Quantum electrodynamics in finite volume and nonrelativistic effective field theories
NASA Astrophysics Data System (ADS)
Fodor, Z.; Hoelbling, C.; Katz, S. D.; Lellouch, L.; Portelli, A.; Szabo, K. K.; Toth, B. C.
2016-04-01
Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.
Finite field-dependent symmetries in perturbative quantum gravity
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker
2014-01-01
In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci-Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin-Vilkovisky (BV) formulation.
Finite field-dependent symmetries in perturbative quantum gravity
Upadhyay, Sudhaker
2014-01-15
In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation. -- Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and anti-BRST transformations are developed in linear and non-linear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and non-linear gauges is established. •Using BV formulation the results are established at quantum level also.
Finite temperature quantum field theory in the functional Schroedinger picture
Lee, H. ); Na, K.; Yee, J.H. )
1995-03-15
We calculate the finite temperature Gaussian effective potential of scalar [phi][sup 4] theory in the functional Schroedinger picture. Our method is the direct generalization of the variational method proposed by Eboli, Jackiw, and Pi for quantum-mechanical systems, and gives the same result as that of Amelino-Camelia and Pi who used the self-consistent composite operator method.
NASA Astrophysics Data System (ADS)
Kormos, Márton; Wu, Jianda; Si, Qimiao
2014-03-01
When the transverse-field Ising chain at its quantum critical point is subjected to a small longitudinal field, the perturbed conformal field theory led to a field theory with an exotic E8 symmetry. Recent neutron scattering experiments have provided evidence for the lightest two particles in this E8 model in the quasi-1D Ising ferromagnet CoNb2O6. While the zero temperature dynamic of the model is well known, its finite-temperature counterpart has not yet been systematically studied. We study the low-frequency dynamical spin structure factor at finite temperatures using the form-factor method. We show that the dominant contribution to the spin dynamics comes from the channel between two lightest particles, and demonstrate how the spin dynamics differ from a diffusion form. Using these results, we determine the temperature dependence of the NMR relaxation rate. We suggest that, for CoNb2O6, measurements of the NMR relaxation rate provide a means to further test the applicability of the E8 model.
Finite temperature quantum field theory in the functional Schrödinger picture
NASA Astrophysics Data System (ADS)
Lee, Hyuk-Jae; Na, Kyunghyun; Yee, Jae Hyung
1995-03-01
We calculate the finite temperature Gaussian effective potential of scalar φ4 theory in the functional Schrödinger picture. Our method is the direct generalization of the variational method proposed by Eboli, Jackiw, and Pi for quantum-mechanical systems, and gives the same result as that of Amelino-Camelia and Pi who used the self-consistent composite operator method.
Finite-temperature scaling at the quantum critical point of the Ising chain in a transverse field
NASA Astrophysics Data System (ADS)
Haelg, Manuel; Huvonen, Dan; Guidi, Tatiana; Quintero-Castro, Diana Lucia; Boehm, Martin; Regnault, Louis-Pierre; Zheludev, Andrey
2015-03-01
Inelastic neutron scattering is used to study the finite-temperature scaling behavior of spin correlations at the quantum critical point in an experimental realization of the one-dimensional Ising model in a transverse field. The target compound is the well-characterized, anisotropic and bond-alternating Heisenberg spin-1 chain material NTENP. The validity and the limitations of the dynamic structure factor scaling are tested, discussed and compared to theoretical predictions. For this purpose neutron data have been collected on the three-axes spectrometers IN14 at ILL and FLEXX at HZB as well as on the time of flight multi-chopper spectrometer LET at ISIS. In addition to the general statement about quantum criticality and universality, present study also reveals new insight into the properties of the spin chain compound NTENP in particular.
NASA Astrophysics Data System (ADS)
Modesto, Leonardo; Piva, Marco; Rachwał, Lesław
2016-07-01
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).
Variational density matrices in quantum field theory at finite temperature and chemical potential
Nadeau, H.
1996-07-01
I evaluate the Helmholtz free energy of finite temperature {lambda}{var_phi}{sup 4} theory, both real and complex, using a variational quadratic {ital ansatz} for the density matrix. Minimizing with respect to the variational parameters produces results identical to those obtained by summing the daisy and superdaisy diagrams. In the nonrelativistic limit this is equivalent to a Hartree-Fock mean field with an effective mass. Quartic terms are then included by means of a relativistic generalization of the hypernetted-chain approximation without exchange terms, called the {open_quote}{open_quote}direct approximation.{close_quote}{close_quote} In this way infinite groups of rings and ladders are summed, giving nonperturbative expressions for the internal energy and four-point function in terms of a small number of Dyson-like integral equations. An expression is obtained for the internal energy of a zero-temperature system in terms of only two variational parameters. Because the hypernetted-chain approximation preserves the Euler-Lagrange variational principle, minimizing the internal energy with respect to these parameters should provide a semiquantitative upper bound on the ground state energy of an interacting relativistic system at zero temperature. For the full finite temperature theory in the direct approximation, there are now three variational parameters and it is necessary to obtain the entropy in a approximation comparable to that for the internal energy. This is done in an analogous manner to the separability approximation of nonrelativistic hypernetted-chain theory. Finally, an improvement on the direct approximation is attained by including exchange terms of all types. This proceeds along the lines of parquet summations, resulting in a set of integral equations that, when solved self-consistently, includes all series and parallel connections of direct and exchange diagrams. {copyright} {ital 1996 The American Physical Society.}
Finite groups and quantum physics
Kornyak, V. V.
2013-02-15
Concepts of quantum theory are considered from the constructive 'finite' point of view. The introduction of a continuum or other actual infinities in physics destroys constructiveness without any need for them in describing empirical observations. It is shown that quantum behavior is a natural consequence of symmetries of dynamical systems. The underlying reason is that it is impossible in principle to trace the identity of indistinguishable objects in their evolution-only information about invariant statements and values concerning such objects is available. General mathematical arguments indicate that any quantum dynamics is reducible to a sequence of permutations. Quantum phenomena, such as interference, arise in invariant subspaces of permutation representations of the symmetry group of a dynamical system. Observable quantities can be expressed in terms of permutation invariants. It is shown that nonconstructive number systems, such as complex numbers, are not needed for describing quantum phenomena. It is sufficient to employ cyclotomic numbers-a minimal extension of natural numbers that is appropriate for quantum mechanics. The use of finite groups in physics, which underlies the present approach, has an additional motivation. Numerous experiments and observations in the particle physics suggest the importance of finite groups of relatively small orders in some fundamental processes. The origin of these groups is unclear within the currently accepted theories-in particular, within the Standard Model.
Spotlighting quantum critical points via quantum correlations at finite temperatures
Werlang, T.; Ribeiro, G. A. P.; Rigolin, Gustavo
2011-06-15
We extend the program initiated by T. Werlang et al. [Phys. Rev. Lett. 105, 095702 (2010)] in several directions. Firstly, we investigate how useful quantum correlations, such as entanglement and quantum discord, are in the detection of critical points of quantum phase transitions when the system is at finite temperatures. For that purpose we study several thermalized spin models in the thermodynamic limit, namely, the XXZ model, the XY model, and the Ising model, all of which with an external magnetic field. We compare the ability of quantum discord, entanglement, and some thermodynamic quantities to spotlight the quantum critical points for several different temperatures. Secondly, for some models we go beyond nearest neighbors and also study the behavior of entanglement and quantum discord for second nearest neighbors around the critical point at finite temperature. Finally, we furnish a more quantitative description of how good all these quantities are in spotlighting critical points of quantum phase transitions at finite T, bridging the gap between experimental data and those theoretical descriptions solely based on the unattainable absolute zero assumption.
A classification of finite quantum kinematics
NASA Astrophysics Data System (ADS)
Tolar, J.
2014-10-01
Quantum mechanics in Hilbert spaces of finite dimension N is reviewed from the number theoretic point of view. For composite numbers N possible quantum kinematics are classified on the basis of Mackey's Imprimitivity Theorem for finite Abelian groups. This yields also a classification of finite Weyl-Heisenberg groups and the corresponding finite quantum kinematics. Simple number theory gets involved through the fundamental theorem describing all finite discrete Abelian groups of order N as direct products of cyclic groups, whose orders are powers of not necessarily distinct primes contained in the prime decomposition of N. The representation theoretic approach is further compared with the algebraic approach, where the basic object is the corresponding operator algebra. The consideration of fine gradings of this associative algebra then brings a fresh look on the relation between the mathematical formalism and physical realizations of finite quantum systems.
Finite-size scaling at quantum transitions
NASA Astrophysics Data System (ADS)
Campostrini, Massimo; Pelissetto, Andrea; Vicari, Ettore
2014-03-01
We develop the finite-size scaling (FSS) theory at quantum transitions. We consider various boundary conditions, such as open and periodic boundary conditions, and characterize the corrections to the leading FSS behavior. Using renormalization-group (RG) theory, we generalize the classical scaling ansatz to describe FSS in the quantum case, classifying the different sources of scaling corrections. We identify nonanalytic corrections due to irrelevant (bulk and boundary) RG perturbations and analytic contributions due to regular backgrounds and analytic expansions of the nonlinear scaling fields. To check the general predictions, we consider the quantum XY chain in a transverse field. For this model exact or numerically accurate results can be obtained by exploiting its fermionic quadratic representation. We study the FSS of several observables, such as the free energy, the energy differences between low-energy levels, correlation functions of the order parameter, etc., confirming the general predictions in all cases. Moreover, we consider bipartite entanglement entropies, which are characterized by the presence of additional scaling corrections, as predicted by conformal field theory.
Quantum finite time availability for parametric oscillators
NASA Astrophysics Data System (ADS)
Hoffmann, Karl Heinz; Schmidt, Kim; Salamon, Peter
2015-06-01
The availability of a thermodynamic system out of equilibrium with its environment describes its ability to perform work in a reversible process which brings it to equilibrium with this environment. Processes in finite time can usually not be performed reversibly thus leading to unavoidable losses. In order to account for these losses the concept of finite time availability was introduced. We here add a new feature through the introduction of quantum finite time availability for an ensemble of parametric oscillators. For such systems there exists a certain critical time, the FEAT time. Quantum finite time availability quantifies the available work from processes which are shorter than the FEAT time of the oscillator ensemble.
Quantum coding with finite resources
NASA Astrophysics Data System (ADS)
Tomamichel, Marco; Berta, Mario; Renes, Joseph M.
2016-05-01
The quantum capacity of a memoryless channel determines the maximal rate at which we can communicate reliably over asymptotically many uses of the channel. Here we illustrate that this asymptotic characterization is insufficient in practical scenarios where decoherence severely limits our ability to manipulate large quantum systems in the encoder and decoder. In practical settings, we should instead focus on the optimal trade-off between three parameters: the rate of the code, the size of the quantum devices at the encoder and decoder, and the fidelity of the transmission. We find approximate and exact characterizations of this trade-off for various channels of interest, including dephasing, depolarizing and erasure channels. In each case, the trade-off is parameterized by the capacity and a second channel parameter, the quantum channel dispersion. In the process, we develop several bounds that are valid for general quantum channels and can be computed for small instances.
Quantum coding with finite resources
Tomamichel, Marco; Berta, Mario; Renes, Joseph M.
2016-01-01
The quantum capacity of a memoryless channel determines the maximal rate at which we can communicate reliably over asymptotically many uses of the channel. Here we illustrate that this asymptotic characterization is insufficient in practical scenarios where decoherence severely limits our ability to manipulate large quantum systems in the encoder and decoder. In practical settings, we should instead focus on the optimal trade-off between three parameters: the rate of the code, the size of the quantum devices at the encoder and decoder, and the fidelity of the transmission. We find approximate and exact characterizations of this trade-off for various channels of interest, including dephasing, depolarizing and erasure channels. In each case, the trade-off is parameterized by the capacity and a second channel parameter, the quantum channel dispersion. In the process, we develop several bounds that are valid for general quantum channels and can be computed for small instances. PMID:27156995
Quantum channels with a finite memory
NASA Astrophysics Data System (ADS)
Bowen, Garry; Mancini, Stefano
2004-01-01
In this paper we study quantum communication channels with correlated noise effects, i.e., quantum channels with memory. We derive a model for correlated noise channels that includes a channel memory state. We examine the case where the memory is finite, and derive bounds on the classical and quantum capacities. For the entanglement-assisted and unassisted classical capacities it is shown that these bounds are attainable for certain classes of channel. Also, we show that the structure of any finite-memory state is unimportant in the asymptotic limit, and specifically, for a perfect finite-memory channel where no information is lost to the environment, achieving the upper bound implies that the channel is asymptotically noiseless.
Categorical Formulation of Finite-Dimensional Quantum Algebras
NASA Astrophysics Data System (ADS)
Vicary, Jamie
2011-06-01
We describe how †-Frobenius monoids give the correct categorical description of certain kinds of finite-dimensional `quantum algebras'. We develop the concept of an involution monoid, and use it to construct a correspondence between finite-dimensional C*-algebras and certain types of †-Frobenius monoids in the category of Hilbert spaces. Using this technology, we recast the spectral theorems for commutative C*-algebras and for normal operators into an explicitly categorical language, and we examine the case that the results of measurements do not form finite sets, but rather objects in a finite Boolean topos. We describe the relevance of these results for topological quantum field theory.
Quantum algorithms and the finite element method
NASA Astrophysics Data System (ADS)
Montanaro, Ashley; Pallister, Sam
2016-03-01
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretizes the parameter space and finds an approximate solution by solving a large system of linear equations. Here we investigate the extent to which the finite element method can be accelerated using an efficient quantum algorithm for solving linear equations. We consider the representative general question of approximately computing a linear functional of the solution to a boundary value problem and compare the quantum algorithm's theoretical performance with that of a standard classical algorithm—the conjugate gradient method. Prior work claimed that the quantum algorithm could be exponentially faster but did not determine the overall classical and quantum run times required to achieve a predetermined solution accuracy. Taking this into account, we find that the quantum algorithm can achieve a polynomial speedup, the extent of which grows with the dimension of the partial differential equation. In addition, we give evidence that no improvement of the quantum algorithm can lead to a superpolynomial speedup when the dimension is fixed and the solution satisfies certain smoothness properties.
Mironov, A. ); Zabrodin, A. )
1992-06-30
Using the finite-size effects, the scaling dimensions and correlation functions of the main operators in continuous and lattice models of 1d spinless Bose-gas with pairwise interaction of rather general form are obtained. The long-wave properties of these systems can be described by the Gaussian model with central charge c = 1. The disorder operators of the extended Gaussian model are found to correspond to some nonlocal operators in the XXZ Heisenberg antiferromagnet. This same approach is applicable to fermionic systems. Scaling dimensions of operators and correlation functions in the systems of interacting Fermi-particles are obtained. This paper presents a universal treatment for 1d systems of different kinds which is independent of the exact integrability and which gives universal expressions for critical exponents through the thermodynamic characteristics of the system.
Nonperturbative Quantum Field Evolution
NASA Astrophysics Data System (ADS)
Zhao, Xingbo; Ilderton, Anton; Maris, Pieter; Vary, James P.
2014-06-01
We introduce a nonperturbative, first-principles approach to time-dependent problems in quantum field theory. In this approach, the time-evolution of quantum field configurations is calculated in real time and at the amplitude level. This method is particularly suitable for treating systems interacting with a time-dependent background field. As a test problem, we apply this approach to QED and study electron acceleration and the associated photon emission in a time- and space-dependent electromagnetic background field.
High resolution finite volume scheme for the quantum hydrodynamic equations
NASA Astrophysics Data System (ADS)
Lin, Chin-Tien; Yeh, Jia-Yi; Chen, Jiun-Yeu
2009-03-01
The theory of quantum fluid dynamics (QFD) helps nanotechnology engineers to understand the physical effect of quantum forces. Although the governing equations of quantum fluid dynamics and classical fluid mechanics have the same form, there are two numerical simulation problems must be solved in QFD. The first is that the quantum potential term becomes singular and causes a divergence in the numerical simulation when the probability density is very small and close to zero. The second is that the unitarity in the time evolution of the quantum wave packet is significant. Accurate numerical evaluations are critical to the simulations of the flow fields that are generated by various quantum fluid systems. A finite volume scheme is developed herein to solve the quantum hydrodynamic equations of motion, which significantly improve the accuracy and stability of this method. The QFD equation is numerically implemented within the Eulerian method. A third-order modified Osher-Chakravarthy (MOC) upwind-centered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a second-order central finite volume scheme was used to map the quantum potential field. An explicit Runge-Kutta method is used to perform the time integration to achieve fast convergence of the proposed scheme. In order to meet the numerical result can conform to the physical phenomenon and avoid numerical divergence happening due to extremely low probability density, the minimum value setting of probability density must exceed zero and smaller than certain value. The optimal value was found in the proposed numerical approach to maintain a converging numerical simulation when the minimum probability density is 10 -5 to 10 -12. The normalization of the wave packet remains close to unity through a long numerical simulation and the deviations from 1.0 is about 10 -4. To check the QFD finite difference numerical computations, one- and two-dimensional particle motions were
Thermal Phase Transitions in Finite Quantum Systems
Dean, D.J.
2001-10-18
In this Proceedings, the author will describe the behavior of two different quantum-mechanical systems as a function of increasing temperature. While these systems are somewhat different, the questions addressed are very similar, namely, how does one describe transitions in phase of a finite many-body system; how does one recognize these transitions in practical calculations; and how may one obtain the order of the transition.
Finite-size scaling for quantum criticality using the finite-element method.
Antillon, Edwin; Wehefritz-Kaufmann, Birgit; Kais, Sabre
2012-03-01
Finite size scaling for the Schrödinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite-element method was shown to be a powerful numerical method for ab initio electronic-structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite-element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, local density approximation, and an "exact" formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems. PMID:22587208
Finite-size scaling for quantum criticality using the finite-element method
NASA Astrophysics Data System (ADS)
Antillon, Edwin; Wehefritz-Kaufmann, Birgit; Kais, Sabre
2012-03-01
Finite size scaling for the Schrödinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite-element method was shown to be a powerful numerical method for ab initio electronic-structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite-element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, local density approximation, and an “exact” formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems.
Simplified Quantum Transport Theory for Finite Bias and Temperature
NASA Astrophysics Data System (ADS)
Zhang, Xiaoguang; Wu, Yuning; Pantelides, Sokrates
We reformulate the Landauer-Buttiker formula for quantum transport by explicitly accounting for the energy and bias voltage dependence of the transmission probability. Under the assumption of a constant electric field, a simple formula for the differential conductance under a finite bias and at a finite temperature is derived that does not require a nonequilibrium self-consistent calculation. Calculation for the tunneling current through Au-Benzendithiol-Au molecular junction shows excellent agreement with the nonequilibrium Green's function (NEGF) method at zero temperature. Temperature dependent I-V curves for a number of devices are demonstrated. Supported by NSF Grant 1508898.
Multiscale quantum simulation of quantum field theory using wavelets
NASA Astrophysics Data System (ADS)
Brennen, Gavin K.; Rohde, Peter; Sanders, Barry C.; Singh, Sukhwinder
2015-09-01
A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field degrees of freedom in a wavelet basis—a multiscale description of the theory. Since wavelet families can be constructed to have compact support at all resolutions, this encoding allows for quantum simulations to create particle excitations which are local at some chosen scale and provides a natural way to associate observables in the theory to finite-resolution detectors.
NASA Astrophysics Data System (ADS)
Steffens, A.; Riofrío, C. A.; Hübener, R.; Eisert, J.
2014-12-01
We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product states (cMPS), a complete set of variational states grasping states in one-dimensional quantum field theory. We innovate a practical method, making use of and developing tools in estimation theory used in the context of compressed sensing such as Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum field states based on low-order correlation functions. In the absence of a phase reference, we highlight how specific higher order correlation functions can still be predicted. We exemplify the functioning of the approach by reconstructing randomized cMPS from their correlation data and study the robustness of the reconstruction for different noise models. Furthermore, we apply the method to data generated by simulations based on cMPS and using the time-dependent variational principle. The presented approach is expected to open up a new window into experimentally studying continuous quantum systems, such as those encountered in experiments with ultra-cold atoms on top of atom chips. By virtue of the analogy with the input-output formalism in quantum optics, it also allows for studying open quantum systems.
Least-squares finite element methods for quantum chromodynamics
Ketelsen, Christian; Brannick, J; Manteuffel, T; Mccormick, S
2008-01-01
A significant amount of the computational time in large Monte Carlo simulations of lattice quantum chromodynamics (QCD) is spent inverting the discrete Dirac operator. Unfortunately, traditional covariant finite difference discretizations of the Dirac operator present serious challenges for standard iterative methods. For interesting physical parameters, the discretized operator is large and ill-conditioned, and has random coefficients. More recently, adaptive algebraic multigrid (AMG) methods have been shown to be effective preconditioners for Wilson's discretization of the Dirac equation. This paper presents an alternate discretization of the Dirac operator based on least-squares finite elements. The discretization is systematically developed and physical properties of the resulting matrix system are discussed. Finally, numerical experiments are presented that demonstrate the effectiveness of adaptive smoothed aggregation ({alpha}SA ) multigrid as a preconditioner for the discrete field equations resulting from applying the proposed least-squares FE formulation to a simplified test problem, the 2d Schwinger model of quantum electrodynamics.
Characterizing finite-dimensional quantum behavior
NASA Astrophysics Data System (ADS)
Navascués, Miguel; Feix, Adrien; Araújo, Mateus; Vértesi, Tamás
2015-10-01
We study and extend the semidefinite programming (SDP) hierarchies introduced in Navascués and Vértesi [Phys. Rev. Lett. 115, 020501 (2015), 10.1103/PhysRevLett.115.020501] for the characterization of the statistical correlations arising from finite-dimensional quantum systems. First, we introduce the dimension-constrained noncommutative polynomial optimization (NPO) paradigm, where a number of polynomial inequalities are defined and optimization is conducted over all feasible operator representations of bounded dimensionality. Important problems in device-independent and semi-device-independent quantum information science can be formulated (or almost formulated) in this framework. We present effective SDP hierarchies to attack the general dimension-constrained NPO problem (and related ones) and prove their asymptotic convergence. To illustrate the power of these relaxations, we use them to derive a number of dimension witnesses for temporal and Bell-type correlation scenarios, and also to bound the probability of success of quantum random access codes.
Quantum emitters dynamically coupled to a quantum field
Acevedo, O. L.; Quiroga, L.; Rodríguez, F. J.; Johnson, N. F.
2013-12-04
We study theoretically the dynamical response of a set of solid-state quantum emitters arbitrarily coupled to a single-mode microcavity system. Ramping the matter-field coupling strength in round trips, we quantify the hysteresis or irreversible quantum dynamics. The matter-field system is modeled as a finite-size Dicke model which has previously been used to describe equilibrium (including quantum phase transition) properties of systems such as quantum dots in a microcavity. Here we extend this model to address non-equilibrium situations. Analyzing the system’s quantum fidelity, we find that the near-adiabatic regime exhibits the richest phenomena, with a strong asymmetry in the internal collective dynamics depending on which phase is chosen as the starting point. We also explore signatures of the crossing of the critical points on the radiation subsystem by monitoring its Wigner function; then, the subsystem can exhibit the emergence of non-classicality and complexity.
Quantum algorithms for quantum field theories.
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. PMID:22654052
Quaternionic quantum field theory
Adler, S.L.
