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1

Cloning in nonlinear Hamiltonian quantum and hybrid mechanics

Possibility of state cloning is analyzed in two types of generalizations of quantum mechanics with nonlinear evolution. It is first shown that nonlinear Hamiltonian quantum mechanics does not admit cloning without the cloning machine. It is then demonstrated that the addition of the cloning machine, treated as a quantum or as a classical system, makes the cloning possible by nonlinear Hamiltonian evolution. However, a special type of quantum-classical theory, known as the mean-field Hamiltonian hybrid mechanics, does not admit cloning by natural evolution. The latter represents an example of a theory where it appears to be possible to communicate between two quantum systems at super-luminal speed, but at the same time it is impossible to clone quantum pure states.

D. Arsenovic; N. Buric; D. B. Popovic; M. Radonjic; S. Prvanovic

2014-11-17

2

Isometric operators, isospectral Hamiltonians, and supersymmetric quantum mechanics

Isometric operators are used to provide a unified theory of the three established procedures for generating one-parameter families of isospectral Hamiltonians. All members of the same family of isospectral Hamiltonians are unitarily equivalent, and the unitary transformations between them form a group isomorphic with the additive group of real numbers. The theory is generalized by including the parameter identifying a member of an isospectral family as a new variable. The unitary transformations within a family correspond to translations in the parameter space. The generator of infinitesimal translations represents a conserved quantity in the extended theory. Isometric operators are then applied to the development of models of supersymmetric quantum mechanics. In addition to the standard models based on the Darboux procedure, I show how to construct models based on the Abraham-Moses and Pursey procedures. The formalism shows that the Nieto ambiguity present in all models of supersymmetric quantum mechanics can be interpreted as a renormalization of the ground state of the supersymmetric system. This allows a generalization of supersymmetric quantum mechanics analogous to that developed for systems of isospectral Hamiltonians.

Pursey, D.L.

1986-04-15

3

Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant. -- Highlights: •Self-adjoint extension theory and contact interactions. •Application of self-adjoint extensions to supersymmetry. •Contact interactions in finite volume with Robin boundary condition.

Al-Hashimi, M.H., E-mail: hashimi@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Salman, M., E-mail: msalman@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Shalaby, A., E-mail: amshalab@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Physics Department, Faculty of Science, Mansoura University (Egypt); Wiese, U.-J., E-mail: wiese@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA (United States)

2013-10-15

4

The general aim of this paper is to extend the Modal-Hamiltonian interpretation of quantum mechanics to the case of relativistic quantum mechanics with gauge U(1) elds. In this case we propose that the actual- valued observables are the Casimir operators of the Poincar\\'e group and of the group U(1) of the internal symmetry of the theory. Moreover, we also show that the magnitudes that acquire actual values in the relativistic and in the non-relativistic cases are correctly related through the adequate limit.

Juan Sebastián Ardenghi; Mario Castagnino; Olimpia Lombardi

2010-12-05

5

The Interpretation of Quantum-Mechanical Models with Non-Hermitian Hamiltonians and Real Spectra

We study the quantum-mechanical interpretation of models with non-Hermitian Hamiltonians and real spectra. We set up a general framework for the analysis of such systems in terms of Hermitian Hamiltonians defined in the usual Hilbert space $L_2(-\\\\infty,\\\\infty)$. Special emphasis is put on the correct definition of the algebra of physical observables. Within this scheme we consider various examples, including the

R. Kretschmer; L. Szymanowski

2001-01-01

6

Holomorphic quantum mechanics with a quadratic Hamiltonian constraint

A finite-dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic, and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator algebra. The different representations yield drastically different Hilbert spaces. In particular, all the spaces obtained in the antiholomorphic representation violate classical expectations for the spectra of certain operators, whereas

Jorma Louko

1993-01-01

7

We present an ab initio polarizable representation of classical molecular mechanics (MM) atoms by employing an angular momentum-based expansion scheme of the point charges into partial wave orbitals. The charge density represented by these orbitals can be fully polarized, and for hybrid quantum-mechanical-molecular-mechanical (QM\\/MM) calculations, mutual polarization within the QM\\/MM Hamiltonian can be obtained. We present the mathematical formulation and

P. K. Biswas; Valentin Gogonea

2008-01-01

8

The linearity of quantum mechanics from the perspective of Hamiltonian cellular automata

NASA Astrophysics Data System (ADS)

We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped reversibly on continuum equations describing a set of bandwidth limited harmonic oscillators. They represent the Schrödinger equation. However, modifications reflecting the bandwidth limit are incorporated, i.e., the presence of a time (or length) scale. When this discreteness scale is taken to zero, the usual results are obtained. Thus, the linearity of quantum mechanics can be traced to the postulated action principle of such cellular automata and its conservation laws to discrete ones. The cellular automaton conservation laws are in one-to-one correspondence with those of the related quantum mechanical model, while admissible symmetries are not.

Elze, Hans-Thomas

2014-04-01

9

NASA Astrophysics Data System (ADS)

We provide a reviewlike introduction to the quantum mechanical formalism related to non-Hermitian Hamiltonian systems with real eigenvalues. Starting with the time-independent framework, we explain how to determine an appropriate domain of a non-Hermitian Hamiltonian and pay particular attention to the role played by PJ symmetry and pseudo-Hermiticity. We discuss the time evolution of such systems having in particular the question in mind of how to couple consistently an electric field to pseudo-Hermitian Hamiltonians. We illustrate the general formalism with three explicit examples: (i) the generalized Swanson Hamiltonians, which constitute non-Hermitian extensions of anharmonic oscillators, (ii) the spiked harmonic oscillator, which exhibits explicit super-symmetry, and (iii) the - x 4-potential, which serves as a toy model for the quantum field theoretical ?4-theory.

Faria, C. F. M.; Fring, A.

2007-04-01

10

Programmable quantum simulation by dynamic Hamiltonian engineering

Quantum simulation is a promising near term application for mesoscale quantum information processors, with the potential to solve computationally intractable problems at the scale of just a few dozen interacting quantum systems. Recent experiments in a range of technical platforms have demonstrated the basic functionality of quantum simulation applied to quantum magnetism, quantum phase transitions, and relativistic quantum mechanics. In all cases, the underlying hardware platforms restrict the achievable inter-particle interaction, forming a serious constraint on the ability to realize a versatile, programmable quantum simulator. In this work, we address this problem by developing novel sequences of unitary operations that engineer desired effective Hamiltonians in the time-domain. The result is a hybrid programmable analog simulator permitting a broad class of interacting spin-lattice models to be generated starting only with an arbitrary long-range native inter-particle interaction and single-qubit addressing. Specifically, our approach permits the generation of all symmetrically coupled translation-invariant two-body Hamiltonians with homogeneous on-site terms, a class which includes all spin-1/2 XYZ chains, but generalized to include long-range couplings. Building on previous work proving that universal simulation is possible using both entangling gates and single-qubit unitaries, we show that determining the "program" of unitary pulses to implement an arbitrary spin Hamiltonian can be formulated as a linear program that runs in polynomial time and scales efficiently in hardware resources. Our analysis extends from circuit model quantum information to adiabatic quantum evolutions, where our approach allows for the creation of non-native ground state solutions to a computation.

David L. Hayes; Steven T. Flammia; Michael J. Biercuk

2014-06-18

11

Quantum Hamiltonian Physics with Supercomputers

NASA Astrophysics Data System (ADS)

The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark-gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed.

Vary, James P.

2014-06-01

12

Hamiltonian Learning and Certification Using Quantum Resources

NASA Astrophysics Data System (ADS)

In recent years quantum simulation has made great strides, culminating in experiments that existing supercomputers cannot easily simulate. Although this raises the possibility that special purpose analog quantum simulators may be able to perform computational tasks that existing computers cannot, it also introduces a major challenge: certifying that the quantum simulator is in fact simulating the correct quantum dynamics. We provide an algorithm that, under relatively weak assumptions, can be used to efficiently infer the Hamiltonian of a large but untrusted quantum simulator using a trusted quantum simulator. We illustrate the power of this approach by showing numerically that it can inexpensively learn the Hamiltonians for large frustrated Ising models, demonstrating that quantum resources can make certifying analog quantum simulators tractable.

Wiebe, Nathan; Granade, Christopher; Ferrie, Christopher; Cory, D. G.

2014-05-01

13

Hamiltonian learning and certification using quantum resources.

In recent years quantum simulation has made great strides, culminating in experiments that existing supercomputers cannot easily simulate. Although this raises the possibility that special purpose analog quantum simulators may be able to perform computational tasks that existing computers cannot, it also introduces a major challenge: certifying that the quantum simulator is in fact simulating the correct quantum dynamics. We provide an algorithm that, under relatively weak assumptions, can be used to efficiently infer the Hamiltonian of a large but untrusted quantum simulator using a trusted quantum simulator. We illustrate the power of this approach by showing numerically that it can inexpensively learn the Hamiltonians for large frustrated Ising models, demonstrating that quantum resources can make certifying analog quantum simulators tractable. PMID:24877920

Wiebe, Nathan; Granade, Christopher; Ferrie, Christopher; Cory, D G

2014-05-16

14

NASA Astrophysics Data System (ADS)

Introduction; Part I. Basic Features of Quantum Mechanics: 1. From classical mechanics to quantum mechanics; 2. Quantum observable and states; 3. Quantum dynamics; 4. Examples of quantum dynamics; 5. Density matrix; Part II. More Advanced Topics: 6. Angular momentum and spin; 7. Identical particles; 8. Symmetries and conservation laws; 9. The measurement problem; Part III. Matter and Light: 10. Perturbations and approximation methods; 11. Hydrogen and helium atoms; 12. Hydrogen molecular ion; 13. Quantum optics; Part IV. Quantum Information: State and Correlations: 14. Quantum theory of open systems; 15. State measurement in quantum mechanics; 16. Entanglement: non-separability; 17. Entanglement: quantum information; References; Index.

Auletta, Gennaro; Fortunato, Mauro; Parisi, Giorgio

2014-01-01

15

Non-Hermitian quantum Hamiltonians with PT symmetry

We formulate quantum mechanics for non-Hermitian Hamiltonians that are invariant under PT, where P is the parity and T denotes time reversal, for the case that time-reversal symmetry is odd (T{sup 2}=-1), generalizing prior work for the even case (T{sup 2}=1). We discover an analog of Kramer's theorem for PT quantum mechanics, present a prototypical example of a PT quantum system with odd time reversal, and discuss potential applications of the formalism.

Jones-Smith, Katherine; Mathur, Harsh [Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106-7079 (United States)

2010-10-15

16

Hamiltonian mechanics of stochastic acceleration.

We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems. PMID:24266476

Burby, J W; Zhmoginov, A I; Qin, H

2013-11-01

17

Adiabatic quantum optimization with the wrong Hamiltonian

NASA Astrophysics Data System (ADS)

Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement these Hamiltonians will be imperfect and limited in its precision. Even small perturbations and imprecisions can have profound effects on the nature of the ground state. Here we consider an imperfect implementation of adiabatic quantum optimization and show that, for a widely applicable random control noise model, quantum stabilizer encodings are able to reduce the effective noise magnitude and thus improve the likelihood of a successful computation or simulation. This reduction builds upon two design principles: summation of equivalent logical operators to increase the energy scale of the encoded optimization problem, and the inclusion of a penalty term comprising the sum of the code stabilizer elements. We illustrate our findings with an Ising ladder and show that classical repetition coding drastically increases the probability that the ground state of a perturbed model is decodable to that of the unperturbed model, while using only realistic two-body interaction. Finally, we note that the repetition encoding is a special case of quantum stabilizer encodings, and show that this in principle allows us to generalize our results to many types of analog quantum information processing, albeit at the expense of many-body interactions.

Young, Kevin C.; Blume-Kohout, Robin; Lidar, Daniel A.

2013-12-01

18

PT-symmetric quantum mechanics

This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition H†=H on the Hamiltonian, where † represents the mathematical operation of complex conjugation and matrix transposition. This conventional Hermiticity condition is sufficient to ensure that the Hamiltonian H has a real spectrum. However, replacing this mathematical condition by the weaker and more physical requirement

Carl M. Bender; Stefan Boettcher; Peter N. Meisinger

1999-01-01

19

Uncertainty relation for non-Hamiltonian quantum systems

General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schroedinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications.

Tarasov, Vasily E. [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)] [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)

2013-01-15

20

Evolution Law of Quantum Observables from Classical Hamiltonian in Non-Commutative Phase Space

The evolution equations of quantum observables are derived from the classical Hamiltonian equations of motion with the only additional assumption that the phase space is non-commutative. The demonstration of the quantum evolution laws is quite general; it does not rely on any assumption on the operator nature of x and p and is independent of the quantum mechanical formalism.

Daniela Dragoman

2006-04-11

21

Estimation of many-body quantum Hamiltonians via compressive sensing

We develop an efficient and robust approach for quantum measurement of nearly sparse many-body quantum Hamiltonians based on the method of compressive sensing. This work demonstrates that with only O(sln(d)) experimental ...

Shabani, A.

22

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction; 2. Mathematical preliminaries; 3. The rules of quantum mechanics; 4. The connection between the fundamental rules and wave mechanics; 5. Further illustrations of the rules of quantum mechanics; 6. Further developments in one-dimensional wave mechanics; 7. The theory of angular momentum; 8. Wave mechanics in three dimensions: hydrogenic atoms; 9. Time-independent approximations for bound state problems; 10. Applications of static perturbation theory; 11. Identical particles; 12. Atomic structure; 13. Molecules; 14. The stability of matter; 15. Photons; 16. Interaction of non-relativistic charged particles and radiation; 17. Further topics in perturbation theory; 18. Scattering; 19. Special relativity and quantum mechanics: the Klein–Gordon equation; 20. The Dirac equation; 21. Interaction of a relativistic spin 1/2 particle with an external electromagnetic field; 22. The Dirac field; 23. Interaction between relativistic electrons, positrons, and photons; 24. The quantum mechanics of weak interactions; 25. The quantum measurement problem; Appendix A: useful inequalities for quantum mechanics; Appendix B: Bell's inequality; Appendix C: spin of the photon: vector spherical waves; Works cited; Bibliography; Index.

Commins, Eugene D.

2014-10-01

23

NSDL National Science Digital Library

This website contains a number of descriptions of quantum mechanical phenomena, using 3D animations to illustrate the physics. The goal is to introduce basic concepts and phenomena using simulations rather than complex mathematics. The time-dependence of quantum systems is a focus of this material.

De Raedt, Hans; Michielsen, Kristel

2010-03-25

24

PT quantum mechanics - Recent results

Most quantum physicists believe that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under matrix transposition and complex conjugation) to be sure that the energy eigenvalues are real and that time evolution is unitary. However, the non-Dirac-hermitian Hamiltonian H p{sup 2}+ix{sup 3} has a real positive discrete spectrum and generates unitary time evolution and defines a fully consistent and physical quantum theory. Evidently, Dirac Hermiticity is too restrictive. While H = p{sup 2}+ix{sup 3} is not Dirac Hermitian, it is PT symmetric (invariant under combined space reflection P and time reversal T). Another PT-symmetric Hamiltonian whose energy levels are real, positive and discrete is H = p{sup 2}-x{sup 4}, which contains an upside-down potential. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics and quantum field theory are extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past two years some of these properties have been verified in laboratory experiments. Here, we first discuss PT-symmetric Hamiltonians at a simple intuitive level and explain why the energy levels of such Hamiltonians may be real, positive, and discrete. Second, we describe a recent experiment in which the PT phase transition was observed. Third, we briefly mention that PT-symmetric theories can be useful at a fundamental level. While the double-scaling limit of an O(N)-symmetric g{phi}{sup 4} quantum field theory appears to be inconsistent because the critical value of g is negative, this limit is in fact not inconsistent because the critical theory is PT symmetric.

Bender, Carl M. [Physics Department, Washington University, St. Louis, MO 63130 (United States)

2012-09-26

25

Time and a physical Hamiltonian for quantum gravity.

We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. PMID:22540782

Husain, Viqar; Paw?owski, Tomasz

2012-04-01

26

On the Hamiltonian Description of Fluid Mechanics

We suggest the Hamiltonian approach for fluid mechanics based on the dynamics, formulated in terms of Lagrangian variables. The construction of the canonical variables of the fluid sheds a light of the origin of Clebsh variables, introduced in the previous century. The developed formalism permits to relate the circulation conservation (Tompson theorem) with the invariance of the theory with respect to special diffiomorphisms and establish also the new conservation laws. We discuss also the difference of the Eulerian and Lagrangian description, pointing out the incompleteness of the first. The constructed formalism is also applicable for ideal plasma. We conclude with several remarks on the quantization of the fluid.

