum Physics (World Scientific, 2013)]. In this review, we study several types of decay — decay in the average, decay in the Lp-sense, and pointwise decay — of the Fourier-Stieltjes transform of a measure, usually identified with the spectral measure, which appear naturally in different mathematical and physical settings. In particular, decay in the Lp-sense is related both to pointwise decay and to decay in the average and, from a physical standpoint, relates to a rigorous form of the time-energy uncertainty relation. Both decay on the average and in the Lp-sense are related to spectral properties, in particular, absolute continuity of the spectral measure. The study of pointwise decay for singular continuous measures (Rajchman measures) provides a bridge between ergodic theory, number theory and analysis, including the method of stationary phase. The theory is illustrated by some new results in the theory of sparse models.

Applied Mathematical Methods in Theoretical Physics

NASA Astrophysics Data System (ADS)

Masujima, Michio

2005-04-01

All there is to know about functional analysis, integral equations and calculus of variations in a single volume. This advanced textbook is divided into two parts: The first on integral equations and the second on the calculus of variations. It begins with a short introduction to functional analysis, including a short review of complex analysis, before continuing a systematic discussion of different types of equations, such as Volterra integral equations, singular integral equations of Cauchy type, integral equations of the Fredholm type, with a special emphasis on Wiener-Hopf integral equations and Wiener-Hopf sum equations. After a few remarks on the historical development, the second part starts with an introduction to the calculus of variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory. Throughout the book, the author presents over 150 problems and exercises -- many from such branches of physics as quantum mechanics, quantum statistical mechanics, and quantum field theory -- together with outlines of the solutions in each case. Detailed solutions are given, supplementing the materials discussed in the main text, allowing problems to be solved making direct use of the method illustrated. The original references are given for difficult problems. The result is complete coverage of the mathematical tools and techniques used by physicists and applied mathematicians Intended for senior undergraduates and first-year graduates in science and engineering, this is equally useful as a reference and self-study guide.

Relativistic Quantum Metrology: Exploiting relativity to improve quantum measurement technologies

PubMed Central

Ahmadi, Mehdi; Bruschi, David Edward; Sabín, Carlos; Adesso, Gerardo; Fuentes, Ivette

2014-01-01

We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects. PMID:24851858

Relativistic quantum metrology: exploiting relativity to improve quantum measurement technologies.

PubMed

Ahmadi, Mehdi; Bruschi, David Edward; Sabín, Carlos; Adesso, Gerardo; Fuentes, Ivette

2014-05-22

We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects.

Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths.

PubMed

Yang, Wen; Ma, Wen-Long; Liu, Ren-Bao

2017-01-01

Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since the 1950s, semi-classical noise theories have been developed for understanding electron spin decoherence. In spin-based solid-state quantum technologies, the relevant systems are in the nanometer scale and nuclear spin baths are quantum objects which require a quantum description. Recently, quantum pictures have been established to understand the decoherence and quantum many-body theories have been developed to quantitatively describe this phenomenon. Anomalous quantum effects have been predicted and some have been experimentally confirmed. A systematically truncated cluster-correlation expansion theory has been developed to account for the many-body correlations in nanoscale nuclear spin baths that are built up during electron spin decoherence. The theory has successfully predicted and explained a number of experimental results in a wide range of physical systems. In this review, we will cover this recent progress. The limitations of the present quantum many-body theories and possible directions for future development will also be discussed.

Fokker-Planck equation of the reduced Wigner function associated to an Ohmic quantum Langevin dynamics

NASA Astrophysics Data System (ADS)

Colmenares, Pedro J.

2018-05-01

This article has to do with the derivation and solution of the Fokker-Planck equation associated to the momentum-integrated Wigner function of a particle subjected to a harmonic external field in contact with an ohmic thermal bath of quantum harmonic oscillators. The strategy employed is a simplified version of the phenomenological approach of Schramm, Jung, and Grabert of interpreting the operators as c numbers to derive the quantum master equation arising from a twofold transformation of the Wigner function of the entire phase space. The statistical properties of the random noise comes from the integral functional theory of Grabert, Schramm, and Ingold. By means of a single Wigner transformation, a simpler equation than that mentioned before is found. The Wigner function reproduces the known results of the classical limit. This allowed us to rewrite the underdamped classical Langevin equation as a first-order stochastic differential equation with time-dependent drift and diffusion terms.

Density functional theory calculation of refractive indices of liquid-forming silicon oil compounds

NASA Astrophysics Data System (ADS)

Lee, Sanghun; Park, Sung Soo; Hagelberg, Frank

2012-02-01

A combination of quantum chemical calculation and molecular dynamics simulation is applied to compute refractive indices of liquid-forming silicon oils. The densities of these species are obtained from molecular dynamics simulations based on the NPT ensemble while the molecular polarizabilities are evaluated by density functional theory. This procedure is shown to yield results well compatible with available experimental data, suggesting that it represents a robust and economic route for determining the refractive indices of liquid-forming organic complexes containing silicon.

Electronic Structures of Strained InAs x P1-x by Density Functional Theory.

PubMed

Lee, Seung Mi; Kim, Min-Young; Kim, Young Heon

2018-09-01

We investigated the effects of strain on the electronic structures of InAsxP1-x using quantum mechanical density functional theory calculations. The electronic band gap and electron effective mass decreased with the increase of the uniaxial tensile strain along the [0001] direction of wurtzite InAs0.75P0.25. Therefore, faster electron movements are expected. These theoretical results are in good agreement with the experimental measurements of InAs0.75P0.25 nanowire.

The potential of using quantum theory to build models of cognition.

PubMed

Wang, Zheng; Busemeyer, Jerome R; Atmanspacher, Harald; Pothos, Emmanuel M

2013-10-01

Quantum cognition research applies abstract, mathematical principles of quantum theory to inquiries in cognitive science. It differs fundamentally from alternative speculations about quantum brain processes. This topic presents new developments within this research program. In the introduction to this topic, we try to answer three questions: Why apply quantum concepts to human cognition? How is quantum cognitive modeling different from traditional cognitive modeling? What cognitive processes have been modeled using a quantum account? In addition, a brief introduction to quantum probability theory and a concrete example is provided to illustrate how a quantum cognitive model can be developed to explain paradoxical empirical findings in psychological literature. © 2013 Cognitive Science Society, Inc.

Differentiable representations of finite dimensional Lie groups in rigged Hilbert spaces

NASA Astrophysics Data System (ADS)

Wickramasekara, Sujeewa

The inceptive motivation for introducing rigged Hilbert spaces (RHS) in quantum physics in the mid 1960's was to provide the already well established Dirac formalism with a proper mathematical context. It has since become clear, however, that this mathematical framework is lissome enough to accommodate a class of solutions to the dynamical equations of quantum physics that includes some which are not possible in the normative Hilbert space theory. Among the additional solutions, in particular, are those which describe aspects of scattering and decay phenomena that have eluded the orthodox quantum physics. In this light, the RHS formulation seems to provide a mathematical rubric under which various phenomenological observations and calculational techniques, commonly known in the study of resonance scattering and decay as ``effective theories'' (e.g., the Wigner- Weisskopf method), receive a unified theoretical foundation. These observations lead to the inference that a theory founded upon the RHS mathematics may prove to be of better utility and value in understanding quantum physical phenomena. This dissertation primarily aims to contribute to the general formalism of the RHS theory of quantum mechanics by undertaking a study of differentiable representations of finite dimensional Lie groups. In particular, it is shown that a finite dimensional operator Lie algebra G in a rigged Hilbert space can be always integrated, provided one parameter integrability holds true for the elements of any basis for G . This result differs from and extends the well known integration theorem of E. Nelson and the subsequent works of others on unitary representations in that it does not require any assumptions on the existence of analytic vectors. Also presented here is a construction of a particular rigged Hilbert space of Hardy class functions that appears useful in formulating a relativistic version of the RHS theory of resonances and decay. As a contexture for the construction, a synopsis of the new relativistic theory is presented.

Holographic description of a quantum black hole on a computer.

PubMed

Hanada, Masanori; Hyakutake, Yoshifumi; Ishiki, Goro; Nishimura, Jun

2014-05-23

Black holes have been predicted to radiate particles and eventually evaporate, which has led to the information loss paradox and implies that the fundamental laws of quantum mechanics may be violated. Superstring theory, a consistent theory of quantum gravity, provides a possible solution to the paradox if evaporating black holes can actually be described in terms of standard quantum mechanical systems, as conjectured from the theory. Here, we test this conjecture by calculating the mass of a black hole in the corresponding quantum mechanical system numerically. Our results agree well with the prediction from gravity theory, including the leading quantum gravity correction. Our ability to simulate black holes offers the potential to further explore the yet mysterious nature of quantum gravity through well-established quantum mechanics. Copyright © 2014, American Association for the Advancement of Science.