1985-08-19
We show that a quaternionic quantum field theory can be formulated when the numbers of bosonic and fermionic degrees of freedom are equal and the fermions, as well as the bosons, obey a second-order wave equation. The theory is initially defined in terms of a quaternion-imaginary Lagrangian using the Feynman sum over histories. A Schroedinger equation can be derived from the functional integral, which identifies the quaternion-imaginary quantum Hamiltonian. Conversely, the transformation theory based on this Hamiltonian can be used to rederive the functional-integral formulation.
Supersymmetric Quantum Field Theories
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2005-03-01
We consider some supersymmetric multiplets in a purely quantum framework. A crucial point is to ensure the positivity of the scalar product in the Hilbert space of the quantum system. For the vector multiplet we obtain some discrepancies with respect to the literature in the expression of the super-propagator and we prove that the model is consistent only for positive mass. The gauge structure is constructed purely deductive and leads to the necessity of introducing scalar ghost superfields, in analogy to the usual gauge theories. Then we consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence.
Quantum algorithms for quantum field theories
NASA Astrophysics Data System (ADS)
Jordan, Stephen
2015-03-01
Ever since Feynman's original proposal for quantum computers, one of the primary applications envisioned has been efficient simulation of other quantum systems. In fact, it has been conjectured that quantum computers would be universal simulators, which can simulate all physical systems using computational resources that scale polynomially with the system's number of degrees of freedom. Quantum field theories have posed a challenge in that the set of degrees of freedom is formally infinite. We show how quantum computers, if built, could nevertheless efficiently simulate certain quantum field theories at bounded energy scales. Our algorithm includes a new state preparation technique which we believe may find additional applications in quantum algorithms. Joint work with Keith Lee and John Preskill.
Understanding quantum entanglement by thermo field dynamics
NASA Astrophysics Data System (ADS)
Hashizume, Yoichiro; Suzuki, Masuo
2013-09-01
We propose a new method to understand quantum entanglement using the thermo field dynamics (TFD) described by a double Hilbert space. The entanglement states show a quantum-mechanically complicated behavior. Our new method using TFD makes it easy to understand the entanglement states, because the states in the tilde space in TFD play a role of tracer of the initial states. For our new treatment, we define an extended density matrix on the double Hilbert space. From this study, we make a general formulation of this extended density matrix and examine some simple cases using this formulation. Consequently, we have found that we can distinguish intrinsic quantum entanglement from the thermal fluctuations included in the definition of the ordinary quantum entanglement at finite temperatures. Through the above examination, our method using TFD can be applied not only to equilibrium states but also to non-equilibrium states. This is shown using some simple finite systems in the present paper.
Finite-temperature Dynamics and Quantum Criticality in a Model for Insulating Magnets
NASA Astrophysics Data System (ADS)
Wu, Jianda; Yang, Wang; Wu, Congjun; Si, Qimiao
Theoretical understanding of the finite-temperature dynamics in quantum critical systems is a challenging problem, due to the mixing of thermal and quantum fluctuations. Recently, neutron scattering experiments in the three-dimensional quantum dimmer material TlCuCl3 under pressure tuning have mapped out the magnetic dynamics at finite temperatures in the quantum critical regime, thereby providing the opportunity for systematic understandings. In this work, we calculate the spin spectral function of an O (n) symmetric field theory using a field-theory procedure to two loops. We calculate the temperature dependence of the energy and damping rate of the spin excitations in the quantum critical regime, demonstrate a good agreement with the experimental results, and determine the parameter regime of the field theory that is appropriate for TlCuCl3. From our calculations we can also suggest further experimental means to test the applicability of the underlying field theory in this and related systems.
Observable measure of quantum coherence in finite dimensional systems.
Girolami, Davide
2014-10-24
Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology, and cryptography. Yet, there is no universally efficient method for quantifying coherence either in theoretical or in experimental practice. I introduce a framework for measuring quantum coherence in finite dimensional systems. I define a theoretical measure which satisfies the reliability criteria established in the context of quantum resource theories. Then, I present an experimental scheme implementable with current technology which evaluates the quantum coherence of an unknown state of a d-dimensional system by performing two programmable measurements on an ancillary qubit, in place of the O(d2) direct measurements required by full state reconstruction. The result yields a benchmark for monitoring quantum effects in complex systems, e.g., certifying nonclassicality in quantum protocols and probing the quantum behavior of biological complexes. PMID:25379903
Symmetry and Degeneracy in Quantum Mechanics. Self-Duality in Finite Spin Systems
ERIC Educational Resources Information Center
Osacar, C.; Pacheco, A. F.
2009-01-01
The symmetry of self-duality (Savit 1980 "Rev. Mod. Phys. 52" 453) of some models of statistical mechanics and quantum field theory is discussed for finite spin blocks of the Ising chain in a transverse magnetic field. The existence of this symmetry in a specific type of these blocks, and not in others, is manifest by the degeneracy of their…
Vector fields and Loop Quantum Cosmology
Artymowski, Michał; Lalak, Zygmunt E-mail: Zygmunt.Lalak@fuw.edu.pl
2011-09-01
In the context of the Loop Quantum Cosmology we have analysed the holonomy correction to the classical evolution of the simplified Bianchi I model in the presence of vector fields. For the Universe dominated by a massive vector field or by a combination of a scalar field and a vector field a smooth transition between Kasner-like and Kasner-unlike solutions for a Bianchi I model has been demonstrated. In this case a lack of initial curvature singularity and a finite maximal energy density appear already at the level of General Relativity, which simulates a classical Big Bounce.
Translation operator for finite dmensional electromagnetic fields
Howard, A.Q. Jr.
1981-04-01
Computation of electromagnetic fields in particular applications is usually accompanied by the adhoc assumption that the field contains a finite number of degrees of freedom. Herein, this assumption is made at the outset. It is shown that if an annular region between two closed surfaces contains no sources or sinks and is isotropic, lossless and homogeneous, a unique translation operator can be defined algebraically. Conservation of energy defines the translation operator T to within an arbitrary unitary transformation. The conditions of causality, unitarity and energy conservation are shown to uniquely determine T. Both scalar and vector fields are treated. In both of these cases, frequency and time domain transforms are computed. The transform T is compared with the analagous one as derived from the time domain Stratton-Chu Formulation. The application to a radiation condition boundary constraint on finite difference and finite element computations is discussed.
Super-renormalizable or finite Lee-Wick quantum gravity
NASA Astrophysics Data System (ADS)
Modesto, Leonardo
2016-08-01
We propose a class of multidimensional higher derivative theories of gravity without extra real degrees of freedom besides the graviton field. The propagator shows up the usual real graviton pole in k2 = 0 and extra complex conjugates poles that do not contribute to the absorptive part of the physical scattering amplitudes. Indeed, they may consistently be excluded from the asymptotic observable states of the theory making use of the Lee-Wick and Cutkosky, Landshoff, Olive and Polkinghorne prescription for the construction of a unitary S-matrix. Therefore, the spectrum consists of the graviton and short lived elementary unstable particles that we named "anti-gravitons" because of their repulsive contribution to the gravitational potential at short distance. However, another interpretation of the complex conjugate pairs is proposed based on the Calmet's suggestion, i.e. they could be understood as black hole precursors long established in the classical theory. Since the theory is CPT invariant, the conjugate complex of the micro black hole precursor can be interpreted as a white hole precursor consistently with the 't Hooft complementarity principle. It is proved that the quantum theory is super-renormalizable in even dimension, i.e. only a finite number of divergent diagrams survive, and finite in odd dimension. Furthermore, turning on a local potential of the Riemann tensor we can make the theory finite in any dimension. The singularity-free Newtonian gravitational potential is explicitly computed for a range of higher derivative theories. Finally, we propose a new super-renormalizable or finite Lee-Wick standard model of particle physics.
Variational Equation for Quantum Number Projection at Finite Temperature
NASA Astrophysics Data System (ADS)
Tanabe, Kosai; Nakada, Hitoshi
2008-04-01
To describe phase transitions in a finite system at finite temperature, we develop a formalism of the variation-after-projection (VAP) of quantum numbers based on the thermofield dynamics (TFD). We derive a new Bardeen-Cooper-Schrieffer (BCS)-type equation by variating the free energy with approximate entropy without violating Peierls inequality. The solution to the new BCS equation describes the S-shape in the specific heat curve and the superfluid-to-normal phase transition caused by the temperature effect. It simulates the exact quantum Monte Carlo results well.
Sudden change of geometric quantum discord in finite temperature reservoirs
Hu, Ming-Liang Sun, Jian
2015-03-15
We investigate sudden change (SC) behaviors of the distance-based measures of geometric quantum discords (GQDs) for two non-interacting qubits subject to the two-sided and the one-sided thermal reservoirs. We found that the GQDs defined by different distances exhibit different SCs, and thus the SCs are the combined result of the chosen discord measure and the property of a state. We also found that the thermal reservoir may generate states having different orderings related to different GQDs. These inherent differences of the GQDs reveal that they are incompatible in characterizing quantum correlations both quantitatively and qualitatively. - Highlights: • Comparable study of different distance-based geometric quantum discords. • Evolution of the geometric quantum discords in finite temperature reservoirs. • Different geometric quantum discords exhibit distinct sudden changes. • Nonunique states ordering imposed by different geometric quantum discords.
Studies in quantum field theory
NASA Astrophysics Data System (ADS)
Polmar, S. K.
The theoretical physics group at Washington University has been devoted to the solution of problems in theoretical and mathematical physics. All of the personnel on this task have a similar approach to their research in that they apply sophisticated analytical and numerical techniques to problems primarily in quantum field theory. Specifically, this group has worked on quantum chromodynamics, classical Yang-Mills fields, chiral symmetry breaking condensates, lattice field theory, strong-coupling approximations, perturbation theory in large order, nonlinear waves, 1/N expansions, quantum solitons, phase transitions, nuclear potentials, and early universe calculations.
Mathematics of Quantization and Quantum Fields
NASA Astrophysics Data System (ADS)
Dereziński, Jan; Gérard, Christian
2013-03-01
Preface; 1. Vector spaces; 2. Operators in Hilbert spaces; 3. Tensor algebras; 4. Analysis in L2(Rd); 5. Measures; 6. Algebras; 7. Anti-symmetric calculus; 8. Canonical commutation relations; 9. CCR on Fock spaces; 10. Symplectic invariance of CCR in finite dimensions; 11. Symplectic invariance of the CCR on Fock spaces; 12. Canonical anti-commutation relations; 13. CAR on Fock spaces; 14. Orthogonal invariance of CAR algebras; 15. Clifford relations; 16. Orthogonal invariance of the CAR on Fock spaces; 17. Quasi-free states; 18. Dynamics of quantum fields; 19. Quantum fields on space-time; 20. Diagrammatics; 21. Euclidean approach for bosons; 22. Interacting bosonic fields; Subject index; Symbols index.
Quantum spectral dimension in quantum field theory
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca; Modesto, Leonardo; Nardelli, Giuseppe
2016-03-01
We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where, instead of a transition amplitude, one has a probability density solving a nonrelativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higher-order and nonlocal dispersion relations in classical and quantum gravity; (c) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension dS of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension D. In particular, in the presence of higher momentum powers it changes with the scale, dropping from D in the infrared (IR) to a value dSUV ≤ D in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value dSUV = 2 for any dimension D.
Electric fields and quantum wormholes
NASA Astrophysics Data System (ADS)
Engelhardt, Dalit; Freivogel, Ben; Iqbal, Nabil
2015-09-01
Electric fields can thread a classical Einstein-Rosen bridge. Maldacena and Susskind have recently suggested that in a theory of dynamical gravity the entanglement of ordinary perturbative quanta should be viewed as creating a quantum version of an Einstein-Rosen bridge between the particles, or a "quantum wormhole." We demonstrate within low-energy effective field theory that there is a precise sense in which electric fields can also thread such quantum wormholes. We define a nonperturbative "wormhole susceptibility" that measures the ease of passing an electric field through any sort of wormhole. The susceptibility of a quantum wormhole is suppressed by powers of the U (1 ) gauge coupling relative to that for a classical wormhole but can be made numerically equal with a sufficiently large amount of entangled matter.
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…
Quantum mechanics in finite-dimensional Hilbert space
NASA Astrophysics Data System (ADS)
de la Torre, A. C.; Goyeneche, D.
2003-01-01
The quantum mechanical formalism for the position and momentum of a particle on a one-dimensional lattice is developed. Some mathematical features characteristic of finite-dimensional Hilbert spaces are compared with the infinite-dimensional case. The construction of an unbiased basis for state determination is discussed.
Finite field-energy and interparticle potential in logarithmic electrodynamics
NASA Astrophysics Data System (ADS)
Gaete, Patricio; Helayël-Neto, José
2014-03-01
We pursue an investigation of logarithmic electrodynamics, for which the field energy of a point-like charge is finite, as happens in the case of the usual Born-Infeld electrodynamics. We also show that, contrary to the latter, logarithmic electrodynamics exhibits the feature of birefringence. Next, we analyze the lowest-order modifications for both logarithmic electrodynamics and for its non-commutative version, within the framework of the gauge-invariant path-dependent variables formalism. The calculation shows a long-range correction (-type) to the Coulomb potential for logarithmic electrodynamics. Interestingly enough, for its non-commutative version, the interaction energy is ultraviolet finite. We highlight the role played by the new quantum of length in our analysis.
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J.; Lamata, L.; Egusquiza, I. L.; Gerritsma, R.; Roos, C. F.; Garcia-Ripoll, J. J.; Solano, E.
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Fractional quantum Hall effect in a tilted magnetic field
NASA Astrophysics Data System (ADS)
Papić, Z.
2013-06-01
We discuss the orbital effect of a tilted magnetic field on the quantum Hall effect in parabolic quantum wells. Many-body states realized at the fractional (1)/(3) and (1)/(2) filling of the second electronic subband are studied using finite-size exact diagonalization. In both cases, we obtain the phase diagram consisting of a fractional quantum Hall fluid phase that persists for moderate tilts, and eventually undergoes a direct transition to the stripe phase. It is shown that tilting of the field probes the geometrical degree of freedom of fractional quantum Hall fluids, and can be partly related to the effect of band-mass anisotropy.
Bounding the Set of Finite Dimensional Quantum Correlations.
Navascués, Miguel; Vértesi, Tamás
2015-07-10
We describe a simple method to derive high performance semidefinite programing relaxations for optimizations over complex and real operator algebras in finite dimensional Hilbert spaces. The method is very flexible, easy to program, and allows the user to assess the behavior of finite dimensional quantum systems in a number of interesting setups. We use this method to bound the strength of quantum nonlocality in Bell scenarios where the dimension of the parties is bounded from above. We derive new results in quantum communication complexity and prove the soundness of the prepare-and-measure dimension witnesses introduced in Gallego et al., Phys. Rev. Lett. 105, 230501 (2010). Finally, we propose a new dimension witness that can distinguish between classical, real, and complex two-level systems. PMID:26207454
Finite key analysis for symmetric attacks in quantum key distribution
Meyer, Tim; Kampermann, Hermann; Kleinmann, Matthias; Bruss, Dagmar
2006-10-15
We introduce a constructive method to calculate the achievable secret key rate for a generic class of quantum key distribution protocols, when only a finite number n of signals is given. Our approach is applicable to all scenarios in which the quantum state shared by Alice and Bob is known. In particular, we consider the six state protocol with symmetric eavesdropping attacks, and show that for a small number of signals, i.e., below n{approx}10{sup 4}, the finite key rate differs significantly from the asymptotic value for n{yields}{infinity}. However, for larger n, a good approximation of the asymptotic value is found. We also study secret key rates for protocols using higher-dimensional quantum systems.
Continuous wavelet transform in quantum field theory
NASA Astrophysics Data System (ADS)
Altaisky, M. V.; Kaputkina, N. E.
2013-07-01
We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar ϕ4 theory, quantum electrodynamics, and quantum chromodynamics. The method of continuous wavelet transform in quantum field theory, presented by Altaisky [Phys. Rev. D 81, 125003 (2010)] for the scalar ϕ4 theory, consists in substitution of the local fields ϕ(x) by those dependent on both the position x and the resolution a. The substitution of the action S[ϕ(x)] by the action S[ϕa(x)] makes the local theory into a nonlocal one and implies the causality conditions related to the scale a, the region causality [J. D. Christensen and L. Crane, J. Math. Phys. (N.Y.) 46, 122502 (2005)]. These conditions make the Green functions G(x1,a1,…,xn,an)=⟨ϕa1(x1)…ϕan(xn)⟩ finite for any given set of regions by means of an effective cutoff scale A=min(a1,…,an).
Quantum fields in curved spacetime
NASA Astrophysics Data System (ADS)
Hollands, Stefan; Wald, Robert M.
2015-04-01
We review the theory of quantum fields propagating in an arbitrary, classical, globally hyperbolic spacetime. Our review emphasizes the conceptual issues arising in the formulation of the theory and presents known results in a mathematically precise way. Particular attention is paid to the distributional nature of quantum fields, to their local and covariant character, and to microlocal spectrum conditions satisfied by physically reasonable states. We review the Unruh and Hawking effects for free fields, as well as the behavior of free fields in deSitter spacetime and FLRW spacetimes with an exponential phase of expansion. We review how nonlinear observables of a free field, such as the stress-energy tensor, are defined, as well as time-ordered-products. The "renormalization ambiguities" involved in the definition of time-ordered products are fully characterized. Interacting fields are then perturbatively constructed. Our main focus is on the theory of a scalar field, but a brief discussion of gauge fields is included. We conclude with a brief discussion of a possible approach towards a nonperturbative formulation of quantum field theory in curved spacetime and some remarks on the formulation of quantum gravity.
Quantum state discrimination bounds for finite sample size
Audenaert, Koenraad M. R.; Mosonyi, Milan; Verstraete, Frank
2012-12-15
In the problem of quantum state discrimination, one has to determine by measurements the state of a quantum system, based on the a priori side information that the true state is one of the two given and completely known states, {rho} or {sigma}. In general, it is not possible to decide the identity of the true state with certainty, and the optimal measurement strategy depends on whether the two possible errors (mistaking {rho} for {sigma}, or the other way around) are treated as of equal importance or not. Results on the quantum Chernoff and Hoeffding bounds and the quantum Stein's lemma show that, if several copies of the system are available then the optimal error probabilities decay exponentially in the number of copies, and the decay rate is given by a certain statistical distance between {rho} and {sigma} (the Chernoff distance, the Hoeffding distances, and the relative entropy, respectively). While these results provide a complete solution to the asymptotic problem, they are not completely satisfying from a practical point of view. Indeed, in realistic scenarios one has access only to finitely many copies of a system, and therefore it is desirable to have bounds on the error probabilities for finite sample size. In this paper we provide finite-size bounds on the so-called Stein errors, the Chernoff errors, the Hoeffding errors, and the mixed error probabilities related to the Chernoff and the Hoeffding errors.
(Studies in quantum field theory)
Not Available
1990-01-01
During the period 4/1/89--3/31/90 the theoretical physics group supported by Department of Energy Contract No. AC02-78ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity.
Exemplifying Quantum Systems in a Finite Element Basis
Young, Toby D.
2009-08-13
This paper presents a description of the abstractions required for the expression and solution of the linear single-particle Schroedinger equation in a finite element basis. This paper consists of two disparate themes: First, to layout and establish the foundations of finite element analysis as an approximate numerical solution to extendable quantum mechanical systems; and second, to promote a high-performance open-source computational model for the approximate numerical solution to quantum mechanical systems. The structural foundation of the one-and two-dimensional time-independent Schroedinger equation describing an infinite potential well is explored and a brief overview of the hierarchal design of the computational library written in C++ is given.
Realization schemes for quantum instruments in finite dimensions
Chiribella, Giulio; Perinotti, Paolo; D'Ariano, Giacomo Mauro
2009-04-15
We present a general dilation scheme for quantum instruments with continuous outcome space in finite dimensions, in terms of a measurement on a finite-dimensional ancilla, described by a positive operator valued measure (POVM). The general result is then applied to a large class of instruments generated by operator frames, which contains group-covariant instruments as a particular case and allows one to construct dilation schemes based on a measurement on the ancilla followed by a conditional feed-forward operation on the output. In the case of tight operator frames, our construction generalizes quantum teleportation and telecloning, producing a whole family of generalized teleportation schemes in which the instrument is realized via a joint POVM at the sender combined with a conditional feed-forward operation at the receiver.
Transitional steady states of exchange dynamics between finite quantum systems.
Jeon, Euijin; Yi, Juyeon; Kim, Yong Woon
2016-08-01
We examine energy and particle exchange between finite-sized quantum systems and find a new form of nonequilibrium state. The exchange rate undergoes stepwise evolution in time, and its magnitude and sign dramatically change according to system size differences. The origin lies in interference effects contributed by multiply scattered waves at system boundaries. Although such characteristics are utterly different from those of true steady state for infinite systems, Onsager's reciprocal relation remains universally valid. PMID:27627275
Finite-key security analysis for multilevel quantum key distribution
NASA Astrophysics Data System (ADS)
Brádler, Kamil; Mirhosseini, Mohammad; Fickler, Robert; Broadbent, Anne; Boyd, Robert
2016-07-01
We present a detailed security analysis of a d-dimensional quantum key distribution protocol based on two and three mutually unbiased bases (MUBs) both in an asymptotic and finite-key-length scenario. The finite secret key rates (in bits per detected photon) are calculated as a function of the length of the sifted key by (i) generalizing the uncertainly relation-based insight from BB84 to any d-level 2-MUB QKD protocol and (ii) by adopting recent advances in the second-order asymptotics for finite block length quantum coding (for both d-level 2- and 3-MUB QKD protocols). Since the finite and asymptotic secret key rates increase with d and the number of MUBs (together with the tolerable threshold) such QKD schemes could in principle offer an important advantage over BB84. We discuss the possibility of an experimental realization of the 3-MUB QKD protocol with the orbital angular momentum degrees of freedom of photons.
Finite-temperature scaling of quantum coherence near criticality in a spin chain
NASA Astrophysics Data System (ADS)
Cheng, Weiwen; Zhang, Zhijun; Gong, Longyan; Zhao, Shengmei
2016-06-01
We explore quantum coherence, inherited from Wigner-Yanase skew information, to analyze quantum criticality in the anisotropic XY chain model at finite temperature. Based on the exact solutions of the Hamiltonian, the quantum coherence contained in a nearest-neighbor spin pairs reduced density matrix ρ is obtained. The first-order derivative of the quantum coherence is non-analytic around the critical point at sufficient low temperature. The finite-temperature scaling behavior and the universality are verified numerically. In particular, the quantum coherence can also detect the factorization transition in such a model at sufficient low temperature. We also show that quantum coherence contained in distant spin pairs can characterize quantum criticality and factorization phenomena at finite temperature. Our results imply that quantum coherence can serve as an efficient indicator of quantum criticality in such a model and shed considerable light on the relationships between quantum phase transitions and quantum information theory at finite temperature.
Finiteness of entanglement entropy in a quantum black hole
NASA Astrophysics Data System (ADS)
Wen, Wen-Yu
2016-03-01
A logarithmic but divergent term usually appears in the computation of entanglement entropy circumferencing a black hole, while the leading quantum correction to the Bekenstein-Hawking entropy also takes the logarithmic form. A quench model of CFT within finite Euclidean time was proposed by Kuwakino and Wen (JHEP, 05 (2015) 099) to regard this logarithmic term as entanglement between radiation and the black hole, and this proposal was justified by the alternative sign for n-partite quantum information. However, this preliminary form suffers from the notorious divergence at its low-temperature limit. In this letter, we propose a modified form for black-hole entanglement entropy such that the divergence sickness can be cured. We discuss the final stage of a black hole due to this modification and its relation to the Rényi entropy, higher-loop quantum correction and higher-spin black holes.