I. Antoniou; G. P. Pronko

2001-06-14

27

The Scattering Matrix and Associated Formulas in Hamiltonian Mechanics

NASA Astrophysics Data System (ADS)

We prove two new identities in scattering theory in Hamiltonian mechanics and discuss the analogy between these identities and their counterparts in quantum scattering theory. These identities involve the Poincaré scattering map, which is analogous to the scattering matrix. The first of our identities states that the Calabi invariant of the Poincaré scattering map can be expressed as the regularised phase space volume. This is analogous to the Birman-Krein formula. The second identity relates the Poincaré scattering map to the total time delay and is analogous to the Eisenbud-Wigner formula.

Buslaev, Vladimir; Pushnitski, Alexander

2010-01-01

28

The multidimensional N=4 supersymmetric (SUSY) quantum mechanics (QM) is constructed using the superfield approach. As a result, the component form of the classical and quantum Lagrangian and Hamiltonian is obtained. In the SUSY QM considered, both classical and quantum N=4 algebras include central charges, and this opens various possibilities for partial supersymmetry breaking. It is shown that quantum-mechanical models with

E. E. Donets; A. Pashnev; J. Juan Rosales; M. M. Tsulaia

2000-01-01

29

Supersymmetric q-deformed quantum mechanics

A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.

Traikia, M. H.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)

2012-06-27

30

Fast Universal Quantum Computation with Railroad-switch Local Hamiltonians

We present two universal models of quantum computation with a time-independent, frustration-free Hamiltonian. The first construction uses 3-local (qubit) projectors, and the second one requires only 2-local qubit-qutrit projectors. We build on Feynman's Hamiltonian computer idea and use a railroad-switch type clock register. The resources required to simulate a quantum circuit with L gates in this model are O(L) small-dimensional quantum systems (qubits or qutrits), a time-independent Hamiltonian composed of O(L) local, constant norm, projector terms, the possibility to prepare computational basis product states, a running time O(L log^2 L), and the possibility to measure a few qubits in the computational basis. Our models also give a simplified proof of the universality of 3-local Adiabatic Quantum Computation.

Daniel Nagaj

2009-08-28

31

-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter–antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantum mechanics. PMID:23509390

Bender, Carl M; DeKieviet, Maarten; Klevansky, S. P.

2013-01-01

32

Fast Universal Quantum Computation with Railroad-switch Local Hamiltonians

We present two universal models of quantum computation with a time-independent, frustration-free Hamiltonian. The first construction uses 3-local (qubit) projectors, and the second one requires only 2-local qubit-qutrit projectors. We build on Feynman's Hamiltonian computer idea and use a novel railroad-switch clock register, inspired by the triangle Hamiltonian of Eldar et al. The resources required to simulate a quantum circuit with L gates in this model are O(L) small-dimensional quantum systems (qubits or qutrits), a time-independent Hamiltonian composed of O(L) local, constant norm, projector terms, the possibility to prepare computational basis product states, a running time O(L log^2 L), and the possibility to measure a few qubits in the computational basis. Our models also give a simplified proof of the universality of Adiabatic Quantum Computation. Nevertheless, it is not the power of the adiabatic theorem, but Feynman's idea and the dynamics of a quantum walk in 1D that give our frustration-free Ham...

Nagaj, Daniel

2009-01-01

33

Emergent mechanics, quantum and un-quantum

NASA Astrophysics Data System (ADS)

There is great interest in quantum mechanics as an "emergent" phenomenon. The program holds that nonobvious patterns and laws can emerge from complicated physical systems operating by more fundamental rules. We find a new approach where quantum mechanics itself should be viewed as an information management tool not derived from physics nor depending on physics. The main accomplishment of quantum-style theory comes in expanding the notion of probability. We construct a map from macroscopic information as data" to quantum probability. The map allows a hidden variable description for quantum states, and efficient use of the helpful tools of quantum mechanics in unlimited circumstances. Quantum dynamics via the time-dependent Shroedinger equation or operator methods actually represents a restricted class of classical Hamiltonian or Lagrangian dynamics, albeit with different numbers of degrees of freedom. We show that under wide circumstances such dynamics emerges from structureless dynamical systems. The uses of the quantum information management tools are illustrated by numerical experiments and practical applications

Ralston, John P.

2013-10-01

34

Minkowski Space and Quantum Mechanics

NASA Astrophysics Data System (ADS)

A paradigm shift distinguishes general relativity from classical mechanics. In general relativity the energy-momentum tensor is the effective cause of the ontological space-time curvature and vice-versa, while in classical physics, the structure of space-time is treated as an accidental cause, serving only as a backdrop against which the laws of physics unfold. This split in turn is inherited by quantum mechanics, which is usually developed by changing classical (including special relativity) Hamiltonians into quantum wave equations.

O'Hara, Paul

35

The Hamiltonian Mechanics of Stochastic Acceleration

We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.

J. W. Burby; A. I. Zhmoginov; H. Qin

2013-12-13

36

The Hamiltonian Mechanics of Stochastic Acceleration

We show how to nd the physical Langevin equation describing the trajectories of particles un- dergoing collisionless stochastic acceleration. These stochastic di erential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.

Burby, J. W.

2013-07-17

37

Lagrangian and Hamiltonian Geometries. Applications to Analytical Mechanics

The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or evolution equations) of these Mechanics are derived from the variational calculus applied to the integral of action and these can be studied by using the methods of Lagrangian or Hamiltonian geometries. More general, the notions of higher order Lagrange or Hamilton spaces have been introduced and developed by the present author. The applications led to the notions of Lagrangian or Hamiltonian Analytical Mechanics of higher order. For short, in this text we aim to solve some difficult problems: The problem of geometrization of classical non conservative mechanical systems; The foundations of geometrical theory of new mechanics: Finslerian, Lagrangian and Hamiltonian;To determine the evolution equations of the classical mechanical systems for whose external forces depend on the higher order accelerations. My colleagues Professors M. Anastasiei, I. Bucataru, I. Mihai, K. Stepanovici made important remarks and suggestions and Mrs. Carmen Savin prepared an excellent print-form of the hand-written text. Many thanks to all of them.

Radu Miron

2012-03-19

38

Hamiltonian mechanics of generalized eikonal waves

In accordance with the Keller-Maslov global WKB theory, a semiclassical scalar wave field is best encoded as a triple consisting of (i) a Lagrangian submanifold $\\Lambda$ in the ray phase space, (ii) a density $\\mu$ on $\\Lambda$, and (iii) an overall phase factor $\\phi$. We present the Hamiltonian structure of the Cauchy problem for such a "geometric semiclassical state" in the special case where the wave operator is Hermetian. Variational, symplectic, and Poisson formulations of the time evolution equations for $(\\Lambda,\\mu,\\phi)$ are identitfied. Because we work in terms of the Keller-Maslov global WKB ansatz, as opposed to the more restrictive $\\psi=a \\exp(i S/\\epsilon)$, all of our results are insensitive to the presence of caustics. In particular, because the variational principle is insensitive to caustics, the latter may be used to construct structure-perserving numerical integrators for scalar wave equations.

J. W. Burby; H. Qin

2014-05-07

39

Quantum integrals of motion for variable quadratic Hamiltonians

We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

Cordero-Soto, Ricardo, E-mail: ricardojavier81@gmail.co [Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804 (United States); Suazo, Erwin, E-mail: erwin.suazo@upr.ed [Department of Mathematical Sciences, University of Puerto Rico, Mayaquez, call box 9000, PR 00681-9000 (Puerto Rico); Suslov, Sergei K., E-mail: sks@asu.ed [School of Mathematical and Statistical Sciences and Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804 (United States)

2010-09-15

40

NASA Astrophysics Data System (ADS)

A development of quantum theory that was initiated in the 1920s by Werner Heisenberg (1901-76) and Erwin Schrödinger (1887-1961). The theory drew on a proposal made in 1925 Prince Louis de Broglie (1892-1987), that particles have wavelike properties (the wave-particle duality) and that an electron, for example, could in some respects be regarded as a wave with a wavelength that depended on its mo...

Murdin, P.

2000-11-01

41

A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Lévy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Lévy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and

Nikolai Laskin

2000-01-01

42

Third-order differential ladder operators and supersymmetric quantum mechanics

NASA Astrophysics Data System (ADS)

Hierarchies of one-dimensional Hamiltonians in quantum mechanics admitting third-order differential ladder operators are studied. Each Hamiltonian has associated three-step Darboux (pseudo)-cycles and Painlevé IV equations as a closure condition. The whole hierarchy is generated applying some operations on the cycles. These operations are investigated in the frame of supersymmetric quantum mechanics and mainly involve algebraic manipulations. A consistent geometric representation for the hierarchy and cycles is built that also helps in understanding the operations. Three kinds of hierarchies are distinguished and a realization based on the harmonic oscillator Hamiltonian is supplied, giving an interpretation for the spectral properties of the Hamiltonians of each hierarchy.

Mateo, J.; Negro, J.

2008-02-01

43

More on Exact $\\CP$-Symmetric Quantum Mechanics

In this article, we discussed certain properties of non-Hermitian $\\CP$-symmetry Hamiltonian, and it is shown that a consistent physical theory of quantum mechanics can be built on a ${\\cal C} \\CP$-symmetry Hamiltonian. In particular, we show that these theories have unitary time evolution, and conservation probability. Furthermore, transition from quantum mechanics to classical mechanics is investigate and it is found that the Ehrenfest theorem is satisfied.

Khaled Saaidi

2003-09-15

44

Participation spectroscopy and entanglement Hamiltonian of quantum spin models

NASA Astrophysics Data System (ADS)

Shannon-Rényi entropies and associated participation spectra quantify how much a many-body wave-function is localized in a given configuration basis. Using these tools, we present an analysis of the ground-state wave functions of various quantum spin systems in one and two dimensions. General ideas and a review of the current status of this field are first given, with a particular emphasis on universal subleading terms characterizing different quantum phases of matter, and associated transitions. We highlight the connection with the related entanglement entropies and spectra when this is possible. In a second part, new results are presented for the participation spectra of interacting spin models, mostly based on quantum Monte Carlo simulations, but also using perturbation theory in some cases. For full antiferromagnetic one-dimensional systems, participation spectra are analyzed in terms of ferromagnetic domain walls which experience a pairwise attractive interaction. This confinement potential is either linear for long-range Néel order, or logarithmic for quasi-long-range order. The case of subsystems is also analyzed in great detail for a 2d dimerized Heisenberg model undergoing a quantum phase transition between a gapped paramagnet and a Néel phase. Participation spectra of line shaped (1d) sub-systems are quantitatively compared with finite temperature participation spectra of ansatz effective boundary (1d) entanglement Hamiltonians. While short-range models describe almost perfectly the gapped side, the Néel regime is best compared using long-range effective Hamiltonians. Spectral comparisons performed using Kullback-Leibler divergences, a tool potentially useful for entanglement spectra, provide a quantitative way to identify both the best boundary entanglement Hamiltonian and effective temperature.

Luitz, David J.; Laflorencie, Nicolas; Alet, Fabien

2014-08-01

45

Mechanical analogues of spin Hamiltonians and dynamics

NASA Astrophysics Data System (ADS)

Bloch et al. mapped the precession of the spin-half in a magnetic field of variable magnitude and direction to the rotations of a rigid sphere rolling on a curved surface utilizing SU(2)-SO(3) isomorphism. This formalism is extended to study the behaviour of spin-orbit interactions and the mechanical analogy for Rashba-Dresselhauss spin-orbit interaction in two dimensions is presented by making its spin states isomorphic to the rotations of a rigid sphere rolling on a ring. The change in phase of spin is represented by the angle of rotation of sphere after a complete revolution. In order to develop the mechanical analogy for the spin filter, we find that perfect spin filtration of down spin makes the sphere to rotate at some unique angles and the perfect spin filtration of up spin causes the rotations with certain discrete frequencies.

Kaur, Harjeet; Jain, Sudhir R.; Malik, Sham S.

2014-01-01

46

Error suppression in Hamiltonian based quantum computation using energy penalties

We consider the use of quantum error detecting codes, together with energy penalties against leaving the codespace, as a method for suppressing environmentally induced errors in Hamiltonian based quantum computation. This method was introduced in [1] in the context of quantum adiabatic computation, but we consider it more generally. Specifically, we consider a computational Hamiltonian, which has been encoded using the logical qubits of a single-qubit error detecting code, coupled to an environment of qubits by interaction terms that act one-locally on the system. Energy penalty terms are added that penalize states outside of the codespace. We prove that in the limit of infinitely large penalties, one-local errors are completely suppressed, and we derive some bounds for the finite penalty case. Our proof technique involves exact integration of the Schrodinger equation, making no use of master equations or their assumptions. We perform long time numerical simulations on a small (one logical qubit) computational system coupled to an environment and the results suggest that the energy penalty method achieves even greater protection than our bounds indicate.

Adam D. Bookatz; Edward Farhi; Leo Zhou

2014-07-06

47

Lie-Poisson integrators in Hamiltonian fluid mechanics

This thesis explores the application of geometric mechanics to problems in 2D, incompressible, inviscid fluid mechanics. The main motivation is to try to develop symplectic integration algorithms to model the Hamiltonian structure of inviscid fluid flow. The main manifestation of this Hamiltonian or conservative nature is the preservation of the infinite family of Casimirs parametrized by the body integrals of vorticity in the 2D case. The main difficulties encountered in trying to model the Hamiltonian structure of a fluid mechanical system are that the configuration space for the Hamiltonian flow is an infinite dimensional Frechet space and that the phase space is not symplectic but Lie-Poisson. Therefore, an appropriate finite mode truncation must be constructed under the constraint that it too remains Poisson and in some sense converges to the infinite dimensional parent manifold. With such a truncation in hand, there still remains the obstacle of non-symplectic structure. This geometry invalidates the application of traditional symplectic integrators and requires a more sophisticated algorithm. The authors develop a Lie-Poisson truncation on the Lie group SU(N) for the Euler equations on the special geometry of a twice periodic domain in R[sup 2]. They show that this finite dimensional analog is compatible with the Arnold[5] formulation of Hamiltonian mechanics on Lie groups with a left or right invariant metric. They then proceed to review the Lie-Poisson integration literature and to develop Hamilton-Jacobi type symplectic algorithms for a broad class of Lie groups. For this same class of groups, they also succeed in constructing an explicit Lie-Poisson algorithm which radically improves computational speed over the current implicit schema. They test this new algorithm against a Hamilton-Jacobi implicit technique with favorable results.

Ryan, B.J.

1993-01-01

48

Quantum mechanics with explicit time dependence

We investigate quantum mechanical Hamiltonians with explicit time dependence. We find a class of models in which an analogue of the time-independent Schrödinger equation exists. Among the models in this class is a new exactly soluble model, the harmonic oscillator with frequency inversely proportional to time.

John Rogers; Donald Spector

1992-01-01

49

Timeless path integral for relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of a timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all possible paths in the constraint surface specified by the (relativistic) Hamiltonian constraint, and each path contributes with a phase identical to the classical action divided by ?. The timeless path integral manifests the timeless feature as it is completely independent of the parametrization for paths. For the special case that the Hamiltonian constraint is a quadratic polynomial in momenta, the transition amplitude admits the timeless Feynman's path integral over the (relativistic) configuration space. Meanwhile, the difference between relativistic quantum mechanics and conventional nonrelativistic (with time) quantum mechanics is elaborated on in light of the timeless path integral.

Chiou, Dah-Wei

2013-06-01

50

Quantum Mechanics II (Undergraduate)

, and applications of quantum mechanics to materials science/solid-state physics. Grades: Homework: 15%, Midertm: 40 other selected topics from quantum information (see the QUNET reference) and solid-state physics. All

Nickrent, Daniel L.

51

Coherent states for quantum systems with a trilinear boson Hamiltonian

We introduce a set of coherent states which are associated with quantum systems governed by a trilinear boson Hamiltonian. These states are produced by the action of a nonunitary displacement operator on a reference state and can be equivalently defined by some eigenvalue equations. The system prepared initially in the reference state will evolve into the coherent state during the first instants of the interaction process. Some properties of the coherent states are discussed. In particular, the resolution of the identity is derived and the related analytic representation in the complex plane is developed. It is shown that this analytic representation coincides with a double representation based on the Glauber coherent states of the pump mode and on the SU(1,1) Perelomov coherent states of the signal-idler system. Entanglement between the field modes and photon statistics of the coherent states are studied. Connections between the coherent states and the long-time evolution induced by the trilinear Hamiltonian are considered.