Classical Field Theory and the Stress-Energy Tensor

NASA Astrophysics Data System (ADS)

Swanson, Mark S.

2015-09-01

This book is a concise introduction to the key concepts of classical field theory for beginning graduate students and advanced undergraduate students who wish to study the unifying structures and physical insights provided by classical field theory without dealing with the additional complication of quantization. In that regard, there are many important aspects of field theory that can be understood without quantizing the fields. These include the action formulation, Galilean and relativistic invariance, traveling and standing waves, spin angular momentum, gauge invariance, subsidiary conditions, fluctuations, spinor and vector fields, conservation laws and symmetries, and the Higgs mechanism, all of which are often treated briefly in a course on quantum field theory. The variational form of classical mechanics and continuum field theory are both developed in the time-honored graduate level text by Goldstein et al (2001). An introduction to classical field theory from a somewhat different perspective is available in Soper (2008). Basic classical field theory is often treated in books on quantum field theory. Two excellent texts where this is done are Greiner and Reinhardt (1996) and Peskin and Schroeder (1995). Green's function techniques are presented in Arfken et al (2013).

A Philosophical Approach to Quantum Field Theory

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-01-01

Preface; Acknowledgements; 1. Approach to quantum field theory; 2. Scalar field theory; 3. Quantum electrodynamics; 4. Perspectives; Appendix A. An efficient perturbation scheme; Appendix B. Properties of Dirac matrices; Appendix C. Baker-Campbell-Hausdorff formulas; References; Author index; Subject index.

Strong Quantum Coherence between Fermi Liquid Mahan Excitons

NASA Astrophysics Data System (ADS)

Paul, J.; Stevens, C. E.; Liu, C.; Dey, P.; McIntyre, C.; Turkowski, V.; Reno, J. L.; Hilton, D. J.; Karaiskaj, D.

2016-04-01

In modulation doped quantum wells, the excitons are formed as a result of the interactions of the charged holes with the electrons at the Fermi edge in the conduction band, leading to the so-called "Mahan excitons." The binding energy of Mahan excitons is expected to be greatly reduced and any quantum coherence destroyed as a result of the screening and electron-electron interactions. Surprisingly, we observe strong quantum coherence between the heavy hole and light hole excitons. Such correlations are revealed by the dominating cross-diagonal peaks in both one-quantum and two-quantum two-dimensional Fourier transform spectra. Theoretical simulations based on the optical Bloch equations where many-body effects are included phenomenologically reproduce well the experimental spectra. Time-dependent density functional theory calculations provide insight into the underlying physics and attribute the observed strong quantum coherence to a significantly reduced screening length and collective excitations of the many-electron system.

Strong Quantum Coherence between Fermi Liquid Mahan Excitons.

PubMed

Paul, J; Stevens, C E; Liu, C; Dey, P; McIntyre, C; Turkowski, V; Reno, J L; Hilton, D J; Karaiskaj, D

2016-04-15

In modulation doped quantum wells, the excitons are formed as a result of the interactions of the charged holes with the electrons at the Fermi edge in the conduction band, leading to the so-called "Mahan excitons." The binding energy of Mahan excitons is expected to be greatly reduced and any quantum coherence destroyed as a result of the screening and electron-electron interactions. Surprisingly, we observe strong quantum coherence between the heavy hole and light hole excitons. Such correlations are revealed by the dominating cross-diagonal peaks in both one-quantum and two-quantum two-dimensional Fourier transform spectra. Theoretical simulations based on the optical Bloch equations where many-body effects are included phenomenologically reproduce well the experimental spectra. Time-dependent density functional theory calculations provide insight into the underlying physics and attribute the observed strong quantum coherence to a significantly reduced screening length and collective excitations of the many-electron system.

Quantum-circuit refrigerator

NASA Astrophysics Data System (ADS)

Tan, Kuan Yen; Partanen, Matti; Lake, Russell E.; Govenius, Joonas; Masuda, Shumpei; Möttönen, Mikko

2017-05-01

Quantum technology promises revolutionizing applications in information processing, communications, sensing and modelling. However, efficient on-demand cooling of the functional quantum degrees of freedom remains challenging in many solid-state implementations, such as superconducting circuits. Here we demonstrate direct cooling of a superconducting resonator mode using voltage-controllable electron tunnelling in a nanoscale refrigerator. This result is revealed by a decreased electron temperature at a resonator-coupled probe resistor, even for an elevated electron temperature at the refrigerator. Our conclusions are verified by control experiments and by a good quantitative agreement between theory and experimental observations at various operation voltages and bath temperatures. In the future, we aim to remove spurious dissipation introduced by our refrigerator and to decrease the operational temperature. Such an ideal quantum-circuit refrigerator has potential applications in the initialization of quantum electric devices. In the superconducting quantum computer, for example, fast and accurate reset of the quantum memory is needed.

Prospect of quantum anomalous Hall and quantum spin Hall effect in doped kagome lattice Mott insulators.

PubMed

Guterding, Daniel; Jeschke, Harald O; Valentí, Roser

2016-05-17

Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. We introduce a new strategy for realizing these effects, namely by hole and electron doping kagome lattice Mott insulators through, for instance, chemical substitution. As an example, we apply this new approach to the natural mineral herbertsmithite. We prove the feasibility of the proposed modifications by performing ab-initio density functional theory calculations and demonstrate the occurrence of the predicted effects using realistic models. Our results herald a new family of quantum anomalous Hall and quantum spin Hall insulators at affordable energy/temperature scales based on kagome lattices of transition metal ions.

Using Conceptual Metaphor and Functional Grammar to Explore How Language Used in Physics Affects Student Learning

ERIC Educational Resources Information Center

Brookes, David T.; Etkina, Eugenia

2007-01-01

This paper introduces a theory about the role of language in learning physics. The theory is developed in the context of physics students and physicists talking and writing about the subject of quantum mechanics. We found that physicists' language encodes different varieties of analogical models through the use of grammar and conceptual metaphor.…

Bare Quantum Null Energy Condition.

PubMed

Fu, Zicao; Marolf, Donald

2018-02-16

The quantum null energy condition (QNEC) is a conjectured relation between a null version of quantum field theory energy and derivatives of quantum field theory von Neumann entropy. In some cases, divergences cancel between these two terms and the QNEC is intrinsically finite. We study the more general case here where they do not and argue that a QNEC can still hold for bare (unrenormalized) quantities. While the original QNEC applied only to locally stationary null congruences in backgrounds that solve semiclassical theories of quantum gravity, at least in the formal perturbation theory at a small Planck length, the quantum focusing conjecture can be viewed as the special case of our bare QNEC for which the metric is on shell.

Bare Quantum Null Energy Condition

NASA Astrophysics Data System (ADS)

Fu, Zicao; Marolf, Donald

2018-02-01

The quantum null energy condition (QNEC) is a conjectured relation between a null version of quantum field theory energy and derivatives of quantum field theory von Neumann entropy. In some cases, divergences cancel between these two terms and the QNEC is intrinsically finite. We study the more general case here where they do not and argue that a QNEC can still hold for bare (unrenormalized) quantities. While the original QNEC applied only to locally stationary null congruences in backgrounds that solve semiclassical theories of quantum gravity, at least in the formal perturbation theory at a small Planck length, the quantum focusing conjecture can be viewed as the special case of our bare QNEC for which the metric is on shell.

Sulfate radical oxidation of aromatic contaminants: a detailed assessment of density functional theory and high-level quantum chemical methods.

PubMed

Pari, Sangavi; Wang, Inger A; Liu, Haizhou; Wong, Bryan M

2017-03-22

Advanced oxidation processes that utilize highly oxidative radicals are widely used in water reuse treatment. In recent years, the application of sulfate radical (SO 4 ˙ - ) as a promising oxidant for water treatment has gained increasing attention. To understand the efficiency of SO 4 ˙ - in the degradation of organic contaminants in wastewater effluent, it is important to be able to predict the reaction kinetics of various SO 4 ˙ - -driven oxidation reactions. In this study, we utilize density functional theory (DFT) and high-level wavefunction-based methods (including computationally-intensive coupled cluster methods), to explore the activation energies of SO 4 ˙ - -driven oxidation reactions on a series of benzene-derived contaminants. These high-level calculations encompass a wide set of reactions including 110 forward/reverse reactions and 5 different computational methods in total. Based on the high-level coupled-cluster quantum calculations, we find that the popular M06-2X DFT functional is significantly more accurate for OH - additions than for SO 4 ˙ - reactions. Most importantly, we highlight some of the limitations and deficiencies of other computational methods, and we recommend the use of high-level quantum calculations to spot-check environmental chemistry reactions that may lie outside the training set of the M06-2X functional, particularly for water oxidation reactions that involve SO 4 ˙ - and other inorganic species.