Quantum entanglement of localized excited states at finite temperature
NASA Astrophysics Data System (ADS)
Caputa, Pawel; Simón, Joan; Štikonas, Andrius; Takayanagi, Tadashi
2015-01-01
In this work we study the time evolutions of (Renyi) entanglement entropy of locally excited states in two dimensional conformal field theories (CFTs) at finite temperature. We consider excited states created by acting with local operators on thermal states and give both field theoretic and holographic calculations. In free field CFTs, we find that the growth of Renyi entanglement entropy at finite temperature is reduced compared to the zero temperature result by a small quantity proportional to the width of the localized excitations. On the other hand, in finite temperature CFTs with classical gravity duals, we find that the entanglement entropy approaches a characteristic value at late time. This behaviour does not occur at zero temperature. We also study the mutual information between the two CFTs in the thermofield double (TFD) formulation and give physical interpretations of our results.
Properties of dipolar bosonic quantum gases at finite temperatures
NASA Astrophysics Data System (ADS)
Boudjemâa, Abdelâali
2016-07-01
The properties of ultracold quantum gases of bosons with dipole–dipole interaction are investigated at finite temperature in the frame of representative ensembles theory. Self-consistent coupled equations of motion are derived for the condensate and the non-condensate components. Corrections due to the dipolar interaction to condensate depletion, the anomalous density and thermodynamic quantities such as the ground state energy, the equation of state, the compressibility and the presure are calculated in the homogeneous case at both zero and finite temperatures. Effects of interaction and temperature on the structure factor are also discussed. Within the realm of the local density approximation, we generalize our results to the case of a trapped dipolar gas.
A finite Zitterbewegung model for relativistic quantum mechanics
Noyes, H.P.
1990-02-19
Starting from steps of length h/mc and time intervals h/mc{sup 2}, which imply a quasi-local Zitterbewegung with velocity steps {plus minus}c, we employ discrimination between bit-strings of finite length to construct a necessary 3+1 dimensional event-space for relativistic quantum mechanics. By using the combinatorial hierarchy to label the strings, we provide a successful start on constructing the coupling constants and mass ratios implied by the scheme. Agreement with experiments is surprisingly accurate. 22 refs., 1 fig.
Finite temperature static charge screening in quantum plasmas
NASA Astrophysics Data System (ADS)
Eliasson, B.; Akbari-Moghanjoughi, M.
2016-07-01
The shielding potential around a test charge is calculated, using the linearized quantum hydrodynamic formulation with the statistical pressure and Bohm potential derived from finite temperature kinetic theory, and the temperature effects on the force between ions is assessed. The derived screening potential covers the full range of electron degeneracy in the equation of state of the plasma electrons. An attractive force between shielded ions in an arbitrary degenerate plasma exists below a critical temperature and density. The effect of the temperature on the screening potential profile qualitatively describes the ion-ion bound interaction strength and length variations. This may be used to investigate physical properties of plasmas and in molecular-dynamics simulations of fermion plasma. It is further shown that the Bohm potential including the kinetic corrections has a profound effect on the Thomson scattering cross section in quantum plasmas with arbitrary degeneracy.
Towards quantum turbulence in finite temperature Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Lan, Shanquan; Tian, Yu; Zhang, Hongbao
2016-07-01
Motivated by the various indications that holographic superfluid is BCS like at the standard quantization but BEC like at the alternative quantization, we have implemented the alternative quantization in the dynamical holographic superfluid for the first time. With this accomplishment, we further initiate the detailed investigation of quantum turbulence in finite temperature BEC by a long time stable numerical simulation of bulk dynamics, which includes the two body decay of vortex number caused by vortex pair annihilation, the onset of superfluid turbulence signaled by Kolmogorov scaling law, and a direct energy cascade demonstrated by injecting energy to the turbulent superfluid. All of these results share the same patterns as the holographic superfluid at the standard quantization, thus suggest that these should be universal features for quantum turbulence at temperatures order of the critical temperature.
Quantum perceptron over a field and neural network architecture selection in a quantum computer.
da Silva, Adenilton José; Ludermir, Teresa Bernarda; de Oliveira, Wilson Rosa
2016-04-01
In this work, we propose a quantum neural network named quantum perceptron over a field (QPF). Quantum computers are not yet a reality and the models and algorithms proposed in this work cannot be simulated in actual (or classical) computers. QPF is a direct generalization of a classical perceptron and solves some drawbacks found in previous models of quantum perceptrons. We also present a learning algorithm named Superposition based Architecture Learning algorithm (SAL) that optimizes the neural network weights and architectures. SAL searches for the best architecture in a finite set of neural network architectures with linear time over the number of patterns in the training set. SAL is the first learning algorithm to determine neural network architectures in polynomial time. This speedup is obtained by the use of quantum parallelism and a non-linear quantum operator. PMID:26878722
Improved Algorithm For Finite-Field Normal-Basis Multipliers
NASA Technical Reports Server (NTRS)
Wang, C. C.
1989-01-01
Improved algorithm reduces complexity of calculations that must precede design of Massey-Omura finite-field normal-basis multipliers, used in error-correcting-code equipment and cryptographic devices. Algorithm represents an extension of development reported in "Algorithm To Design Finite-Field Normal-Basis Multipliers" (NPO-17109), NASA Tech Briefs, Vol. 12, No. 5, page 82.
Approximation to the quantum planar rotor coupled to a finite temperature bath
NASA Astrophysics Data System (ADS)
López Vázquez, P. C.; García, A.
2016-05-01
An approximation to the description of the dynamics of a quantum planar rotor coupled to a finite temperature bath is derived by considering a microscopic model of interaction based on an angular momentum exchange with two different environments coupled independently to the positive and negative angular momentum spectrum. A non-Lindblad master equation is derived for this microscopic model by using the Born–Markov approximation in the weak coupling limit. We show that under this approximation the rotor dynamics presents the correct damping behavior of the motion and the thermal state reached by the rotor is in the form of Boltzmann distribution. The case of the quantum rotor in an external uniform field and the quantum kicked rotor are briefly discussed as exemplification.
Twistor Diagrams and Quantum Field Theory.
NASA Astrophysics Data System (ADS)
O'Donald, Lewis
Available from UMI in association with The British Library. Requires signed TDF. This thesis uses twistor diagram theory, as developed by Penrose (1975) and Hodges (1990c), to try to approach some of the difficulties inherent in the standard quantum field theoretic description of particle interactions. The resolution of these issues is the eventual goal of the twistor diagram program. First twistor diagram theory is introduced from a physical view-point, with the aim of studying larger diagrams than have been typically explored. Methods are evolved to tackle the double box and triple box diagrams. These lead to three methods of constructing an amplitude for the double box, and two ways for the triple box. Next this theory is applied to translate the channels of a Yukawa Feynman diagram, which has more than four external states, into various twistor diagrams. This provides a test of the skeleton hypothesis (of Hodges, 1990c) in these cases, and also shows that conformal breaking must enter into twistor diagrams before the translation of loop level Feynman diagrams. The issue of divergent Feynman diagrams is then considered. By using a twistor equivalent of the sum-over -states idea of quantum field theory, twistor translations of loop diagrams are conjectured. The various massless propagator corrections and vacuum diagrams calculated give results consistent with Feynman theory. Two diagrams are also found that give agreement with the finite parts of the Feynman "fish" diagrams of phi^4 -theory. However it is found that a more rigorous translation for the time-like fish requires new boundaries to be added to the twistor sum-over-states. The twistor diagram obtained is found to give the finite part of the relevant Feynman diagram.
Externally controlled local magnetic field in a conducting mesoscopic ring coupled to a quantum wire
Maiti, Santanu K.
2015-01-14
In the present work, the possibility of regulating local magnetic field in a quantum ring is investigated theoretically. The ring is coupled to a quantum wire and subjected to an in-plane electric field. Under a finite bias voltage across the wire a net circulating current is established in the ring which produces a strong magnetic field at its centre. This magnetic field can be tuned externally in a wide range by regulating the in-plane electric field, and thus, our present system can be utilized to control magnetic field at a specific region. The feasibility of this quantum system in designing spin-based quantum devices is also analyzed.
Decoherence in an interacting quantum field theory: Thermal case
Koksma, Jurjen F.; Prokopec, Tomislav; Schmidt, Michael G.
2011-04-15
We study the decoherence of a renormalized quantum field theoretical system. We consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. Using out-of-equilibrium field theory techniques at finite temperatures, we show that the Gaussian von Neumann entropy for a pure quantum state asymptotes to the interacting thermal entropy. The decoherence rate can be well described by the single particle decay rate in our model. Connecting to electroweak baryogenesis scenarios, we moreover study the effects on the entropy of a changing mass of the system field. Finally, we compare our correlator approach to existing approaches to decoherence in the simple quantum mechanical analogue of our field theoretical model. The entropy following from the perturbative master equation suffers from physically unacceptable secular growth.
Quantum dynamics at finite temperature: Time-dependent quantum Monte Carlo study
NASA Astrophysics Data System (ADS)
Christov, Ivan P.
2016-08-01
In this work we investigate the ground state and the dissipative quantum dynamics of interacting charged particles in an external potential at finite temperature. The recently devised time-dependent quantum Monte Carlo (TDQMC) method allows a self-consistent treatment of the system of particles together with bath oscillators first for imaginary-time propagation of Schrödinger type of equations where both the system and the bath converge to their finite temperature ground state, and next for real time calculation where the dissipative dynamics is demonstrated. In that context the application of TDQMC appears as promising alternative to the path-integral related techniques where the real time propagation can be a challenge.
Measuring finite quantum geometries via quasi-coherent states
NASA Astrophysics Data System (ADS)
Schneiderbauer, Lukas; Steinacker, Harold C.
2016-07-01
We develop a systematic approach to determine and measure numerically the geometry of generic quantum or ‘fuzzy’ geometries realized by a set of finite-dimensional Hermitian matrices. The method is designed to recover the semi-classical limit of quantized symplectic spaces embedded in {{{R}}}d including the well-known examples of fuzzy spaces, but it applies much more generally. The central tool is provided by quasi-coherent states, which are defined as ground states of Laplace- or Dirac operators corresponding to localized point branes in target space. The displacement energy of these quasi-coherent states is used to extract the local dimension and tangent space of the semi-classical geometry, and provides a measure for the quality and self-consistency of the semi-classical approximation. The method is discussed and tested with various examples, and implemented in an open-source Mathematica package.
Modern Quantum Field Theory II - Proceeeings of the International Colloquium
NASA Astrophysics Data System (ADS)
Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.
1995-08-01
* Finite Quantum Physics and Noncommutative Geometry * Higgs as Gauge Field and the Standard Model * Canonical Quantisation of an Off-Conformal Theory * Deterministic Quantum Mechanics in One Dimension * Spin-Statistics Relations for Topological Geons in 2+1 Quantum Gravity * Generalized Fock Spaces * Geometrical Expression for Short Distance Singularities in Field Theory * 5. Mathematics and Quantum Field Theory * Knot Invariants from Quantum Field Theories * Infinite Grassmannians and Moduli Spaces of G-Bundles * A Review of an Algebraic Geometry Approach to a Model Quantum Field Theory on a Curve (Abstract) * 6. Integrable Models * Spectral Representation of Correlation Functions in Two-Dimensional Quantum Field Theories * On Various Avatars of the Pasquier Algebra * Supersymmetric Integrable Field Theories and Eight Vertex Free Fermion Models (Abstract) * 7. Lattice Field Theory * From Kondo Model and Strong Coupling Lattice QCD to the Isgur-Wise Function * Effective Confinement from a Logarithmically Running Coupling (Abstract)
Quantum fields in toroidal topology
Khanna, F.C.; Malbouisson, A.P.C.; Santana, A.E.
2011-10-15
The standard representation of c*-algebra is used to describe fields in compactified space-time dimensions characterized by topologies of the type {Gamma}{sub D}{sup d}=(S{sup 1}){sup d}xM{sup D-d}. The modular operator is generalized to introduce representations of isometry groups. The Poincare symmetry is analyzed and then we construct the modular representation by using linear transformations in the field modes, similar to the Bogoliubov transformation. This provides a mechanism for compactification of the Minkowski space-time, which follows as a generalization of the Fourier integral representation of the propagator at finite temperature. An important result is that the 2x2 representation of the real-time formalism is not needed. The end result on calculating observables is described as a condensate in the ground state. We initially analyze the free Klein-Gordon and Dirac fields, and then formulate non-abelian gauge theories in {Gamma}{sub D}{sup d}. Using the S-matrix, the decay of particles is calculated in order to show the effect of the compactification. - Highlights: > C*-algebra is used to describe fields in compactified space-time dimensions. > The space-time is characterized by toroidal topologies. > Representations of the Poincare group are studied by using the modular operator. > We derive non-abelian gauge theories in compactified regions of space-time. > We show the compactification effect in the decay of particles using the S-matrix.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Sifting attacks in finite-size quantum key distribution
NASA Astrophysics Data System (ADS)
Pfister, Corsin; Lütkenhaus, Norbert; Wehner, Stephanie; Coles, Patrick J.
2016-05-01
A central assumption in quantum key distribution (QKD) is that Eve has no knowledge about which rounds will be used for parameter estimation or key distillation. Here we show that this assumption is violated for iterative sifting, a sifting procedure that has been employed in some (but not all) of the recently suggested QKD protocols in order to increase their efficiency. We show that iterative sifting leads to two security issues: (1) some rounds are more likely to be key rounds than others, (2) the public communication of past measurement choices changes this bias round by round. We analyze these two previously unnoticed problems, present eavesdropping strategies that exploit them, and find that the two problems are independent. We discuss some sifting protocols in the literature that are immune to these problems. While some of these would be inefficient replacements for iterative sifting, we find that the sifting subroutine of an asymptotically secure protocol suggested by Lo et al (2005 J. Cryptol. 18 133–65), which we call LCA sifting, has an efficiency on par with that of iterative sifting. One of our main results is to show that LCA sifting can be adapted to achieve secure sifting in the finite-key regime. More precisely, we combine LCA sifting with a certain parameter estimation protocol, and we prove the finite-key security of this combination. Hence we propose that LCA sifting should replace iterative sifting in future QKD implementations. More generally, we present two formal criteria for a sifting protocol that guarantee its finite-key security. Our criteria may guide the design of future protocols and inspire a more rigorous QKD analysis, which has neglected sifting-related attacks so far.
Lorentz symmetry breaking as a quantum field theory regulator
Visser, Matt
2009-07-15
Perturbative expansions of quantum field theories typically lead to ultraviolet (short-distance) divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. I shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory and discuss its implications. In particular, I shall quantify just 'how much' Lorentz symmetry breaking is required to fully regulate the quantum theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Horava's recent article [Phys. Rev. D 79, 084008 (2009)] on 3+1 dimensional quantum gravity.
Lorentz symmetry breaking as a quantum field theory regulator
NASA Astrophysics Data System (ADS)
Visser, Matt
2009-07-01
Perturbative expansions of quantum field theories typically lead to ultraviolet (short-distance) divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. I shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory and discuss its implications. In particular, I shall quantify just “how much” Lorentz symmetry breaking is required to fully regulate the quantum theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Hořava’s recent article [Phys. Rev. DPRVDAQ1550-7998 79, 084008 (2009)10.1103/PhysRevD.79.084008] on 3+1 dimensional quantum gravity.
Quantum de Finetti theorems and mean-field theory from quantum phase space representations
NASA Astrophysics Data System (ADS)
Trimborn, F.; Werner, R. F.; Witthaut, D.
2016-04-01
We introduce the number-conserving quantum phase space description as a versatile tool to address fundamental aspects of quantum many-body systems. Using phase space methods we prove two alternative versions of the quantum de Finetti theorem for finite-dimensional bosonic quantum systems, which states that a reduced density matrix of a many-body quantum state can be approximated by a convex combination of product states where the error is proportional to the inverse particle number. This theorem provides a formal justification for the mean-field description of many-body quantum systems, as it shows that quantum correlations can be neglected for the calculation of few-body observables when the particle number is large. Furthermore we discuss methods to derive the exact evolution equations for quantum phase space distribution functions as well as upper and lower bounds for the ground state energy. As an important example, we consider the Bose-Hubbard model and show that the mean-field dynamics is given by a classical phase space flow equivalent to the discrete Gross-Pitaevskii equation.
A VLSI single chip 8-bit finite field multiplier
NASA Technical Reports Server (NTRS)
Deutsch, L. J.; Shao, H. M.; Hsu, I. S.; Truong, T. K.
1985-01-01
A Very Large Scale Integration (VLSI) architecture and layout for an 8-bit finite field multiplier is described. The algorithm used in this design was developed by Massey and Omura. A normal basis representation of finite field elements is used to reduce the multiplication complexity. It is shown that a drastic improvement was achieved in this design. This multiplier will be used intensively in the implementation of an 8-bit Reed-Solomon decoder and in many other related projects.
Quantum field theory in spaces with closed timelike curves
NASA Astrophysics Data System (ADS)
Boulware, David G.
1992-11-01
Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Extension of Nelson's stochastic quantization to finite temperature using thermo field dynamics
NASA Astrophysics Data System (ADS)
Kobayashi, K.; Yamanaka, Y.
2011-08-01
We present an extension of Nelson's stochastic quantum mechanics to finite temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can show that Ito's stochastic equations for tilde and non-tilde particle positions reproduce the TFD-type Schrödinger equation which is equivalent to the Liouville-von Neumann equation. In our formalism, the drift terms in the Ito's stochastic equation have the temperature dependence and the thermal fluctuation is induced through the correlation of the non-tilde and tilde particles. We show that our formalism satisfies the position-momentum uncertainty relation at finite temperature.
Finite-size version of the excitonic instability in graphene quantum dots
Paananen, Tomi; Egger, Reinhold
2011-10-15
By a combination of Hartree-Fock simulations, exact diagonalization, and perturbative calculations, we investigate the ground-state properties of disorder-free circular quantum dots formed in a graphene monolayer. Taking the reference chemical potential at the Dirac point, we study N{<=}15 interacting particles, where the fine structure constant {alpha} parametrizes the Coulomb interaction. We explore three different models: (i) Sucher's positive projection (''no-pair'') approach, (ii) a more general Hamiltonian conserving both N and the number of additional electron-hole pairs, and (iii) the full quantum electrodynamics problem, where only N is conserved. We find that electron-hole pair production is important for {alpha} > or approx. 1. This corresponds to a reconstruction of the filled Dirac sea and is a finite-size version of the bulk excitonic instability. We also address the effects of an orbital magnetic field.
Holographic geometry of cMERA for quantum quenches and finite temperature
NASA Astrophysics Data System (ADS)
Mollabashi, Ali; Naozaki, Masahiro; Ryu, Shinsei; Takayanagi, Tadashi
2014-03-01
We study the time evolution of cMERA (continuous MERA) under quantum quenches in free field theories. We calculate the corresponding holographic metric using the proposal in arXiv:1208.3469 and confirm that it qualitatively agrees with its gravity dual given by a half of the AdS black hole spacetime, argued by Hartman and Maldacena in arXiv:1303.1080. By doubling the cMERA for the quantum quench, we give an explicit construction of finite temperature cMERA. We also study cMERA in the presence of chemical potential and show that there is an enhancement of metric in the infrared region corresponding to the Fermi energy.
Continuous Time Finite State Mean Field Games
Gomes, Diogo A.; Mohr, Joana Souza, Rafael Rigao
2013-08-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N{yields}{infinity} of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.
Wouters, Sebastian; Limacher, Peter A; Van Neck, Dimitri; Ayers, Paul W
2012-04-01
We have implemented the sweep algorithm for the variational optimization of SU(2) U(1) (spin and particle number) invariant matrix product states (MPS) for general spin and particle number invariant fermionic Hamiltonians. This class includes non-relativistic quantum chemical systems within the Born-Oppenheimer approximation. High-accuracy ab initio finite field results of the longitudinal static polarizabilities and second hyperpolarizabilities of one-dimensional hydrogen chains are presented. This allows to assess the performance of other quantum chemical methods. For small basis sets, MPS calculations in the saturation regime of the optical response properties can be performed. These results are extrapolated to the thermodynamic limit. PMID:22482543
A generalized algorithm to design finite field normal basis multipliers
NASA Technical Reports Server (NTRS)
Wang, C. C.
1986-01-01
Finite field arithmetic logic is central in the implementation of some error-correcting coders and some cryptographic devices. There is a need for good multiplication algorithms which can be easily realized. Massey and Omura recently developed a new multiplication algorithm for finite fields based on a normal basis representation. Using the normal basis representation, the design of the finite field multiplier is simple and regular. The fundamental design of the Massey-Omura multiplier is based on a design of a product function. In this article, a generalized algorithm to locate a normal basis in a field is first presented. Using this normal basis, an algorithm to construct the product function is then developed. This design does not depend on particular characteristics of the generator polynomial of the field.
Quantum decomposition of random walk on Cayley graph of finite group
NASA Astrophysics Data System (ADS)
Kang, Yuanbao
2016-09-01
In the paper, A quantum decomposition (QD, for short) of random walk on Cayley graph of finite group is introduced, which contains two cases. One is QD of quantum random walk operator (QRWO, for short), another is QD of Quantum random walk state (QRWS, for short). Using these findings, I finally obtain some applications for quantum random walk (QRW, for short), which are of interest in the study of QRW, highlighting the role played by QRWO and QRWS.
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; Weedbrook, Christian
2015-12-14
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; Weedbrook, Christian
2015-12-14
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonicmore » quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.« less
Collective field theory for quantum Hall states
NASA Astrophysics Data System (ADS)
Laskin, M.; Can, T.; Wiegmann, P.
2015-12-01
We develop a collective field theory for fractional quantum Hall (FQH) states. We show that in the leading approximation for a large number of particles, the properties of Laughlin states are captured by a Gaussian free field theory with a background charge. Gradient corrections to the Gaussian field theory arise from the covariant ultraviolet regularization of the theory, which produces the gravitational anomaly. These corrections are described by a theory closely related to the Liouville theory of quantum gravity. The field theory simplifies the computation of correlation functions in FQH states and makes manifest the effect of quantum anomalies.
Entanglement Entropy in Quantum Spin Chains with Finite Range Interaction
NASA Astrophysics Data System (ADS)
Its, A. R.; Mezzadri, F.; Mo, M. Y.
2008-11-01
We study the entropy of entanglement of the ground state in a wide family of one-dimensional quantum spin chains whose interaction is of finite range and translation invariant. Such systems can be thought of as generalizations of the XY model. The chain is divided in two parts: one containing the first consecutive L spins; the second the remaining ones. In this setting the entropy of entanglement is the von Neumann entropy of either part. At the core of our computation is the explicit evaluation of the leading order term as L → ∞ of the determinant of a block-Toeplitz matrix with symbol Φ(z) = left(begin{array}{cc} iλ & g(z) \\ g^{-1}(z) & i λ right), where g( z) is the square root of a rational function and g(1/ z) = g -1( z). The asymptotics of such determinant is computed in terms of multi-dimensional theta-functions associated to a hyperelliptic curve {mathcal{L}} of genus g ≥ 1, which enter into the solution of a Riemann-Hilbert problem. Phase transitions for these systems are characterized by the branch points of {mathcal{L}} approaching the unit circle. In these circumstances the entropy diverges logarithmically. We also recover, as particular cases, the formulae for the entropy discovered by Jin and Korepin [14] for the XX model and Its, Jin and Korepin [12, 13] for the XY model.