C. Brif

1996-08-14

52

Effective quantum memory Hamiltonian from local two-body interactions

In [Phys. Rev. A 88, 062313 (2013)] we proposed and studied a model for a self-correcting quantum memory in which the energetic cost for introducing a defect in the memory grows without bounds as a function of system size. This positive behavior is due to attractive long-range interactions mediated by a bosonic field to which the memory is coupled. The crucial ingredients for the implementation of such a memory are the physical realization of the bosonic field as well as local five-body interactions between the stabilizer operators of the memory and the bosonic field. Here, we show that both of these ingredients appear in a low-energy effective theory of a Hamiltonian that involves only two-body interactions between neighboring spins. In particular, we consider the low-energy, long-wavelength excitations of an ordered Heisenberg ferromagnet (magnons) as a realization of the bosonic field. Furthermore, we present perturbative gadgets for generating the required five-spin operators. Our Hamiltonian involving only local two-body interactions is thus expected to exhibit self-correcting properties as long as the noise affecting it is in the regime where the effective low-energy description remains valid.

Adrian Hutter; Fabio L. Pedrocchi; James R. Wootton; Daniel Loss

2014-05-13

53

Statistical mechanics based on fractional classical and quantum mechanics

The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantum mechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantum mechanics, we have calculated the thermodynamical properties for the black body radiation, studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac statistics.

Korichi, Z.; Meftah, M. T., E-mail: mewalid@yahoo.com [Physics Department, LRPPS Laboratory, Ouargla University, Ouargla 30000 (Algeria)

2014-03-15

54

Quantum-Merlin-Arthur-complete problems for stoquastic Hamiltonians and Markov matrices

We show that finding the lowest eigenvalue of a 3-local symmetric stochastic matrix is Quantum-Merlin-Arthur-complete (QMA-complete). We also show that finding the highest energy of a stoquastic Hamiltonian is QMA-complete and that adiabatic quantum computation using certain excited states of a stoquastic Hamiltonian is universal. We also show that adiabatic evolution in the ground state of a stochastic frustration-free Hamiltonian is universal. Our results give a QMA-complete problem arising in the classical setting of Markov chains and adiabatically universal Hamiltonians that arise in many physical systems.

Jordan, Stephen P.; Gosset, David; Love, Peter J. [Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States); Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 6-304, Cambridge, Massachusetts 02139 (United States); Department of Physics, Haverford College, 370 Lancaster Avenue, Haverford, Pennsylvania 19041, USA, and Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States)

2010-03-15

55

Advanced Visual Quantum Mechanics

NSDL National Science Digital Library

This page provides links to a range of teaching materials for use in an upper-level undergraduate quantum mechanics course. These are developed from some of the concepts of the Visual Quantum Mechanics course for high school and introductory college classes. Materials inlcude tutorial activities in concepts of energy diagrams, probability, and wavefunctions, and some computer activities.

Axmann, Wally; Group, Kansas S.

2004-04-04

56

A classical analog of the quantum mechanical model of three Josephson junctions in a loop

It is shown that the time-dependent Schrödinger equation for a quantum mechanical system may be recast as a nonlinear flow if the Hamiltonian is a functional of the state of the system. This implies the possibility of deterministic chaos in this quantum mechanical system. If a classical Hamiltonian can be found that generates an identical flow, then a classical analog

R. H. Parmenter; L. Y. Yu

1995-01-01

57

NASA Astrophysics Data System (ADS)

We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the BLG-model and the ABJM-model compactified on a torus are N = 16 and N = 12 superconformal gauged quantum mechanics. After integrating out the auxiliary gauge fields we find OSp (16 | 2) and SU (1 , 1 | 6) quantum mechanics from the reduced systems. The curved Riemann surface is taken as a holomorphic curve in a Calabi-Yau space to preserve supersymmetry and we present a prescription of the topological twisting. We find the N = 8 superconformal gauged quantum mechanics that may describe the motion of two wrapped M2-branes in a K3 surface.

Okazaki, Tadashi

2015-01-01

58

We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the BLG-model and the ABJM-model compactified on a torus are N = 16 and N = 12 superconformal gauged quantum mechanics. After integrating out the auxiliary gauge fields we find OSp(16|2) and SU(1,1|6) quantum mechanics from the reduced systems. The curved Riemann surface is taken as a holomorphic curve in a Calabi-Yau space to preserve supersymmetry and we present a prescription of the topological twisting. We find the N = 8 superconformal gauged quantum mechanics that may describe the motion of two wrapped M2-branes in a K3 surface.

Tadashi Okazaki

2014-11-03

59

NASA Astrophysics Data System (ADS)

We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.

Kapustin, Anton

2013-06-01

60

Quantum Mechanical Models of Turing Machines That Dissipate No Energy

Quantum mechanical Hamiltonian models of Turing machines are constructed here on a finite lattice of spin- 1\\/2 systems. The models do not dissipate any energy and they operate at the quantum limit in that the system (energy uncertainty)\\/(computation speed) is close to the limit given by the time-energy uncertainty principle.

Paul Benioff

1982-01-01

61

NSDL National Science Digital Library

Visual Quantum Mechanics provides illustrations of quantum mechanics using computer-generated animations. Visualizations provide learning experiences for beginners and offer new insights to the advanced student or researcher. This project includes the development of multimedia software for teaching and scientific software for the solution of the Shrodinger equation and the visualization of these solutions in two and three dimensions. The materials presented here are related to two texts by the author.

Thaller, Bernd

2004-07-10

62

Can PT-Symmetric Quantum Mechanics be a Viable Alternative Quantum Theory?

Update: A time-independent $n\\times n$ PT-symmetric (and symmetric) Hamiltonian is diagonalizable since it has all distinct real eigenvalues and the resulting diagonal matrix is a real symmetric matrix. The diagonalization results an isometry so there shouldn't be any issue with unitarity and unfortunately this very elementary mathematical fact somehow did not draw the authors' attention. However, PT-symmetric quantum mechanics is not out of trouble. For time-dependent PT-symmetric (and symmetric) Hamiltonians (even $2\\times 2$ ones) the authors observed that there is a violation of unitarity. Moreover, the first named author showed in his recent article arXiv:1312.7738 that PT-symmetric quantum mechanics is indeed a certain kind of Hermitian quantum mechanics and that in order for time-evolution to be unitary with respect to $J$-inner product (one that gives rise to a Hilbert space structure on the space of state functions), the potential energy operator $V(x)$ must be real. This means that those complex PT-symmetric Hamiltonians that have been studied by physicists are unfortunately unphysical. The first named author discussed in a subsequent article arXiv:1401.5149 that while finite-state PT-symmetric quantum mechanics with time-independent Hamiltonians is not physically any different from Hermitian quantum mechanics, PT-symmetric quantum mechanics exhibits a distinctive symmetry from that of Hermitian quantum mechanics.

Sungwook Lee; Lawrence R. Mead

2014-05-18

63

Quantum ballistic evolution in quantum mechanics: Application to quantum computers

Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single-step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators T is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e., motion restricted to a collection of nonintersecting or distinct

Paul Benioff

1996-01-01

64

Adaptive Perturbation Theory I: Quantum Mechanics

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be treatable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, H, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. This paper introduces the method in the context of the pure anharmonic oscillator and then goes on to apply it to the case of tunneling between both symmetric and asymmetric minima. It concludes with an introduction to the extension of these methods to the discussion of a quantum field theory. A more complete discussion of this issue will be given in the second paper in this series, and it will show how to use the method of adaptive perturbation theory to non-perturbatively extract the structure of mass, wavefunction and coupling constant renormalization.

Weinstein, Marvin; /SLAC

2005-10-19

65

Models of Damped Oscillators in Quantum Mechanics

We consider several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schroedinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time-evolution of the expectation values of the energy related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator.

Ricardo Cordero-Soto; Erwin Suazo; Sergei K. Suslov

2009-06-04

66

Probability in Quantum Mechanics

The concept of probability played an important role in the very beginning of ? quantum theory, when Max Planck (1858–1947)\\u000a postulated the discrete emission and absorption of radiation in a ? black body radiation. The quantum statistical mechanics\\u000a developed by Planck and his successors has extraordinary consequences treated elsewhere in this Compendium. Here, however,\\u000a the emphasis will be upon the

Abner Shimony

67

Topological rigidity of Hamiltonian loops and quantum homology

. This paper studies the question of when a loop ?={?\\u000a \\u000a t\\u000a \\u000a }0?\\u000a \\u000a \\u000a \\u000a t\\u000a \\u000a \\u000a \\u000a ?1 in the group Symp(M,?) of symplectomorphisms of a symplectic manifold (M,?) is isotopic to a loop that is generated by a time-dependent Hamiltonian function. (Loops with this property are said to\\u000a be Hamiltonian.) Our main result is that Hamiltonian loops are rigid in the following

François Lalonde; Dusa McDuff; Leonid Polterovich

1999-01-01

68

Complex square well - a new exactly solvable quantum mechanical model

Recently, a class of -invariant quantum mechanical models described by the non-Hermitian Hamiltonian H = p2+x2(ix) was studied. It was found that the energy levels for this theory are real for all 0. Here, the limit as is examined. It is shown that in this limit, the theory becomes exactly solvable. A generalization of this Hamiltonian, H = p2+x2M(ix) (M

Carl M. Bender; Stefan Boettcher; H. F. Jones; Van M Savage

1999-01-01

69

Quantum Error Suppression with Commuting Hamiltonians: Two Local is Too Local

NASA Astrophysics Data System (ADS)

We consider error suppression schemes in which quantum information is encoded into the ground subspace of a Hamiltonian comprising a sum of commuting terms. Since such Hamiltonians are gapped, they are considered natural candidates for protection of quantum information and topological or adiabatic quantum computation. However, we prove that they cannot be used to this end in the two-local case. By making the favorable assumption that the gap is infinite, we show that single-site perturbations can generate a degeneracy splitting in the ground subspace of this type of Hamiltonian which is of the same order as the magnitude of the perturbation, and is independent of the number of interacting sites and their Hilbert space dimensions, just as in the absence of the protecting Hamiltonian. This splitting results in decoherence of the ground subspace, and we demonstrate that for natural noise models the coherence time is proportional to the inverse of the degeneracy splitting. Our proof involves a new version of the no-hiding theorem which shows that quantum information cannot be approximately hidden in the correlations between two quantum systems. The main reason that two-local commuting Hamiltonians cannot be used for quantum error suppression is that their ground subspaces have only short-range (two-body) entanglement.

Marvian, Iman; Lidar, Daniel A.

2014-12-01

70

NSDL National Science Digital Library

Visual Quantum Mechanics provides illustrations of quantum mechanics using computer-generated animations. Visualizations provide learning experiences for beginners and offer new insights to the advanced student or researcher. This project includes the development of multimedia software for teaching and scientific software for the solution of the Shrodinger equation and the visualization of these solutions in two and three dimensions. The materials presented here are related to two texts by the author. A German translation is also available. Quicktime is needed to view these movies.

Thaller, Bernd

2009-05-14

71

TIME IN QUANTUM MECHANICS A Thesis by KIMBERLY R. CHAPIN Submitted to Texas A8M University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Approved as to style and content by: Marian O. Scully (Chair... of Committee) Edward S. Fry (Member) aan Laane (Member) Thomas W. Adair, III (Head of Department) August 1997 Major Subject: Physics TIME IN QIJANTUM MECHANICS A Thesis by KIMBERLY R. CHAPIN Submitted to the Oflice of Graduate Studies of Texas A...

Chapin, Kimberly R.

2012-06-07

72

QUICK QUANTUM MECHANICS ---Introduction ---

to their students. Thus, it was natural that the historical evolution of quantum mechanics relied on some aspects sin 2 ` â?? OE 2 ] \\Gamma V (r) : (2) The time evolution of the system is given once we determine, replace it by q(t) + ffif (t) where ffif (t) is completely arbitrary except for the facts

Jackson, Andrew D.

73

Quantum Simulation of Pairing Hamiltonians with Nearest-Neighbor Interacting Qubits

Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum simulators are physical setups able to simulate other quantum systems efficiently that are intractable on classical computers. Based on solid-state qubit systems with various types of nearest-neighbor interactions, we propose a complete set of algorithms for simulating pairing Hamiltonians. Fidelity of the target states corresponding to each algorithm is numerically studied. We also compare algorithms designed for different types of experimentally available Hamiltonians and analyze their complexity. Furthermore, we design a measurement scheme to extract energy spectra from the simulators. Our simulation algorithms might be feasible with state-of-the-art technology in solid-state quantum devices.

Zhixin Wang; Xiu Gu; Lian-Ao Wu; Yu-xi Liu

2014-11-19

74

Quantum Mechanical Models of Solids

NSDL National Science Digital Library

This web site contains the class notes for a course on Quantum Mechanical Models of Solids. Topics cover basic quantum mechanics, crystallography, exchange-correlation, metals, and semiconductors. The site also includes a list of useful books and references.

Heggie, Malcom; Martinez, Irene S.; Venables, John, 1936-

2010-08-24

75

TRANSIENT QUANTUM MECHANICAL PROCESSES

Our principal objective has centered on the development of sophisticated computational techniques to solve the time-dependent Schroedinger equation that governs the evolution of quantum mechanical systems. We have perfected two complementary methods, discrete variable representation and real space product formula, that show great promise in solving these complicated temporal problems. We have applied these methods to the interaction of laser light with molecules with the intent of not only investigating the basic mechanisms but also devising schemes for actually controlling the outcome of microscopic processes. Lasers now exist that produce pulses of such short duration as to probe a molecular process many times within its characteristic period--allowing the actual observation of an evolving quantum mechanical system. We have studied the potassium dimer as an example and found agreement with experimental changes in the intermediate state populations as a function of laser frequency--a simple control prescription. We have also employed elaborate quantum chemistry programs to improve the accuracy of basic input such as bound-bound and bound-free coupling moments. These techniques have far-ranging applicability; for example, to trapped quantum systems at very low temperatures such as Bose-Einstein condensates.

L. COLLINS; J. KRESS; R. WALKER

1999-07-01

76

"Velocities" in Quantum Mechanics

The present paper deals with some kind of quantum ``velocity'' which is introduced by the method of hydrodynamical analogy. It is found that this ``velocity'' is in general irrotational, namely, a vorticity vanishes, and then a velocity potential must exist in quantum mechanics. In some elementary examples of stable systems we will see what the ``velocities'' are. In particular, the two-dimensional flows of these examples can be expressed by complex velocity potentials whose real and imaginary parts are the velocity potentials and stream functions, respectively.

Shimbori, T; Shimbori, Toshiki; Kobayashi, Tsunehiro

2000-01-01

77

"Velocities" in Quantum Mechanics

The present paper deals with some kind of quantum ``velocity'' which is introduced by the method of hydrodynamical analogy. It is found that this ``velocity'' is in general irrotational, namely, a vorticity vanishes, and then a velocity potential must exist in quantum mechanics. In some elementary examples of stable systems we will see what the ``velocities'' are. In particular, the two-dimensional flows of these examples can be expressed by complex velocity potentials whose real and imaginary parts are the velocity potentials and stream functions, respectively.

Toshiki Shimbori; Tsunehiro Kobayashi

2000-04-21

78

The quantum field theories (QFT) constructed in [1,2] include phenomenology of interest. The constructions approximate: scattering by $1/r$ and Yukawa potentials in non-relativistic approximations; and the first contributing order of the Feynman series for Compton scattering. To have a semi-norm, photon states are constrained to transverse polarizations and for Compton scattering, the constructed cross section deviates at large momentum exchanges from the cross section prediction of the Feynman rules. Discussion includes the incompatibility of canonical quantization with the constructed interacting fields, and the role of interpretations of quantum mechanics in realizing QFT.

Glenn Eric Johnson

2014-12-21

79

Probabilistic Interpretation of Quantum Mechanics

The probabilistic interpretation of quantum mechanics is based on Born's 1926 papers and von Neumann's formal account of quantum\\u000a mechanics in ? Hilbert space. According to Max Born (1882–1970), the quantum mechanical ? wave function ? does not have any\\u000a direct physical meaning, whereas its square ???2 is a probability [1] ? Born rule, probability in quantum mechanics. According to

Brigitte Falkenburg; Peter Mittelstaedt

80

Path Integrals in Quantum Mechanics

Jean Zinn-Justin's textbook Path Integrals in Quantum Mechanics aims to familiarize the reader with the path integral as a calculational tool in quantum mechanics and field theory. The emphasis is on quantum statistical mechanics, starting with the partition function Tr exp(-? H) and proceeding through the diffusion equation to barrier penetration problems and their semiclassical limit. The 'real time' path

J Louko

2005-01-01

81

Quantum Teleportation Under the Effect of Dissipative Environment and Hamiltonian XY Model

NASA Astrophysics Data System (ADS)

By supposing that the quantum channel is affected by the Hamiltonian XY model, quantum teleportation is studied in the absence and presence of a dissipative environment. We find that the dynamics of the average of fidelity and entanglement of the channel depend on which qubits interact with the environment and magnitude of parameters of the Hamiltonian. In the case that the qubits of quantum channel interact with environment, a critical value of entanglement is needed to keep quantum advantage at infinite time. We also find that, the most destructive case is that the qubit to be teleported is subject to an environment. It is shown that quantum advantage may be lost even in the absence of an environment.