The ground state magnetic moment and susceptibility of a two electron Gaussian quantum dot

NASA Astrophysics Data System (ADS)

Boda, Aalu; Chatterjee, Ashok

2018-04-01

The problem of two interacting electrons moving in a two-dimensional semiconductor quantum dot with Gaussian confinement under the influence of an external magnetic field is studied by using a method of numerical diagonalization of the Hamiltonian matrix with in the effective-mass approximation. The energy spectrum is calculated as a function of the magnetic field. We find the ground state magnetic moment and the magnetic susceptibility show zero temperature diamagnetic peaks due to exchange induced singlet-triplet oscillations. The position and the number of these peaks depend on the size of the quantum dot and also strength of the electro-electron interaction. The theory is applied to a GaAs quantum dot.

Interferometric Computation Beyond Quantum Theory

NASA Astrophysics Data System (ADS)

Garner, Andrew J. P.

2018-03-01

There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer. There has been recent foundational interest in theories beyond quantum theory. Here, we present a generalized formulation of computation in the context of a many-armed interferometer, and explore how theories can differ from quantum theory and still perform distributed calculations in this set-up. We shall see that quaternionic quantum theory proves a suitable candidate, whereas box-world does not. We also find that a classical hidden variable model first presented by Spekkens (Phys Rev A 75(3): 32100, 2007) can also be used for this type of computation due to the epistemic restriction placed on the hidden variable.

Exceptional quantum geometry and particle physics

NASA Astrophysics Data System (ADS)

Dubois-Violette, Michel

2016-11-01

Based on an interpretation of the quark-lepton symmetry in terms of the unimodularity of the color group SU (3) and on the existence of 3 generations, we develop an argumentation suggesting that the "finite quantum space" corresponding to the exceptional real Jordan algebra of dimension 27 (the Euclidean Albert algebra) is relevant for the description of internal spaces in the theory of particles. In particular, the triality which corresponds to the 3 off-diagonal octonionic elements of the exceptional algebra is associated to the 3 generations of the Standard Model while the representation of the octonions as a complex 4-dimensional space C ⊕C3 is associated to the quark-lepton symmetry (one complex for the lepton and 3 for the corresponding quark). More generally it is suggested that the replacement of the algebra of real functions on spacetime by the algebra of functions on spacetime with values in a finite-dimensional Euclidean Jordan algebra which plays the role of "the algebra of real functions" on the corresponding almost classical quantum spacetime is relevant in particle physics. This leads us to study the theory of Jordan modules and to develop the differential calculus over Jordan algebras (i.e. to introduce the appropriate notion of differential forms). We formulate the corresponding definition of connections on Jordan modules.

Integrable model for density-modulated quantum condensates: Solitons passing through a soliton lattice.

PubMed

Takahashi, Daisuke A

2016-06-01

An integrable model possessing inhomogeneous ground states is proposed as an effective model of nonuniform quantum condensates such as supersolids and Fulde-Ferrell-Larkin-Ovchinnikov superfluids. The model is a higher-order analog of the nonlinear Schrödinger equation. We derive an n-soliton solution via the inverse scattering theory with elliptic-functional background and reveal various kinds of soliton dynamics such as dark soliton billiards, dislocations, gray solitons, and envelope solitons. We also provide the exact bosonic and fermionic quasiparticle eigenstates and show their tunneling phenomena. The solutions are expressed by a determinant of theta functions.

Weak values of a quantum observable and the cross-Wigner distribution.

PubMed

de Gosson, Maurice A; de Gosson, Serge M

2012-01-09

We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor here is the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar theory and time-frequency analysis. It allows us to express weak values using a complex probability distribution. We suggest that our approach seems to confirm that the weak value of an observable is, as conjectured by several authors, due to the interference of two wavefunctions, one coming from the past, and the other from the future.

Absorption, autoionization, and predissociation in molecular hydrogen: High-resolution spectroscopy and multichannel quantum defect theory.

PubMed

Sommavilla, M; Merkt, F; Mezei, J Zs; Jungen, Ch

2016-02-28

Absorption and photoionization spectra of H2 have been recorded at a resolution of 0.09 and 0.04 cm(-1), respectively, between 125,600 cm(-1) and 126,000 cm(-1). The observed Rydberg states belong to series (n = 10 - 14) converging on the first vibrationally excited level of the X (2)Σ(g)(+) state of H2(+), and of lower members of series converging on higher vibrational levels. The observed resonances are characterized by the competition between autoionization, predissociation, and fluorescence. The unprecedented resolution of the present experimental data leads to a full characterization of the predissociation/autoionization profiles of many resonances that had not been resolved previously. Multichannel quantum defect theory is used to predict the line positions, widths, shapes, and intensities of the observed spectra and is found to yield quantitative agreement using previously determined quantum defect functions as the unique set of input parameters.

Quantum ergodicity in the SYK model

NASA Astrophysics Data System (ADS)

Altland, Alexander; Bagrets, Dmitry

2018-05-01

We present a replica path integral approach describing the quantum chaotic dynamics of the SYK model at large time scales. The theory leads to the identification of non-ergodic collective modes which relax and eventually give way to an ergodic long time regime (describable by random matrix theory). These modes, which play a role conceptually similar to the diffusion modes of dirty metals, carry quantum numbers which we identify as the generators of the Clifford algebra: each of the 2N different products that can be formed from N Majorana operators defines one effective mode. The competition between a decay rate quickly growing in the order of the product and a density of modes exponentially growing in the same parameter explains the characteristics of the system's approach to the ergodic long time regime. We probe this dynamics through various spectral correlation functions and obtain favorable agreement with existing numerical data.

Quantum metabolism explains the allometric scaling of metabolic rates.

PubMed

Demetrius, Lloyd; Tuszynski, J A

2010-03-06

A general model explaining the origin of allometric laws of physiology is proposed based on coupled energy-transducing oscillator networks embedded in a physical d-dimensional space (d = 1, 2, 3). This approach integrates Mitchell's theory of chemi-osmosis with the Debye model of the thermal properties of solids. We derive a scaling rule that relates the energy generated by redox reactions in cells, the dimensionality of the physical space and the mean cycle time. Two major regimes are found corresponding to classical and quantum behaviour. The classical behaviour leads to allometric isometry while the quantum regime leads to scaling laws relating metabolic rate and body size that cover a broad range of exponents that depend on dimensionality and specific parameter values. The regimes are consistent with a range of behaviours encountered in micelles, plants and animals and provide a conceptual framework for a theory of the metabolic function of living systems.

Quantum Crystallography: Density Matrix-Density Functional Theory and the X-Ray Diffraction Experiment

NASA Astrophysics Data System (ADS)

Soirat, Arnaud J. A.

Density Matrix Theory is a Quantum Mechanical formalism in which the wavefunction is eliminated and its role taken over by reduced density matrices. The interest of this is that, it allows one, in principle, to calculate any electronic property of a physical system, without having to solve the Schrodinger equation, using only two entities much simpler than an N-body wavefunction: first and second -order reduced density matrices. In practice, though, this very promising possibility faces the tremendous theoretical problem of N-representability, which has been solved for the former, but, until now, voids any hope of theoretically determining the latter. However, it has been shown that single determinant reduced density matrices of any order may be recovered from coherent X-ray diffraction data, if one provides a proper Quantum Mechanical description of the Crystallography experiment. A deeper investigation of this method is the purpose of this work, where we, first, further study the calculation of X-ray reduced density matrices N-representable by a single Slater determinant. In this context, we independently derive necessary and sufficient conditions for the uniqueness of the method. We then show how to account for electron correlation in this model. For the first time, indeed, we derive highly accurate, yet practical, density matrices approximately N-representable by correlated-determinant wavefunctions. The interest of such a result lies in the Quantum Mechanical validity of these density matrices, their property of being entirely obtainable from X-ray coherent diffraction data, their very high accuracy conferred by this known property of the N-representing wavefunction, as well as their definition as explicit functionals of the density. All of these properties are finally used in both a theoretical and a numerical application: in the former, we show that these density matrices may be used in the context of Density Functional Theory to highly accurately determine the unknown HK functional, associated with the theorem of Hohenberg and Kohn. The latter is provided by the calculation of helium correlation energy, where we test approximating the second-order density function by the leading term of its McLaurin's series expansion.