Dynamical renormalization group approach to relaxation in quantum field theory
NASA Astrophysics Data System (ADS)
Boyanovsky, D.; de Vega, H. J.
2003-10-01
The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that goes beyond the scope of Bloch-Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths.
NASA Astrophysics Data System (ADS)
Wu, Jianda; Kormos, Marton; Si, Qimiao
2013-03-01
When the transverse field Ising chain at its quantum critical point is subjected to a small longitudinal field, the perturbed conformal field theory led to a field theory with an exotic E8 symmetry. Recent neutron scattering experiments have provided evidence for the lightest two particles in this E8 model in the quasi-1D Ising ferromagnet CoNb2O6. While the zero temperature dynamics of the model is well known, its finite-temperature counterpart has not yet been systematically studied. We study the low-frequency dynamical structure factor at finite temperatures using the form-factor method. We show that the dominant contribution to the dynamical structure factor comes from the scattering between two lightest particles, and discuss the implications of our results for the NMR relaxation rate.
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).
A cascadic monotonic time-discretized algorithm for finite-level quantum control computation
NASA Astrophysics Data System (ADS)
Ditz, P.; Borzi`, A.
2008-03-01
A computer package (CNMS) is presented aimed at the solution of finite-level quantum optimal control problems. This package is based on a recently developed computational strategy known as monotonic schemes. Quantum optimal control problems arise in particular in quantum optics where the optimization of a control representing laser pulses is required. The purpose of the external control field is to channel the system's wavefunction between given states in its most efficient way. Physically motivated constraints, such as limited laser resources, are accommodated through appropriately chosen cost functionals. Program summaryProgram title: CNMS Catalogue identifier: ADEB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADEB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 770 No. of bytes in distributed program, including test data, etc.: 7098 Distribution format: tar.gz Programming language: MATLAB 6 Computer: AMD Athlon 64 × 2 Dual, 2:21 GHz, 1:5 GB RAM Operating system: Microsoft Windows XP Word size: 32 Classification: 4.9 Nature of problem: Quantum control Solution method: Iterative Running time: 60-600 sec
Quantum field perturbation theory revisited
NASA Astrophysics Data System (ADS)
Matone, Marco
2016-03-01
Schwinger's formalism in quantum field theory can be easily implemented in the case of scalar theories in D dimension with exponential interactions, such as μDexp (α ϕ ). In particular, we use the relation exp (α δ/δ J (x ) )exp (-Z0[J ])=exp (-Z0[J +αx]) with J the external source, and αx(y )=α δ (y -x ). Such a shift is strictly related to the normal ordering of exp (α ϕ ) and to a scaling relation which follows by renormalizing μ . Next, we derive a new formulation of perturbation theory for the potentials V (ϕ )=λ/n ! :ϕn: , using the generating functional associated to :exp (α ϕ ):. The Δ (0 )-terms related to the normal ordering are absorbed at once. The functional derivatives with respect to J to compute the generating functional are replaced by ordinary derivatives with respect to auxiliary parameters. We focus on scalar theories, but the method is general and similar investigations extend to other theories.
Quantum enhanced estimation of a multi-dimensional field
NASA Astrophysics Data System (ADS)
Datta, Animesh; Baumgratz, Tillmann
We present a framework for the quantum-enhanced estimation of multiple parameters corresponding to non-commuting unitary generators. We derive the quantum Fisher information matrix to put a lower bound on the total variance of all the parameters involved. We present the conditions for the attainment of the multi-parameter bound, which is not guaranteed unlike the quantum metrology of single parameters. Our study also reveals that too much quantum entanglement may be detrimental to attaining the Heisenberg scaling in the estimation of unitarily generated parameters. One particular case of our framework is the simultaneous estimation of all three components of a magnetic field. We propose a probe state that demonstrates that the simultaneous estimation of the three components is better than the precision of estimating the three components individually. We provide realistic measurements that come close to attaining the quantum limit, exhibiting the advantage of simultaneous quantum estimation even in the case of non-commuting generators. Our work applies to precision estimation any Hamiltonian, and may be employed in efficient process tomography and verification. Our theoretical proposal can be implement in any finite dimensional quantum system such as trapped ions and nitrogen vacancy centres in diamond. Acknowledgement: UK EPSRC.
Continuum regularization of quantum field theory
Bern, Z.
1986-04-01
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
Quantum fields out of thermal equilibrium
Eboli, O.; Jackiw, R.; Pi, S.
1988-06-15
The isoentropic, but energy-nonconserving, time evolution of mixed quantum states is studied in quantum mechanics and quantum field theory. A variational principle, which gives the Liouville--von Neumann equation, is implemented approximately by making a Gaussian Ansatz for the density matrix. The dynamical equations governing the parameters that define the Ansatz satisfy equations variously analogous to the Schroedinger equation and to mechanical problems. Interesting nonequilibrium evolution is found in special cases, as, for example, when the analog Schroedinger equation gives rise to reflectionless transmission. For field theory in an external, time-dependent metric we obtain equations that were previously derived in the many-field (spherical-model) limit.
Quantum simulation of quantum field theory using continuous variables
NASA Astrophysics Data System (ADS)
Marshall, Kevin; Pooser, Raphael; Siopsis, George; Weedbrook, Christian
2015-12-01
The year 1982 is often credited as the year that theoretical quantum computing was started with a keynote speech by Richard Feynman, who proposed a universal quantum simulator, the idea being that if you had such a machine you could in principle "imitate any quantum system, including the physical world." With that in mind, we present an algorithm for a continuous-variable quantum computing architecture which gives an exponential speedup over the best-known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is believed to be hard using a classical computer. Building on this, we give an experimental implementation based on continuous-variable states that is feasible with today's technology.
Finite temperature quantum critical transport near the Mott transition
NASA Astrophysics Data System (ADS)
Terletska, Hanna; Dobrosavljevic, Vladimir
2010-03-01
We use Dynamical Mean-Field Theory to study incoherent transport above the critical end-point temperature Tc of the single band Hubbard model at half-filling. By employing an eigenvalue analysis for the free energy functional, we are able to precisely identify the crossover temperature T*(U) separating the Fermi liquid and the Mott insulating regimes. Our calculations demonstrate that a broad parameter range exist around the crossover line, where the family of resistivity curves displays simple scaling behavior. This is interpreted as a manifestation of quantum criticality controlled by the T=0 Mott transition, which is ``interrupted'' by the emergence of the coexistence dome at T < Tc . We argue that in situations where the critical temperature Tc is significantly reduced, so that the coexistence region is reduced or even absent (as in two-band, particle-hole asymmetric models, where this is found even in the clean d->∞ limit [1, 2]), similar critical scaling properties should persist down to much lower temperatures, resembling quantum critical transport similar to that found in a number of experiments [2]. [1] A. Amaricci, G. Sordi, and M. J. Rosenberg, Phys. Rev. Lett. 101, 146403 (2008) [2] A. Camjayi, K. Haule, V. Dobrosavljevic, and G. Kotliar, Nature Physics, 4, 932 (2008)
Quantum entanglement of local operators in conformal field theories.
Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
2014-03-21
We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles. PMID:24702348
Miller, D.; Milton, K.A.; Siegemund-Broka, S. )
1992-07-15
This is the first in a series of papers dealing with four-dimensional quantum electrodynamics on a finite-element lattice. We begin by studying the canonical structure of the theory without interactions. This tells us how to construct momentum expansions for the field operators. Next we examine the interaction term in the Dirac equation. We construct the transfer matrix explicitly in the temporal gauge, and show that it is unitary. Therefore, fermion canonical anticommutation relations hold at each lattice site. Finally, we expand the interaction term to second order in the temporal-lattice spacing and deduce the magnetic moment of the electron in a background field, consistent with the continuum value of {ital g}=2.
Fields and Laplacians on Quantum Geometries
NASA Astrophysics Data System (ADS)
Thürigen, Johannes
2015-01-01
In fundamentally discrete approaches to quantum gravity such as loop quantum gravity, spin-foam models, group field theories or Regge calculus observables are functions on discrete geometries. We present a bra-ket formalism of function spaces and discrete calculus on abstract simplicial complexes equipped with geometry and apply it to the mentioned theories of quantum gravity. In particular we focus on the quantum geometric Laplacian and discuss as an example the expectation value of the heat kernel trace from which the spectral dimension follows.
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.
Relativistic Quantum Mechanics and Field Theory
NASA Astrophysics Data System (ADS)
Gross, Franz
1999-04-01
An accessible, comprehensive reference to modern quantum mechanics and field theory. In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics. Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field. With a strong emphasis on applications to practical problems as well as calculations, Dr. Gross provides complete, up-to-date coverage of both elementary and advanced topics essential for a well-rounded understanding of the field. Developing the material at a level accessible even to newcomers to quantum mechanics, the book begins with topics that every physicist should know-quantization of the electromagnetic field, relativistic one body wave equations, and the theoretical explanation of atomic decay. Subsequent chapters prepare readers for advanced work, covering such major topics as gauge theories, path integral techniques, spontaneous symmetry breaking, and an introduction to QCD, chiral symmetry, and the Standard Model. A special chapter is devoted to relativistic bound state wave equations-an important topic that is often overlooked in other books. Clear and concise throughout, Relativistic Quantum Mechanics and Field Theory boasts examples from atomic and nuclear physics as well as particle physics, and includes appendices with background material. It is an essential reference for anyone working in quantum mechanics today.
Ultrafast dynamics of finite Hubbard clusters: A stochastic mean-field approach
NASA Astrophysics Data System (ADS)
Lacroix, Denis; Hermanns, S.; Hinz, C. M.; Bonitz, M.
2014-09-01
Finite lattice models are a prototype for interacting quantum systems and capture essential properties of condensed matter systems. With the dramatic progress in ultracold atoms in optical lattices, finite fermionic Hubbard systems have become directly accessible in experiments, including their ultrafast dynamics far from equilibrium. Here, we present a theoretical approach that is able to treat these dynamics in any dimension and fully includes inhomogeneity effects. The method consists in stochastic sampling of mean-field trajectories and is—for not too large two-body interaction strength—found to be much more accurate than time-dependent mean-field at the same order of numerical costs. Furthermore, it can well compete with recent nonequilibrium Green function approaches using second-order Born approximation, which are of substantially larger complexity. The performance of the stochastic mean-field approach is demonstrated for Hubbard clusters with up to 512 particles in one, two, and three dimensions.
NASA Astrophysics Data System (ADS)
Wang, Tianyi; Yu, Song; Gu, Wanyi
2016-03-01
In continuous-variable quantum key distribution, detectors are necessarily coarse grained and of finite range. We analyze the impact of both features and demonstrate that while coarse graining adds a fixed error to the estimated excess noise, finite range degrades the estimation accuracy of both transmission and excess noise. Moreover, the inaccurate estimation due to finite range may results in secret key rate underestimation, even misjudgment of security. To compensate these consequences, tuning the modulation variance is a possible way.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
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.
Spin-polarized electron-hole quantum bilayers: finite layer width and mass-asymmetric effects
NASA Astrophysics Data System (ADS)
Gangadhar Nayak, Mukesh; Saini, Lalit Kumar
2013-03-01
The influence of mass-asymmetry and finite layer width in phase-transition from the liquid-state to the density-modulated ground-state of the spin-polarized electron-hole quantum bilayers (EHBL) is explored within the Singwi, Tosi, Land and Sjölander (qSTLS) approach. At the same number density of electrons and holes, in addition to the stronger interlayer correlations, the mass-asymmetry also shows stronger intralayer correlations in the hole layer than that of the electron layer. This change in the behaviour of correlations affects the ground-state of the spin-polarized EHBL system. Interestingly, we notice the enhancement of critical density for the onset of Wigner crystallization as compared to the recent results of spin-polarized mass-symmetric EHBL system. Pair-correlation function and local-field correction factor show a strong in-phase oscillations at the instability region. Further, we find that the inclusion of finite layer width weakens the intralayer correlations. As a result, the critical density for Wigner crystallization is lowered. The present results are compared with the recent results of spin-polarized (and unpolarized) mass-symmetric EHBL with zero (finite) layer width. Contribution to the Topical Issue "Excitonic Processes in Condensed Matter, Nanostructured and Molecular Materials", edited by Maria Antonietta Loi, Jasper Knoester and Paul H. M. van Loosdrecht.
Tomograms for open quantum systems: In(finite) dimensional optical and spin systems
NASA Astrophysics Data System (ADS)
Thapliyal, Kishore; Banerjee, Subhashish; Pathak, Anirban
2016-03-01
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In realistic experimental conditions, quantum states are exposed to the ambient environment and hence subject to effects like decoherence and dissipation, which are dealt with here, consistently, using the formalism of open quantum systems. This is extremely relevant from the perspective of experimental implementation and issues related to state reconstruction in quantum computation and communication. These considerations are also expected to affect the quasiprobability distribution obtained from experimentally generated tomograms and nonclassicality observed from them.
Mean-field analysis of quantum annealing with XX-type terms
NASA Astrophysics Data System (ADS)
Nishimori, Hidetoshi
I analyze the role of XX-type terms in quantum annealing for a few mean-field systems including the Ising ferromagnet and the Hopfield model, both with many-body interactions. The XX-type terms are shown to be effective to remove first-order quantum phase transitions, which exist in the conventional implementation of quantum annealing using only transverse fields. This means an exponential increase in efficiency, and is suggestive for the design of quantum annealers. I will discuss how and why this phenomenon emerges and what may happen on realistic finite-dimensional lattices.
Systematic study of finite-size effects in quantum Monte Carlo calculations of real metallic systems
Azadi, Sam Foulkes, W. M. C.
2015-09-14
We present a systematic and comprehensive study of finite-size effects in diffusion quantum Monte Carlo calculations of metals. Several previously introduced schemes for correcting finite-size errors are compared for accuracy and efficiency, and practical improvements are introduced. In particular, we test a simple but efficient method of finite-size correction based on an accurate combination of twist averaging and density functional theory. Our diffusion quantum Monte Carlo results for lithium and aluminum, as examples of metallic systems, demonstrate excellent agreement between all of the approaches considered.
Finiteness of the vacuum energy density in quantum electrodynamics
NASA Astrophysics Data System (ADS)
Manoukian, Edward B.
1983-03-01
Recent interest in the finiteness problem of the vacuum energy density (VED) in finite QED has motivated us to reexamine this problem in the light of an analysis we have carried out earlier. By a loopwise summation procedure, supplemented by a renormalization-group analysis, we study the finiteness of the VED with α, the renormalized fine-structure constant, fixed in the process as the (infinite order) zero of the eigenvalue condition F[1](x)|x=α=0∞, and with the electron mass totally dynamical of origin. We propose a possible finite solution for the VED in QED which may require only one additional eigenvalue condition for α.
Quantum jump model for a system with a finite-size environment
NASA Astrophysics Data System (ADS)
Suomela, S.; Kutvonen, A.; Ala-Nissila, T.
2016-06-01
Measuring the thermodynamic properties of open quantum systems poses a major challenge. A calorimetric detection has been proposed as a feasible experimental scheme to measure work and fluctuation relations in open quantum systems. However, the detection requires a finite size for the environment, which influences the system dynamics. This process cannot be modeled with the standard stochastic approaches. We develop a quantum jump model suitable for systems coupled to a finite-size environment. We use the method to study the common fluctuation relations and prove that they are satisfied.
Interacting quantum fields and the chronometric principle
Segal, I. E.
1976-01-01
A form of interaction in quantum field theory is described that is physically intrinsic rather than superimposed via a postulated nonlinearity on a hypothetical free field. It derives from the extension to general symmetries of the distinction basic for the chronometric cosmology between the physical (driving) and the observed energies, together with general precepts of quantum field theory applicable to nonunitary representations. The resulting interacting field is covariant, causal, involves real particle production, and is devoid of nontrivial ultraviolet divergences. Possible physical applications are discussed. PMID:16592353
Consensus networks with time-delays over finite fields
NASA Astrophysics Data System (ADS)
Li, Xiuxian; Su, Housheng; Chen, Michael Z. Q.
2016-05-01
In this paper, we investigate the consensus problem in networks with time-delays over finite fields. The delays are categorised into three cases: single constant delay, multiple constant delays, and time-varying bounded delays. For all cases, some sufficient and necessary conditions for consensus are derived. Furthermore, assuming that the communication graph is strongly connected, some of the obtained necessary conditions reveal that the conditions for consensus with time-delays over finite fields depend not only on the diagonal entries but also on the off-diagonal entries, something that is intrinsically distinct from the case over real numbers (where having at least one nonzero diagonal entry is a sufficient and necessary condition to guarantee consensus). In addition, it is shown that delayed networks cannot achieve consensus when the interaction graph is a tree if the corresponding delay-free networks cannot reach consensus, which is consistent with the result over real numbers. As for average consensus, we show that it can never be achieved for delayed networks over finite fields, although it indeed can be reached under several conditions for delay-free networks over finite fields. Finally, networks with time-varying delays are discussed and one sufficient condition for consensus is presented by graph-theoretic method.
Quantum Cylindrical Waves and Parametrized Field Theory
NASA Astrophysics Data System (ADS)
Varadarajan, Madhavan
In this article, we review some illustrative results in the study of two related toy models for quantum gravity, namely cylindrical waves (which are cylindrically symmetric gravitational fields)and parametrized field theory (which is just free scalar field theory on a flat space-time in generally covariant disguise). In the former, we focus on the phenomenon of unexpected large quantum gravity effects in regions of weak classical gravitational fields and on an analysis of causality in a quantum geometry. In the latter, we focus on Dirac quantization, argue that this is related to the unitary implementability of free scalar field evolution along curved foliations of the flat space-time and review the relevant results for unitary implementability.
Quantum processes: A Whiteheadian interpretation of quantum field theory
NASA Astrophysics Data System (ADS)
Bain, Jonathan
Quantum processes: A Whiteheadian interpretation of quantum field theory is an ambitious and thought-provoking exercise in physics and metaphysics, combining an erudite study of the very complex metaphysics of A.N. Whitehead with a well-informed discussion of contemporary issues in the philosophy of algebraic quantum field theory. Hättich's overall goal is to construct an interpretation of quantum field theory. He does this by translating key concepts in Whitehead's metaphysics into the language of algebraic quantum field theory. In brief, this Hättich-Whitehead (H-W, hereafter) interpretation takes "actual occasions" as the fundamental ontological entities of quantum field theory. An actual occasion is the result of two types of processes: a "transition process" in which a set of initial possibly-possessed properties for the occasion (in the form of "eternal objects") is localized to a space-time region; and a "concrescence process" in which a subset of these initial possibly-possessed properties is selected and actualized to produce the occasion. Essential to these processes is the "underlying activity", which conditions the way in which properties are initially selected and subsequently actualized. In short, under the H-W interpretation of quantum field theory, an initial set of possibly-possessed eternal objects is represented by a Boolean sublattice of the lattice of projection operators determined by a von Neumann algebra R (O) associated with a region O of Minkowski space-time, and the underlying activity is represented by a state on R (O) obtained by conditionalizing off of the vacuum state. The details associated with the H-W interpretation involve imposing constraints on these representations motivated by principles found in Whitehead's metaphysics. These details are spelled out in the three sections of the book. The first section is a summary and critique of Whitehead's metaphysics, the second section introduces the formalism of algebraic quantum field
Universal order parameters and quantum phase transitions: a finite-size approach.
Shi, Qian-Qian; Zhou, Huan-Qiang; Batchelor, Murray T
2015-01-01
We propose a method to construct universal order parameters for quantum phase transitions in many-body lattice systems. The method exploits the H-orthogonality of a few near-degenerate lowest states of the Hamiltonian describing a given finite-size system, which makes it possible to perform finite-size scaling and take full advantage of currently available numerical algorithms. An explicit connection is established between the fidelity per site between two H-orthogonal states and the energy gap between the ground state and low-lying excited states in the finite-size system. The physical information encoded in this gap arising from finite-size fluctuations clarifies the origin of the universal order parameter. We demonstrate the procedure for the one-dimensional quantum formulation of the q-state Potts model, for q = 2, 3, 4 and 5, as prototypical examples, using finite-size data obtained from the density matrix renormalization group algorithm. PMID:25567585
Nontransverse factorizing fields and entanglement in finite spin systems
NASA Astrophysics Data System (ADS)
Cerezo, M.; Rossignoli, R.; Canosa, N.
2015-12-01
We determine the conditions for the existence of nontransverse factorizing magnetic fields in general spin arrays with anisotropic X Y Z couplings of arbitrary range. It is first shown that a uniform, maximally aligned, completely separable eigenstate can exist just for fields hs parallel to a principal plane and forming four straight lines in the field space, with the alignment direction different from that of hs and determined by the anisotropy. Such a state always becomes a nondegenerate ground state for sufficiently strong (yet finite) fields along these lines, in both ferromagnetic and antiferromagnetic-type systems. In antiferromagnetic chains, this field coexists with the nontransverse factorizing field hs' associated with a degenerate Néel-type separable ground state, which is shown to arise at a level crossing in a finite chain. It is also demonstrated for arbitrary spin that pairwise entanglement reaches full range in the vicinity of both hs and hs', vanishing at hs but approaching small yet finite side limits at hs', which are analytically determined. The behavior of the block entropy and entanglement spectrum in their vicinity is also analyzed.
Normal basis of finite field GF(2 super m)
NASA Technical Reports Server (NTRS)
Pei, D. Y.; Wang, C. C.; Omura, J. K.
1986-01-01
Massey and Omura (1981) recently developed a new multiplication algorithm for Galois fields based on the normal basis representation. This algorithm shows a much simpler way to perform multiplication in finite field than the conventional method. The necessary and sufficient conditions are presented for an element to generate a normal basis in the field GF(2 super m), where m = 2 super k p super n and p super n has two as a primitive root. This result provides a way to find a normal basis in the field.
Regaining quantum incoherence for matter fields
Gonzalez-Driaaaz, P.F. )
1992-01-15
The possible quantum state of wormholes or little baby universes should be described by a nonfactorizable density matrix given by the path integral over the class of asymptotically flat four-geometries and asymptotically vanishing matter-field configurations which suitably match the prescribed data on three-surfaces which do not divide the manifold on the inner boundary. An instanton is here obtained which can represent such a nonsimply connected wormhole manifold, and is used to evaluate the asymptotic effective interaction of the resulting correlated baby universes with ordinary quantum fields at low energies in the Fock representation. It is argued that the demand of locality on the interacting quantum field commutators is no longer valid for correlated baby universes, and it is therefore concluded that quantum coherence in the matter-field sector is lost as a consequence of the interaction with nonsimply connected wormholes. A proposal is advanced that wormholes may provide us with a complementary quantum state sector that would induce the collapse of the state vector in the quantum measurement of any observable for ordinary microscopic matter systems.
Efficiency, Power and Period of a model quantum heat engine working in a finite time
NASA Astrophysics Data System (ADS)
Bekele, Mulugeta; Dima, Tolasa A.; Alemye, Mekuannent; Chegeno, Warga
We take a spin-half quantum particle undergoing Carnot type cyclic process in a finite time assisted by two heat reservoirs and an external magnetic field. We find that the power of the heat engine is maximum at a particular period of the cyclic process and efficiency at the maximum power is at least half of the Carnot efficiency. We further apply the Omega-criterion for a figure of merit representing a compromise between useful power and lost power determining the corresponding efficiency for the optimization criterion to be at least three fourth of the Carnot efficiency. The authers are thankful to the International Science programme, IPS, Uppsala, Sweden for their support to our research lab.