Pourkarimi, Mohammad Reza; Rahnama, Majid

2014-04-01

82

Time Asymmetric Quantum Mechanics

The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone--von Neumann theorem, the solutions of the dynamical equations, the Schr\\"odinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width $\\Gamma$ and exponentially decaying states of lifetime $\\tau=\\frac{\\hbar}{\\Gamma}$ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution $t_{0}\\leq tbeginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.

Arno R. Bohm; Manuel Gadella; Piotr Kielanowski

2011-09-03

83

Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Evolution of quantum circuits faces two major challenges: complex and huge search space and the high costs of simulating quantum circuits on classical computers. Here, we use the group leaders optimization algorithm to decompose a given unitary matrix into a proper-minimum cost quantum gate sequence. We test the method on the known decompositions of Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, and the sender part of the quantum teleportation. Using this procedure, we present the circuit designs for the simulation of the unitary propagators of the Hamiltonians for the hydrogen and the water molecules. The approach is general and can be applied to generate the sequence of quantum gates for larger molecular systems. PMID:21495747

Daskin, Anmer; Kais, Sabre

2011-04-14

84

Quantum Mechanics Survey (QMS)

NSDL National Science Digital Library

This 31-question research-based multiple-choice test is designed to evaluate studentsâ conceptual understanding of quantum mechanics in junior-level courses. The survey is based on investigations of studentsâ difficulties in quantum mechanics and should be given in a 50-minute period. Statistical results have shown the survey to be reliable and valid. A summary of the construction and analysis of the survey is available in Surveying studentsâ understanding of quantum mechanics in one spatial dimension, Am. J. Phys. 80 (3), 252-259. This assessment is free for use by instructors in their classroom. However, as it takes years of development effort to create and validate reliable assessment instruments, the file is password-protected. Furthermore, the author requests that 1. students are not given copies following examination; and 2. none of the questions are incorporated into web-based question delivery systems without adequate security to prevent printing or unauthorized access by students. To obtain the password, please send a request with your name, email, institution, and a link to a page at your institution that confirms you are an instructor.

Singh, Chandralekha; Zhu, Guangtian

2012-04-29

85

A solvable quantum-mechanical model with nonlinear transformation laws

Summary A quantum-mechanical model with three degrees of freedom and a nonlinearly realized Lorentz group is solved exactly. Moreover,\\u000a it is shown that even after breaking the symmetry by a linearly transforming term the model remains solvable. In both cases\\u000a the spectrum of the Hamiltonian is investigated and found to be positive.

G. Velo; J. Wess

1971-01-01

86

Taming the zoo of supersymmetric quantum mechanical models

NASA Astrophysics Data System (ADS)

We show that in many cases nontrivial and complicated supersymmetric quantum mechanical (SQM) models can be obtained from the simple model describing free dynamics in flat complex space by two operations: (i) Hamiltonian reduction and (ii) similarity transformation of the complex supercharges. We conjecture that it is true for any SQM model.

Smilga, A. V.

2013-05-01

87

Scattering in PT-symmetric quantum mechanics

A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with Hermiticity, T invariance and PT invariance.

Cannata, Francesco [Istituto Nazionale di Fisica Nucleare, Sezione di Bologna and Dipartimento di Fisica dell' Universita, Via Irnerio 46, I 40126 Bologna (Italy)]. E-mail: Francesco.Cannata@bo.infn.it; Dedonder, Jean-Pierre [GMPIB Universite Paris 7 - Denis-Diderot, 2 Place Jussieu, F-75251, Paris Cedex 05 (France)]. E-mail: dedonder@paris7.jussieu.fr; Ventura, Alberto [Ente Nuove Tecnologie, Energia e Ambiente, Bologna and Istituto Nazionale di Fisica Nucleare, Sezione di Bologna (Italy)]. E-mail: Alberto.Ventura@bologna.enea.it

2007-02-15

88

Supersymmetric quantum mechanics and its applications

The Hamiltonian in Supersymmetric Quantum Mechanics is defined in terms of charges that obey the same algebra as that of the generators of supersymmetry in field theory. The consequences of this symmetry for the spectra of the component parts that constitute the supersymmetric system are explored. The implications of supersymmetry for the solutions of the Schroedinger equation, the Dirac equation, the inverse scattering theory and the multi-soliton solutions of the KdV equation are examined. Applications to scattering problems in Nuclear Physics with specific reference to singular potentials which arise from considerations of supersymmetry will be discussed.

Sukumar, C.V. [Wadham College, University of Oxford, Oxford OX1 3PN (United Kingdom)

2004-12-23

89

Kinetic potentials in quantum mechanics

NASA Astrophysics Data System (ADS)

Suppose that the Hamiltonian H=-?+vf(r) represents the energy of a particle which moves in an attractive central potential and obeys nonrelativistic quantum mechanics. The discrete eigenvalues Enl=Fnl(v) of H may be expressed as a Legendre transformation Fnl(v)=mins?0(s+vfŻnl(s)), n=1,2,3,..., l=0,1,2,..., where the ``kinetic potentials'' fŻnl(s) associated with f(r) are defined by fŻnl(s) =infDnl sup??Dnl, ???=1 ? ?(r) f ([?,-??)/s]1/2r)?(r)d3r, and Dnl is an n-dimensional subspace of L2(R3) labeled by Ylm(?,?), m=0, and contained in the domain D(H) of H. If the potential has the form f(r)=?Ni=1 g(i)( f(i)(r)) then in many interesting cases it turns out that the corresponding kinetic potentials can be closely approximated by ?Ni=1 g(i)( fŻnl(i)(s)). This nice behavior of the kinetic potentials leads to a constructive global approximation theory for Schrödinger eigenvalues. As an illustration, detailed recipes are provided for arbitrary linear combinations of power-law potentials and the log potential. For the linear plus Coulomb potential and the quartic anharmonic oscillator the approximate eigenvalues are compared to accurate values found by numerical integration.

Hall, Richard L.

1984-09-01

90

Construction of bilinear control Hamiltonians using the series product and quantum feedback

We show that it is possible to construct closed quantum systems governed by a bilinear Hamiltonian depending on an arbitrary input signal. This is achieved by coupling the system to a quantum input field and performing a feedback of the output field back into the system to cancel out the stochastic effects, with the signal being added to the field between these events and later subtracted. Here we assume the zero time delay limit between the various connections and operations.

J. Gough

2008-07-26

91

The ground state problem for a quantum Hamiltonian model describing friction

The ground state problem for a quantum Hamiltonian model describing friction Laurent Bruneau friction introduced in [4]. This model consists of a particle which interacts with a bosonic reservoir is violated in the case of linear friction, but satis#28;ed when the friction force is proportional

92

(N+1)-dimensional quantum mechanical model for a closed universe

A quantum mechanical model for an (N+1)-dimensional universe arising from a quantum fluctuation is outlined. (3+1) dimensions are a closed, infinitely expanding universe, and the remaining N-3 dimensions are compact. The (3+1) noncompact dimensions are modeled by quantizing a canonical Hamiltonian description of a homogeneous isotropic universe. It is assumed that gravity and the strong-electroweak (SEW) force had equal strengths

T. R. Mongan

1999-01-01

93

Dynamical noncommutative quantum mechanics

NASA Astrophysics Data System (ADS)

We study some basic and interesting quantum mechanical systems in dynamical noncommutative spaces in which the space-space commutation relations are position dependent. It is observed that the fundamental objects in the dynamical noncommutative space introduced here are string-like. We show that the Stark effect can be employed to determine whether the noncommutativity of space is dynamical or non-dynamical. It appears that unlike a non-dynamical case there is a fundamental energy ??2/m in this dynamical space.

Alavi, S. A.; Abbaspour, S.

2014-01-01

94

Advanced Concepts in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction: the need for a quantum theory; 2. Experimental foundations of quantum theory; 3. Waves and particles; 4. Schrödinger picture, Heisenberg picture and probabilistic aspects; 5. Integrating the equations of motion; 6. Elementary applications: 1-dimensional problems; 7. Elementary applications: multidimensional problems; 8. Coherent states and related formalism; 9. Introduction to spin; 10. Symmetries in quantum mechanics; 11. Approximation methods; 12. Modern pictures of quantum mechanics; 13. Formulations of quantum mechanics and their physical implications; 14. Exam problems; Glossary of geometric concepts; References; Index.

Esposito, Giampiero; Marmo, Giuseppe; Miele, Gennaro; Sudarshan, George

2014-11-01

95

Topological color codes and two-body quantum lattice Hamiltonians

Topological color codes are among the stabilizer codes with remarkable properties from the quantum information perspective. In this paper, we construct a lattice, the so-called ruby lattice, with coordination number 4 ...

Kargarian, M.

96

Emission of Cherenkov Radiation as a Mechanism for Hamiltonian Friction

We study the motion of a heavy tracer particle weakly coupled to a dense, weakly interacting Bose gas exhibiting Bose-Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations. We prove that if the initial speed of the tracer particle is above the speed of sound in the Bose gas, and for a suitable class of initial states of the Bose gas, the particle decelerates due to emission of Cherenkov radiation of sound waves, and its motion approaches a uniform motion at the speed of sound, as time tends to infinity.

Juerg Froehlich; Zhou Gang

2014-07-28

97

Nontrivial systems and the necessity of the scalar quantum mechanics axioms

We discuss the necessity of the axioms of scalar quantum mechanics introduced by Paschke and clearly demonstrate their geometric and/or physical meaning. We show that reasonable nonrelativistic quantum mechanics is exactly specified by the axioms. A system describing the electric Aharonov-Bohm effect is presented. It illustrates the topological obstructions for the existence of a Hamiltonian.

Kotulek, Jan [Mathematical Institute, Silesian University at Opava, Na Rybnicku 1, 746 01 Opava (Czech Republic)

2009-06-15

98

EVENTUM MECHANICS OF QUANTUM TRAJECTORIES: CONTINUAL MEASUREMENTS, QUANTUM PREDICTIONS

EVENTUM MECHANICS OF QUANTUM TRAJECTORIES: CONTINUAL MEASUREMENTS, QUANTUM PREDICTIONS AND FEEDBACK CONTROL VIACHESLAV P BELAVKIN Abstract. Quantum mechanical systems exhibit an inherently probabilistic on the basis of an independent-increment model for quantum noise and nondemolition causal- ity principle

Belavkin, Viacheslav P.

99

From Quantum Mechanics to Thermodynamics?

From Quantum Mechanics to Thermodynamics? Dresden, 22.11.2004 Jochen Gemmer UniversitÂ¨at Osnabr to thermodynamical behavior Â· Quantum approach to thermodynamical behavior Â· The route to equilibrium Â· Summary of thermodynamical behavior entirely on the basis of Hamilton models and SchrÂ¨odinger-type quantum dynamics. Â· define

Steinhoff, Heinz-JĂĽrgen

100

Chaos and Statistical Mechanics in the Hamiltonian Mean Field Model

We study the dynamical and statistical behavior of the Hamiltonian Mean Field (HMF) model in order to investigate the relation between microscopic chaos and phase transitions. HMF is a simple toy model of $N$ fully-coupled rotators which shows a second order phase transition. The canonical thermodynamical solution is briefly recalled and its predictions are tested numerically at finite $N$. The Vlasov stationary solution is shown to give the same consistency equation of the canonical solution and its predictions for rotator angle and momenta distribution functions agree very well with numerical simulations. A link is established between the behavior of the maximal Lyapunov exponent and that of thermodynamical fluctuations, expressed by kinetic energy fluctuations or specific heat. The extensivity of chaos in the $N \\to \\infty$ limit is tested through the scaling properties of Lyapunov spectra and of the Kolmogorov-Sinai entropy. Chaotic dynamics provides the mixing property in phase space necessary for obtaining equilibration; however, the relaxation time to equilibrium grows with $N$, at least near the critical point. Our results constitute an interesting bridge between Hamiltonian chaos in many degrees of freedom systems and equilibrium thermodynamics.

Vito Latora; Andrea Rapisarda; Stefano Ruffo

1998-03-13

101

Quantum mechanics probes superspace

We study quantum mechanics in one space dimension in the stochastic formalism. We show that the partition function of the theory is, in fact, equivalent to that of a model, whose action is explicitly invariant (up to surface terms) under supersymmetry transformations--but whose invariance under the stochastic identities is not obvious, due to an apparent mismatch between fermions and bosons. The resolution of the riddle is that one "fermion" is a gauge artifact and, upon fixing the local, fermionic symmetry, called $\\kappa-$symmetry, we recover the stochastic partition function. The "fermions" do not propagate in the bulk, since their kinetic term is a total derivative. Their contribution to the action is through an ultra--local bilinear term, that may be exactly integrated out, as long as the superpotential has a unique minimum and we obtain a local action for the scalar. When the superpotential does not have a unique minimum, we use a Hubbard-Stratonovich transformation of the kinetic term to obtain an action in terms of the Fourier transform of the velocity, a kind of duality transformation. The classical particle thus moves in a medium of dipoles, that parametrize the quantum fluctuations and the classical trajectory $\\phi(\\tau)$, becomes a chiral superfield, $(\\phi(\\tau),\\psi_\\alpha(\\tau),F(\\tau))$, when quantum effects are taken into account. The observable superpartner of the scalar, however, is the fermion bilinear and thus, while supersymmetry may be realized, the observable partner excitations are not degenerate in mass. We compute the stochastic identities of the auxiliary field, using a lattice regularization of the equivalent "bosonic" action, for the case of a superpotential with a single minimum. We show that the lattice action can be expressed as an ultra--local functional of the auxiliary field, up to terms that vanish with the lattice spacing.

S. Nicolis

2014-05-05

102

Zitterbewegung in Quantum Mechanics

NASA Astrophysics Data System (ADS)

The possibility that zitterbewegung opens a window to particle substructure in quantum mechanics is explored by constructing a particle model with structural features inherent in the Dirac equation. This paper develops a self-contained dynamical model of the electron as a lightlike particle with helical zitterbewegung and electromagnetic interactions. The model admits periodic solutions with quantized energy, and the correct magnetic moment is generated by charge circulation. It attributes to the electron an electric dipole moment rotating with ultrahigh frequency, and the possibility of observing this directly as a resonance in electron channeling is analyzed in detail. Correspondence with the Dirac equation is discussed. A modification of the Dirac equation is suggested to incorporate the rotating dipole moment.

Hestenes, David

2010-01-01

103

The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can be represented in a Hilbert space, that a self-adjoint operator is associated to any observable, that the result of a measure must be the eigen value of the operator and appear with the usual probability. Furthermore an equivalent of the Wigner's theorem holds, which leads to the Schr\\"{o}dinger equation. These results are based on well known mathematics, and do not involve any specific hypothesis in Physics. They validate and explain the methods currently used, which are made simpler and safer, and open new developments. In the second edition of this paper important developments have been added about interacting systems and the transitions of phases.

Jean-Paul Metailié; Jean Claude Dutailly

2014-08-20

104

Supersymmetric Quantum Mechanics of Scattering

In the quantum mechanics of collision problems we must consider scattering states of the system. For these states, the wave functions do not remain in Hilbert space, but they are expressible in terms of generalized functions of a Gel'fand triplet. Supersymmetric quantum mechanics for dealing with the scattering states is here proposed.

Shimbori, T; Shimbori, Toshiki; Kobayashi, Tsunehiro

2001-01-01

105

Supersymmetric Quantum Mechanics of Scattering

In the quantum mechanics of collision problems we must consider scattering states of the system. For these states, the wave functions do not remain in Hilbert space, but they are expressible in terms of generalized functions of a Gel'fand triplet. Supersymmetric quantum mechanics for dealing with the scattering states is here proposed.

Toshiki Shimbori; Tsunehiro Kobayashi

2000-10-27

106

Supersymmetric quantum mechanics of scattering

In the quantum mechanics of collision problems we must consider scattering states of the system. For these states, the wave functions do not remain in Hilbert space, but they are expressible in terms of generalized functions of a Gel'fand triplet. Supersymmetric quantum mechanics for dealing with the scattering states is here proposed.