Time Asymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Bohm, Arno R.; Gadella, Manuel; Kielanowski, Piotr

2011-09-01

The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.

Signatures of bifurcation on quantum correlations: Case of the quantum kicked top

NASA Astrophysics Data System (ADS)

Bhosale, Udaysinh T.; Santhanam, M. S.

2017-01-01

Quantum correlations reflect the quantumness of a system and are useful resources for quantum information and computational processes. Measures of quantum correlations do not have a classical analog and yet are influenced by classical dynamics. In this work, by modeling the quantum kicked top as a multiqubit system, the effect of classical bifurcations on measures of quantum correlations such as the quantum discord, geometric discord, and Meyer and Wallach Q measure is studied. The quantum correlation measures change rapidly in the vicinity of a classical bifurcation point. If the classical system is largely chaotic, time averages of the correlation measures are in good agreement with the values obtained by considering the appropriate random matrix ensembles. The quantum correlations scale with the total spin of the system, representing its semiclassical limit. In the vicinity of trivial fixed points of the kicked top, the scaling function decays as a power law. In the chaotic limit, for large total spin, quantum correlations saturate to a constant, which we obtain analytically, based on random matrix theory, for the Q measure. We also suggest that it can have experimental consequences.

Multiple choices of time in quantum cosmology

NASA Astrophysics Data System (ADS)

Małkiewicz, Przemysław

2015-07-01

It is often conjectured that a choice of time function merely sets up a frame for the quantum evolution of the gravitational field, meaning that all choices should be in some sense compatible. In order to explore this conjecture (and the meaning of compatibility), we develop suitable tools for determining the relation between quantum theories based on different time functions. First, we discuss how a time function fixes a canonical structure on the constraint surface. The presentation includes both the kinematical and the reduced perspective, and the relation between them. Second, we formulate twin theorems about the existence of two inequivalent maps between any two deparameterizations, a formal canonical and a coordinate one. They are used to separate the effects induced by choice of clock and other factors. We show, in an example, how the spectra of quantum observables are transformed under the change of clock and prove, via a general argument, the existence of choice-of-time-induced semiclassical effects. Finally, we study an example, in which we find that the semiclassical discrepancies can in fact be arbitrarily large for dynamical observables. We conclude that the values of critical energy density or critical volume in the bouncing scenarios of quantum cosmology cannot in general be at the Planck scale, and always need to be given with reference to a specific time function.

Thermalization dynamics of two correlated bosonic quantum wires after a split

NASA Astrophysics Data System (ADS)

Huber, Sebastian; Buchhold, Michael; Schmiedmayer, Jörg; Diehl, Sebastian

2018-04-01

Cherently splitting a one-dimensional Bose gas provides an attractive, experimentally established platform to investigate many-body quantum dynamics. At short enough times, the dynamics is dominated by the dephasing of single quasiparticles, and well described by the relaxation towards a generalized Gibbs ensemble corresponding to the free Luttinger theory. At later times on the other hand, the approach to a thermal Gibbs ensemble is expected for a generic, interacting quantum system. Here, we go one step beyond the quadratic Luttinger theory and include the leading phonon-phonon interactions. By applying kinetic theory and nonequilibrium Dyson-Schwinger equations, we analyze the full relaxation dynamics beyond dephasing and determine the asymptotic thermalization process in the two-wire system for a symmetric splitting protocol. The major observables are the different phonon occupation functions and the experimentally accessible coherence factor, as well as the phase correlations between the two wires. We demonstrate that, depending on the splitting protocol, the presence of phonon collisions can have significant influence on the asymptotic evolution of these observables, which makes the corresponding thermalization dynamics experimentally accessible.

Quantum statistical mechanics of dense partially ionized hydrogen

NASA Technical Reports Server (NTRS)

Dewitt, H. E.; Rogers, F. J.

1972-01-01

The theory of dense hydrogen plasmas beginning with the two component quantum grand partition function is reviewed. It is shown that ionization equilibrium and molecular dissociation equilibrium can be treated in the same manner with proper consideration of all two-body states. A quantum perturbation expansion is used to give an accurate calculation of the equation of state of the gas for any degree of dissociation and ionization. The statistical mechanical calculation of the plasma equation of state is intended for stellar interiors. The general approach is extended to the calculation of the equation of state of the outer layers of large planets.

Classical and Quantum Thermal Physics

NASA Astrophysics Data System (ADS)

Prasad, R.

2016-11-01

List of figures; List of tables; Preface; Acknowledgement; Dedication; 1. The kinetic theory of gases; 2. Ideal to real gas, viscosity, conductivity and diffusion; 3. Thermodynamics: definitions and Zeroth law; 4. First Law of Thermodynamics and some of its applications; 5. Second Law of Thermodynamics and some of its applications; 6. TdS equations and their applications; 7. Thermodynamic functions, potentials, Maxwell equations, the Third Law and equilibrium; 8. Some applications of thermodynamics to problems of physics and engineering; 9. Application of thermodynamics to chemical reactions; 10. Quantum thermodynamics; 11. Some applications of quantum thermodynamics; 12. Introduction to the thermodynamics of irreversible processes; Index.

Probing quantum gravity through exactly soluble midi-superspaces I

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ashtekar, A.; Pierri, M.

1996-12-01

It is well-known that the Einstein-Rosen solutions to the 3+1- dimensional vacuum Einstein{close_quote}s equations are in one to one correspondence with solutions of 2+1-dimensional general relativity coupled to axi-symmetric, zero rest mass scalar fields. We first re-examine the quantization of this midi-superspace paying special attention to the asymptotically flat boundary conditions and to certain functional analytic subtleties associated with regularization. We then use the resulting quantum theory to analyze several conceptual and technical issues of quantum gravity. {copyright} {ital 1996 American Institute of Physics.}

The Effect of Temperature and Electric Field on a Quantum Pseudodot Qubit

NASA Astrophysics Data System (ADS)

Chen, Ying-Cong; Xiao, Jing-Lin

2018-02-01

The electron's probability density (EPD) and the oscillating period (OP) of an electron confined by a three-dimensional RbCl quantum pseudodot (QPD) are studied. Calculations are performed by employing variational method of Pekar type (VMPT) and the quantum statistics theory (QST).The influences of the temperature and electric field on the EPD and the OP of the RbCl QPD qubit have been derived in detail. According to the obtained results, it is observed that the EPD and the OP increase (decrease) with raising temperature at lower (higher) temperature region. They are decaying functions of the electric field.

Discrete-to-continuous transition in quantum phase estimation

NASA Astrophysics Data System (ADS)

Rządkowski, Wojciech; Demkowicz-Dobrzański, Rafał

2017-09-01

We analyze the problem of quantum phase estimation in which the set of allowed phases forms a discrete N -element subset of the whole [0 ,2 π ] interval, φn=2 π n /N , n =0 ,⋯,N -1 , and study the discrete-to-continuous transition N →∞ for various cost functions as well as the mutual information. We also analyze the relation between the problems of phase discrimination and estimation by considering a step cost function of a given width σ around the true estimated value. We show that in general a direct application of the theory of covariant measurements for a discrete subgroup of the U(1 ) group leads to suboptimal strategies due to an implicit requirement of estimating only the phases that appear in the prior distribution. We develop the theory of subcovariant measurements to remedy this situation and demonstrate truly optimal estimation strategies when performing a transition from discrete to continuous phase estimation.