Quantum Otto cycle with inner friction: finite-time and disorder effects
NASA Astrophysics Data System (ADS)
Alecce, A.; Galve, F.; Lo Gullo, N.; Dell'Anna, L.; Plastina, F.; Zambrini, R.
2015-07-01
The concept of inner friction, by which a quantum heat engine is unable to follow adiabatically its strokes and thus dissipates useful energy, is illustrated in an exact physical model where the working substance consists of an ensemble of misaligned spins interacting with a magnetic field and performing the Otto cycle. The effect of this static disorder under a finite-time cycle gives a new perspective of the concept of inner friction under realistic settings. We investigate the efficiency and power of this engine and relate its performance to the amount of friction from misalignment and to the temperature difference between heat baths. Finally we propose an alternative experimental implementation of the cycle where the spin is encoded in the degree of polarization of photons.
A quantum relaxation-time approximation for finite fermion systems
Reinhard, P.-G.; Suraud, E.
2015-03-15
We propose a relaxation time approximation for the description of the dynamics of strongly excited fermion systems. Our approach is based on time-dependent density functional theory at the level of the local density approximation. This mean-field picture is augmented by collisional correlations handled in relaxation time approximation which is inspired from the corresponding semi-classical picture. The method involves the estimate of microscopic relaxation rates/times which is presently taken from the well established semi-classical experience. The relaxation time approximation implies evaluation of the instantaneous equilibrium state towards which the dynamical state is progressively driven at the pace of the microscopic relaxation time. As test case, we consider Na clusters of various sizes excited either by a swift ion projectile or by a short and intense laser pulse, driven in various dynamical regimes ranging from linear to strongly non-linear reactions. We observe a strong effect of dissipation on sensitive observables such as net ionization and angular distributions of emitted electrons. The effect is especially large for moderate excitations where typical relaxation/dissipation time scales efficiently compete with ionization for dissipating the available excitation energy. Technical details on the actual procedure to implement a working recipe of such a quantum relaxation approximation are given in appendices for completeness.
PT-Symmetric Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2011-09-01
In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H†) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.
Backlund Transformation in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Burt, Philip
1996-11-01
Solutions of nonlinear field equations with polynomial nonlin earities are well known(P.B.Burt,Quantum Mechanics and Nonlinear Waves,Harwood Academic,Chur,1981).These solutions have been used to describe spin zero systems with self interactions. General- izations to systmes of fermions and bosons with various inter- actions lend themselves to description of quantum field theories with proper normalization. No ultraviolet divergences occur in such theories. The solutions themselves represent weak Backlund transformation of the nonlinear field equations and the related Klein Gordonequation(C.Rogers and W.F.Ames,Nonlinear Boundary Value Problems in Science and Engineering, Academic Press,New York,1989).
The facets of relativistic quantum field theory
NASA Astrophysics Data System (ADS)
Dosch, H. G.; Müller, V. F.
2010-04-01
Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.
The facets of relativistic quantum field theory
NASA Astrophysics Data System (ADS)
Dosch, H. G.; Müller, V. F.
2011-04-01
Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.
Quantum number theoretic transforms on multipartite finite systems.
Vourdas, A; Zhang, S
2009-06-01
A quantum system composed of p-1 subsystems, each of which is described with a p-dimensional Hilbert space (where p is a prime number), is considered. A quantum number theoretic transform on this system, which has properties similar to those of a Fourier transform, is studied. A representation of the Heisenberg-Weyl group in this context is also discussed. PMID:19488175
Quantum Enhanced Estimation of a Multidimensional Field
NASA Astrophysics Data System (ADS)
Baumgratz, Tillmann; Datta, Animesh
2016-01-01
We present a framework for the quantum enhanced estimation of multiple parameters corresponding to noncommuting unitary generators. Our formalism provides a recipe for the simultaneous estimation of all three components of a magnetic field. We propose a probe state that surpasses the precision of estimating the three components individually, and we discuss measurements that come close to attaining the quantum limit. Our study also reveals that too much quantum entanglement may be detrimental to attaining the Heisenberg scaling in the estimation of unitarily generated parameters.
Computing Gravitational Fields of Finite-Sized Bodies
NASA Technical Reports Server (NTRS)
Quadrelli, Marco
2005-01-01
A computer program utilizes the classical theory of gravitation, implemented by means of the finite-element method, to calculate the near gravitational fields of bodies of arbitrary size, shape, and mass distribution. The program was developed for application to a spacecraft and to floating proof masses and associated equipment carried by the spacecraft for detecting gravitational waves. The program can calculate steady or time-dependent gravitational forces, moments, and gradients thereof. Bodies external to a proof mass can be moving around the proof mass and/or deformed under thermoelastic loads. An arbitrarily shaped proof mass is represented by a collection of parallelepiped elements. The gravitational force and moment acting on each parallelepiped element of a proof mass, including those attributable to the self-gravitational field of the proof mass, are computed exactly from the closed-form equation for the gravitational potential of a parallelepiped. The gravitational field of an arbitrary distribution of mass external to a proof mass can be calculated either by summing the fields of suitably many point masses or by higher-order Gauss-Legendre integration over all elements surrounding the proof mass that are part of a finite-element mesh. This computer program is compatible with more general finite-element codes, such as NASTRAN, because it is configured to read a generic input data file, containing the detailed description of the finiteelement mesh.
Quantum stability of chameleon field theories.
Upadhye, Amol; Hu, Wayne; Khoury, Justin
2012-07-27
Chameleon scalar fields are dark-energy candidates which suppress fifth forces in high density regions of the Universe by becoming massive. We consider chameleon models as effective field theories and estimate quantum corrections to their potentials. Requiring that quantum corrections be small, so as to allow reliable predictions of fifth forces, leads to an upper bound m<0.0073(ρ/10 g cm(-3))(1/3) eV for gravitational-strength coupling whereas fifth force experiments place a lower bound of m>0.0042 eV. An improvement of less than a factor of two in the range of fifth force experiments could test all classical chameleon field theories whose quantum corrections are well controlled and couple to matter with nearly gravitational strength regardless of the specific form of the chameleon potential. PMID:23006073
Dual field theories of quantum computation
NASA Astrophysics Data System (ADS)
Vanchurin, Vitaly
2016-06-01
Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N +1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state and so the initial and final dual field theory conditions are described by these two quantum computational states. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2 N , but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N -torus
Probability distributions for quantum stress tensors measured in a finite time interval
NASA Astrophysics Data System (ADS)
Fewster, Christopher J.; Ford, L. H.
2015-11-01
A meaningful probability distribution for measurements of a quantum stress tensor operator can only be obtained if the operator is averaged in time or in spacetime. This averaging can be regarded as a description of the measurement process. Realistic measurements can be expected to begin and end at finite times, which means that they are described by functions with compact support, which we will also take to be smooth. Here we study the probability distributions for stress tensor operators averaged with such functions of time, in the vacuum state of a massless free field. Our primary aim is to understand the asymptotic form of the distribution which describes the probability of large vacuum fluctuations. Our approach involves asymptotic estimates for the high moments of the distribution. These estimates in turn may be used to obtain estimates for the asymptotic form of the probability distribution. Our results show that averaging over a finite interval results in a probability distribution which falls more slowly than for the case of Lorentzian averaging, and both fall more slowly than exponentially. This indicates that vacuum fluctuations effects can dominate over thermal fluctuations in some circumstances.
Mean Field Analysis of Quantum Annealing Correction
NASA Astrophysics Data System (ADS)
Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A.
2016-06-01
Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p -body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p =2 , where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p ≥3 , where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.
Mean Field Analysis of Quantum Annealing Correction.
Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A
2016-06-01
Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder. PMID:27314705
Quantum interactions between nonperturbative vacuum fields
Millo, R.; Faccioli, P.; Scorzato, L.
2010-04-01
We develop an approach to investigate the nonperturbative dynamics of quantum field theories, in which specific vacuum field fluctuations are treated as the low-energy dynamical degrees of freedom, while all other vacuum field configurations are explicitly integrated out from the path integral. We show how to compute the effective interaction between the vacuum field degrees of freedom both perturbatively (using stochastic perturbation theory) and fully nonperturbatively (using lattice field theory simulations). The present approach holds to all orders in the couplings and does not rely on the semiclassical approximation.
FDIPS: Finite Difference Iterative Potential-field Solver
NASA Astrophysics Data System (ADS)
Toth, Gabor; van der Holst, Bartholomeus; Huang, Zhenguang
2016-06-01
FDIPS is a finite difference iterative potential-field solver that can generate the 3D potential magnetic field solution based on a magnetogram. It is offered as an alternative to the spherical harmonics approach, as when the number of spherical harmonics is increased, using the raw magnetogram data given on a grid that is uniform in the sine of the latitude coordinate can result in inaccurate and unreliable results, especially in the polar regions close to the Sun. FDIPS is written in Fortran 90 and uses the MPI library for parallel execution.
Finite geometry effects of field-aligned currents
NASA Technical Reports Server (NTRS)
Fung, Shing F.; Hoffman, R. A.
1992-01-01
Results are presented of model calculations of the magnetic field produced by finite current regions that would be measured by a spaceborne magnetometer. Conditions were examined under which the infinite current sheet approximation can be applied to the calculation of the field-aligned current (FAC) density, using satellite magnetometer data. The accuracy of the three methods used for calculating the current sheet normal direction with respect to the spacecraft trajectory was assessed. It is shown that the model can be used to obtain the position and the orientation of the spacecraft trajectory through the FAC region.
Quantum fields near phantom-energy ''sudden'' singularities
Calderon, Hector H.
2008-08-15
This paper is committed to calculations near a type of future singularity driven by phantom energy. At the singularities considered, the scale factor remains finite but its derivative diverges. The general behavior of barotropic phantom energy producing this singularity is calculated under the assumption that near the singularity such fluid is the dominant contributor. We use the semiclassical formula for renormalized stress tensors of conformally invariant fields in conformally flat spacetimes and analyze the softening/enhancing of the singularity due to quantum vacuum contributions. This dynamical analysis is then compared to results from thermodynamical considerations. In both cases, the vacuum states of quantized scalar and spinor fields strengthen the accelerating expansion near the singularity whereas the vacuum states of vector fields weaken it.
3-D Finite Element Analyses of the Egan Cavern Field
Klamerus, E.W.; Ehgartner, B.L.
1999-02-01
Three-dimensional finite element analyses were performed for the two gas-filled storage caverns at the Egan field, Jennings dome, Louisiana. The effects of cavern enlargement on surface subsidence, storage loss, and cavern stability were investigated. The finite element model simulated the leaching of caverns to 6 and 8 billion cubic feet (BCF) and examined their performance at various operating conditions. Operating pressures varied from 0.15 psi/ft to 0.9 psi/ft at the bottom of the lowest cemented casing. The analysis also examined the stability of the web or pillar of salt between the caverns under differential pressure loadings. The 50-year simulations were performed using JAC3D, a three dimensional finite element analysis code for nonlinear quasistatic solids. A damage criterion based on onset of dilatancy was used to evaluate cavern instability. Dilation results from the development of microfractures in salt and, hence, potential increases in permeability onset occurs well before large scale failure. The analyses predicted stable caverns throughout the 50-year period for the range of pressures investigated. Some localized salt damage was predicted near the bottom walls of the caverns if the caverns are operated at minimum pressure for long periods of time. Volumetric cavern closures over time due to creep were moderate to excessive depending on the salt creep properties and operating pressures. However, subsidence above the cavern field was small and should pose no problem, to surface facilities.
Global effects in quaternionic quantum field theory
NASA Astrophysics Data System (ADS)
Brumby, S. P.; Joshi, G. C.
1996-12-01
We present some striking global consequences of a model quaternionic quantum field theory which is locally complex. We show how making the quaternionic structure a dynamical quantity naturally leads to the prediction of cosmic strings and nonbaryonic hot dark matter candidates.
Theory of finite size effects for electronic quantum Monte Carlo calculations of liquids and solids
NASA Astrophysics Data System (ADS)
Holzmann, Markus; Clay, Raymond C.; Morales, Miguel A.; Tubman, Norm M.; Ceperley, David M.; Pierleoni, Carlo
2016-07-01
Concentrating on zero temperature quantum Monte Carlo calculations of electronic systems, we give a general description of the theory of finite size extrapolations of energies to the thermodynamic limit based on one- and two-body correlation functions. We introduce effective procedures, such as using the potential and wave function split up into long and short range functions to simplify the method, and we discuss how to treat backflow wave functions. Then we explicitly test the accuracy of our method to correct finite size errors on example hydrogen and helium many-body systems and show that the finite size bias can be drastically reduced for even small systems.
Distance and coupling dependence of entanglement in the presence of a quantum field
NASA Astrophysics Data System (ADS)
Hsiang, J.-T.; Hu, B. L.
2015-12-01
We study the entanglement between two coupled detectors, the internal degrees of freedom of which are modeled by harmonic oscillators, interacting with a common quantum field, paying special attention to two less studied yet important features: finite separation and direct coupling. Distance dependence is essential in quantum teleportation and relativistic quantum information considerations. The presence of a quantum field as the environment accords an indirect interaction between the two oscillators at finite separation of a non-Markovian nature which competes with the direct coupling between them. The interplay between these two factors results in a rich variety of interesting entanglement behaviors at late times. We show that the entanglement behavior reported in prior work assuming no separation between the detectors can at best be a transient effect at very short times and claims that such behaviors represent late-time entanglement are misplaced. Entanglement between the detectors with direct coupling enters in the consideration of macroscopic quantum phenomena and other frontline issues. We find that with direct coupling entanglement between the two detectors can sustain over a finite distance, in contrast to the no direct coupling case reported before, where entanglement cannot survive at a separation more than a few inverse high-frequency cutoff scales. This work provides a functional platform for systematic investigations into the entanglement behavior of continuous variable quantum systems, such as used in quantum electro- and optomechanics.
Finite strain crack tip fields in soft incompressible elastic solids.
Krishnan, Venkat R; Hui, Chung Yuen; Long, Rong
2008-12-16
A finite element model (FEM) is used to study the behavior of the large deformation field near the tip of a crack in a soft incompressible plane stress fracture specimen loaded in mode I. Results are obtained for the case of a neo-Hookean solid (ideal rubber) and a hyperelastic solid with exponentially hardening behavior. In contrast to the predictions of linear elastic fracture mechanics (LEFM), the near tip stress fields are dominated by the opening stress which shows a 1/R singularity for the neo-Hookean material and a -1/(R ln R) singularity for the exponential hardening solid. We found very similar qualitative behavior in the near tip stress fields despite the very large difference in strain hardening behavior of the two material models. Our result shows that the near tip opening stress is controlled by the far field energy release rate for large applied loads. PMID:19053624
Finite- to zero-range relativistic mean-field interactions
Niksic, T.; Vretenar, D.; Lalazissis, G. A.; Ring, P.
2008-03-15
We study the relation between the finite-range (meson-exchange) and zero-range (point-coupling) representations of effective nuclear interactions in the relativistic mean-field framework. Starting from the phenomenological interaction DD-ME2 with density-dependent meson-nucleon couplings, we construct a family of point-coupling effective interactions for different values of the strength parameter of the isoscalar-scalar derivative term. In the meson-exchange picture this corresponds to different values of the {sigma}-meson mass. The parameters of the isoscalar-scalar and isovector-vector channels of the point-coupling interactions are adjusted to nuclear matter and ground-state properties of finite nuclei. By comparing results for infinite and semi-infinite nuclear matter, ground-state masses, charge radii, and collective excitations, we discuss constraints on the parameters of phenomenological point-coupling relativistic effective interaction.
Quantum dynamics in strong fluctuating fields
NASA Astrophysics Data System (ADS)
Goychuk, Igor; Hänggi, Peter
A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems, such as e.g. nonadiabatic electron transfer in proteins, can be treated in terms of quantum relaxation processes which couple to one or several fluctuating environments. A thermal equilibrium environment can conveniently be modelled by a thermal bath of harmonic oscillators. An archetype situation provides a two-state dissipative quantum dynamics, commonly known under the label of a spin-boson dynamics. An interesting and nontrivial physical situation emerges, however, when the quantum dynamics evolves far away from thermal equilibrium. This occurs, for example, when a charge transferring medium possesses nonequilibrium degrees of freedom, or when a strong time-dependent control field is applied externally. Accordingly, certain parameters of underlying quantum subsystem acquire stochastic character. This may occur, for example, for the tunnelling coupling between the donor and acceptor states of the transferring electron, or for the corresponding energy difference between electronic states which assume via the coupling to the fluctuating environment an explicit stochastic or deterministic time-dependence. Here, we review the general theoretical framework which is based on the method of projector operators, yielding the quantum master equations for systems that are exposed to strong external fields. This allows one to investigate on a common basis, the influence of nonequilibrium fluctuations and periodic electrical fields on those already mentioned dynamics and related quantum transport processes. Most importantly, such strong fluctuating fields induce a whole variety of nonlinear and nonequilibrium phenomena. A characteristic feature of such dynamics is the absence of thermal (quantum) detailed balance.ContentsPAGE1. Introduction5262. Quantum dynamics in stochastic fields531 2.1. Stochastic Liouville equation531 2.2. Non-Markovian vs. Markovian discrete
Metric quantum field theory: A preliminary look
Watson, W.N.
1988-01-01
Spacetime coordinates are involved in uncertainty relations; spacetime itself appears to exhibit curvature. Could the continua associated with field variables exhibit curvature This question, as well as the ideas that (a) difficulties with quantum theories of gravitation may be due to their formulation in an incorrect analogy with other quantum field theories, (b) spacetime variables should not be any more basic than others for describing physical phenomena, and (c) if field continua do not exhibit curvature, the reasons would be of interest, motivated the formulation of a theory of variable curvature and torsion in the electromagnetic four-potential's reciprocal space. Curvature and torsion equation completely analogous to those for a gauge theory of gravitation (the Einstein-Cartan-Sciama-Kibble theory) are assumed for this continuum. The interaction-Hamiltonian density of this theory, to a first approximation, implies that in addition to the Maxwell-Dirac field interaction of ordinary quantum electrodynamics, there should also be an interaction between Dirac-field vector and pseudovector currents unmediated by photons, as well as other interactions involving two or three Dirac-field currents interacting with the Maxwell field at single spacetime events. Calculations expressing Bhabha-scattering cross sections for incident beams with parallel spins differ from those of unmodified quantum electrodynamics by terms of first order in the gravitational constant of the theory, but the corresponding cross section for unpolarized incident beams differs from that of the unmodified theory only by terms of higher order in that constant. Undesirable features of the present theory include its nonrenormalizability, the obscurity of the meaning of its inverse field operator, and its being based on electrodynamics rather than electroweak dynamics.
Integrable structures in quantum field theory
NASA Astrophysics Data System (ADS)
Negro, Stefano
2016-08-01
This review was born as notes for a lecture given at the Young Researchers Integrability School (YRIS) school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the mid-nineties by Bazhanov, Lukyanov and Zamolodchikov and, as such, called BLZ. This method can be interpreted as a field theory version of the quantum inverse scattering, also known as the algebraic Bethe ansatz. Starting with the case of conformal field theories (CFTs) we show how to build the field theory analogues of commuting transfer T matrices and Baxter Q-operators of integrable lattice models. These objects contain the complete information of the integrable structure of the theory, viz. the integrals of motion, and can be used, as we will show, to derive the thermodynamic Bethe ansatz and nonlinear integral equations. This same method can be easily extended to the description of integrable structures of certain particular massive deformations of CFTs; these, in turn, can be described as quantum group reductions of the quantum sine-Gordon model and it is an easy step to include this last theory in the framework of BLZ approach. Finally we show an interesting and surprising connection of the BLZ structures with classical objects emerging from the study of classical integrable models via the inverse scattering transform method. This connection goes under the name of ODE/IM correspondence and we will present it for the specific case of quantum sine-Gordon model only.
BOOK REVIEW: Finite Element and Boundary Element Applications in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Ueta, Tsuyoshi
2003-08-01
L Ramdas Ram-Mohan Oxford: Oxford University Press (2002) £26.50 (paperback), ISBN 0-19-852522-2 Although this book is one of the Oxford Texts in Applied and Engineering Mathematics, we may think of it as a physics book. It explains how to solve the problem of quantum mechanics using the finite element method (FEM) and the boundary element method (BEM). Many examples analysing actual problems are also shown. As for the ratio of the number of pages of FEM and BEM, the former occupies about 80%. This is, however, reasonable reflecting the flexibility of FEM. Although many explanations of FEM and BEM exist, most are written using special mathematical expressions and numerical computation fields. However, this book is written in the `language of physicists' throughout. I think that it is very readable and easy to understand for physicists. In the derivation of FEM and the argument on calculation accuracy, the action integral and a variation principle are used consistently. In the numerical computation of matrices, such as simultaneous equations and eigen value problems, a description of important points is also fully given. Moreover, the practical problems which become important in the electron device design field and the condensed matter physics field are dealt with as example computations, so that this book is very practical and applicable. It is characteristic and interesting that FEM is applied to solve the Schrödinger and Poisson equations consistently, and to the solution of the Ginzburg--Landau equation in superconductivity. BEM is applied to treat electric field enhancements due to surface plasmon excitations at metallic surfaces. A number of references are cited at the end of all the chapters, and this is very helpful. The description of quantum mechanics is also made appropriately and the actual application of quantum mechanics in condensed matter physics can also be surveyed. In the appendices, the mathematical foundation, such as numerical quadrature
Finite-time quantum-to-classical transition for a Schroedinger-cat state
Paavola, Janika; Hall, Michael J. W.; Paris, Matteo G. A.; Maniscalco, Sabrina
2011-07-15
The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schroedinger-cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum-to-classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well-defined physical meaning and allow a deeper understanding of the quantum-to-classical transition. Our analysis shows that, for most nonclassicality measures, the Schroedinger-cat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a ''sudden death''. In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.
"Quantum Field Theory and QCD"
Jaffe, Arthur M.
2006-02-25
This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 18-19, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.
Detecting Large Quantum Fisher Information with Finite Measurement Precision
NASA Astrophysics Data System (ADS)
Fröwis, Florian; Sekatski, Pavel; Dür, Wolfgang
2016-03-01
We propose an experimentally accessible scheme to determine the lower bounds on the quantum Fisher information (QFI), which ascertains multipartite entanglement or usefulness for quantum metrology. The scheme is based on comparing the measurement statistics of a state before and after a small unitary rotation. We argue that, in general, the limited resolution of collective observables prevents the detection of large QFI. This can be overcome by performing an additional operation prior to the measurement. We illustrate the power of this protocol for present-day spin-squeezing experiments, where the same operation used for the preparation of the initial spin-squeezed state improves also the measurement precision and hence the lower bound on the QFI by 2 orders of magnitude. We also establish a connection to the Leggett-Garg inequalities. We show how to simulate a variant of the inequalities with our protocol and demonstrate that large QFI is necessary for their violation with coarse-grained detectors.
Tight finite-key analysis for quantum cryptography
NASA Astrophysics Data System (ADS)
Tomamichel, Marco; Lim, Charles Ci Wen; Gisin, Nicolas; Renner, Renato
2012-01-01
Despite enormous theoretical and experimental progress in quantum cryptography, the security of most current implementations of quantum key distribution is still not rigorously established. One significant problem is that the security of the final key strongly depends on the number, M, of signals exchanged between the legitimate parties. Yet, existing security proofs are often only valid asymptotically, for unrealistically large values of M. Another challenge is that most security proofs are very sensitive to small differences between the physical devices used by the protocol and the theoretical model used to describe them. Here we show that these gaps between theory and experiment can be simultaneously overcome by using a recently developed proof technique based on the uncertainty relation for smooth entropies.