Toshiki Shimbori; Tsunehiro Kobayashi

2001-01-01

107

Quantum mechanism helps agents combat \\

Quantum strategies have been successfully applied to game theory for years.\\u000aHowever, as a reverse problem of game theory, the theory of mechanism design is\\u000aignored by physicists. In this paper, the theory of mechanism design is\\u000ageneralized to a quantum domain. The main result is that by virtue of a quantum\\u000amechanism, agents who satisfy a certain condition can

Haoyang Wu

2010-01-01

108

NASA Astrophysics Data System (ADS)

In this thesis we derive minimal effective Hamiltonians from more detailed theories which are used to predict novel quantum phases of solid state and atomic and molecular systems. We consider the solid state systems of transition metal dichalcogenides, strands of stretched poly (CG)-poly (CG) DNA, and carbon nanotubes. The cold atomic and molecular systems we consider are alkali atoms in the F = 2 hyperfine state and dipolar molecules in an optical lattice.

Barnett, Ryan

109

Classical and Quantum Mechanical Waves

NSDL National Science Digital Library

This web site consists of lecture notes in classical and quantum mechanical waves. The notes include the basics of classical waves including connections to mechanical oscillators, wave packets, and acoustic and electromagnetic waves. The final section outlines the key concepts of the quantum mechanical wave equation including probability and current, free and bound states, time dependent perturbation theory, and radiation. Visual Python and Maple animations are included for download.

Riley, Lewis

2006-07-22

110

Ab initio no core calculations of light nuclei and preludes to Hamiltonian quantum field theory

Recent advances in ab initio quantum many-body methods and growth in computer power now enable highly precise calculations of nuclear structure. The precision has attained a level sufficient to make clear statements on the nature of 3-body forces in nuclear physics. Total binding energies, spin-dependent structure effects, and electroweak properties of light nuclei play major roles in pinpointing properties of the underlying strong interaction. Eventually,we anticipate a theory bridge with immense predictive power from QCD through nuclear forces to nuclear structure and nuclear reactions. Light front Hamiltonian quantum field theory offers an attractive pathway and we outline key elements.

Vary, J.P.; Maris, P.; /Iowa State U.; Shirokov, A.M.; /Iowa State U. /SINP, Moscow; Honkanen, H.; li, J.; /Iowa State U.; Brodsky, S.J.; /SLAC; Harindranath, A.; /Saha Inst.; Teramond, G.F.de; /Costa Rica U.

2009-08-03

111

Ab initio no core calculations of light nuclei and preludes to Hamiltonian quantum field theory

Recent advances in ab initio quantum many-body methods and growth in computer power now enable highly precise calculations of nuclear structure. The precision has attained a level sufficient to make clear statements on the nature of 3-body forces in nuclear physics. Total binding energies, spin-dependent structure effects, and electroweak properties of light nuclei play major roles in pinpointing properties of the underlying strong interaction. Eventually, we anticipate a theory bridge with immense predictive power from QCD through nuclear forces to nuclear structure and nuclear reactions. Light front Hamiltonian quantum field theory offers an attractive pathway and we outline key elements.

Vary, J. P.; Maris, P.; Honkanen, H.; Li, J. [Department of Physics and Astronomy, Iowa State University, Ames, Iowa, 50011 (United States); Shirokov, A. M. [Department of Physics and Astronomy, Iowa State University, Ames, Iowa, 50011 (United States); Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119991 (Russian Federation); Brodsky, S. J. [SLAC National Accelerator Laboratory, Stanford University, Menlo Park, California (United States); Harindranath, A. [Theory Group, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata, 700064 (India); Teramond, G. F. de [Universidad de Costa Rica, San Jose (Costa Rica)

2009-12-17

112

Spin decoherence from Hamiltonian dynamics in quantum dots

The dynamics of a spin-1/2 particle coupled to a nuclear spin bath through an isotropic Heisenberg interaction is studied as a model for the spin decoherence in quantum dots. The time-dependent polarization of the central spin is calculated as a function of the bath-spin distribution and the polarizations of the initial bath state. For short times, the polarization of the central spin shows a Gaussian decay, and at later times it is revived displaying nonmonotonic time dependence. The decoherence time scale depends on moments of the bath-spin distribution, and also on the polarization strengths in various bath-spin channels. The bath polarizations have a tendency to increase the decoherence time scale. The effective dynamics of the central spin polarization is shown to be described by a master equation with non-Markovian features.

Bhaktavatsala Rao, D. D.; Ravishankar, V.; Subrahmanyam, V. [Department of Physics, Indian Institute of Technology, Kanpur-208016 (India)

2006-08-15

113

Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm proposed by Wu, Byrd, and Lidar [Phys. Rev. Lett. 89, 057904 (2002).10.1103/PhysRevLett.89.057904] to find the low-lying spectrum of a pairing Hamiltonian. While the number of elementary quantum gates required scales polynomially with the size of the system, it increases inversely to the desired error bound E. Making such simulations robust to decoherence using fault tolerance requires an additional factor of approximately 1/E gates. These constraints, along with the effects of control errors, are illustrated using a three qubit NMR system. PMID:17026087

Brown, Kenneth R; Clark, Robert J; Chuang, Isaac L

2006-08-01

114

From the unitary operator used for implementing two-state discrete-time quantum walk on one-, two- and three- dimensional lattice we obtain a two-component Dirac-like Hamiltonian. In particular, using different pairs of Pauli basis as position translation states we obtain three different form of Hamiltonians for evolution on one-dimensional lattice. We extend this to two- and three-dimensional lattices using different Pauli basis states as position translation states for each dimension and show that the external coin operation, which is necessary for one-dimensional walk is not a necessary requirement for a walk on higher dimensions but can serve as an additional resource to control the dynamics. The two-component Hamiltonian we present here for quantum walk on different lattices can serve as a general framework to simulate, control, and study the dynamics of quantum systems governed by Dirac-like Hamiltonian. PMID:24088731

Chandrashekar, C. M.

2013-01-01

115

Quantum-mechanical Maxwell's demon

A Maxwell's demon is a device that gets information and trades it in for thermodynamic advantage, in apparent (but not actual) contradiction to the second law of thermodynamics. Quantum-mechanical versions of Maxwell's demon exhibit features that classical versions do not: in particular, a device that gets information about a quantum system disturbs it in the process. This paper proposes experimentally

Seth Lloyd

1997-01-01

116

Solvable quantum mechanical model in two-dimensional space

A one-particle non-relativistic quantum mechanical solvable model in two-dimensional space is given. The Hamiltonian is the sum of kinetic and interaction parts. Interactions are separable and can be centred at n arbitrary points of the plane. Conditions for the existence and for the number of bound states in finite linear chains are formulated in terms of the parameters of the

E. de Prunelé

2006-01-01

117

N + 1 dimensional quantum mechanical model for a closed universe

A quantum mechanical model for an N + 1 dimensional universe arising from a\\u000aquantum fluctuation is outlined. (3 + 1) dimensions are a closed\\u000ainfinitely-expanding universe and the remaining N - 3 dimensions are compact.\\u000aThe (3 + 1) non-compact dimensions are modeled by quantizing a canonical\\u000aHamiltonian description of a homogeneous isotropic universe. It is assumed\\u000agravity and

T. R. Mongan

1999-01-01

118

Twist deformation of rotationally invariant quantum mechanics

Noncommutative quantum mechanics in 3D is investigated in the framework of an abelian Drinfeld twist which deforms a given Hopf algebra structure. Composite operators (of coordinates and momenta) entering the Hamiltonian have to be reinterpreted as primitive elements of a dynamical Lie algebra which could be either finite (for the harmonic oscillator) or infinite (in the general case). The deformed brackets of the deformed angular momenta close the so(3) algebra. On the other hand, undeformed rotationally invariant operators can become, under deformation, anomalous (the anomaly vanishes when the deformation parameter goes to zero). The deformed operators, Taylor-expanded in the deformation parameter, can be selected to minimize the anomaly. We present the deformations (and their anomalies) of undeformed rotationally invariant operators corresponding to the harmonic oscillator (quadratic potential), the anharmonic oscillator (quartic potential), and the Coulomb potential.

Chakraborty, B. [S.N. Bose National Center for Basic Sciences, JD Block, Sector III, Salt-Lake, Kolkata-700098 (India); Kuznetsova, Z. [UFABC, Rua Catequese 242, Bairro Jardim, cep 09090-400, Santo Andre (Brazil); Toppan, F. [CBPF, Rua Dr. Xavier Sigaud 150, cep 22290-180, Rio de Janeiro (Brazil)

2010-11-15

119

Quantum mechanics and the psyche

In this paper we apply the last developments of the theory of measurement in quantum mechanics to the phenomenon of consciousness\\u000a and especially to the awareness of unconscious components. Various models of measurement in quantum mechanics can be distinguished\\u000a by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness

G. Galli Carminati; F. Martin

2008-01-01

120

We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a ...

Ajoy, Ashok

121

Topological Characterization of Fractional Quantum Hall Ground States from Microscopic Hamiltonians

NASA Astrophysics Data System (ADS)

We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall Hamiltonian. To find the set of degenerate ground states, we employ the infinite density matrix renormalization group method based on the matrix-product state representation of fractional quantum Hall states on an infinite cylinder. To study localized quasiparticles of a chosen topological charge, we use pairs of degenerate ground states as boundary conditions for the infinite density matrix renormalization group. We then show that the wave function obtained on the infinite cylinder geometry can be adapted to a torus of arbitrary modular parameter, which allows us to explicitly calculate the non-Abelian Berry connection associated with the modular T transformation. As a result, the quantum dimensions, topological spins, quasiparticle charges, chiral central charge, and Hall viscosity of the phase can be obtained using data contained entirely in the entanglement spectrum of an infinite cylinder.

Zaletel, Michael P.; Mong, Roger S. K.; Pollmann, Frank

2013-06-01

122

Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians.

We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall Hamiltonian. To find the set of degenerate ground states, we employ the infinite density matrix renormalization group method based on the matrix-product state representation of fractional quantum Hall states on an infinite cylinder. To study localized quasiparticles of a chosen topological charge, we use pairs of degenerate ground states as boundary conditions for the infinite density matrix renormalization group. We then show that the wave function obtained on the infinite cylinder geometry can be adapted to a torus of arbitrary modular parameter, which allows us to explicitly calculate the non-Abelian Berry connection associated with the modular T transformation. As a result, the quantum dimensions, topological spins, quasiparticle charges, chiral central charge, and Hall viscosity of the phase can be obtained using data contained entirely in the entanglement spectrum of an infinite cylinder. PMID:25167520

Zaletel, Michael P; Mong, Roger S K; Pollmann, Frank

2013-06-01

123

An Introduction to Quantum Mechanics

NSDL National Science Digital Library

This Ohio State website provides an introduction to the principles of quantum mechanics as a supplement to the "discussion of hydrogen and many-electron orbitals commonly found in general chemistry text books." Users can find informative text and graphics explaining Classical Mechanics, uncertainty, Pauli Principle, stationary states, and much more. Through the tutorial, students can explore how physical objects can be perceived as both particles and waves. With the Macromedia Shockwave plug-in, visitors can hear discussions of the quantum mechanics topics covered.

Hanlin, Heath

124

Quantum Mechanics: Fundamentals

This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience.That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried's well-known book published by Benjamin in 1966. This was written as a text for

A Whitaker

2004-01-01

125

NSDL National Science Digital Library

This web site outlines a set of undergraduate physics labs that investigate quantum interference and entanglement with photons. The labs are designed for simplicity and low cost. A description of the lab set up, background information, the lab manual, and several articles on both the curriculum development and research performed in the lab are provided.

Galvez, Enrique; Holbrow, Charles

2005-04-16

126

The symplectic egg in classical and quantum mechanics

NASA Astrophysics Data System (ADS)

Symplectic geometry is the language of Classical Mechanics in its Hamiltonian formulation, and it also plays a crucial role in Quantum Mechanics. Symplectic geometry seemed to be well understood until 1985, when the mathematician Gromov discovered a surprising and unexpected property of canonical transformations: the non-squeezing theorem. Gromov's result, nicknamed the "principle of the symplectic camel," seems at first sight to be an abstruse piece of pure mathematics. It turns out that it has fundamental—and unsuspected—consequences in the interpretations of both Classical and Quantum Mechanics, because it is essentially a classical form of the uncertainty principle. We invite the reader to a journey taking us from Gromov's non-squeezing theorem and its dynamical interpretation to the quantum uncertainty principle, opening the way to new insights.

de Gosson, Maurice A.

2013-05-01

127

Quantum Mechanics: Sum Over Paths

NSDL National Science Digital Library

Created by Edwin F. Taylor a former professor at the Department of Physics at the Massachusetts Institute of Technology, this material describes methods of presenting quantum mechanics using the path-integral formulation. Included are links to a paper and presentation outlining the method, software to simulate the path integrals, and student workbook materials. This course has been used for introducing quantum physics to high school teachers.

Taylor, Edwin F.

2009-05-26

128

Large scale quantum mechanical enzymology

for Physics were awarded to the predominant developers of the theory of quantum mechanics (QM). These laureates were Max Planck, Niels Bohr, Louis de Broglie, Werner Heisenberg, Erwin Schro¨dinger and Paul Dirac, in chronological order. In addition, Albert... Einstein’s significant contributions cannot go unmentioned. These theoretical insights laid the foundations for the quantum chemical approach that won Walter Kohn and John Pople the prize for Chemistry in 1998. Considering earlier works, Johannes Diderik...

Lever, Greg

2014-10-07

129

Locality and Nonlinear Quantum Mechanics

Nonlinear modifications of quantum mechanics generically lead to nonlocal effects which violate relativistic causality. We study these effects using the functional Schrodinger equation for quantum fields and identify a type of nonlocality which causes nearly instantaneous entanglement of spacelike separated systems. We describe a simple example involving widely separated wave-packet (coherent) states, showing that nonlinearity in the Schrodinger evolution causes spacelike entanglement, even in free field theory.

Chiu Man Ho; Stephen D. H. Hsu

2015-01-09

130

Quantum Mechanical Earth: Where Orbitals Become Orbits

ERIC Educational Resources Information Center

Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…

Keeports, David

2012-01-01

131

Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics

NASA Astrophysics Data System (ADS)

In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called quantum annealing. The most typical instance is quantum adiabatic computation based on the adiabatic theorem. The quantum adiabatic computation as discussed in the other chapter, unfortunately, has a crucial bottleneck for a part of the optimization problems. We here introduce several recent trials to overcome such a weakpoint by use of developments in statistical mechanics. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.

Ohzeki, Masayuki

2013-09-01

132

BOOK REVIEW: Relativistic Quantum Mechanics

NASA Astrophysics Data System (ADS)

The aim of relativistic quantum mechanics is to describe the finer details of the structure of atoms and molecules, where relativistic effects become nonnegligible. It is a sort of intermediate realm, between the familiar nonrelativistic quantum mechanics and fully relativistic quantum field theory, and thus it lacks the simplicity and elegance of both. Yet it is a necessary tool, mostly for quantum chemists. Pilkuhn's book offers to this audience an up-to-date survey of these methods, which is quite welcome since most previous textbooks are at least ten years old. The point of view of the author is to start immediately in the relativistic domain, following the lead of Maxwell's equations rather than classical mechanics, and thus to treat the nonrelativistic version as an approximation. Thus Chapter 1 takes off from Maxwell's equations (in the noncovariant Coulomb gauge) and gradually derives the basic aspects of Quantum Mechanics in a rather pedestrian way (states and observables, Hilbert space, operators, quantum measurement, scattering,. Chapter 2 starts with the Lorentz transformations, then continues with the Pauli spin equation and the Dirac equation and some of their applications (notably the hydrogen atom). Chapter 3 is entitled `Quantum fields and particles', but falls short of treating quantum field theory properly: only creation/annihilation operators are considered, for a particle in a box. The emphasis is on two-electron states (the Pauli principle, the Foldy--Wouthuysen elimination of small components of Dirac spinors, Breit projection operators. Chapter 4 is devoted to scattering theory and the description of relativistic bound states. Chapter 5, finally, covers hyperfine interactions and radiative corrections. As we said above, relativistic quantum mechanics is by nature limited in scope and rather inelegant and Pilkuhn's book is no exception. The notation is often heavy (mostly noncovariant) and the mathematical level rather low. The central topic is the description of atoms and molecules, including relativistic effects. The author fulfils this program in a reasonable way and offers a valuable tool to the targeted audience. I am not overly enthusiastic about the end result, but I might be prejudiced. Clearly, going further would require the full power of quantum field theory, but this is clearly beyond the scope of the book.

Antoine, J.-P.

2004-01-01

133

Quantum mechanical force field for water with explicit electronic polarization

A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 10{sup 6} self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across biological ion channels through membranes.