Equations of state and stability of MgSiO 3 perovskite and post-perovskite phases from quantum Monte Carlo simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Yangzheng; Cohen, Ronald E.; Stackhouse, Stephen

2014-11-10

In this study, we have performed quantum Monte Carlo (QMC) simulations and density functional theory calculations to study the equations of state of MgSiO 3 perovskite (Pv, bridgmanite) and post-perovskite (PPv) up to the pressure and temperature conditions of the base of Earth's lower mantle. The ground-state energies were derived using QMC simulations and the temperature-dependent Helmholtz free energies were calculated within the quasiharmonic approximation and density functional perturbation theory. The equations of state for both phases of MgSiO 3 agree well with experiments, and better than those from generalized gradient approximation calculations. The Pv-PPv phase boundary calculated from ourmore » QMC equations of state is also consistent with experiments, and better than previous local density approximation calculations. Lastly, we discuss the implications for double crossing of the Pv-PPv boundary in the Earth.« less

Role of information theoretic uncertainty relations in quantum theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jizba, Petr, E-mail: p.jizba@fjfi.cvut.cz; ITP, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin; Dunningham, Jacob A., E-mail: J.Dunningham@sussex.ac.uk

2015-04-15

Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) Rényi entropy and its related entropy power. This allows us to find a new class of information-theoretic uncertainty relations (ITURs). The potency of such uncertainty relations in quantum mechanics is illustrated with a simple two-energy-level model where they outperform both the usual Robertson–Schrödinger uncertainty relation and Shannon entropy based uncertainty relation. In the continuous case the ensuing entropy power uncertainty relations are discussed in the context of heavy tailed wave functions and Schrödinger cat states. Again,more » improvement over both the Robertson–Schrödinger uncertainty principle and Shannon ITUR is demonstrated in these cases. Further salient issues such as the proof of a generalized entropy power inequality and a geometric picture of information-theoretic uncertainty relations are also discussed.« less

Universal conductivity in a two-dimensional superfluid-to-insulator quantum critical system.

PubMed

Chen, Kun; Liu, Longxiang; Deng, Youjin; Pollet, Lode; Prokof'ev, Nikolay

2014-01-24

We compute the universal conductivity of the (2+1)-dimensional XY universality class, which is realized for a superfluid-to-Mott insulator quantum phase transition at constant density. Based on large-scale Monte Carlo simulations of the classical (2+1)-dimensional J-current model and the two-dimensional Bose-Hubbard model, we can precisely determine the conductivity on the quantum critical plateau, σ(∞) = 0.359(4)σQ with σQ the conductivity quantum. The universal conductivity curve is the standard example with the lowest number of components where the bottoms-up AdS/CFT correspondence from string theory can be tested and made to use [R. C. Myers, S. Sachdev, and A. Singh, Phys. Rev. D 83, 066017 (2011)]. For the first time, the shape of the σ(iω(n)) - σ(∞) function in the Matsubara representation is accurate enough for a conclusive comparison and establishes the particlelike nature of charge transport. We find that the holographic gauge-gravity duality theory for transport properties can be made compatible with the data if temperature of the horizon of the black brane is different from the temperature of the conformal field theory. The requirements for measuring the universal conductivity in a cold gas experiment are also determined by our calculation.

Implementation of a channelized Hotelling observer model to assess image quality of x-ray angiography systems.

PubMed

Favazza, Christopher P; Fetterly, Kenneth A; Hangiandreou, Nicholas J; Leng, Shuai; Schueler, Beth A

2015-01-01

Evaluation of flat-panel angiography equipment through conventional image quality metrics is limited by the scope of standard spatial-domain image quality metric(s), such as contrast-to-noise ratio and spatial resolution, or by restricted access to appropriate data to calculate Fourier domain measurements, such as modulation transfer function, noise power spectrum, and detective quantum efficiency. Observer models have been shown capable of overcoming these limitations and are able to comprehensively evaluate medical-imaging systems. We present a spatial domain-based channelized Hotelling observer model to calculate the detectability index (DI) of our different sized disks and compare the performance of different imaging conditions and angiography systems. When appropriate, changes in DIs were compared to expectations based on the classical Rose model of signal detection to assess linearity of the model with quantum signal-to-noise ratio (SNR) theory. For these experiments, the estimated uncertainty of the DIs was less than 3%, allowing for precise comparison of imaging systems or conditions. For most experimental variables, DI changes were linear with expectations based on quantum SNR theory. DIs calculated for the smallest objects demonstrated nonlinearity with quantum SNR theory due to system blur. Two angiography systems with different detector element sizes were shown to perform similarly across the majority of the detection tasks.

Evidence of quantum phase transition in real-space vacuum entanglement of higher derivative scalar quantum field theories.

PubMed

Kumar, S Santhosh; Shankaranarayanan, S

2017-11-17

In a bipartite set-up, the vacuum state of a free Bosonic scalar field is entangled in real space and satisfies the area-law- entanglement entropy scales linearly with area of the boundary between the two partitions. In this work, we show that the area law is violated in two spatial dimensional model Hamiltonian having dynamical critical exponent z = 3. The model physically corresponds to next-to-next-to-next nearest neighbour coupling terms on a lattice. The result reported here is the first of its kind of violation of area law in Bosonic systems in higher dimensions and signals the evidence of a quantum phase transition. We provide evidence for quantum phase transition both numerically and analytically using quantum Information tools like entanglement spectra, quantum fidelity, and gap in the energy spectra. We identify the cause for this transition due to the accumulation of large number of angular zero modes around the critical point which catalyses the change in the ground state wave function due to the next-to-next-to-next nearest neighbor coupling. Lastly, using Hubbard-Stratanovich transformation, we show that the effective Bosonic Hamiltonian can be obtained from an interacting fermionic theory and provide possible implications for condensed matter systems.

Multi-orbital non-crossing approximation from maximally localized Wannier functions: the Kondo signature of copper phthalocyanine on Ag(100).

PubMed

Korytár, Richard; Lorente, Nicolás

2011-09-07

We have developed a multi-orbital approach to compute the electronic structure of a quantum impurity using the non-crossing approximation. The calculation starts with a mean-field evaluation of the system's electronic structure using a standard quantum chemistry code; here we use density functional theory (DFT). We transformed the one-electron structure into an impurity Hamiltonian by using maximally localized Wannier functions. Hence, we have developed a method to study the Kondo effect in systems based on an initial one-electron calculation. We have applied our methodology to a copper phthalocyanine molecule chemisorbed on Ag(100), and we have described its spectral function for three different cases where the molecule presents a single spin or two spins with ferro- and anti-ferromagnetic exchange couplings. We find that the use of broken-symmetry mean-field theories such as Kohn-Sham DFT cannot deal with the complexity of the spin of open-shell molecules on metal surfaces and extra modeling is needed. © 2011 IOP Publishing Ltd

Quantum electrodynamical time-dependent density functional theory for many-electron systems on a lattice

NASA Astrophysics Data System (ADS)

Farzanehpour, Mehdi; Tokatly, Ilya; Nano-Bio Spectroscopy Group; ETSF Scientific Development Centre Team

2015-03-01

We present a rigorous formulation of the time-dependent density functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic mode, which is equivalent to the single mode spin-boson model or the quantum Rabi model. For this system we prove that the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate, provided the initial state and the density satisfy a set of well defined conditions. Then we generalize the formalism to many interacting electrons on a lattice coupled to multiple photonic modes and prove the general mapping theorem. We also show that for a system evolving from the ground state of a lattice Hamiltonian any density with a continuous second time derivative is locally v-representable. Spanish Ministry of Economy and Competitiveness (Grant No. FIS2013-46159-C3-1-P), Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT578-13), COST Actions CM1204 (XLIC) and MP1306 (EUSpec).

Chain representations of Open Quantum Systems and Lieb-Robinson like bounds for the dynamics

NASA Astrophysics Data System (ADS)

Woods, Mischa

2013-03-01

This talk is concerned with the mapping of the Hamiltonian of open quantum systems onto chain representations, which forms the basis for a rigorous theory of the interaction of a system with its environment. This mapping progresses as an interaction which gives rise to a sequence of residual spectral densities of the system. The rigorous mathematical properties of this mapping have been unknown so far. Here we develop the theory of secondary measures to derive an analytic, expression for the sequence solely in terms of the initial measure and its associated orthogonal polynomials of the first and second kind. These mappings can be thought of as taking a highly nonlocal Hamiltonian to a local Hamiltonian. In the latter, a Lieb-Robinson like bound for the dynamics of the open quantum system makes sense. We develop analytical bounds on the error to observables of the system as a function of time when the semi-infinite chain in truncated at some finite length. The fact that this is possible shows that there is a finite ``Speed of sound'' in these chain representations. This has many implications of the simulatability of open quantum systems of this type and demonstrates that a truncated chain can faithfully reproduce the dynamics at shorter times. These results make a significant and mathematically rigorous contribution to the understanding of the theory of open quantum systems; and pave the way towards the efficient simulation of these systems, which within the standard methods, is often an intractable problem. EPSRC CDT in Controlled Quantum Dynamics, EU STREP project and Alexander von Humboldt Foundation

Quantum theory and human perception of the macro-world.