Tight finite-key analysis for quantum cryptography.
Tomamichel, Marco; Lim, Charles Ci Wen; Gisin, Nicolas; Renner, Renato
2012-01-01
Despite enormous theoretical and experimental progress in quantum cryptography, the security of most current implementations of quantum key distribution is still not rigorously established. One significant problem is that the security of the final key strongly depends on the number, M, of signals exchanged between the legitimate parties. Yet, existing security proofs are often only valid asymptotically, for unrealistically large values of M. Another challenge is that most security proofs are very sensitive to small differences between the physical devices used by the protocol and the theoretical model used to describe them. Here we show that these gaps between theory and experiment can be simultaneously overcome by using a recently developed proof technique based on the uncertainty relation for smooth entropies. PMID:22252558
Matter-enhanced transition probabilities in quantum field theory
Ishikawa, Kenzo Tobita, Yutaka
2014-05-15
The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the S-matrix, S[T], that satisfies the boundary condition at T. Using S[T], the finite-size corrections of the form of 1/T are found. The corrections to Fermi’s golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths. -- Highlights: •S-matrix S[T] for the finite-time interval in relativistic field theory. •S[T] satisfies the boundary condition and gives correction of 1/T . •The large corrections for light particles breaks Lorentz invariance. •The corrections have implications to neutrino experiments.
Quantum fields on closed timelike curves
Pienaar, J. L.; Myers, C. R.; Ralph, T. C.
2011-12-15
Recently, there has been much interest in the evolution of quantum particles on closed timelike curves (CTCs). However, such models typically assume pointlike particles with only two degrees of freedom; a very questionable assumption given the relativistic setting of the problem. We show that it is possible to generalize the Deutsch model of CTCs to fields using the equivalent circuit formalism. We give examples for coherent, squeezed, and single-photon states interacting with the CTC via a beamsplitter. The model is then generalized further to account for the smooth transition to normal quantum mechanics as the CTC becomes much smaller than the size of the modes interacting on it. In this limit, we find that the system behaves like a standard quantum-mechanical feedback loop.
Cellular automata based byte error correcting codes over finite fields
NASA Astrophysics Data System (ADS)
Köroğlu, Mehmet E.; Şiap, İrfan; Akın, Hasan
2012-08-01
Reed-Solomon codes are very convenient for burst error correction which occurs frequently in applications, but as the number of errors increase, the circuit structure of implementing Reed-Solomon codes becomes very complex. An alternative solution to this problem is the modular and regular structure of cellular automata which can be constructed with VLSI economically. Therefore, in recent years, cellular automata have became an important tool for error correcting codes. For the first time, cellular automata based byte error correcting codes analogous to extended Reed-Solomon codes over binary fields was studied by Chowdhury et al. [1] and Bhaumik et al. [2] improved the coding-decoding scheme. In this study cellular automata based double-byte error correcting codes are generalized from binary fields to primitive finite fields Zp.
Neutrino oscillations: Quantum mechanics vs. quantum field theory
Akhmedov, Evgeny Kh.; Kopp, Joachim
2010-01-01
A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
Finite Difference Elastic Wave Field Simulation On GPU
NASA Astrophysics Data System (ADS)
Hu, Y.; Zhang, W.
2011-12-01
Numerical modeling of seismic wave propagation is considered as a basic and important aspect in investigation of the Earth's structure, and earthquake phenomenon. Among various numerical methods, the finite-difference method is considered one of the most efficient tools for the wave field simulation. However, with the increment of computing scale, the power of computing has becoming a bottleneck. With the development of hardware, in recent years, GPU shows powerful computational ability and bright application prospects in scientific computing. Many works using GPU demonstrate that GPU is powerful . Recently, GPU has not be used widely in the simulation of wave field. In this work, we present forward finite difference simulation of acoustic and elastic seismic wave propagation in heterogeneous media on NVIDIA graphics cards with the CUDA programming language. We also implement perfectly matched layers on the graphics cards to efficiently absorb outgoing waves on the fictitious edges of the grid Simulations compared with the results on CPU platform shows reliable accuracy and remarkable efficiency. This work proves that GPU can be an effective platform for wave field simulation, and it can also be used as a practical tool for real-time strong ground motion simulation.
Magnetic field homogeneity perturbations in finite Halbach dipole magnets.
Turek, Krzysztof; Liszkowski, Piotr
2014-01-01
Halbach hollow cylinder dipole magnets of a low or relatively low aspect ratio attract considerable attention due to their applications, among others, in compact NMR and MRI systems for investigating small objects. However, a complete mathematical framework for the analysis of magnetic fields in these magnets has been developed only for their infinitely long precursors. In such a case the analysis is reduced to two-dimensions (2D). The paper details the analysis of the 3D magnetic field in the Halbach dipole cylinders of a finite length. The analysis is based on three equations in which the components of the magnetic flux density Bx, By and Bz are expanded to infinite power series of the radial coordinate r. The zeroth term in the series corresponds to a homogeneous magnetic field Bc, which is perturbed by the higher order terms due to a finite magnet length. This set of equations is supplemented with an equation for the field profile B(z) along the magnet axis, presented for the first time. It is demonstrated that the geometrical factors in the coefficients of particular powers of r, defined by intricate integrals are the coefficients of the Taylor expansion of the homogeneity profile (B(z)-Bc)/Bc. As a consequence, the components of B can be easily calculated with an arbitrary accuracy. In order to describe perturbations of the field due to segmentation, two additional equations are borrowed from the 2D theory. It is shown that the 2D approach to the perturbations generated by the segmentation can be applied to the 3D Halbach structures unless r is not too close to the inner radius of the cylinder ri. The mathematical framework presented in the paper was verified with great precision by computations of B by a highly accurate integration of the magnetostatic Coulomb law and utilized to analyze the inhomogeneity of the magnetic field in the magnet with the accuracy better than 1 ppm. PMID:24316186
Finite-key analysis for measurement-device-independent quantum key distribution
NASA Astrophysics Data System (ADS)
Song, Ting-Ting; Wen, Qiao-Yan; Guo, Fen-Zhuo; Tan, Xiao-Qing
2012-08-01
The length of signal pulses is finite in practical quantum key distribution. The finite-key analysis of an unconditional quantum key distribution is a burning problem, and the efficient quantum key distribution protocol suitable for practical implementation, measurement-device-independent quantum key distribution (MDI QKD), was proposed very recently. We give the finite-key analysis of MDI QKD, which removes all detector side channels and generates many orders of key rate higher than that of full-device-independent quantum key distribution. The secure bound of the ultimate key rate is obtained under the statistical fluctuations of relative frequency, which can be applied directly to practical threshold detectors with low detection efficiency and highly lossy channels. The bound is evaluated for reasonable values of the observed parameters. The simulation shows that the secure distance is around 10 km when the number of sifted data is 1010. Moreover the secure distance would be much longer in practice because of some simplified treatments used in our paper.
Model for noncancellation of quantum electric field fluctuations
Parkinson, Victor; Ford, L. H.
2011-12-15
A localized charged particle oscillating near a reflecting boundary is considered as a model for noncancellation of vacuum fluctuations. Although the mean velocity of the particle is sinusoidal, the velocity variance produced by vacuum fluctuations can either grow or decrease linearly in time, depending upon the product of the oscillation frequency and the distance to the boundary. This amounts to heating or cooling arising from noncancellation of electric field fluctuations, which are otherwise anticorrelated in time. Similar noncancellations arise in quantum field effects in time-dependent curved space-times. We give some estimates of the magnitude of the effect, and discuss its potential observability. We also compare the effects of vacuum fluctuations with the shot noise due to emission of a finite number of photons. We find that the two effects can be comparable in magnitude, but have distinct characteristics, and hence could be distinguished in an experiment.
Locality and entanglement in bandlimited quantum field theory
NASA Astrophysics Data System (ADS)
Pye, Jason; Donnelly, William; Kempf, Achim
2015-11-01
We consider a model for a Planck-scale ultraviolet cutoff which is based on Shannon sampling. Shannon sampling originated in information theory, where it expresses the equivalence of continuous and discrete representations of information. When applied to quantum field theory, Shannon sampling expresses a hard ultraviolet cutoff in the form of a bandlimitation. This introduces nonlocality at the cutoff scale in a way that is more subtle than a simple discretization of space: quantum fields can then be represented as either living on continuous space or, entirely equivalently, as living on any one lattice whose average spacing is sufficiently small. We explicitly calculate vacuum entanglement entropies in 1 +1 dimensions and we find a transition between logarithmic and linear scaling of the entropy, which is the expected 1 +1 dimensional analog of the transition from an area to a volume law. We also use entanglement entropy and mutual information as measures to probe in detail the localizability of the field degrees of freedom. We find that, even though neither translation nor rotation invariance are broken, each field degree of freedom occupies an incompressible volume of space, indicating a finite information density.
Locality and entanglement in bandlimited quantum field theory
NASA Astrophysics Data System (ADS)
Pye, Jason; Donnelly, William; Kempf, Achim
We consider a model for a Planck scale ultraviolet cutoff which is based on Shannon sampling. Shannon sampling originated in information theory, where it expresses the equivalence of continuous and discrete representations of information. When applied to quantum field theory, Shannon sampling expresses a hard ultraviolet cutoff in the form of a bandlimitation. This introduces nonlocality at the cutoff scale in a way that is more subtle than a simple discretization of space: quantum fields can then be represented as either living on continuous space or, entirely equivalently, as living on any one lattice whose average spacing is sufficiently small. We explicitly calculate vacuum entanglement entropies in 1+1 dimensions and we find a transition between logarithmic and linear scaling of the entropy, which is the expected 1+1 dimensional analog of the transition from an area to a volume law. We also use entanglement entropy and mutual information as measures to probe in detail the localizability of the field degrees of freedom. We find that, even though neither translation nor rotation invariance are broken, each field degree of freedom occupies an incompressible volume of space, indicating a finite information density.
Remote State Preparation for Quantum Fields
NASA Astrophysics Data System (ADS)
Ber, Ran; Zohar, Erez
2016-07-01
Remote state preparation is generation of a desired state by a remote observer. In spite of causality, it is well known, according to the Reeh-Schlieder theorem, that it is possible for relativistic quantum field theories, and a "physical" process achieving this task, involving superoscillatory functions, has recently been introduced. In this work we deal with non-relativistic fields, and show that remote state preparation is also possible for them, hence obtaining a Reeh-Schlieder-like result for general fields. Interestingly, in the nonrelativistic case, the process may rely on completely different resources than the ones used in the relativistic case.
He, Qi-Liang; Xu, Jing-Bo; Yao, Dao-Xin; Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996 ; Zhang, Ye-Qi
2013-07-15
We investigate the dynamics of quantum correlation between two noninteracting qubits each inserted in its own finite-temperature environment with 1/f spectral density. It is found that the phenomenon of sudden transition between classical and quantum decoherence exists in the system when two qubits are initially prepared in X-type quantum states, and the transition time depends on the initial-state of two qubits, the qubit–environment coupling constant and the temperature of the environment. Furthermore, we explore the influence of dynamical decoupling pulses on the transition time and show that it can be prolonged by applying the dynamical decoupling pulses. -- Highlights: •The sudden transition phenomenon from finite-temperature environments is studied. •The transition time depends on the environment temperature and the system parameters. •The transition time can be prolonged by applying the dynamical decoupling pulses.
Marchiolli, Marcelo A.; Ruzzi, Maurizio; Galetti, Diogenes
2005-10-15
By means of a mod(N)-invariant operator basis, s-parametrized phase-space functions associated with bounded operators in a finite-dimensional Hilbert space are introduced in the context of the extended Cahill-Glauber formalism, and their properties are discussed in details. The discrete Glauber-Sudarshan, Wigner, and Husimi functions emerge from this formalism as specific cases of s-parametrized phase-space functions where, in particular, a hierarchical process among them is promptly established. In addition, a phase-space description of quantum tomography and quantum teleportation is presented and new results are obtained.
Functional representation for fermionic quantum fields
NASA Astrophysics Data System (ADS)
Floreanini, R.; Jackiw, R.
1988-04-01
A functional representation for fermionic quantum fields is developed in analogy to familiar results for bosonic fields. The infinite Clifford algebra of the field anticommutator is realized reducibly on a Grassmann functional space. On this space, transformation groups may be represented without normal ordering with respect to a Fock vacuum, and a projective representation for the two-dimensional conformal group is found, which is compared to the corresponding representation in terms of bosonic fields. When a quadratic Hamiltonian for the Fermi fields is posited, a Fock space can be constructed after a prescription for filling the Dirac sea is selected. Different filling prescriptions lead to inequivalent Fock spaces within the functional space. Explicit eigenfunctionals exhibit the peculiarities of fermionic field theory, such as fractional charge, Berry's phase, and anomalies.
Quantum-corrected finite entropy of noncommutative acoustic black holes
NASA Astrophysics Data System (ADS)
Anacleto, M. A.; Brito, F. A.; Luna, G. C.; Passos, E.; Spinelly, J.
2015-11-01
In this paper we consider the generalized uncertainty principle in the tunneling formalism via Hamilton-Jacobi method to determine the quantum-corrected Hawking temperature and entropy for 2 + 1-dimensional noncommutative acoustic black holes. In our results we obtain an area entropy, a correction logarithmic in leading order, a correction term in subleading order proportional to the radiation temperature associated with the noncommutative acoustic black holes and an extra term that depends on a conserved charge. Thus, as in the gravitational case, there is no need to introduce the ultraviolet cut-off and divergences are eliminated.
Detecting Large Quantum Fisher Information with Finite Measurement Precision.
Fröwis, Florian; Sekatski, Pavel; Dür, Wolfgang
2016-03-01
We propose an experimentally accessible scheme to determine the lower bounds on the quantum Fisher information (QFI), which ascertains multipartite entanglement or usefulness for quantum metrology. The scheme is based on comparing the measurement statistics of a state before and after a small unitary rotation. We argue that, in general, the limited resolution of collective observables prevents the detection of large QFI. This can be overcome by performing an additional operation prior to the measurement. We illustrate the power of this protocol for present-day spin-squeezing experiments, where the same operation used for the preparation of the initial spin-squeezed state improves also the measurement precision and hence the lower bound on the QFI by 2 orders of magnitude. We also establish a connection to the Leggett-Garg inequalities. We show how to simulate a variant of the inequalities with our protocol and demonstrate that large QFI is necessary for their violation with coarse-grained detectors. PMID:26991166
Thermalization of field driven quantum systems
Fotso, H.; Mikelsons, K.; Freericks, J. K.
2014-01-01
There is much interest in how quantum systems thermalize after a sudden change, because unitary evolution should preclude thermalization. The eigenstate thermalization hypothesis resolves this because all observables for quantum states in a small energy window have essentially the same value; it is violated for integrable systems due to the infinite number of conserved quantities. Here, we show that when a system is driven by a DC electric field there are five generic behaviors: (i) monotonic or (ii) oscillatory approach to an infinite-temperature steady state; (iii) monotonic or (iv) oscillatory approach to a nonthermal steady state; or (v) evolution to an oscillatory state. Examining the Hubbard model (which thermalizes under a quench) and the Falicov-Kimball model (which does not), we find both exhibit scenarios (i–iv), while only Hubbard shows scenario (v). This shows richer behavior than in interaction quenches and integrability in the absence of a field plays no role. PMID:24736404
GPU and APU computations of Finite Time Lyapunov Exponent fields
NASA Astrophysics Data System (ADS)
Conti, Christian; Rossinelli, Diego; Koumoutsakos, Petros
2012-03-01
We present GPU and APU accelerated computations of Finite-Time Lyapunov Exponent (FTLE) fields. The calculation of FTLEs is a computationally intensive process, as in order to obtain the sharp ridges associated with the Lagrangian Coherent Structures an extensive resampling of the flow field is required. The computational performance of this resampling is limited by the memory bandwidth of the underlying computer architecture. The present technique harnesses data-parallel execution of many-core architectures and relies on fast and accurate evaluations of moment conserving functions for the mesh to particle interpolations. We demonstrate how the computation of FTLEs can be efficiently performed on a GPU and on an APU through OpenCL and we report over one order of magnitude improvements over multi-threaded executions in FTLE computations of bluff body flows.
Quantum field theories in spaces with neutral signatures
NASA Astrophysics Data System (ADS)
Pavšič, Matej
2013-04-01
We point out that quantum field theories based on the concept of Clifford space and Clifford algebra valued-fields involve both positive and negative energies. This is a consequence of the indefinite signature (p, q) of the Clifford space. When the signature is neutral, p = q, then vacuum energy vanishes and there is no cosmological constant problem. A question of the stability of such theories in the presence of interactions arises. We investigate a toy model of the harmonic oscillator in the space M1,1. We have found that in the presence of certain interactions the amplitude of oscillations can remain finite. In general this is not the case and the amplitude grows to infinity, but only when the two frequencies are exactly the same. When they are even slightly different, the amplitude remains finite and the system is stable. We show how such oscillator comes from the Stueckelberg action in curved space, and how it can be generalized to field theories.
Zeno effect and ergodicity in finite-time quantum measurements
Sokolovski, D.
2011-12-15
We demonstrate that an attempt to measure a nonlocal in time quantity, such as the time average {sub T} of a dynamical variable A, by separating Feynman paths into ever narrower exclusive classes traps the system in eigensubspaces of the corresponding operator A. Conversely, in a long measurement of {sub T} to a finite accuracy, the system explores its Hilbert space and is driven to a universal steady state in which the von Neumann ensemble average of A coincides with {sub T}. Both effects are conveniently analyzed in terms of singularities and critical points of the corresponding amplitude distribution and the Zeno-like behavior is shown to be a consequence of the conservation of probability.
Open systems dynamics for propagating quantum fields
NASA Astrophysics Data System (ADS)
Baragiola, Ben Quinn
In this dissertation, I explore interactions between matter and propagating light. The electromagnetic field is modeled as a Markovian reservoir of quantum harmonic oscillators successively streaming past a quantum system. Each weak and fleeting interaction entangles the light and the system, and the light continues its course. In the context of quantum tomography or metrology one attempts, using measure- ments of the light, to extract information about the quantum state of the system. An inevitable consequence of these measurements is a disturbance of the system's quantum state. These ideas focus on the system and regard the light as ancillary. It serves its purpose as a probe or as a mechanism to generate interesting dynamics or system states but is eventually traced out, leaving the reduced quantum state of the system as the primary mathematical subject. What, then, when the state of light itself harbors intrinsic self-entanglement? One such set of states, those where a traveling wave packet is prepared with a defi- nite number of photons, is a focal point of this dissertation. These N-photon states are ideal candidates as couriers in quantum information processing device. In con- trast to quasi-classical states, such as coherent or thermal fields, N-photon states possess temporal mode entanglement, and local interactions in time have nonlocal consequences. The reduced state of a system probed by an N-photon state evolves in a non-Markovian way, and to describe its dynamics one is obliged to keep track of the field's evolution. I present a method to do this for an arbitrary quantum system using a set of coupled master equations. Many models set aside spatial degrees of freedom as an unnecessary complicating factor. By doing so the precision of predictions is limited. Consider a ensemble of cold, trapped atomic spins dispersively probed by a paraxial laser beam. Atom-light coupling across the ensemble is spatially inhomogeneous as is the radiation pattern of
The amplitude of quantum field theory
Medvedev, B.V. ); Pavlov, V.P.; Polivanov, M.K. ); Sukhanov, A.D. )
1989-05-01
General properties of the transition amplitude in axiomatic quantum field theory are discussed. Bogolyubov's axiomatic method is chosen as the variant of the theory. The axioms of this method are analyzed. In particular, the significance of the off-shell extension and of the various forms of the causality condition are examined. A complete proof is given of the existence of a single analytic function whose boundary values are the amplitudes of all channels of a process with given particle number.
Effective field theory out of equilibrium: Brownian quantum fields
NASA Astrophysics Data System (ADS)
Boyanovsky, D.
2015-06-01
The emergence of an effective field theory out of equilibrium is studied in the case in which a light field—the system—interacts with very heavy fields in a finite temperature bath. We obtain the reduced density matrix for the light field, its time evolution is determined by an effective action that includes the influence action from correlations of the heavy degrees of freedom. The non-equilibrium effective field theory yields a Langevin equation of motion for the light field in terms of dissipative and noise kernels that obey a generalized fluctuation dissipation relation. These are completely determined by the spectral density of the bath which is analyzed in detail for several cases. At T = 0 we elucidate the effect of thresholds in the renormalization aspects and the asymptotic emergence of a local effective field theory with unitary time evolution. At T\
NASA Astrophysics Data System (ADS)
Gustin, C.; Faniel, S.; Hackens, B.; Melinte, S.; Shayegan, M.; Bayot, V.
2003-12-01
We report on conductance fluctuations of ballistic quantum dots in a strictly parallel magnetic field B. The quantum dots are patterned in two-dimensional electron gases (2DEG’s), confined to 15- and 45-nm-thick GaAs quantum wells (QW) with one and two occupied subbands at B=0, respectively. For both dots we observe universal conductance fluctuations (UCF’s) and, in the case of the wide QW dot, a reduction in their amplitude at large B. Our data suggest that the finite thickness of the 2DEG and the orbital effect are responsible for the parallel B-induced UCF’s.
Markovian evolution of classical and quantum correlations in transverse-field XY model
NASA Astrophysics Data System (ADS)
Pal, A. K.; Bose, I.
2012-08-01
The transverse-field XY model in one dimension is a well-known spin model for which the ground state properties and excitation spectrum are known exactly. The model has an interesting phase diagram describing quantum phase transitions (QPTs) belonging to two different universality classes. These are the transverse-field Ising model and the XX model universality classes with both the models being special cases of the transverse-field XY model. In recent years, quantities related to quantum information theoretic measures like entanglement, quantum discord (QD) and fidelity have been shown to provide signatures of QPTs. Another interesting issue is that of decoherence to which a quantum system is subjected due to its interaction, represented by a quantum channel, with an environment. In this paper, we determine the dynamics of different types of correlations present in a quantum system, namely, the mutual information I( ρ AB ), the classical correlations C( ρ AB ) and the quantum correlations Q( ρ AB ), as measured by the quantum discord, in a two-qubit state. The density matrix of this state is given by the nearest-neighbour reduced density matrix obtained from the ground state of the transverse-field XY model in 1d. We assume Markovian dynamics for the time-evolution due to system-environment interactions. The quantum channels considered include the bit-flip, bit-phase-flip and phase-flip channels. Two different types of dynamics are identified for the channels in one of which the quantum correlations are greater in magnitude than the classical correlations in a finite time interval. The origins of the different types of dynamics are further explained. For the different channels, appropriate quantities associated with the dynamics of the correlations are identified which provide signatures of QPTs. We also report results for further-neighbour two-qubit states and finite temperatures.
Finite Element Modeling for Megagauss Magnetic Field Generation
NASA Astrophysics Data System (ADS)
Martinez, David
2005-10-01
Applying external magnetic fields with MegaGauss strength is needed for hot plasma confinement and stabilization. We investigate the possibility of generating ultra-high magnetic fields with the fast z-pinch generator ``Zebra'' for experiments at the NTF. Zebra can produce a load a current of 1 MA in 100 ns. To design appropriate loads we use FemlabootnotetextFemlab 3 -- multi-physics, finite-element modeling program by Comsol AB, 2004 and ScreamerootnotetextScreamer -- A Pulsed Power Design Tool developed at SNL by M. L. Kiefer, K. L. Fugelso, K. W. Struve, and M. M. Widner. to simulate the magnetic field. Screamer predicts the load current using a detailed model of Zebra and helps optimize the operation. Using the information from Screamer, Femlab is able to calculate the magnetic field, heating, and stress on the conductor. All these effects must be taken into consideration to determine the integrity of the coil until maximum field is reached. The presentation will include simulation results for single- and multi-turn coils, as well as quasi-force-free inductors.