Han, Jaebeom; Mazack, Michael J. M.; Zhang, Peng; Truhlar, Donald G.; Gao, Jiali [Department of Chemistry and Supercomputing Institute, University of Minnesota, 207 Pleasant Street, SE, Minneapolis, Minnesota 55455-0431 (United States)] [Department of Chemistry and Supercomputing Institute, University of Minnesota, 207 Pleasant Street, SE, Minneapolis, Minnesota 55455-0431 (United States)

2013-08-07

134

Quantum mechanical force field for water with explicit electronic polarization

A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 106 self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across biological ion channels through membranes. PMID:23927266

Han, Jaebeom; Mazack, Michael J. M.; Zhang, Peng; Truhlar, Donald G.; Gao, Jiali

2013-01-01

135

NASA Astrophysics Data System (ADS)

We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. Throughout the paper, we adopt the partitioning of the total Hamiltonian into the system part, the bath part, and their coupling. We rederive many equalities which are available in the literature and obtain a number of new equalities for nonequilibrium classical and quantum systems. Our results can be useful for determining partition functions and (generalized) free energies through simulations or measurements performed on nonequilibrium systems.

Gelin, M. F.; Kosov, D. S.

2008-07-01

136

NASA Astrophysics Data System (ADS)

We introduce a highest weight type representation of the Rovelli-Smolin algebra of loop observables for quantum gravity. In terms of this representation, new solutions of the hamiltonian and diffeomorphism constraints are given. Assuming the locality of the quantum hamiltonian constraint we show that any functional depending on the generalized link class of the disjoint union of arbitrary simple loops is a solution. Finally we argue that this is the general solution in the irreducible representation space. On leave of absence from the Departamento de Fisica Teorica, Universidad de Valencia, and IFIC, Centro Mixto Universidad de Valencia - CSIC, Burjassot, Spain.

Aldaya, V.; Navarro-Salas, J.

1991-04-01

137

Remarks on osmosis, quantum mechanics, and gravity

Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.

Carroll, Robert

2011-01-01

138

Remarks on osmosis, quantum mechanics, and gravity

Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.

Robert Carroll

2011-04-03

139

Non-exponential decay in Quantum Mechanics and Quantum Field Theory

NASA Astrophysics Data System (ADS)

We describe some salient features as well as some recent developments concerning short-time deviations from the exponential decay law in the context of Quantum Mechanics by using the Lee Hamiltonian approach and Quantum Field Theory by using relativistic Lagrangians. In particular, the case in which two decay channels are present is analyzed: the ratio of decay probability densities, which is a constant equal to the ratio of decay widths in the exponential limit, shows in general sizable fluctuations which persist also at long times.

Giacosa, Francesco

2014-10-01

140

OSP: Quantum-mechanical Measurement

NSDL National Science Digital Library

This set of quantum mechanics java applets, part of the Open Source Physics project, provides simulations that demonstrate the effect of measurement on the time-dependence of quantum states. Exercises are available that demonstrate the results of measurement of energy, position, and momentum on states in potential wells (square well, harmonic oscillator, asymmetric well, etc). Eigenstates, superpositions of eigenstates, and wave packets can all be studied. Tutorials are also available. The material stresses the measurement of a quantum-mechanical wave function. The simulations can be delivered either through the OSP Launcher interface or embedded in html pages. The source code is available, and users are invited to contribute to the collection's development by submitting improvements. The simulations are available through the "View attached documents" link below.

Belloni, Mario; Christian, Wolfgang

2006-06-27

141

Basic Concepts for a Quantum Mechanical Theory of Events

A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. As a key feature, the laws are formulated in terms of quantum events rather than of particle states. Temporal and spatial coordinates of a quantum event are treated on equal footing, namely as self-adjoint operators on a Hilbert space. The theory is not based upon Lagrangian or Hamiltonian mechanics, and breaks with the concept of a continuously flowing time. The physical object under consideration is a spinless particle exposed to an external potential. The theory also accounts for particle-antiparticle pair creation and annihilation, and is therefore not a single-particle theory in the usual sense. The Maxwell equations are derived as a straightforward consequence of certain fundamental commutation relations. In the non-relativistic limit and in the limit of vanishing time uncertainty, the Schr\\"odinger equation of a spinless particle exposed to an external electromagnetic field is obtained.

Kim J. Bostroem

2005-03-21

142

Quantum mechanics and brain uncertainty.

This paper argues that molecular governing structures (such as receptors, gating molecules, or ionic channels) which operate pervasively in the brain, often with small number particle systems (as, for example, at the surfaces of membranes, synaptic clefts, or macromolecules), may plausibly be vehicles for the transmutation of quantum mechanical fluctuations to normal-level neural signaling. PMID:17125159

Macgregor, Ronald J

2006-09-01

143

Nine formulations of Quantum Mechanics

NSDL National Science Digital Library

This article provides a comprehensive review of the various formulations of quantum mechanics. The article contains a brief description of each formulation, advantages/disadvantages, application notes, and recommended references for. Recommended references include textbooks using the formulation background information and influential publications.

Styer, Dan; Balkin, Miranda; Becker, Kathryn; Wotherspoon, Tim; Forth, Scott; Kramer, Mark

2005-04-16

144

Quantum Mechanics Of Consciousness

A phenomenological approach using the states of spin-like observables is developed to understand the nature of consciousness and the totality of experience. The three states of consciousness are taken to form the triplet of eigenstates of a spin-one entity and are derived as the triplet resulting from the composition of two spins by treating the subject and the object as interacting two-state, spin-half systems with external and internal projections. The state of deep sleep is analysed in the light of this phenomenological approach and a novel understanding of the status of the individual consciousness in this state is obtained. The resulting fourth state i.e. the singlet state is interpreted to correspond to the superconscious state of intuitive experience and is justified by invoking the concept of the universal consciousness as the underlying source of all individual states of experience. It is proposed that the individual experiences result from the operations of four individualizing observables which project out the individual from the universal. The one-to-one correspondence between the individual and the universal states of experience is brought out and their identity in the fourth state is established by showing that all individualizing quantum numbers become zero in this state leaving no trace of any individuality.

Rajat Kumar Pradhan

2009-07-28

145

NASA Astrophysics Data System (ADS)

While a microscopic system is usually governed by canonical Hamiltonian mechanics, that of a macroscopic system is often noncanonical, reflecting a degenerate Poisson structure underlying the coarse-grained phase space. Probing into symplectic leaves (local structures in a foliated phase space), we may be able to elucidate the order of transition from micro to macro. The Lagrangian guides our analysis. We formulate canonized Hamiltonian systems of Hall magnetohydrodynamics (HMHD) which have a hierarchized set of canonical variables; the simplest system is the subclass in which the ion vorticity and magnetic field have integral surfaces. Renormalizing the singularity scaled by the reciprocal Hall parameter (as the ion vorticity surfaces and the magnetic surfaces are set to merge), we delineate the singular limit to ideal magnetohydrodynamics (MHD). The formulated canonical equations will be useful in the study of ordered structures and dynamics (with integrable vortex lines) in HMHD and their singular limit to MHD, such as magnetic confinement systems, shocks or vortical dynamics.

Yoshida, Z.; Hameiri, E.

2013-08-01

146

Quantum Mechanics: Structures, Axioms and Paradoxes

Quantum Mechanics: Structures, Axioms and Paradoxes Diederik Aerts Center Leo Apostel, Brussels show that two of the traditional axioms of quantum ax- iomatics are not satisfied for these `in between., 1999, "Quantum Mechanics; Structures, Axioms and Paradoxes", in Quantum Structures and the Nature

Aerts, Diederik

147

A quantum mechanical model of interference

In this paper an ideal quantum mechanical model of interference is constructed, in particular, the role of the quantum mechanical phase difference of two harmonic modes on the interference picture is investigated.

A. Shalom; J. Zak

1973-01-01

148

Star Products for Relativistic Quantum Mechanics

The star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. We want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in the proper time formulation.

P. Henselder

2007-05-24

149

Quantum Mechanics of Black Holes

NASA Astrophysics Data System (ADS)

The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.

Witten, Edward

2012-08-01

150

First Day Handout Phys 430: Quantum Mechanics

First Day Handout Phys 430: Quantum Mechanics (Dated: 18 August 2014) Meeting times: MWF 1:00-1:50 Room: Neckers 410 Text: "Introduction to Quantum Mechanics," 2nd Edition, by D. Griffiths. Instructor Interpretation (e) The Uncertainty Principle (f) Dirac Notation 4. Chapter 4: Quantum Mechanics in Three

Nickrent, Daniel L.

151

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Review of Quantum Mechanics In general, particles

152

On the interpretation of quantum mechanics

After a brief discussion of the reasons for the complete failure of a deterministic interpretation of quantum mechanics (§ 1)Niels Bohr's ideas on quantum mechanics are exposed. The importance of Bohr's idea on the necessity of combining the quantum-mechanical description of atomic objects with a classical description of the instruments is stressed (§ 2).It is pointed out, however, that the

V. A. Fock

1957-01-01

153

On the interpretation of quantum mechanics

After a brief discussion of the reasons for the complete failure of a deterministic interpretation of quantum mechanics (§ 1) Niels Bohr's ideas on quantum mechanics are exposed. The importance of Bohr's idea on the necessity of combining the quantum-mechanical description of atomic objects with a classical description of the instruments is stressed (§ 2). It is pointed out, however,

V. A. Fock

1957-01-01

154

Relativistic Quantum Mechanics and Field Theory

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

Franz Gross

1999-01-01

155

Although time measurements are routinely performed in laboratories, their theoretical description is still an open problem. Correspondingly, the status of the energy-time uncertainty relation is unsettled. In the first part of this work the necessity of positive operator valued measures (POVM) as descriptions of every quantum experiment is reviewed, as well as the suggestive role played by the probability current in time measurements. Furthermore, it is shown that no POVM exists, which approximately agrees with the probability current on a very natural set of wave functions; nevertheless, the choice of the set is crucial, and on more restrictive sets the probability current does provide a good arrival time prediction. Some ideas to experimentally detect quantum effects in time measurements are discussed. In the second part of the work the energy-time uncertainty relation is considered, in particular for a model of alpha decay for which the variance of the energy can be calculated explicitly, and the variance of time can be estimated. This estimate is tight for systems with long lifetimes, in which case the uncertainty relation is shown to be satisfied. Also the linewidth-lifetime relation is shown to hold, but contrary to the common expectation, it is found that the two relations behave independently, and therefore it is not possible to interpret one as a consequence of the other. To perform the mentioned analysis quantitative scattering estimates are necessary. To this end, bounds of the form $\\|1_Re^{-iHt}\\psi\\|_2^2 \\leq C t^{-3}$ have been derived, where $\\psi$ denotes the initial state, $H$ the Hamiltonian, $R$ a positive constant, and $C$ is explicitly known. As intermediate step, bounds on the derivatives of the $S$-matrix in the form $\\|1_K S^{(n)}\\|_\\infty \\leq C_{n,K} $ have been established, with $n=1,2,3$, and the constants $C_{n,K}$ explicitly known.

Nicola Vona

2014-03-11

156

Nonlinear Boundaries in Quantum Mechanics

Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a linear boundary condition, but not both. Further analysis shows that non-linear boundaries for the ring restore gauge invariance but lead unexpectedly to eigenfunctions with a continuous eigenvalue spectrum, a discreet subset of which forms a Hilbert space with energy bands. This Hilbert space maintains the principle of superposition of eigenfunctions despite the nonlinearity. The momentum operator remains Hermitian. If physical reality requires gauge invariance, it would appear that quantum mechanics should incorporate these nonlinear boundary conditions.

Arthur Davidson

2011-06-22

157

Hamiltonian formulation of quantum error correction and correlated noise: Effects of syndrome lost to the environment 12 . However, as we discuss below, QEC can very effectively slow down this loss of Physics, Duke University, Box 90305, Durham, North Carolina 27708-0305, USA 2 Department of Physics

Baranger, Harold U.

158

Ab-Initio Hamiltonian Approach to Light Nuclei And to Quantum Field Theory

Nuclear structure physics is on the threshold of confronting several long-standing problems such as the origin of shell structure from basic nucleon-nucleon and three-nucleon interactions. At the same time those interactions are being developed with increasing contact to QCD, the underlying theory of the strong interactions, using effective field theory. The motivation is clear - QCD offers the promise of great predictive power spanning phenomena on multiple scales from quarks and gluons to nuclear structure. However, new tools that involve non-perturbative methods are required to build bridges from one scale to the next. We present an overview of recent theoretical and computational progress with a Hamiltonian approach to build these bridges and provide illustrative results for the nuclear structure of light nuclei and quantum field theory.

Vary, J.P.; /Iowa State U.; Honkanen, H.; /Iowa State U.; Li, Jun; /Iowa State U.; Maris, P.; /Iowa State U.; Shirokov, A.M.; /SINP, Moscow; Brodsky, S.J.; /SLAC /Stanford U., Phys. Dept.; Harindranath, A.; /Saha Inst.; de Teramond, G.F.; /Costa Rica U.; Ng, E.G.; /LBL, Berkeley; Yang, C.; /LBL, Berkeley; Sosonkina, M.; /Ames Lab

2012-06-22

159

Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology

We investigate the origin of the arrow of time in quantum mechanics in the\\u000acontext of quantum cosmology. The ``Copenhagen'' quantum mechanics of measured\\u000asubsystems incorporates a fundamental arrow of time. Extending discussions of\\u000aAharonov, Bergmann and Lebovitz, Griffiths, and others we investigate a\\u000ageneralized quantum mechanics for cosmology that utilizes both an initial and a\\u000afinal density matrix to

Murray Gell-Mann; James B. Hartle

1993-01-01

160

Two dogmas about quantum mechanics

We argue that the intractable part of the measurement problem -- the 'big' measurement problem -- is a pseudo-problem that depends for its legitimacy on the acceptance of two dogmas. The first dogma is John Bell's assertion that measurement should never be introduced as a primitive process in a fundamental mechanical theory like classical or quantum mechanics, but should always be open to a complete analysis, in principle, of how the individual outcomes come about dynamically. The second dogma is the view that the quantum state has an ontological significance analogous to the significance of the classical state as the 'truthmaker' for propositions about the occurrence and non-occurrence of events, i.e., that the quantum state is a representation of physical reality. We show how both dogmas can be rejected in a realist information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. The Everettian, too, regards the 'big' measurement problem as a pseudo-problem, because the Everettian rejects the assumption that measurements have definite outcomes, in the sense that one particular outcome, as opposed to other possible outcomes, actually occurs in a quantum measurement process. By contrast with the Everettians, we accept that measurements have definite outcomes. By contrast with the Bohmians and the GRW 'collapse' theorists who add structure to the theory and propose dynamical solutions to the 'big' measurement problem, we take the problem to arise from the failure to see the significance of Hilbert space as a new kinematic framework for the physics of an indeterministic universe, in the sense that Hilbert space imposes kinematic (i.e., pre-dynamic) objective probabilistic constraints on correlations between events.

Jeffrey Bub; Itamar Pitowsky

2007-12-27

161

Adaptive Perturbation Theory: Quantum Mechanics and Field Theory

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, H, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. In this talk I will introduce the method in the context of the pure anharmonic oscillator and then apply it to the case of tunneling between symmetric minima. After that, I will show how this method can be applied to field theory. In that discussion I will show how one can non-perturbatively extract the structure of mass, wavefunction and coupling constant renormalization.

Weinstein, Marvin; /SLAC

2005-10-19

162

Quantum Mechanics in symmetry language

We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better understood in this view. In particular, the abstract concept of symmetry provides a basis-independent definition for observables. Moreover, we show that the apparent projection/collapse of the state as the final step of measurement or decoherence is the result of breaking of symmetries. This phenomenon is comparable with a phase transition by spontaneous symmetry breaking, and makes the process of decoherence and classicality a natural fate of complex systems consisting of many interacting subsystems. Additionally, we demonstrate that the property of state space as a vector space representing symmetries is more fundamental than being an abstract Hilbert space, and its $L2$ integrability can be obtained from the imposed condition of being a representation of a symmetry group and general properties of probability distributions.

Houri Ziaeepour

2014-09-17

163

Quantum Mechanics Beyond Hilbert Space

NASA Astrophysics Data System (ADS)

Going Beyond Hilbert Space Why? The Different Formalisms What Does One Obtain? The Mathematical Formalism Rigged Hilbert Spaces Scales and Lattices of Hilbert Spaces Partial Inner Product Spaces Operators on PIP-Spaces Application in Quantum Mechanics: The Fock-Bargmann Representation - Revisited A RHS of Entire Functions A LHS of Entire Functions Around ? Application in Scattering Theory RHS: Resonances, Gamow Vectors, Arrow of Time LHS: Integral Equations vs. Complex Scaling Conclusion

Antoine, J.-P.