PubMed

Aerts, Diederik

2014-01-01

We investigate the question of 'why customary macroscopic entities appear to us humans as they do, i.e., as bounded entities occupying space and persisting through time', starting from our knowledge of quantum theory, how it affects the behavior of such customary macroscopic entities, and how it influences our perception of them. For this purpose, we approach the question from three perspectives. Firstly, we look at the situation from the standard quantum angle, more specifically the de Broglie wavelength analysis of the behavior of macroscopic entities, indicate how a problem with spin and identity arises, and illustrate how both play a fundamental role in well-established experimental quantum-macroscopical phenomena, such as Bose-Einstein condensates. Secondly, we analyze how the question is influenced by our result in axiomatic quantum theory, which proves that standard quantum theory is structurally incapable of describing separated entities. Thirdly, we put forward our new 'conceptual quantum interpretation', including a highly detailed reformulation of the question to confront the new insights and views that arise with the foregoing analysis. At the end of the final section, a nuanced answer is given that can be summarized as follows. The specific and very classical perception of human seeing-light as a geometric theory-and human touching-only ruled by Pauli's exclusion principle-plays a role in our perception of macroscopic entities as ontologically stable entities in space. To ascertain quantum behavior in such macroscopic entities, we will need measuring apparatuses capable of its detection. Future experimental research will have to show if sharp quantum effects-as they occur in smaller entities-appear to be ontological aspects of customary macroscopic entities. It remains a possibility that standard quantum theory is an incomplete theory, and hence incapable of coping ultimately with separated entities, meaning that a more general theory will be needed.

Algorithmic information theory and the hidden variable question

NASA Technical Reports Server (NTRS)

Fuchs, Christopher

1992-01-01

The admissibility of certain nonlocal hidden-variable theories are explained via information theory. Consider a pair of Stern-Gerlach devices with fixed nonparallel orientations that periodically perform spin measurements on identically prepared pairs of electrons in the singlet spin state. Suppose the outcomes are recorded as binary strings l and r (with l sub n and r sub n denoting their n-length prefixes). The hidden-variable theories considered here require that there exists a recursive function which may be used to transform l sub n into r sub n for any n. This note demonstrates that such a theory cannot reproduce all the statistical predictions of quantum mechanics. Specifically, consider an ensemble of outcome pairs (l,r). From the associated probability measure, the Shannon entropies H sub n and H bar sub n for strings l sub n and pairs (l sub n, r sub n) may be formed. It is shown that such a theory requires that the absolute value of H bar sub n - H sub n be bounded - contrasting the quantum mechanical prediction that it grow with n.

Non-local boxes and their implementation in Minecraft

NASA Astrophysics Data System (ADS)

Simnacher, Timo Yannick

PR-boxes are binary devices connecting two remote parties satisfying x AND y = a + b mod 2, where x and y denote the binary inputs and a and b are the respective outcomes without signaling. These devices are named after their inventors Sandu Popescu and Daniel Rohrlich and saturate the Clauser-Horne-Shimony-Holt (CHSH) inequality. This Bell-like inequality bounds the correlation that can exist between two remote, non-signaling, classical systems described by local hidden variable theories. Experiments have now convincingly shown that quantum entanglement cannot be explained by local hidden variable theories. Furthermore, the CHSH inequality provides a method to distinguish quantum systems from super-quantum correlations. The correlation between the outputs of the PR-box goes beyond any quantum entanglement. Though PR-boxes would have impressive consequences, as far as we know they are not physically realizable. However, by introducing PR-boxes to Minecraft as part of the redstone system, which simulates the electrical components for binary computing, we can experience the consequences of super-quantum correlations. For instance, Wim van Dam proved that two parties can use a sufficient number of PR-boxes to compute any Boolean function f(x,y) with only one bit of communication.

Nexus: A modular workflow management system for quantum simulation codes

NASA Astrophysics Data System (ADS)

Krogel, Jaron T.

2016-01-01

The management of simulation workflows represents a significant task for the individual computational researcher. Automation of the required tasks involved in simulation work can decrease the overall time to solution and reduce sources of human error. A new simulation workflow management system, Nexus, is presented to address these issues. Nexus is capable of automated job management on workstations and resources at several major supercomputing centers. Its modular design allows many quantum simulation codes to be supported within the same framework. Current support includes quantum Monte Carlo calculations with QMCPACK, density functional theory calculations with Quantum Espresso or VASP, and quantum chemical calculations with GAMESS. Users can compose workflows through a transparent, text-based interface, resembling the input file of a typical simulation code. A usage example is provided to illustrate the process.

Influence of scattering processes on electron quantum states in nanowires

PubMed Central

Galenchik, Vadim; Borzdov, Andrei; Borzdov, Vladimir; Komarov, Fadei

2007-01-01

In the framework of quantum perturbation theory the self-consistent method of calculation of electron scattering rates in nanowires with the one-dimensional electron gas in the quantum limit is worked out. The developed method allows both the collisional broadening and the quantum correlations between scattering events to be taken into account. It is an alternativeper seto the Fock approximation for the self-energy approach based on Green’s function formalism. However this approach is free of mathematical difficulties typical to the Fock approximation. Moreover, the developed method is simpler than the Fock approximation from the computational point of view. Using the approximation of stable one-particle quantum states it is proved that the electron scattering processes determine the dependence of electron energy versus its wave vector.

Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts.

PubMed

Knizia, Gerald

2013-11-12

Modern quantum chemistry can make quantitative predictions on an immense array of chemical systems. However, the interpretation of those predictions is often complicated by the complex wave function expansions used. Here we show that an exceptionally simple algebraic construction allows for defining atomic core and valence orbitals, polarized by the molecular environment, which can exactly represent self-consistent field wave functions. This construction provides an unbiased and direct connection between quantum chemistry and empirical chemical concepts, and can be used, for example, to calculate the nature of bonding in molecules, in chemical terms, from first principles. In particular, we find consistency with electronegativities (χ), C 1s core-level shifts, resonance substituent parameters (σR), Lewis structures, and oxidation states of transition-metal complexes.

Evidence for a first-order liquid-liquid transition in high-pressure hydrogen from ab initio simulations

PubMed Central

Morales, Miguel A.; Pierleoni, Carlo; Schwegler, Eric; Ceperley, D. M.

2010-01-01

Using quantum simulation techniques based on either density functional theory or quantum Monte Carlo, we find clear evidence of a first-order transition in liquid hydrogen, between a low conductivity molecular state and a high conductivity atomic state. Using the temperature dependence of the discontinuity in the electronic conductivity, we estimate the critical point of the transition at temperatures near 2,000 K and pressures near 120 GPa. Furthermore, we have determined the melting curve of molecular hydrogen up to pressures of 200 GPa, finding a reentrant melting line. The melting line crosses the metalization line at 700 K and 220 GPa using density functional energetics and at 550 K and 290 GPa using quantum Monte Carlo energetics. PMID:20566888

Towards topological quantum computer

NASA Astrophysics Data System (ADS)

Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An.

2018-01-01

Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.

Assessing the quantum physics impacts on future x-ray free-electron lasers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmitt, Mark J.; Anisimov, Petr Mikhaylovich

A new quantum mechanical theory of x-ray free electron lasers (XFELs) has been successfully developed that has placed LANL at the forefront of the understanding of quantum effects in XFELs. Our quantum theory describes the interaction of relativistic electrons with x-ray radiation in the periodic magnetic field of an undulator using the same mathematical formalism as classical XFEL theory. This places classical and quantum treatments on the same footing and allows for a continuous transition from one regime to the other eliminating the disparate analytical approaches previously used. Moreover, Dr. Anisimov, the architect of this new theory, is now consideredmore » a resource in the international FEL community for assessing quantum effects in XFELs.« less

Quantum-like model of unconscious–conscious dynamics

PubMed Central

Khrennikov, Andrei

2015-01-01

We present a quantum-like model of sensation–perception dynamics (originated in Helmholtz theory of unconscious inference) based on the theory of quantum apparatuses and instruments. We illustrate our approach with the model of bistable perception of a particular ambiguous figure, the Schröder stair. This is a concrete model for unconscious and conscious processing of information and their interaction. The starting point of our quantum-like journey was the observation that perception dynamics is essentially contextual which implies impossibility of (straightforward) embedding of experimental statistical data in the classical (Kolmogorov, 1933) framework of probability theory. This motivates application of nonclassical probabilistic schemes. And the quantum formalism provides a variety of the well-approved and mathematically elegant probabilistic schemes to handle results of measurements. The theory of quantum apparatuses and instruments is the most general quantum scheme describing measurements and it is natural to explore it to model the sensation–perception dynamics. In particular, this theory provides the scheme of indirect quantum measurements which we apply to model unconscious inference leading to transition from sensations to perceptions. PMID:26283979