Exact scattering matrix of graphs in magnetic field and quantum noise
Caudrelier, Vincent; Mintchev, Mihail; Ragoucy, Eric
2014-08-15
We consider arbitrary quantum wire networks modelled by finite, noncompact, connected quantum graphs in the presence of an external magnetic field. We find a general formula for the total scattering matrix of the network in terms of its local scattering properties and its metric structure. This is applied to a quantum ring with N external edges. Connecting the external edges of the ring to heat reservoirs, we study the quantum transport on the graph in ambient magnetic field. We consider two types of dynamics on the ring: the free Schrödinger and the free massless Dirac equations. For each case, a detailed study of the thermal noise is performed analytically. Interestingly enough, in presence of a magnetic field, the standard linear Johnson-Nyquist law for the low temperature behaviour of the thermal noise becomes nonlinear. The precise regime of validity of this effect is discussed and a typical signature of the underlying dynamics is observed.
Finite-temperature quantum fluctuations in two-dimensional Fermi superfluids
NASA Astrophysics Data System (ADS)
Bighin, G.; Salasnich, L.
2016-01-01
In two-dimensional systems with a continuous symmetry, the Mermin-Wagner-Hohenberg theorem precludes spontaneous symmetry breaking and condensation at finite temperature. The Berezinskii-Kosterlitz-Thouless critical temperature marks the transition from a superfluid phase characterized by quasicondensation and algebraic long-range order, to a normal phase in which vortex proliferation completely destroys superfluidity. As opposed to conventional off-diagonal long-range order typical of three-dimensional superfluid systems, algebraic long-range order is driven by quantum and thermal fluctuations strongly enhanced in reduced dimensionality. Motivated by this unique scenario and by the very recent experimental realization of trapped quasi-two-dimensional fermionic clouds, we include one-loop Gaussian fluctuations in the theoretical description of resonant Fermi superfluids in two dimensions demonstrating that first sound, second sound, and also critical temperature are strongly renormalized, away from their mean-field values. In particular, we prove that in the intermediate- and strong-coupling regimes, these quantities are radically different when Gaussian fluctuations are taken into account. Our one-loop theory shows good agreement with very recent experimental data on the Berezinskii-Kosterlitz-Thouless critical temperature [Phys. Rev. Lett. 115, 010401 (2015)], 10.1103/PhysRevLett.115.010401 and on the first sound velocity, giving predictions for the second sound as a function of interaction strength and temperature that are open for experimental verification.
Finite-key analysis of a practical decoy-state high-dimensional quantum key distribution
NASA Astrophysics Data System (ADS)
Bao, Haize; Bao, Wansu; Wang, Yang; Zhou, Chun; Chen, Ruike
2016-05-01
Compared with two-level quantum key distribution (QKD), high-dimensional QKD enables two distant parties to share a secret key at a higher rate. We provide a finite-key security analysis for the recently proposed practical high-dimensional decoy-state QKD protocol based on time-energy entanglement. We employ two methods to estimate the statistical fluctuation of the postselection probability and give a tighter bound on the secure-key capacity. By numerical evaluation, we show the finite-key effect on the secure-key capacity in different conditions. Moreover, our approach could be used to optimize parameters in practical implementations of high-dimensional QKD.
On the finite-temperature quantum electrodynamics of gravitational acceleration
NASA Astrophysics Data System (ADS)
Barton, G.
1989-12-01
The temperature-dependent quantum-electrodynamic corrections to the Helmholtz free energy F of a particle at rest, and to its inertial mass minert, are the same: ΔF=Δminert=πe2(kT)2/3m. By contrast, the correction to the total energy U=F+TS is ΔU=-ΔF. Donoghue, Holstein, and Robinett have pointed out that if (as the equivalence principle appears to imply) weight is proportional to total energy, then the gravitational acceleration of a particle inside a blackbody cavity becomes g(m+ΔU)/(m+ΔF)~=g(1-2ΔF/m)
Jain, Shweta Sharma, Prerana; Chhajlani, R. K.
2015-07-31
The Jeans instability of self-gravitating quantum plasma is examined considering the effects of viscosity, finite Larmor radius (FLR) corrections and rotation. The analysis is done by normal mode analysis theory with the help of relevant linearized perturbation equations of the problem. The general dispersion relation is obtained using the quantum magneto hydrodynamic model. The modified condition of Jeans instability is obtained and the numerical calculations have been performed to show the effects of various parameters on the growth rate of Jeans instability.
On Energy-Momentum Transfer of Quantum Fields
NASA Astrophysics Data System (ADS)
Herdegen, Andrzej
2014-10-01
We prove the following theorem on bounded operators in quantum field theory: if , then , where D( x) is a function weakly decaying in spacelike directions, are creation/annihilation parts of an appropriate time derivative of B, G is any positive, bounded, non-increasing function in , and is any finite complex Borel measure; creation/annihilation operators may be also replaced by with . We also use the notion of energy-momentum scaling degree of B with respect to a submanifold (Steinmann-type, but in momentum space, and applied to the norm of an operator). These two tools are applied to the analysis of singularities of . We prove, among others, the following statement (modulo some more specific assumptions): outside p = 0 the only allowed contributions to this functional which are concentrated on a submanifold (including the trivial one—a single point) are Dirac measures on hypersurfaces (if the decay of D is not to slow).
Semianalytical quantum model for graphene field-effect transistors
Pugnaghi, Claudio; Grassi, Roberto Gnudi, Antonio; Di Lecce, Valerio; Gnani, Elena; Reggiani, Susanna; Baccarani, Giorgio
2014-09-21
We develop a semianalytical model for monolayer graphene field-effect transistors in the ballistic limit. Two types of devices are considered: in the first device, the source and drain regions are doped by charge transfer with Schottky contacts, while, in the second device, the source and drain regions are doped electrostatically by a back gate. The model captures two important effects that influence the operation of both devices: (i) the finite density of states in the source and drain regions, which limits the number of states available for transport and can be responsible for negative output differential resistance effects, and (ii) quantum tunneling across the potential steps at the source-channel and drain-channel interfaces. By comparison with a self-consistent non-equilibrium Green's function solver, we show that our model provides very accurate results for both types of devices, in the bias region of quasi-saturation as well as in that of negative differential resistance.
The effect of finite Larmor radius corrections on Jeans instability of quantum plasma
Sharma, Prerana; Chhajlani, R. K.
2013-09-15
The influence of finite Larmor radius (FLR) effects on the Jeans instability of infinitely conducting homogeneous quantum plasma is investigated. The quantum magnetohydrodynamic (QMHD) model is used to formulate the problem. The contribution of FLR is incorporated to the QMHD set of equations in the present analysis. The general dispersion relation is obtained analytically using the normal mode analysis technique which is modified due to the contribution of FLR corrections. From general dispersion relation, the condition of instability is obtained and it is found that Jeans condition is modified due to quantum effect. The general dispersion relation is reduced for both transverse and longitudinal mode of propagations. The condition of gravitational instability is modified due to the presence of both FLR and quantum corrections in the transverse mode of propagation. In longitudinal case, it is found to be unaffected by the FLR effects but modified due to the quantum corrections. The growth rate of Jeans instability is discussed numerically for various values of quantum and FLR corrections of the medium. It is found that the quantum parameter and FLR effects have stabilizing influence on the growth rate of instability of the system.
FINITE ELEMENT MODEL FOR TIDES AND CURRENTS WITH FIELD APPLICATIONS.
Walters, Roy A.
1988-01-01
A finite element model, based upon the shallow water equations, is used to calculate tidal amplitudes and currents for two field-scale test problems. Because tides are characterized by line spectra, the governing equations are subjected to harmonic decomposition. Thus the solution variables are the real and imaginary parts of the amplitude of sea level and velocity rather than a time series of these variables. The time series is recovered through synthesis. This scheme, coupled with a modified form of the governing equations, leads to high computational efficiency and freedom from excessive numerical noise. Two test-cases are presented. The first is a solution for eleven tidal constituents in the English Channel and southern North Sea, and three constituents are discussed. The second is an analysis of the frequency response and tidal harmonics for south San Francisco Bay.
Systolic multiplier for finite fields gf(2/sup m/)
Yeh, C.S.; Reed, I.S.
1983-01-01
A systolic architecture is developed for performing the product-sum computation, ab+c, in the finite field gf(2/sup m/) of 2/sup m/ elements, where a, b and c are arbitrary elements of gf(2/sup m/). The multiplier is a serial-in, serial-out, one-dimensional systolic array. This multiplier for gf(2/sup m/) requires m basic cells. The average time per computation of the multiplier is m time units if a number of computations are computed consecutively. To perform an isolated computation the multiplier requires 3m time units. The architecture is simple and regular and possesses the desirable properties of concurrency and modularity and is well suited for use. 10 references.
Finite element modeling of electromagnetic fields and waves using NASTRAN
NASA Technical Reports Server (NTRS)
Moyer, E. Thomas, Jr.; Schroeder, Erwin
1989-01-01
The various formulations of Maxwell's equations are reviewed with emphasis on those formulations which most readily form analogies with Navier's equations. Analogies involving scalar and vector potentials and electric and magnetic field components are presented. Formulations allowing for media with dielectric and conducting properties are emphasized. It is demonstrated that many problems in electromagnetism can be solved using the NASTRAN finite element code. Several fundamental problems involving time harmonic solutions of Maxwell's equations with known analytic solutions are solved using NASTRAN to demonstrate convergence and mesh requirements. Mesh requirements are studied as a function of frequency, conductivity, and dielectric properties. Applications in both low frequency and high frequency are highlighted. The low frequency problems demonstrate the ability to solve problems involving media inhomogeneity and unbounded domains. The high frequency applications demonstrate the ability to handle problems with large boundary to wavelength ratios.
Systolic multipliers for finite fields GF(2 exp m)
NASA Technical Reports Server (NTRS)
Yeh, C.-S.; Reed, I. S.; Truong, T. K.
1984-01-01
Two systolic architectures are developed for performing the product-sum computation AB + C in the finite field GF(2 exp m) of 2 exp m elements, where A, B, and C are arbitrary elements of GF(2 exp m). The first multiplier is a serial-in, serial-out one-dimensional systolic array, while the second multiplier is a parallel-in, parallel-out two-dimensional systolic array. The first multiplier requires a smaller number of basic cells than the second multiplier. The second multiplier needs less average time per computation than the first multiplier, if a number of computations are performed consecutively. To perform single computations both multipliers require the same computational time. In both cases the architectures are simple and regular and possess the properties of concurrency and modularity. As a consequence, they are well suited for use in VLSI systems.
NASA Astrophysics Data System (ADS)
Shah, Nayana; Lopatin, Andrei
2007-09-01
A microscopic analysis of the superconducting quantum critical point realized via a pair-breaking quantum phase transition is presented. Finite-temperature crossovers are derived for the electrical conductivity, which is a key probe of superconducting fluctuations. By using the diagrammatic formalism for disordered systems, we are able to incorporate the interplay between fluctuating Cooper pairs and electrons, that is outside the scope of a time-dependent Ginzburg-Landau or effective bosonic action formalism. It is essential to go beyond the standard approximation in order to capture the zero-temperature correction which results purely from the (dynamic) quantum fluctuations and dictates the behavior of the conductivity in an entire low-temperature quantum regime. All dynamic contributions are of the same order and conspire to add up to a negative total, thereby inhibiting the conductivity as a result of superconducting fluctuations. On the contrary, the classical and the intermediate regimes are dominated by the positive bosonic channel. Our theory is applicable in one, two, and three dimensions and is relevant for experiments on superconducting nanowires, doubly connected cylinders, thin films, and bulk in the presence of magnetic impurities, magnetic field, or other pair breakers. A window of nonmonotonic behavior is predicted to exist as either the temperature or the pair-breaking parameter is swept.
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D.
2013-10-15
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Finite-momentum condensate of magnetic excitons in a bilayer quantum Hall system
NASA Astrophysics Data System (ADS)
Doretto, R. L.; Morais Smith, C.; Caldeira, A. O.
2012-07-01
We study the bilayer quantum Hall system at total filling factor νT=1 within a bosonization formalism which allows us to approximately treat the magnetic exciton as a boson. We show that in the region where the distance between the two layers is comparable to the magnetic length, the ground state of the system can be seen as a finite-momentum condensate of magnetic excitons provided that the excitation spectrum is gapped. We analyze the stability of such a phase within the Bogoliubov approximation first assuming that only one momentum Q is macroscopically occupied and later we consider the same situation for two modes ±Q. We find strong evidences that a first-order quantum phase transition at small interlayer separation takes place from a zero-momentum condensate phase, which corresponds to Halperin 111 state, to a finite-momentum condensate of magnetic excitons.
Cluster algebra structure on the finite dimensional representations of affine quantum group
NASA Astrophysics Data System (ADS)
Yang, Yan-Min; Ma, Hai-Tao; Lin, Bing-Sheng; Zheng, Zhu-Jun
2015-01-01
In this paper, we prove one case of conjecture given by Hernandez and Leclerc. We give a cluster algebra structure on the Grothendieck ring of a full subcategory of the finite dimensional representations of affine quantum group . As a conclusion, for every exchange relation of cluster algebra, there exists an exact sequence of the full subcategory corresponding to it. Project supported by the National Natural Science Foundation of China (Grant No. 11475178).
Quantum key distribution with finite resources: Secret key rates via Renyi entropies
Abruzzo, Silvestre; Kampermann, Hermann; Mertz, Markus; Bruss, Dagmar
2011-09-15
A realistic quantum key distribution (QKD) protocol necessarily deals with finite resources, such as the number of signals exchanged by the two parties. We derive a bound on the secret key rate which is expressed as an optimization problem over Renyi entropies. Under the assumption of collective attacks by an eavesdropper, a computable estimate of our bound for the six-state protocol is provided. This bound leads to improved key rates in comparison to previous results.
Evidence for a finite-temperature phase transition in a bilayer quantum Hall system.
Champagne, A R; Eisenstein, J P; Pfeiffer, L N; West, K W
2008-03-01
We study the Josephson-like interlayer tunneling signature of the strongly correlated nuT=1 quantum Hall phase in bilayer two-dimensional electron systems as a function of the layer separation, temperature, and interlayer charge imbalance. Our results offer strong evidence that a finite temperature phase transition separates the interlayer coherent phase from incoherent phases which lack strong interlayer correlations. The transition temperature is dependent on both the layer spacing and charge imbalance between the layers. PMID:18352740
Evidence for a Finite-Temperature Phase Transition in a Bilayer Quantum Hall System
NASA Astrophysics Data System (ADS)
Champagne, A. R.; Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W.
2008-03-01
We study the Josephson-like interlayer tunneling signature of the strongly correlated νT=1 quantum Hall phase in bilayer two-dimensional electron systems as a function of the layer separation, temperature, and interlayer charge imbalance. Our results offer strong evidence that a finite temperature phase transition separates the interlayer coherent phase from incoherent phases which lack strong interlayer correlations. The transition temperature is dependent on both the layer spacing and charge imbalance between the layers.
Finite-size analysis of a continuous-variable quantum key distribution
Leverrier, Anthony; Grangier, Philippe
2010-06-15
The goal of this paper is to extend the framework of finite-size analysis recently developed for quantum key distribution to continuous-variable protocols. We do not solve this problem completely here, and we mainly consider the finite-size effects on the parameter estimation procedure. Despite the fact that some questions are left open, we are able to give an estimation of the secret key rate for protocols which do not contain a postselection procedure. As expected, these results are significantly more pessimistic than those obtained in the asymptotic regime. However, we show that recent continuous-variable protocols are able to provide fully secure secret keys in the finite-size scenario, over distances larger than 50 km.
Local hidden variable models for entangled quantum States using finite shared randomness.
Bowles, Joseph; Hirsch, Flavien; Quintino, Marco Túlio; Brunner, Nicolas
2015-03-27
The statistics of local measurements performed on certain entangled states can be reproduced using a local hidden variable (LHV) model. While all known models make use of an infinite amount of shared randomness, we show that essentially all entangled states admitting a LHV model can be simulated with finite shared randomness. Our most economical model simulates noisy two-qubit Werner states using only log_{2}(12)≃3.58 bits of shared randomness. We also discuss the case of positive operator valued measures, and the simulation of nonlocal states with finite shared randomness and finite communication. Our work represents a first step towards quantifying the cost of LHV models for entangled quantum states. PMID:25860723
NASA Astrophysics Data System (ADS)
Wang, Chao; Huang, Peng; Huang, Duan; Lin, Dakai; Zeng, Guihua
2016-02-01
Practical security of the continuous-variable quantum key distribution (CVQKD) system with finite sampling bandwidth of analog-to-digital converter (ADC) at the receiver's side is investigated. We find that the finite sampling bandwidth effects may decrease the lower bound of secret key rate without awareness of the legitimate communicators. This leaves security loopholes for Eve to attack the system. In addition, this effect may restrains the linear relationship of secret key bit rate with repetition rate of the system; subsequently, there is a saturation value for the secret key bit rate with the repetition rate. To resist such kind of effects, we propose a dual sampling detection approach in which two ADCs are employed so that the finite sampling bandwidth effects are removed.
Experimental quantum key distribution with finite-key security analysis for noisy channels
NASA Astrophysics Data System (ADS)
Bacco, Davide; Canale, Matteo; Laurenti, Nicola; Vallone, Giuseppe; Villoresi, Paolo
2013-09-01
In quantum key distribution implementations, each session is typically chosen long enough so that the secret key rate approaches its asymptotic limit. However, this choice may be constrained by the physical scenario, as in the perspective use with satellites, where the passage of one terminal over the other is restricted to a few minutes. Here we demonstrate experimentally the extraction of secure keys leveraging an optimal design of the prepare-and-measure scheme, according to recent finite-key theoretical tight bounds. The experiment is performed in different channel conditions, and assuming two distinct attack models: individual attacks or general quantum attacks. The request on the number of exchanged qubits is then obtained as a function of the key size and of the ambient quantum bit error rate. The results indicate that viable conditions for effective symmetric, and even one-time-pad, cryptography are achievable.
Bilinear covariants and spinor fields duality in quantum Clifford algebras
Abłamowicz, Rafał; Gonçalves, Icaro; Rocha, Roldão da
2014-10-15
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying Z-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, “The unpredictability of quantum gravity,” Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.
Bilinear covariants and spinor fields duality in quantum Clifford algebras
NASA Astrophysics Data System (ADS)
Abłamowicz, Rafał; Gonçalves, Icaro; da Rocha, Roldão
2014-10-01
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying {Z}-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, "The unpredictability of quantum gravity," Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.
Finite-Temperature Spin Dynamics in a Perturbed Quantum Critical Ising Chain with an E8 Symmetry
NASA Astrophysics Data System (ADS)
Wu, Jianda; Kormos, Márton; Si, Qimiao
2014-12-01
A spectrum exhibiting E8 symmetry is expected to arise when a small longitudinal field is introduced in the transverse-field Ising chain at its quantum critical point. Evidence for this spectrum has recently come from neutron scattering measurements in cobalt niobate, a quasi-one-dimensional Ising ferromagnet. Unlike its zero-temperature counterpart, the finite-temperature dynamics of the model has not yet been determined. We study the dynamical spin structure factor of the model at low frequencies and nonzero temperatures, using the form factor method. Its frequency dependence is singular, but differs from the diffusion form. The temperature dependence of the nuclear magnetic resonance (NMR) relaxation rate has an activated form, whose prefactor we also determine. We propose NMR experiments as a means to further test the applicability of the E8 description for CoNb2O6 .
Causality Is Inconsistent With Quantum Field Theory
Wolf, Fred Alan
2011-11-29
Causality in quantum field theory means the vanishing of commutators for spacelike separated fields (VCSSF). I will show that VCSSF is not tenable. For VCSSF to be tenable, and therefore, to have both retarded and advanced propagators vanish in the elsewhere, a superposition of negative energy antiparticle and positive energy particle propagators, traveling forward in time, and a superposition of negative energy particle and positive energy antiparticle propagators, traveling backward in time, are required. Hence VCSSF predicts non-vanishing probabilities for both negative energy particles in the forward-through-time direction and positive energy antiparticles in the backwards-through-time direction. Therefore, since VCSSF is unrealizable in a stable universe, tachyonic propagation must occur in denial of causality.
Maximally polarized states for quantum light fields
Sanchez-Soto, Luis L.; Yustas, Eulogio C.; Bjoerk, Gunnar; Klimov, Andrei B.
2007-10-15
The degree of polarization of a quantum field can be defined as its distance to an appropriate set of states. When we take unpolarized states as this reference set, the states optimizing this degree for a fixed average number of photons N present a fairly symmetric, parabolic photon statistic, with a variance scaling as N{sup 2}. Although no standard optical process yields such a statistic, we show that, to an excellent approximation, a highly squeezed vacuum can be taken as maximally polarized. We also consider the distance of a field to the set of its SU(2) transformed, finding that certain linear superpositions of SU(2) coherent states make this degree to be unity.
NASA Astrophysics Data System (ADS)
Kinross, A. W.; Fu, M.; Munsie, T. J.; Dabkowska, H. A.; Luke, G. M.; Sachdev, Subir; Imai, T.
2014-07-01
The transverse field Ising chain model is ideally suited for testing the fundamental ideas of quantum phase transitions because its well-known T=0 ground state can be extrapolated to finite temperatures. Nonetheless, the lack of appropriate model materials hindered the past effort to test the theoretical predictions. Here, we map the evolution of quantum fluctuations in the transverse field Ising chain based on nuclear magnetic resonance measurements of CoNb2O6, and we demonstrate the finite-temperature effects on quantum criticality for the first time. From the temperature dependence of the Nb93 longitudinal relaxation rate 1/T1, we identify the renormalized classical, quantum critical, and quantum disordered scaling regimes in the temperature (T) vs transverse magnetic field (h ⊥) phase diagram. Precisely at the critical field h⊥c=5.25±0.15 T, we observe a power-law behavior, 1/T1˜T-3/4, as predicted by quantum critical scaling. Our parameter-free comparison between the data and theory reveals that quantum fluctuations persist up to as high as T ˜0.4J, where the intrachain exchange interaction J is the only energy scale of the problem.
Carrier relaxation in (In,Ga)As quantum dots with magnetic field-induced anharmonic level structure
NASA Astrophysics Data System (ADS)
Kurtze, H.; Bayer, M.
2016-07-01
Sophisticated models have been worked out to explain the fast relaxation of carriers into quantum dot ground states after non-resonant excitation, overcoming the originally proposed phonon bottleneck. We apply a magnetic field along the quantum dot heterostructure growth direction to transform the confined level structure, which can be approximated by a Fock-Darwin spectrum, from a nearly equidistant level spacing at zero field to strong anharmonicity in finite fields. This changeover leaves the ground state carrier population rise time unchanged suggesting that fast relaxation is maintained upon considerable changes of the level spacing. This corroborates recent models explaining the relaxation by polaron formation in combination with quantum kinetic effects.