164

Modern Undergraduate Quantum Mechanics Experiments

NSDL National Science Digital Library

The site describes a collection of simplified quantum mechanics experiments developed at Whitman College by Professor Mark Beck. It links to a complete laboratory manual with the following experiments: (1) Spontaneous Parametric Downconversion, (2) Proof of the Existence of Photons, (3) Single Photon Interference, (4) Testing Local Realism Ă la Hardy. The manual also presents documentation for LabView interfaces to the experimental setups. Equipment lists, apparatus pictures, and a collection of links to additional resources is included.

Beck, Mark

2004-07-10

165

Theoretical issues in quantum computing: Graph isomorphism, PageRank, and Hamiltonian determination

NASA Astrophysics Data System (ADS)

This thesis explores several theoretical questions pertaining to quantum computing. First we examine several questions regarding multi-particle quantum random walk-based algorithms for the graph isomorphism problem. We find that there exists a non-trivial difference between continuous-time walks of one and two non-interacting particles as compared to non-interacting walks of three or more particles, in that the latter are able to distinguish many strongly regular graphs (SRGs), a class of graphs with many graph pairs that are difficult to distinguish. We demonstrate analytically where this distinguishing power comes from, and we show numerically that three-particle and four-particle non-interacting continuous-time walks can distinguish many pairs of strongly regular graphs. We additionally show that this distinguishing power, while it grows with particle number, is bounded, so that no continuous-time non-interacting walk of fixed particle number can distinguish all strongly regular graphs. We then investigate the relationship between continuous-time and discrete-time walks, in the context of the graph isomorphism problem. While it has been previously demonstrated numerically that discrete-time walks of non-interacting particles can distinguish some SRGs, we demonstrate where this distinguishing power comes from. We also show that while no continuous-time non-interacting walk of fixed particle number can distinguish SRGs, it remains a possibility that such a discrete-time walk could, leaving open the possibility of a non-trivial difference between discrete-time and continuous-time walks. The last piece of our work on graph isomorphism examines limitations on certain kinds of continuous-time walk-based algorithms for distinguishing graphs. We show that a very general class of continuous-time walk algorithms, with a broad class of allowable interactions, cannot distinguish all graphs. We next consider a previously-proposed quantum adiabatic algorithm for computing the PageRank vector, a necessary step in one of Google's search algorithms. It had been previously believed that this algorithm might offer a non-trivial speedup in preparing the PageRank vector. We demonstrate, however, that when this algorithm is tested on graphs that sufficiently resemble the graph of the World Wide Web, there is no appreciable speedup. Lastly, we consider the problem of Hamiltonian determination. We show that in the high temperature limit, the classical signal processing technique of compressed sensing may be used to recover the Hamiltonian for a system of qubits, provided that the Hamiltonian does not possess too many interactions, i.e., it is "sparse". This new procedure allows for the determination of the Hamiltonian with a number of measurements that can be significantly smaller than required by standard techniques.

Rudinger, Kenneth Michael

166

PT symmetry in classical and quantum statistical mechanics.

PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside the conventional equilibrium statistical mechanics of Hermitian systems. PT-symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviours than Hermitian systems, displaying sinusoidally modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with PT-symmetry include Z(N) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbour Ising model. Quantum many-body problems with a non-zero chemical potential have a natural PT-symmetric representation related to the sign problem. Two-dimensional quantum chromodynamics with heavy quarks at non-zero chemical potential can be solved by diagonalizing an appropriate PT-symmetric Hamiltonian. PMID:23509384

Meisinger, Peter N; Ogilvie, Michael C

2013-04-28

167

Complex solutions to the Painlevé IV equation through supersymmetric quantum mechanics

NASA Astrophysics Data System (ADS)

In this work, supersymmetric quantum mechanics will be used to obtain complex solutions to the Painlevé IV equation with real parameters. We will also focus on the properties of the associated Hamiltonians, i.e. the algebraic structure, the eigenfunctions and the energy spectra

Bermúdez, David; Fernández C., David J.

2012-02-01

168

Physics 216 Spring 2012 Quantum Mechanics of a Charged Particle in an Electromagnetic Field

Physics 216 Spring 2012 Quantum Mechanics of a Charged Particle in an Electromagnetic Field These notes present the Schrodinger equation for a charged particle in an external electromagnetic field. In order to obtain the relevant equation, we first examine the classical Hamiltonian of a charged particle

California at Santa Cruz, University of

169

Game Theory in Categorical Quantum Mechanics

Categorical quantum mechanics, which examines quantum theory via dagger-compact closed categories, gives satisfying high-level explanations to the quantum information procedures such as Bell-type entanglement or complementary observables (\\cite{AC}, \\cite{Co}, \\cite{Co2}). Inspired by the fact that Quantum Game Theory can be seen as branch of quantum information, we express Quantum Game Theory procedures using the topological semantics provided by Categorical Quantum Mechanics. We also investigate Bayesian Games with correlation from this novel point of view while considering the connection between Bayesian game theory and Bell non-locality investigated recently by Brunner and Linden \\cite{BL}.

Ali Nabi Duman

2014-05-17

170

I. BASICS OF STATISTICAL MECHANICS AND QUANTUM MECHANICS Markus Holzmann

I. BASICS OF STATISTICAL MECHANICS AND QUANTUM MECHANICS Markus Holzmann LPMMC, Maison de Magist://www.lptl.jussieu.fr/users/markus/cours.html (Dated: March 1, 2010) We introduce basic concepts of classical and quantum statistical mechanics the basic concepts of statistical mechanics: partition function, free energy, density operators. As examples

171

A new computational method is proposed for ab initio quantum-mechanical\\/molecular-mechanical (QM\\/MM) molecular dynamics (MD) which is limited to time-independent thermodynamic analysis. The idea is to use the mass scaling method combined with multiple-time-scale (MTS) algorithm and an approximate QM\\/MM Hamiltonian derived from the first-order Rayleigh–Schrödinger perturbation theory (PT) in which the electronic polarization is neglected as a first approximation. If

Motoyuki Shiga; Masanori Tachikawa

2007-01-01

172

Quantum mechanical light harvesting mechanisms in photosynthesis

NASA Astrophysics Data System (ADS)

More than 10 million billion photons of light strike a leaf each second. Incredibly, almost every red-coloured photon is captured by chlorophyll pigments and initiates steps to plant growth. Last year we reported that marine algae use quantum mechanics in order to optimize photosynthesis [1], a process essential to its survival. These and other insights from the natural world promise to revolutionize our ability to harness the power of the sun. In a recent review [2] we described the principles learned from studies of various natural antenna complexes and suggested how to utilize that knowledge to shape future technologies. We forecast the need to develop ways to direct and regulate excitation energy flow using molecular organizations that facilitate feedback and control--not easy given that the energy is only stored for a billionth of a second. In this presentation I will describe new results that explain the observation and meaning of quantum-coherent energy transfer. [4pt] [1] Elisabetta Collini, Cathy Y. Wong, Krystyna E. Wilk, Paul M. G. Curmi, Paul Brumer, and Gregory D. Scholes, ``Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature'' Nature 463, 644-648 (2010).[0pt] [2] Gregory D. Scholes, Graham R. Fleming, Alexandra Olaya-Castro and Rienk van Grondelle, ``Lessons from nature about solar light harvesting'' Nature Chem. 3, 763-774 (2011).

Scholes, Gregory

2012-02-01

173

Quantum mechanical effects from deformation theory

We consider deformations of quantum mechanical operators by using the novel construction tool of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a role. Furthermore, a quantum plane can be defined by using the deformation techniques. This in turn gives an experimentally verifiable effect.

Much, A. [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)] [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)

2014-02-15

174

BOOK REVIEWS: Quantum Mechanics: Fundamentals

NASA Astrophysics Data System (ADS)

This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried’s well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Quantum mechanics was already solidly established by 1966, but this second edition gives an indication of progress made and changes in perspective over the last thirty-five years, and also recognises the very substantial increase in knowledge of quantum theory obtained at the undergraduate level. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Their practical importance has now been fully recognised, and a substantial account of them is provided in the new book. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. John Bell’s work of the mid-1960s has led to genuine theoretical and experimental achievement, which has facilitated the development of quantum optics and quantum information theory. Gottfried’s 1966 book played a modest part in this development. When Bell became increasingly irritated with the standard theoretical approach to quantum measurement, Viki Weisskopf repeatedly directed him to Gottfried’s book. Gottfried had devoted a chapter of his book to these matters, titled ‘The Measurement Process and the Statistical Interpretation of Quantum Mechanics’. Gottfried considered the von Neumann or Dirac ‘collapse of state-vector’ (or ‘reduction postulate’ or ‘projection postulate’) was unsatisfactory, as he argued that it led inevitably to the requirement to include ‘consciousness’ in the theory. He replaced this by a more mathematically and conceptually sophisticated treatment in which, following measurement, the density matrix of the correlated measured and measuring systems, rho, is replaced by hat rho, in which the interference terms from rho have been removed. rho represents a pure state, and hat rho a mixture, but Gottfried argued that they are ‘indistinguishable’, and that we may make our replacement, ‘safe in the knowledge that the error will never be found’. Now our combined state is represented as a mixture, it is intuitive, Gottfried argued, to interpret it in a probabilistic way, |cm|2 being the probability of obtaining the mth measurement result. Bell liked Gottfried’s treatment little more than the cruder ‘collapse’ idea of von Neumann, and when, shortly before Bell’s death, his polemical article ‘Against measurement’ was published in the August 1990 issue of Physics World (pages 33-40), his targets included, not only Landau and Lifshitz’s classic Quantum Mechanics, pilloried for its advocacy of old-fashioned collapse, and a paper by van Kampen in Physica, but also Gottfried’s approach. Bell regarded his replacement of rho by hat rho as a ‘butchering’ of the density matrix, and considered, in any case, that even the butchered density matrix should represent co-existence of different terms, not a set of probabilities. Gottfried has replied to Bell ( Physics World, October 1991, pages 34-40; Nature 405, 533-36 (2000)). He has also become a major commentator on Bell’s work, for example editing the section on quantum foundations in the World Scientific edition of Bell’s collected works. Thus it is exceedingly interesting to disco

Whitaker, A.

2004-02-01

175

Davidson potential and SUSYQM in the Bohr Hamiltonian

NASA Astrophysics Data System (ADS)

The Bohr Hamiltonian is modified through the Shape Invariance principle of SUper-SYmmetric Quantum Mechanics for the Davidson potential. The modification is equivalent to a conformal transformation of Bohr's metric, generating a different ?-dependence of the moments of inertia.

Georgoudis, P. E.

2013-06-01

176

Treating Time Travel Quantum Mechanically

The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilising the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their non-linearity and time travel paradoxes. In particular, the "equivalent circuit model"---which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory---is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of new theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features---such as time travel paradoxes, the ability to distinguish non-orthogonal states with certainty, and the ability to clone or delete arbitrary pure states---that are present with D-CTCs and P-CTCs. The problems with non-linear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.

John-Mark A. Allen

2014-01-20

177

A quantum mechanical model of "dark matter"

The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.

V. V. Belokurov; E. T. Shavgulidze

2014-03-28

178

Propagators in polymer quantum mechanics

Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has been used to represent some aspects of the loop quantization in a simpler context, and, on the other, it has been applied to each of the infinite mechanical modes of other systems. Indeed, this polymer approach was recently implemented for the free scalar field propagator. In this work we compute the polymer propagators of the free particle and a particle in a box; amusingly, just as in the non polymeric case, the one of the particle in a box may be computed also from that of the free particle using the method of images. We verify the propagators hereby obtained satisfy standard properties such as: consistency with initial conditions, composition and Green’s function character. Furthermore they are also shown to reduce to the usual Schrödinger propagators in the limit of small parameter ?{sub 0}, the length scale introduced in the polymer dynamics and which plays a role analog of that of Planck length in Quantum Gravity. -- Highlights: •Formulas for propagators of free and particle in a box in polymer quantum mechanics. •Initial conditions, composition and Green’s function character is checked. •Propagators reduce to corresponding Schrödinger ones in an appropriately defined limit. •Results show overall consistency of the polymer framework. •For the particle in a box results are also verified using formula from method of images.

Flores-González, Ernesto, E-mail: eflores@xanum.uam.mx; Morales-Técotl, Hugo A., E-mail: hugo@xanum.uam.mx; Reyes, Juan D., E-mail: jdrp75@gmail.com

2013-09-15

179

NASA Astrophysics Data System (ADS)

We propose a quantum algorithm to obtain the lowest eigenstate of any Hamiltonian simulated by a quantum computer. The proposed algorithm begins with an arbitrary initial state of the simulated system. A finite series of transforms is iteratively applied to the initial state assisted with an ancillary qubit. The fraction of the lowest eigenstate in the initial state is then amplified up to 1. We prove that our algorithm can faithfully work for any arbitrary Hamiltonian in the theoretical analysis. Numerical analyses are also carried out. We firstly provide a numerical proof-of-principle demonstration with a simple Hamiltonian in order to compare our scheme with the so-called "Demon-like algorithmic cooling (DLAC)", recently proposed in Xu (Nat Photonics 8:113, 2014). The result shows a good agreement with our theoretical analysis, exhibiting the comparable behavior to the best `cooling' with the DLAC method. We then consider a random Hamiltonian model for further analysis of our algorithm. By numerical simulations, we show that the total number of iterations is proportional to , where is the difference between the two lowest eigenvalues and is an error defined as the probability that the finally obtained system state is in an unexpected (i.e., not the lowest) eigenstate.

Bang, Jeongho; Lee, Seung-Woo; Lee, Chang-Woo; Jeong, Hyunseok

2015-01-01

180

This paper is concerned with a stochastic dissipativity theory using quadratic-exponential storage functions for open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations. The system is linearly coupled to external boson fields and has a quadratic Hamiltonian which is perturbed by nonquadratic functions of linear combinations of system variables. Such perturbations are similar to those in the classical Lur'e systems and make the quantum dynamics nonlinear. We study their effect on the quantum expectation of the exponential of a positive definite quadratic form of the system variables. This allows conditions to be established for the risk-sensitive stochastic storage function of the quantum system to remain bounded, thus securing boundedness for the moments of system variables of arbitrary order. These results employ a noncommutative analogue of the Doleans-Dade exponential and a multivariate partial differential version of the Gronwall-Bellman lemma.

Igor G. Vladimirov; Ian R. Petersen

2012-05-16

181

Bananaworld: Quantum Mechanics for Primates

This is intended to be a serious paper, in spite of the title. The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, since a theory of information is essentially a theory of probabilistic correlations. To make this clear, it suffices to consider measurements of two binary-valued observables, x with outcomes a = 0 or 1, performed by Alice in a region A, and y with outcomes b = 0 or 1 performed by Bob in a separated region B --or, to emphasize the banality of the phenomena, two ways of peeling a banana, resulting in one of two tastes. The imagined bananas of Bananaworld are non-standard, with operational or phenomenal probabilistic correlations for peelings and tastes that lie outside the polytope of local correlations. The 'no go' theorems tell us that we can't shoe-horn these correlations into a classical correlation polytope, which has the structure of a simplex, by supposing that something has been left out of the story, without giving up fundamental principles that define what we mean by a physical system. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are shown to be generic features of correlations that lie outside the local correlation polytope. As far as the conceptual problems are concerned, we might as well talk about bananas.

Jeffrey Bub

2013-01-08

182

NASA Astrophysics Data System (ADS)

The fluctuation theorems rigorously relate equilibrium ensemble properties of a dynamical system with its evolution under nonequilibrium conditions, beyond the domain of validity of the linear response theory. We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. We adopt the partitioning of the total Hamiltonian into the system part, the bath part, and their coupling. We rederive many equalities which are available in the literature and obtain a number of new equalities for nonequilibrium classical and quantum systems. Our results can be useful for determining partition functions and generalized free energies through simulations or measurements performed on nonequilibrium systems. We derive a semiclassical version of the work theorem and discuss the definition of semicalssical work operator. Phys.Rev. E 78, 011116 (2008)

Kosov, Daniel; Gelin, Maxim

2009-03-01

183

Principles of a 2nd Quantum Mechanics

A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this representation as a reference-and-imbedding-structure, the foundations of an intelligible reconstruction of the Hilbert-Dirac formulation of Quantum Mechanics is developed. Inside this reconstruction the measurement problem as well as the other major problems raised by the quantum mechanical formalism, dissolve.

Mioara Mugur-Schächter

2014-10-23

184

Heisenberg and the Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.

Camilleri, Kristian

2011-09-01

185

Heisenberg and the Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.