Photovoltaic reciprocity and quasi-Fermi level splitting in nanostructure-based solar cells (Conference Presentation)

NASA Astrophysics Data System (ADS)

Aeberhard, Urs

2017-04-01

The photovoltaic reciprocity theory relates the electroluminescence spectrum of a solar cell under applied bias to the external photovoltaic quantum efficiency of the device as measured at short circuit conditions [1]. So far, the theory has been verified for a wide range of devices and material systems and forms the basis of a growing number of luminesecence imaging techniques used in the characterization of photovoltaic materials, cells and modules [2-5]. However, there are also some examples where the theory fails, such as in the case of amorphous silicon. In our contribution, we critically assess the assumptions made in the derivation of the theory and compare its predictions with rigorous formal relations as well as numerical computations in the framework of a comprehensive quantum-kinetic theory of photovoltaics [6] as applied to ultra-thin absorber architectures [7]. One of the main applications of the photovoltaic reciprocity relation is the determination of quasi-Fermi level splittings (QFLS) in solar cells from the measurement of luminescence. In nanostructure-based photovoltaic architectures, the determination of QFLS is challenging, but instrumental to assess the performance potential of the concepts. Here, we use our quasi-Fermi level-free theory to investigate existence and size of QFLS in quantum well and quantum dot solar cells. [1] Uwe Rau. Reciprocity relation between photovoltaic quantum efficiency and electrolumines- cent emission of solar cells. Phys. Rev. B, 76(8):085303, 2007. [2] Thomas Kirchartz and Uwe Rau. Electroluminescence analysis of high efficiency cu(in,ga)se2 solar cells. J. Appl. Phys., 102(10), 2007. [3] Thomas Kirchartz, Uwe Rau, Martin Hermle, Andreas W. Bett, Anke Helbig, and Jrgen H. Werner. Internal voltages in GaInP-GaInAs-Ge multijunction solar cells determined by electro- luminescence measurements. Appl. Phys. Lett., 92(12), 2008. [4] Thomas Kirchartz, Anke Helbig, Wilfried Reetz, Michael Reuter, Jürgen H. Werner, and Uwe Rau. Reciprocity between electroluminescence and quantum efficiency used for the characterization of silicon solar cells. Prog. Photovolt: Res. Appl., 17(6):394-402, 2009. [5] U. Hoyer, M. Wagner, Th. Swonke, J. Bachmann, R. Auer, A. Osvet, and C. J. Brabec. Electroluminescence imaging of organic photovoltaic modules. Appl. Phys. Lett., 97(23), 2010. [6] U. Aeberhard. Theory and simulation of quantum photovoltaic devices based on the non-equilibrium Greens function formalism. J. Comput. Electron., 10:394-413, 2011. [7] U. Aeberhard. Simulation of ultrathin solar cells beyond the limits of the semiclassical bulk picture. IEEE J. Photovolt., 6(3):654-660, 2016.

Fermi liquid, clustering, and structure factor in dilute warm nuclear matter

NASA Astrophysics Data System (ADS)

Röpke, G.; Voskresensky, D. N.; Kryukov, I. A.; Blaschke, D.

2018-02-01

Properties of nuclear systems at subsaturation densities can be obtained from different approaches. We demonstrate the use of the density autocorrelation function which is related to the isothermal compressibility and, after integration, to the equation of state. This way we connect the Landau Fermi liquid theory well elaborated in nuclear physics with the approaches to dilute nuclear matter describing cluster formation. A quantum statistical approach is presented, based on the cluster decomposition of the polarization function. The fundamental quantity to be calculated is the dynamic structure factor. Comparing with the Landau Fermi liquid theory which is reproduced in lowest approximation, the account of bound state formation and continuum correlations gives the correct low-density result as described by the second virial coefficient and by the mass action law (nuclear statistical equilibrium). Going to higher densities, the inclusion of medium effects is more involved compared with other quantum statistical approaches, but the relation to the Landau Fermi liquid theory gives a promising approach to describe not only thermodynamic but also collective excitations and non-equilibrium properties of nuclear systems in a wide region of the phase diagram.

PREFACE: International Conference on Quantum Simulators and Design, Hiroshima, Japan, 3 6 December 2006

NASA Astrophysics Data System (ADS)

Akai, Hisazumi; Oguchi, Tamio

2007-09-01

This special issue of Journal of Physics: Condensed Matter comprises selected papers from the 1st International Conference on Quantum Simulators and Design (QSD2006) held in Hiroshima, Japan, 3-6 December 2006. This conference was organized under the auspices of the Development of New Quantum Simulators and Quantum Design Grant-in-Aid for Scientific Research on Priority Areas, Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT), and Hiroshima University Quantum design is a computational approach to the development of new materials with specified properties and functionalities. The basic ingredient is the use of quantum simulations to design a material that meets a given specification of properties and functionalities. For this to be successful, the quantum simulation should be highly reliable and be applicable to systems of realistic size. A central interest is, therefore, the development of new methods of quantum simulation and quantum design. This includes methods beyond the local density approximation of density functional theory (LDA), order-N methods, methods dealing with excitations and reactions, and so on, as well as the application of these methods to the design of new materials and devices. The field of quantum design has developed rapidly in the past few years and this conference provides an international forum for experimental and theoretical researchers to exchange ideas. A total of 183 delegates from 8 countries participated in the conference. There were 18 invited talks, 16 oral presentations and 100 posters. There were many new ideas and we foresee dramatic progress in the coming years. The 2nd International Conference on Quantum Simulators and Design will be held in Tokyo, Japan, 31 May-3 June 2008.

Equilibrium finite-frequency noise of an interacting mesoscopic capacitor studied in time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole

2018-03-01

We calculate the frequency-dependent equilibrium noise of a mesoscopic capacitor in time-dependent density functional theory (TDDFT). The capacitor is modeled as a single-level quantum dot with on-site Coulomb interaction and tunnel coupling to a nearby reservoir. The noise spectra are derived from linear-response conductances via the fluctuation-dissipation theorem. Thereby, we analyze the performance of a recently derived exchange-correlation potential with time-nonlocal density dependence in the finite-frequency linear-response regime. We compare our TDDFT noise spectra with real-time perturbation theory and find excellent agreement for noise frequencies below the reservoir temperature.

Generalized probability theories: what determines the structure of quantum theory?

NASA Astrophysics Data System (ADS)

Janotta, Peter; Hinrichsen, Haye

2014-08-01

The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical structure of quantum theory. This review paper tries to present the framework and recent results to a broader readership in an accessible manner. To achieve this, we follow a constructive approach. Starting from a few basic physically motivated assumptions we show how a given set of observations can be manifested in an operational theory. Furthermore, we characterize consistency conditions limiting the range of possible extensions. In this framework classical and quantum theory appear as special cases, and the aim is to understand what distinguishes quantum mechanics as the fundamental theory realized in nature. It turns out that non-classical features of single systems can equivalently result from higher-dimensional classical theories that have been restricted. Entanglement and non-locality, however, are shown to be genuine non-classical features.

Problems in particle theory. Technical report - 1993--1994

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adler, S.L.; Wilczek, F.

This report is a progress report on the work of two principal investigators in the broad area of particle physics theory, covering their personal work, that of their coworkers, and their proposed work for the future. One author has worked in the past on various topics in field theory and particle physics, among them current algebras, the physics of neutrino induced reactions, quantum electrodynamics (including strong magnetic field processes), the theory of the axial-vector current anomaly, topics in quantum gravity, and nonlinear models for quark confinement. While much of his work has been analytical, all of the projects listed abovemore » (except for the work on gravity) had phases which required considerable computer work as well. Over the next several years, he proposes to continue or initiate research on the following problems: (1) Acceleration algorithms for the Monte Carlo analysis of lattice field and gauge theories, and more generally, new research in computational neuroscience and pattern recognition. (2) Construction of quaternionic generalizations of complex quantum mechanics and field theory, and their application to composite models of quarks and leptons, and to the problem of unifying quantum theories of matter with general relativity. One author has worked on problems in exotic quantum statistics and its applications to condensed matter systems. His work has also continued on the quantum theory of black holes. This has evolved toward understanding properties of quantum field theory and string theory in incomplete regions of flat space.« less

On a three-dimensional symmetric Ising tetrahedron and contributions to the theory of the dilogarithm and Clausen functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coffey, Mark W.