Multiloop calculations in perturbative quantum field theory
NASA Astrophysics Data System (ADS)
Blokland, Ian Richard
This thesis deals with high-precision calculations in perturbative quantum field theory. In conjunction with detailed experimental measurements, perturbative quantum field theory provides the quantitative framework with which much of modern particle physics is understood. The results of three new theoretical calculations are presented. The first is a definitive resolution of a recent controversy involving the interaction of a muon with a magnetic field. Specifically, the light-by-light scattering contribution to the anomalous magnetic moment of the muon is shown to be of positive sign, thereby decreasing the discrepancy between theory and experiment. Despite this adjustment to the theoretical prediction, the remaining discrepancy might be a subtle signature of new kinds of particles. The second calculation involves the energy levels of a bound state formed from two charged particles of arbitrary masses. By employing recently developed mass expansion techniques, new classes of solutions are obtained for problems in a field of particle physics with a very rich history. The third calculation provides an improved prediction for the decay of a top quark. In order to obtain this result, a large class of multiloop integrals has been solved for the first time. Top quark decay is just one member of a family of interesting physical processes to which these new results apply. Since specialized calculational techniques are essential ingredients in all three calculations, they are motivated and explained carefully in this thesis. These techniques, once automated with symbolic computational software, have recently opened avenues of solution to a wide variety of important problems in particle physics.
Electric Field Screening by the Proximity of Two Knife-Edge Field Emitters of Finite Width
NASA Astrophysics Data System (ADS)
Wong, P.; Tang, W.; Lau, Y. Y.; Hoff, B.
2015-11-01
Field emitter arrays have the potential to provide high current density, low voltage operation, and high pulse repetition for radar and communication. It is well known that packing density of the field emitter arrays significantly affect the emission current. Previously we calculated analytically the electric field profile of two-dimensional knife-edge cathodes with arbitrary separation by using a Schwarz-Christoffel transformation. Here we extend this previous work to include the finite width of two identical emitters. From the electric field profile, the field enhancement factor, thereby the severity of the electric field screening, are determined. It is found that for two identical emitters with finite width, the magnitude of the electric field on the knife-edge cathodes depends strongly on the ratio h / a and h / r , where h is the height of the knife-edge cathode, 2a is the distance between the cathodes, and 2 r represents their width. Particle-in-cell simulations are performed to compare with the analytical results on the emission current distribution. P. Y. Wong was supported by a Directed Energy Summer Scholar internship at Air Force Research Laboratory, Kirtland AFB, and by AFRL Award No. FA9451-14-1-0374.
Four and a Half Axioms for Finite-Dimensional Quantum Probability
NASA Astrophysics Data System (ADS)
Wilce, Alexander
It is an old idea, lately out of fashion but now experiencing a revival, that quantum mechanics may best be understood, not as a physical theory with a problematic probabilistic interpretation, but as something closer to a probability calculus per se. However, from this angle, the rather special C *-algebraic apparatus of quantum probability theory stands in need of further motivation. One would like to find additional principles, having clear physical and/or probabilistic content, on the basis of which this apparatus can be reconstructed. In this paper, I explore one route to such a derivation of finite-dimensional quantum mechanics, by means of a set of strong, but probabilistically intelligible, axioms. Stated very informally, these require that systems appear completely classical as restricted to a single measurement, that different measurements, and likewise different pure states, be equivalent (up to the action of a compact group of symmetries), and that every state be the marginal of a bipartite non-signaling state perfectly correlating two measurements. This much yields a mathematical representation of (basic, discrete) measurements as orthonormal subsets of, and states, by vectors in, an ordered real Hilbert space - in the quantum case, the space of Hermitian operators, with its usual tracial inner product. One final postulate (a simple minimization principle, still in need of a clear interpretation) forces the positive cone of this space to be homogeneous and self-dual and hence, to be the state space of a formally real Jordan algebra. From here, the route to the standard framework of finite-dimensional quantum mechanics is quite short.
NASA Astrophysics Data System (ADS)
Park, Sung-Been; Cha, Min-Chul
2015-11-01
We investigate the finite-size scaling properties of the quantum phase transition in the one-dimensional quantum Ising model with periodic boundary conditions by representing the ground state in matrix product state forms. The infinite time-evolving block decimation technique is used to optimize the states. A trace over a product of the matrices multiplied as many times as the number of sites yields the finite-size effects. For sufficiently large Schmidt ranks, the finite-size scaling behavior determines the critical point and the critical exponents whose values are consistent with the analytical results.
Quantum corrections to the cosmological evolution of conformally coupled fields
Cembranos, Jose A.R.; Olive, Keith A.; Peloso, Marco; Uzan, Jean-Philippe E-mail: olive@physics.umn.edu E-mail: uzan@iap.fr
2009-07-01
Because the source term for the equations of motion of a conformally coupled scalar field, such as the dilaton, is given by the trace of the matter energy momentum tensor, it is commonly assumed to vanish during the radiation dominated epoch in the early universe. As a consequence, such fields are generally frozen in the early universe. Here we compute the finite temperature radiative correction to the source term and discuss its consequences on the evolution of such fields in the early universe. We discuss in particular, the case of scalar tensor theories of gravity which have general relativity as an attractor solution. We show that, in some cases, the universe can experience an early phase of contraction, followed by a non-singular bounce, and standard expansion. This can have interesting consequences for the abundance of thermal relics; for instance, it can provide a solution to the gravitino problem. We conclude by discussing the possible consequences of the quantum corrections to the evolution of the dilaton.
The $\\hbar$ Expansion in Quantum Field Theory
Brodsky, Stanley J.; Hoyer, Paul; /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys.
2010-10-27
We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.
Electromagnetic fields on a quantum scale. I.
Grimes, Dale M; Grimes, Craig A
2002-10-01
This is the first in a series of two articles, the second of which provides an exact electro-magnetic field description of photon emission, absorption, and radiation pattern. Photon energy exchanges are analyzed and shown to be the triggered, regenerative response of a non-local eigenstate electron. This first article presents a model-based, hidden variable analysis of quantum theory that provides the statistical nature of wave functions. The analysis uses the equations of classical electro-magnetism and conservation of energy while modeling an eigenstate electron as a nonlocal entity. Essential to the analysis are physical properties that were discovered and analyzed only after the historical interpretation of quantum mechanics was established: electron non-locality and the standing electro-magnetic energy that accompanies and encompasses an active, electrically small volume. The standing energy produces a driving radiation reaction force that, under certain circumstances, is many orders of magnitude larger than currently accepted values. These properties provide a sufficient basis for the Schrödinger equation as a descriptor of non-relativistic eigenstate electrons in or near equilibrium. The uncertainty principle follows, as does the exclusion principle. The analysis leads to atomic stability and causality in the sense that the status of physical phenomena at any instant specifies the status an instant later. PMID:12908293
NASA Astrophysics Data System (ADS)
Xu, Xing-Lei; Xu, Shi-Min; Li, Hong-Qi
2008-06-01
The quantization of mesoscopic damped circuit involving capacitance-inductance coupling is proposed by the method of thrice linear transformation and damped harmonic oscillator quantization. The quantum fluctuations of the charges and current of each loop are calculated by thermo-field dynamics (TFD) in thermal vacuum state, thermal coherent state and thermal squeezed state, respectively. It is shown that the quantum fluctuations of the charges and current not only depend on circuit inherent parameter and coupled magnitude, but also rely on squeezed coefficients, squeezed angle, environmental temperature and damped resistance. And, because of influence of environmental temperature and damped resistance, the quantum fluctuations increase with increasing temperature and decrease with prolonging time.
NASA Astrophysics Data System (ADS)
Jafari, R.
2012-05-01
The presence of a quantum critical point can significantly affect the thermodynamic properties of a material at finite temperatures. This is reflected, e.g., in the entropy landscape S(T, c) in the vicinity of a quantum critical point, yielding particularly strong variations for varying the tuning parameter c such as magnetic field. In this work we have studied the thermodynamic properties of the quantum compass model in the presence of a transverse field. The specific heat, entropy and cooling rate under an adiabatic demagnetization process have been calculated. During an adiabatic (de)magnetization process temperature drops in the vicinity of a field-induced zero-temperature quantum phase transitions. However close to field-induced quantum phase transitions we observe a large magnetocaloric effect.
Chen, RuiKe; Bao, WanSu; Zhou, Chun; Li, Hongwei; Wang, Yang; Bao, HaiZe
2016-03-21
In recent years, a large quantity of work have been done to narrow the gap between theory and practice in quantum key distribution (QKD). However, most of them are focus on two-party protocols. Very recently, Yao Fu et al proposed a measurement-device-independent quantum cryptographic conferencing (MDI-QCC) protocol and proved its security in the limit of infinitely long keys. As a step towards practical application for MDI-QCC, we design a biased decoy-state measurement-device-independent quantum cryptographic conferencing protocol and analyze the performance of the protocol in both the finite-key and infinite-key regime. From numerical simulations, we show that our decoy-state analysis is tighter than Yao Fu et al. That is, we can achieve the nonzero asymptotic secret key rate in long distance with approximate to 200km and we also demonstrate that with a finite size of data (say 10^{11} to 10^{13} signals) it is possible to perform secure MDI-QCC over reasonable distances. PMID:27136849
Structure of local quantum operations and classical communication: Finite versus infinite rounds
NASA Astrophysics Data System (ADS)
Cohen, Scott M.
2015-04-01
Every measurement that can be implemented by local quantum operations and classical communication (LOCC) using an infinite number of rounds is the limit of a sequence of measurements, where each measurement in the sequence requires only a finite number of rounds. This rather obvious and well-known fact is nonetheless of interest as it shows that these infinite-round measurements can be approximated arbitrarily closely simply by using more and more rounds of communication. Here we demonstrate the perhaps less obvious result that (at least) for bipartite systems, the reverse relationship also holds. Specifically, we show that every finite-round bipartite LOCC measurement is the limit of a continuous sequence of LOCC measurements, where each measurement in that sequence can be implemented by LOCC, but only with the use of an infinite number of rounds. Thus, the set of LOCC measurements that require an infinite number of rounds is dense in the entirety of LOCC, as is the set of finite-round LOCC measurements. This means there exist measurements that can only be implemented by LOCC by using an infinite number of rounds, but can nonetheless be approximated closely by using one round of communication, and actually in some cases, no communication is needed at all. These results follow from a necessary condition presented here for finite-round LOCC, which is extremely simple to check, is very easy to prove, and which can be violated by utilizing an infinite number of rounds.
NASA Astrophysics Data System (ADS)
Boche, H.; Nötzel, J.
2014-12-01
This work is motivated by a quite general question: Under which circumstances are the capacities of information transmission systems continuous? The research is explicitly carried out on finite arbitrarily varying quantum channels (AVQCs). We give an explicit example that answers the recent question whether the transmission of messages over AVQCs can benefit from assistance by distribution of randomness between the legitimate sender and receiver in the affirmative. The specific class of channels introduced in that example is then extended to show that the unassisted capacity does have discontinuity points, while it is known that the randomness-assisted capacity is always continuous in the channel. We characterize the discontinuity points and prove that the unassisted capacity is always continuous around its positivity points. After having established shared randomness as an important resource, we quantify the interplay between the distribution of finite amounts of randomness between the legitimate sender and receiver, the (nonzero) probability of a decoding error with respect to the average error criterion and the number of messages that can be sent over a finite number of channel uses. We relate our results to the entanglement transmission capacities of finite AVQCs, where the role of shared randomness is not yet well understood, and give a new sufficient criterion for the entanglement transmission capacity with randomness assistance to vanish.
Boche, H. E-mail: janis.noetzel@tum.de; Nötzel, J. E-mail: janis.noetzel@tum.de
2014-12-15
This work is motivated by a quite general question: Under which circumstances are the capacities of information transmission systems continuous? The research is explicitly carried out on finite arbitrarily varying quantum channels (AVQCs). We give an explicit example that answers the recent question whether the transmission of messages over AVQCs can benefit from assistance by distribution of randomness between the legitimate sender and receiver in the affirmative. The specific class of channels introduced in that example is then extended to show that the unassisted capacity does have discontinuity points, while it is known that the randomness-assisted capacity is always continuous in the channel. We characterize the discontinuity points and prove that the unassisted capacity is always continuous around its positivity points. After having established shared randomness as an important resource, we quantify the interplay between the distribution of finite amounts of randomness between the legitimate sender and receiver, the (nonzero) probability of a decoding error with respect to the average error criterion and the number of messages that can be sent over a finite number of channel uses. We relate our results to the entanglement transmission capacities of finite AVQCs, where the role of shared randomness is not yet well understood, and give a new sufficient criterion for the entanglement transmission capacity with randomness assistance to vanish.
Tight finite-key analysis for passive decoy-state quantum key distribution under general attacks
NASA Astrophysics Data System (ADS)
Zhou, Chun; Bao, Wan-Su; Li, Hong-Wei; Wang, Yang; Li, Yuan; Yin, Zhen-Qiang; Chen, Wei; Han, Zheng-Fu
2014-05-01
For quantum key distribution (QKD) using spontaneous parametric-down-conversion sources (SPDCSs), the passive decoy-state protocol has been proved to be efficiently close to the theoretical limit of an infinite decoy-state protocol. In this paper, we apply a tight finite-key analysis for the passive decoy-state QKD using SPDCSs. Combining the security bound based on the uncertainty principle with the passive decoy-state protocol, a concise and stringent formula for calculating the key generation rate for QKD using SPDCSs is presented. The simulation shows that the secure distance under our formula can reach up to 182 km when the number of sifted data is 1010. Our results also indicate that, under the same deviation of statistical fluctuation due to finite-size effects, the passive decoy-state QKD with SPDCSs can perform as well as the active decoy-state QKD with a weak coherent source.
Practical continuous-variable quantum key distribution without finite sampling bandwidth effects.
Li, Huasheng; Wang, Chao; Huang, Peng; Huang, Duan; Wang, Tao; Zeng, Guihua
2016-09-01
In a practical continuous-variable quantum key distribution system, finite sampling bandwidth of the employed analog-to-digital converter at the receiver's side may lead to inaccurate results of pulse peak sampling. Then, errors in the parameters estimation resulted. Subsequently, the system performance decreases and security loopholes are exposed to eavesdroppers. In this paper, we propose a novel data acquisition scheme which consists of two parts, i.e., a dynamic delay adjusting module and a statistical power feedback-control algorithm. The proposed scheme may improve dramatically the data acquisition precision of pulse peak sampling and remove the finite sampling bandwidth effects. Moreover, the optimal peak sampling position of a pulse signal can be dynamically calibrated through monitoring the change of the statistical power of the sampled data in the proposed scheme. This helps to resist against some practical attacks, such as the well-known local oscillator calibration attack. PMID:27607653
Quantum field theory in spaces with closed time-like curves
NASA Astrophysics Data System (ADS)
Boulware, D. G.
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27(pi). A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Quantum field theory in spaces with closed time-like curves. [Gott space
Boulware, D.G.
1992-01-01
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27[pi]. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Quantum field theory in spaces with closed time-like curves
Boulware, D.G.
1992-12-31
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27{pi}. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Non-additive probabilities and quantum logic in finite quantum systems
NASA Astrophysics Data System (ADS)
Vourdas, A.
2015-04-01
A quantum system Σ(d) with variables in Z(d) and with Hilbert space H(d), is considered. It is shown that the additivity relation of Kolmogorov probabilities, is not valid in the Birkhoff-von Neumann orthocomplemented modular lattice of subspaces L(d). A second lattice Λ(d) which is distributive and contains the subsystems of Σ(d) is also considered. It is shown that in this case also, the additivity relation of Kolmogorov probabilities is not valid. This suggests that a more general (than Kolmogorov) probability theory is needed, and here we adopt the Dempster-Shafer probability theory. In both of these lattices, there are sublattices which are Boolean algebras, and within these ‘islands’ quantum probabilities are additive.
Accurate 2d finite element calculations for hydrogen in magnetic fields of arbitrary strength
NASA Astrophysics Data System (ADS)
Schimeczek, C.; Wunner, G.
2014-02-01
Recent observations of hundreds of hydrogen-rich magnetic white dwarf stars with magnetic fields up to 105 T (103 MG) have called for more comprehensive and accurate databases for wavelengths and oscillator strengths of the H atom in strong magnetic fields for all states evolving from the field-free levels with principal quantum numbers n≤10. We present a code to calculate the energy eigenvalues and wave functions of such states which is capable of covering the entire regime of field strengths B=0 T to B˜109 T. We achieve this high flexibility by using a two-dimensional finite element expansion of the wave functions in terms of B-splines in the directions parallel and perpendicular to the magnetic field, instead of using asymptotically valid basis expansions in terms of spherical harmonics or Landau orbitals. We have paid special attention to the automation of the program such that the data points for the magnetic field strengths at which the energy of a given state are calculated can be selected automatically. Furthermore, an elaborate method for varying the basis parameters is applied to ensure that the results reach a pre-selected precision, which also can be adjusted freely. Energies and wave functions are stored in a convenient format for further analysis, e.g. for the calculation of transition energies and oscillator strengths. The code has been tested to work for 300 states with an accuracy of better than 10-6 Rydberg across several symmetry subspaces over the entire regime of magnetic field strengths.
Occurrence of discontinuities in the performance of finite-time quantum Otto cycles
NASA Astrophysics Data System (ADS)
Zheng, Yuanjian; Hänggi, Peter; Poletti, Dario
2016-07-01
We study a quantum Otto cycle in which the strokes are performed in finite time. The cycle involves energy measurements at the end of each stroke to allow for the respective determination of work. We then optimize for the work and efficiency of the cycle by varying the time spent in the different strokes and find that the optimal value of the ratio of time spent on each stroke goes through sudden changes as the parameters of this cycle vary continuously. The position of these discontinuities depends on the optimized quantity under consideration such as the net work output or the efficiency.
Finite element basis for the expansion of radial wavefunction in quantum scattering calculations
NASA Astrophysics Data System (ADS)
Hwang, Woonglin; Sup Lee, Yoon; Park, Seung C.
1991-11-01
Radial wavefunctions in quantum scattering calculations are expanded in terms of two shape functions for each finite element. This approach is the R matrix version of Kohn's variational method and also directly applicable to S matrix in the log-derivative version. The linear algebra involved amounts to solving definite banded systems. In this basis set method, R matrix or log-derivative matrix is greatly simplified and the computational effort is linearly proportional to the number of radial basis functions, promising computational efficiencies for large scale calculations. Convergences for test vases are also reasonably rapid.
Anagnostopoulos, Konstantinos N; Hanada, Masanori; Nishimura, Jun; Takeuchi, Shingo
2008-01-18
We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with 16 supercharges at finite temperature. The recently proposed nonlattice simulation enables us to include the effects of fermionic matrices in a transparent and reliable manner. The internal energy nicely interpolates the weak coupling behavior obtained by the high temperature expansion, and the strong coupling behavior predicted from the dual black-hole geometry. The Polyakov line asymptotes at low temperature to a characteristic behavior for a deconfined theory, suggesting the absence of a phase transition. These results provide highly nontrivial evidence for the gauge-gravity duality. PMID:18232852
NASA Astrophysics Data System (ADS)
Hu, Yao-Hua; Tong, Lei; Tan, Yong-Gang; Fang, Mao-Fa
2016-03-01
We demonstrate methods of enhancing robustness of entanglement of two-qubit systems undergoing generalized amplitude damping decoherence using weak measurement and measurement reversal. The results show that the local action of generalized amplitude damping noise can cause sudden death of entanglement, and the weak measurement and measurement reversal is useful for combating generalized amplitude damping decoherence and recovering the entanglement of two entangled qubits. In addition, the results indicate that it would be much more easily implemented by applying quantum measurement reversal on a single-qubit to enhance robustness of entanglement in finite temperature environment, than on both qubits.
Occurrence of discontinuities in the performance of finite-time quantum Otto cycles.
Zheng, Yuanjian; Hänggi, Peter; Poletti, Dario
2016-07-01
We study a quantum Otto cycle in which the strokes are performed in finite time. The cycle involves energy measurements at the end of each stroke to allow for the respective determination of work. We then optimize for the work and efficiency of the cycle by varying the time spent in the different strokes and find that the optimal value of the ratio of time spent on each stroke goes through sudden changes as the parameters of this cycle vary continuously. The position of these discontinuities depends on the optimized quantity under consideration such as the net work output or the efficiency. PMID:27575106
Finite-temperature electron correlations in the framework of a dynamic local-field correction
Schweng, H.K.; Boehm, H.M. )
1993-07-15
The quantum-mechanical version of the Singwi-Tosi-Land-Sjoelander (STLS) approximation is applied to finite temperatures. This approximation has two main advantages. First, it includes a dynamic local-field correction and second, it gives positive values for the pair-distribution function in the short-range region at zero temperature. This is even valid for rather low densities. After a description of the numerical difficulties arising with the use of a dynamic approximation, the results for the static-structure factor and the pair-distribution function are discussed thoroughly. Detailed work is performed on the static part of the local-field correction, with special emphasis put on the investigation of its structure. A peak is found at a wave vector [ital q][approx]2.8 (in units of the Fermi wave vector) for small temperatures, which tends towards higher values of [ital q] with increasing temperature. This peak causes an attractive particle-hole interaction in a certain [ital q] region and thus gives rise to the appearance of a charge-density wave. A parametric description is given for the static local-field correction in order to simplify further applications. Furthermore, the exchange-and-correlation free energy is considered. The results are compared with the STLS results and with the modified convolution approach.
NASA Astrophysics Data System (ADS)
Majka; Staszel, P.; Natowitz, J. B.; Cibor, J.; Hagel, K.; Li, J.; Mdeiwayeh, N.; Wada, R.; Zhao, Y.
1996-10-01
Quantum statistical thermodynamics has been used to calculate the number of available states and their occupation for fermions and bosons at temperature, T_in, of finite nuclear sytems. An apparent temperature of these systems, T_app, has been calculated from double yield ratios of two isotope pairs. The importance of employing the quantum statistics when high densities and/or low temperatures are involved is shown. However, at high temperatures and low densities, the system behaves as a Maxwell-Boltzmann gas. Sequental decays of fragments from excited states influence the double yield ratio observable, causing problems with the temperature extraction. The model has been applied to study the high temperature branch of the "caloric curve".
Warehime, Mick; Alexander, Millard H.
2014-07-14
We restate the application of the finite element method to collinear triatomic reactive scattering dynamics with a novel treatment of the scattering boundary conditions. The method provides directly the reactive scattering wave function and, subsequently, the probability current density field. Visualizing these quantities provides additional insight into the quantum dynamics of simple chemical reactions beyond simplistic one-dimensional models. Application is made here to a symmetric reaction (H+H{sub 2}), a heavy-light-light reaction (F+H{sub 2}), and a heavy-light-heavy reaction (F+HCl). To accompany this article, we have written a MATLAB code which is fast, simple enough to be accessible to a wide audience, as well as generally applicable to any problem that can be mapped onto a collinear atom-diatom reaction. The code and user's manual are available for download from http://www2.chem.umd.edu/groups/alexander/FEM.
NASA Astrophysics Data System (ADS)
Warehime, Mick; Alexander, Millard H.
2014-07-01
We restate the application of the finite element method to collinear triatomic reactive scattering dynamics with a novel treatment of the scattering boundary conditions. The method provides directly the reactive scattering wave function and, subsequently, the probability current density field. Visualizing these quantities provides additional insight into the quantum dynamics of simple chemical reactions beyond simplistic one-dimensional models. Application is made here to a symmetric reaction (H+H2), a heavy-light-light reaction (F+H2), and a heavy-light-heavy reaction (F+HCl). To accompany this article, we have written a MATLAB code which is fast, simple enough to be accessible to a wide audience, as well as generally applicable to any problem that can be mapped onto a collinear atom-diatom reaction. The code and user's manual are available for download from http://www2.chem.umd.edu/groups/alexander/FEM.