2008-04-15

Perturbative quantum field theory for the Ising model at the three-loop level yields a tetrahedral Feynman diagram C(a,b) with masses a and b and four other lines with unit mass. The completely symmetric tetrahedron C{sup Tet}{identical_to}C(1,1) has been of interest from many points of view, with several representations and conjectures having been given in the literature. We prove a conjectured exponentially fast convergent sum for C(1,1), as well as a previously empirical relation for C(1,1) as a remarkable difference of Clausen function values. Our presentation includes propositions extending the theory of the dilogarithm Li{sub 2} and Clausen Cl{sub 2} functions,more » as well as their relation to other special functions of mathematical physics. The results strengthen connections between Feynman diagram integrals, volumes in hyperbolic space, number theory, and special functions and numbers, specifically including dilogarithms, Clausen function values, and harmonic numbers.« less

Microscopic theory of cation exchange in CdSe nanocrystals.

PubMed

Ott, Florian D; Spiegel, Leo L; Norris, David J; Erwin, Steven C

2014-10-10

Although poorly understood, cation-exchange reactions are increasingly used to dope or transform colloidal semiconductor nanocrystals (quantum dots). We use density-functional theory and kinetic Monte Carlo simulations to develop a microscopic theory that explains structural, optical, and electronic changes observed experimentally in Ag-cation-exchanged CdSe nanocrystals. We find that Coulomb interactions, both between ionized impurities and with the polarized nanocrystal surface, play a key role in cation exchange. Our theory also resolves several experimental puzzles related to photoluminescence and electrical behavior in CdSe nanocrystals doped with Ag.

Renormalization in Large Momentum Effective Theory of Parton Physics.

PubMed

Ji, Xiangdong; Zhang, Jian-Hui; Zhao, Yong

2018-03-16

In the large-momentum effective field theory approach to parton physics, the matrix elements of nonlocal operators of quark and gluon fields, linked by straight Wilson lines in a spatial direction, are calculated in lattice quantum chromodynamics as a function of hadron momentum. Using the heavy-quark effective theory formalism, we show a multiplicative renormalization of these operators at all orders in perturbation theory, both in dimensional and lattice regularizations. The result provides a theoretical basis for extracting parton properties through properly renormalized observables in Monte Carlo simulations.

What is Quantum Mechanics? A Minimal Formulation

NASA Astrophysics Data System (ADS)

Friedberg, R.; Hohenberg, P. C.

2018-03-01

This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the presentation is the so-called "microscopic theory", applicable to any closed system S of arbitrary size N, using concepts referring to S alone, without resort to external apparatus or external agents. An example of a similar minimal microscopic theory is the standard formulation of classical mechanics, which serves as the template for a minimal quantum theory. The only substantive assumption required is the replacement of the classical Euclidean phase space by Hilbert space in the quantum case, with the attendant all-important phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the Kochen-Specker-Bell theorem and Gleason's theorem, then lead inevitably to the well-known Born probability rule. For both classical and quantum mechanics, questions of physical implementation and experimental verification of the predictions of the theories are the domain of the macroscopic theory, which is argued to be a special case or application of the more general microscopic theory.

Communication: Photoinduced carbon dioxide binding with surface-functionalized silicon quantum dots.

PubMed

Douglas-Gallardo, Oscar A; Sánchez, Cristián Gabriel; Vöhringer-Martinez, Esteban

2018-04-14

Nowadays, the search for efficient methods able to reduce the high atmospheric carbon dioxide concentration has turned into a very dynamic research area. Several environmental problems have been closely associated with the high atmospheric level of this greenhouse gas. Here, a novel system based on the use of surface-functionalized silicon quantum dots (sf-SiQDs) is theoretically proposed as a versatile device to bind carbon dioxide. Within this approach, carbon dioxide trapping is modulated by a photoinduced charge redistribution between the capping molecule and the silicon quantum dots (SiQDs). The chemical and electronic properties of the proposed SiQDs have been studied with a Density Functional Theory and Density Functional Tight-Binding (DFTB) approach along with a time-dependent model based on the DFTB framework. To the best of our knowledge, this is the first report that proposes and explores the potential application of a versatile and friendly device based on the use of sf-SiQDs for photochemically activated carbon dioxide fixation.

Communication: Photoinduced carbon dioxide binding with surface-functionalized silicon quantum dots

NASA Astrophysics Data System (ADS)

Douglas-Gallardo, Oscar A.; Sánchez, Cristián Gabriel; Vöhringer-Martinez, Esteban

2018-04-01

Nowadays, the search for efficient methods able to reduce the high atmospheric carbon dioxide concentration has turned into a very dynamic research area. Several environmental problems have been closely associated with the high atmospheric level of this greenhouse gas. Here, a novel system based on the use of surface-functionalized silicon quantum dots (sf-SiQDs) is theoretically proposed as a versatile device to bind carbon dioxide. Within this approach, carbon dioxide trapping is modulated by a photoinduced charge redistribution between the capping molecule and the silicon quantum dots (SiQDs). The chemical and electronic properties of the proposed SiQDs have been studied with a Density Functional Theory and Density Functional Tight-Binding (DFTB) approach along with a time-dependent model based on the DFTB framework. To the best of our knowledge, this is the first report that proposes and explores the potential application of a versatile and friendly device based on the use of sf-SiQDs for photochemically activated carbon dioxide fixation.

Determination of structure parameters in strong-field tunneling ionization theory of molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao Songfeng; Jin Cheng; College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou, Gansu 730070

2010-03-15

In the strong field molecular tunneling ionization theory of Tong et al. [Phys. Rev. A 66, 033402 (2002)], the ionization rate depends on the asymptotic wave function of the molecular orbital from which the electron is removed. The orbital wave functions obtained from standard quantum chemistry packages in general are not good enough in the asymptotic region. Here we construct a one-electron model potential for several linear molecules using density functional theory. We show that the asymptotic wave function can be improved with an iteration method and after one iteration accurate asymptotic wave functions and structure parameters are determined. Withmore » the new parameters we examine the alignment-dependent tunneling ionization probabilities for several molecules and compare with other calculations and with recent measurements, including ionization from inner molecular orbitals.« less

Quantum mechanics without the projection postulate and its realistic interpretation

NASA Astrophysics Data System (ADS)

Dieks, D.

1989-11-01

It is widely held that quantum mechanics is the first scientific theory to present scientifically internal, fundamental difficulties for a realistic interpretation (in the philosophical sense). The standard (Copenhagen) interpretation of the quantum theory is often described as the inevitable instrumentalistic response. It is the purpose of the present article to argue that quantum theory does not present fundamental new problems to a realistic interpretation. The formalism of quantum theory has the same states—it will be argued—as the formalisms of older physical theories and is capable of the same kinds of philosophical interpretation. This result is reached via an analysis of what it means to give a realistic interpretation to a theory. The main point of difference between quantum mechanics and other theories—as far as the possibilities of interpretation are concerned—is the special treatment given to measurement by the “projection postulate.” But it is possible to do without this postulate. Moreover, rejection of the projection postulate does not, in spite of what is often maintained in the literature, automatically lead to the many-worlds interpretation of quantum mechanics. A realistic interpretation is possible in which only the reality of one (our) world is recognized. It is argued that the Copenhagen interpretation as expounded by Bohr is not in conflict with the here proposed realistic interpretation of quantum theory.

Theory of time-resolved photoelectron imaging. Comparison of a density functional with a time-dependent density functional approach

NASA Astrophysics Data System (ADS)

Suzuki, Yoshi-ichi; Seideman, Tamar; Stener, Mauro

2004-01-01

Time-resolved photoelectron differential cross sections are computed within a quantum dynamical theory that combines a formally exact solution of the nuclear dynamics with density functional theory (DFT)-based approximations of the electronic dynamics. Various observables of time-resolved photoelectron imaging techniques are computed at the Kohn-Sham and at the time-dependent DFT levels. Comparison of the results serves to assess the reliability of the former method and hence its usefulness as an economic approach for time-domain photoelectron cross section calculations, that is applicable to complex polyatomic systems. Analysis of the matrix elements that contain the electronic dynamics provides insight into a previously unexplored aspect of femtosecond-resolved photoelectron imaging.