Camilleri, Kristian

2009-02-01

186

PT Symmetry in Classical and Quantum Statistical Mechanics

PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside of the conventional equilibrium statistical mechanics of Hermitian systems. PT-symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviors than Hermitian systems, displaying sinusoidally-modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with PT symmetry include Z(N) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbor Ising (ANNNI) model. Quantum many-body problems with a non-zero chemical potential have a natural PT-symmetric representation related to the sign problem. Two-dimensional QCD with heavy quarks at non-zero chemical potential can be solved by diagonalizing an appropriate PT-symmetric Hamiltonian.

Peter N. Meisinger; Michael C. Ogilvie

2012-08-24

187

Quantum Statistical Mechanics. III. Equilibrium Probability

Given are a first principles derivation and formulation of the probabilistic concepts that underly equilibrium quantum statistical mechanics. The transition to non-equilibrium probability is traversed briefly.

Phil Attard

2014-04-10

188

New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis

NASA Astrophysics Data System (ADS)

Loop quantum gravity (LQG) relies heavily on a connection formulation of general relativity such that (1) the connection Poisson commutes with itself and (2) the corresponding gauge group is compact. This can be achieved starting from the Palatini or Holst action when imposing the time gauge. Unfortunately, this method is restricted to D + 1 = 4 spacetime dimensions. However, interesting string theories and supergravity theories require higher dimensions and it would therefore be desirable to have higher dimensional supergravity loop quantizations at one’s disposal in order to compare these approaches. In this series of papers we take first steps toward this goal. The present first paper develops a classical canonical platform for a higher dimensional connection formulation of the purely gravitational sector. The new ingredient is a different extension of the ADM phase space than the one used in LQG which does not require the time gauge and which generalizes to any dimension D > 1. The result is a Yang-Mills theory phase space subject to Gauß, spatial diffeomorphism and Hamiltonian constraint as well as one additional constraint, called the simplicity constraint. The structure group can be chosen to be SO(1, D) or SO(D + 1) and the latter choice is preferred for purposes of quantization.

Bodendorfer, N.; Thiemann, T.; Thurn, A.

2013-02-01

189

This work focuses on the dynamics of a system of quantum multi harmonic oscillators whose Hamiltonian is conic in positions and momenta with time variant coefficients. While it is simple, this system is useful for modeling the dynamics of a number of systems in contemporary sciences where the equations governing spatial or temporal changes are described by sets of ODEs. The dynamical causal models used readily in neuroscience can be indirectly described by these systems. In this work, we want to show that it is possible to describe these systems using quantum wave function type entities and expectations if the dynamic of the system is related to a set of ODEs.

Demiralp, Metin [Istanbul Technical University, Informatics Institute, Group for Science and Methods of Computing, Maslak, 34469, Istanbul (Turkey)

2010-09-30

190

In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ({Dirac_h}/2{pi})=m{sub e}=e=a{sub 0}= 1, have been used unless otherwise stated.

Asplund, Erik; Kluener, Thorsten [Institut fuer Reine und Angewandte Chemie, Carl von Ossietzky Universitaet Oldenburg, Postfach 2503, D-26111 Oldenburg (Germany)

2012-03-28

191

Bohmian Mechanics and the Quantum Revolution

This is a review-essay on ``Speakable and Unspeakable in Quantum Mechanics'' by John Bell and ``The Undivided Universe: An Ontological Interpretation of Quantum Mechanics'' by David Bohm and Basil Hiley. The views of these authors concerning the character of quantum theory and quantum reality---and, in particular, their approaches to the issues of nonlocality, the possibility of hidden variables, and the nature of and desiderata for a satisfactory scientific explanation of quantum phenomena---are contrasted, with each other and with the orthodox approach to these issues.

Sheldon Goldstein

1995-12-26

192

The auxiliary field method in quantum mechanics

The auxiliary field method is a new technique to obtain closed formulae for the solutions of eigenequations in quantum mechanics. The idea is to replace a Hamiltonian $H$ for which analytical solutions are not known by another one $\\tilde H$, including one or more auxiliary fields. For instance, a potential $V(r)$ not solvable is replaced by another one $P(r)$ more familiar, or a semirelativistic kinetic part is replaced by an equivalent nonrelativistic one. The approximation comes from the replacement of the auxiliary fields by pure real constants. The approximant solutions for $H$, eigenvalues and eigenfunctions, are then obtained by the solutions of $\\tilde H$ in which the auxiliary parameters are eliminated by an extremization procedure for the eigenenergies. If $H=T(\\bm p)+V(r)$ and if $P(r)$ is a power law, the approximate eigenvalues can be written $T(p_0)+V(r_0)$, where the mean impulsion $p_0$ is a function of the mean distance $r_0$ and where $r_0$ is determined by an equation which is linked to the generalized virial theorem. The general properties of the method are studied and the connections with the envelope theory presented. This method is first applied to nonrelativistic and semirelativistic two-body systems, with a great variety of potentials. Closed formulae are produced for energies, eigenstates, various observables and critical constants, with sometimes a very good accuracy. The method is then used to solve nonrelativistic and semirelativistic many-body systems with one-body and two-body interactions. For such cases, analytical solutions can only be obtained for systems of identical particles, but several systems of interest for atomic and hadronic physics are studied. General results concerning the many-body critical constants are presented, as well as duality relations existing between approximate and exact eigenvalues.

Bernard Silvestre-Brac; Claude Semay; Fabien Buisseret

2011-01-27

193

Quantum mechanics: A new chapter?

We review the conceptual problems in quantum mechanics on a fundamental level. It is shown that the proposed model of extended electrons and a clear understanding of rotations in three dimensional space solve a large part of these problems, in particular the problems related to the ontological status and physical meaning of wavefunctions. It also solves the problem of non-locality. The experimental results obtained in Yves Couder's group and theoretical results by Gerdard Gr\\"ossing indicate that the wave-like distribution of trajectories of electrons in interference experiments are most likely due to the quantized interactions leading to a discrete set of transferred momenta. A separate experimental confirmation of this interpretation for double-slit interferometry of photons has been given by the group of Steinberg.

Werner A. Hofer

2012-09-05

194

Interactive Learning Tutorials on Quantum Mechanics

NSDL National Science Digital Library

We discuss the development and evaluation of quantum interactive learning tutorials (QuILTs), which are suitable for undergraduate courses in quantum mechanics. QuILTs are based on the investigation of student difficulties in learning quantum physics. They exploit computer-based visualization tools and help students build links between the formal and conceptual aspects of quantum physics without compromising the technical content. They can be used both as supplements to lectures or as self-study tools.

Singh, Chandralekha

2013-08-08

195

Testing quantum mechanics: a statistical approach

NASA Astrophysics Data System (ADS)

As experiments continue to push the quantum-classical boundary using increasingly complex dynamical systems, the interpretation of experimental data becomes more and more challenging: when the observations are noisy, indirect, and limited, how can we be sure that we are observing quantum behavior? This tutorial highlights some of the difficulties in such experimental tests of quantum mechanics, using optomechanics as the central example, and discusses how the issues can be resolved using techniques from statistics and insights from quantum information theory.

Tsang, Mankei

2013-12-01

196

Thermodynamic integration from classical to quantum mechanics

We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.

Habershon, Scott [Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS (United Kingdom); Manolopoulos, David E. [Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ (United Kingdom)

2011-12-14

197

NONEQUILIBRIUM QUANTUM STATISTICAL MECHANICS AND THERMODYNAMICS #

NONEQUILIBRIUM QUANTUM STATISTICAL MECHANICS AND THERMODYNAMICS # Walid K. Abou Salem + Institut f recent progress in deriving the fundamental laws of thermodynamics (0 th , 1 st and 2 nd Âlaw) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and di#erent reversible

198

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Relativity (Why it makes sense) Thursday, May 7

199

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Friday, May 15, 2009 #12;Quark Summary mesons and baryons

200

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Scattering Summary the best way to study

201

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Review of Relativity The laws of physics

202

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification that is naturally solved by string theory Strings vibrating in a variety of ways give rise to particles of different

203

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Friday, June 19, 2009 #12;String Theory Origins We introduced string theory as a possible solution to our

204

Uncertainty and complementarity in axiomatic quantum mechanics

In this work an investigation of the uncertainty principle and the complementarity principle is carried through. A study of the physical content of these principles and their representation in the conventional Hilbert space formulation of quantum mechanics forms a natural starting point for this analysis. Thereafter is presented more general axiomatic framework for quantum mechanics, namely, a probability function formulation

Pekka J. Lahti

1980-01-01

205

PERSPECTIVE Quantum Mechanics of Black Holes

PERSPECTIVE Quantum Mechanics of Black Holes Edward Witten The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived

206

Particle in a box in PT-symmetric quantum mechanics and an electromagnetic analog

NASA Astrophysics Data System (ADS)

In PT-symmetric quantum mechanics a fundamental principle of quantum mechanics, that the Hamiltonian must be Hermitian, is replaced by another set of requirements, including notably symmetry under PT, where P denotes parity and T denotes time reversal. Here we study the role of boundary conditions in PT-symmetric quantum mechanics by constructing a simple model that is the PT-symmetric analog of a particle in a box. The model has the usual particle-in-a-box Hamiltonian but boundary conditions that respect PT symmetry rather than Hermiticity. We find that for a broad class of PT-symmetric boundary conditions the model respects the condition of unbroken PT symmetry, namely, that the Hamiltonian and the symmetry operator PT have simultaneous eigenfunctions, implying that the energy eigenvalues are real. We also find that the Hamiltonian is self-adjoint under the PT-symmetric inner product. Thus we obtain a simple soluble model that fulfills all the requirements of PT-symmetric quantum mechanics. In the second part of this paper we formulate a variational principle for PT-symmetric quantum mechanics that is the analog of the textbook Rayleigh-Ritz principle. Finally we consider electromagnetic analogs of the PT-symmetric particle in a box. We show that the isolated particle in a box may be realized as a Fabry-Perot cavity between an absorbing medium and its conjugate gain medium. Coupling the cavity to an external continuum of incoming and outgoing states turns the energy levels of the box into sharp resonances. Remarkably we find that the resonances have a Breit-Wigner line shape in transmission and a Fano line shape in reflection; by contrast, in the corresponding Hermitian case the line shapes always have a Breit-Wigner form in both transmission and reflection.

Dasarathy, Anirudh; Isaacson, Joshua P.; Jones-Smith, Katherine; Tabachnik, Jason; Mathur, Harsh

2013-06-01

207

Pseudoanalytic function theory is considered to study a two-dimensional supersymmetric quantum mechanics system. Hamiltonian components of the superhamiltonian are factorized in terms of one Vekua and one Bers derivative operators. We show that imaginary and real solutions of a Vekua equation and its Bers derivative are ground state solutions for the superhamiltonian. The two-dimensional Darboux and pseudo-Darboux transformations correspond to Bers derivatives in the complex plane. Results on the completeness of the ground states are obtained. Finally, superpotential is studied in the separable case in terms of transmutation operators. We show how Hamiltonian components of the superhamiltonian are related to the Laplacian operator using these transmutation operators.

Alex Bilodeau; Sébastien Tremblay

2013-07-01

208

Unified theory of exactly and quasiexactly solvable ''discrete'' quantum mechanics. I. Formalism

We present a simple recipe to construct exactly and quasiexactly solvable Hamiltonians in one-dimensional ''discrete'' quantum mechanics, in which the Schroedinger equation is a difference equation. It reproduces all the known ones whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. The recipe also predicts several new ones. An essential role is played by the sinusoidal coordinate, which generates the closure relation and the Askey-Wilson algebra together with the Hamiltonian. The relationship between the closure relation and the Askey-Wilson algebra is clarified.

Odake, Satoru [Department of Physics, Shinshu University, Matsumoto 390-8621 (Japan); Sasaki, Ryu [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)

2010-08-15

209

Noncommutative quantum mechanics: Uniqueness of the functional description

The generalized Weyl transform of index {alpha} is used to implement the time-slice definition of the phase space path integral yielding the Feynman kernel in the case of noncommutative quantum mechanics. As expected, this representation for the Feynman kernel is not unique but labeled by the real parameter {alpha}. We succeed in proving that the {alpha}-dependent contributions disappear at the limit where the time slice goes to zero. This proof of consistency turns out to be intricate because the Hamiltonian involves products of noncommuting operators originating from the noncommutativity. The antisymmetry of the matrix parametrizing the noncommutativity plays a key role in the cancellation mechanism of the {alpha}-dependent terms.

Bemfica, F. S.; Girotti, H. O. [Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970-Porto Alegre, RS (Brazil)

2008-12-15

210

Polymer quantum mechanics and its continuum limit

A rather nonstandard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model.

Corichi, Alejandro [Instituto de Matematicas, Unidad Morelia, Universidad Nacional Autonoma de Mexico, UNAM-Campus Morelia, A. Postal 61-3, Morelia, Michoacan 58090 (Mexico); Departamento de Gravitacion y Teoria de Campos, Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A. Postal 70-543, Mexico D.F. 04510 (Mexico); Institute for Gravitational Physics and Geometry, Physics Department, Pennsylvania State University, University Park, Pennsylvania 16802 (United States); Vukasinac, Tatjana [Facultad de Ingenieria Civil, Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Michoacan 58000 (Mexico); Zapata, Jose A. [Instituto de Matematicas, Unidad Morelia, Universidad Nacional Autonoma de Mexico, UNAM-Campus Morelia, A. Postal 61-3, Morelia, Michoacan 58090 (Mexico)

2007-08-15

211

NASA Astrophysics Data System (ADS)

The role of interfaces and higher bands on the electronic structure of embedded semiconductor quantum dots (QDs) was investigated. The term in the multiband k.p Hamiltonian that captures the effect of interface band mixing was derived starting from the microscopic theory. It was shown, analytically and numerically, that, with such a term included, the right symmetry of the QD system can be captured. It leads to splitting of otherwise degenerate energy levels of the order of several meV. The inclusion of additional higher bands beyond the ones from the standard eight-band model also leads to the reduction of symmetry from an artificially high one to the true atomistic symmetry of the system, however their quantitative effect is weaker. These results prove that the multiband k.p Hamiltonians are fully capable of describing the correct symmetry of a QD.

Tomi?, Stanko; Vukmirovi?, Nenad

2011-09-01

212

Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology

We investigate the origin of the arrow of time in quantum mechanics in the context of quantum cosmology. The ``Copenhagen'' quantum mechanics of measured subsystems incorporates a fundamental arrow of time. Extending discussions of Aharonov, Bergmann and Lebovitz, Griffiths, and others we investigate a generalized quantum mechanics for cosmology that utilizes both an initial and a final density matrix to give a time-neutral formulation without a fundamental arrow of time. Time asymmetries can arise for particular universes from differences between their initial and final conditions. Theories for both would be a goal of quantum cosmology. A special initial condition and a final condition of indifference would be sufficient to explain the observed time asymmetries of the universe. In this essay we ask under what circumstances a completely time symmetric universe, with T-symmetric initial and final condition, could be consistent with the time asymmetries of the limited domain of our experience. We discuss the ap...

Gell-Mann, Murray; Gell-Mann, Murray; Hartle, James B.

1993-01-01

213

Gauging non-Hermitian Hamiltonians

NASA Astrophysics Data System (ADS)

We address the problem of coupling non-Hermitian systems, treated as fundamental rather than effective theories, to the electromagnetic field. In such theories the observables are not the x and p appearing in the Hamiltonian, but quantities X and P constructed by means of the metric operator. Following the analogous procedure of gauging a global symmetry in Hermitian quantum mechanics we find that the corresponding gauge transformation in X implies minimal substitution in the form P ? P - eA(X). We discuss how the relevant matrix elements governing electromagnetic transitions may be calculated in the special case of the Swanson Hamiltonian, where the equivalent Hermitian Hamiltonian h is local, and in the more generic example of the imaginary cubic interaction, where H is local but h is not.

Jones, H. F.

2009-04-01

214

Topological Strings from Quantum Mechanics

We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized theta function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P2, local P1xP1 and local F1. In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.

Alba Grassi; Yasuyuki Hatsuda; Marcos Marino

2014-11-27

215

Operational Axioms for Quantum Mechanics

The mathematical formulation of Quantum Mechanics in terms of complex Hilbert space is derived for finite dimensions, starting from a general definition of physical experiment and from five simple Postulates concerning experimental accessibility and simplicity. For the infinite dimensional case, on the other hand, a C*-algebra representation of physical transformations is derived, starting from just four of the five Postulates via a Gelfand-Naimark-Segal (GNS) construction. The present paper simplifies and sharpens the previous derivation in Ref. [1]. The main ingredient of the axiomatization is the postulated existence of faithful states that allows one to calibrate the experimental apparatus. Such notion is at the basis of the operational definitions of the scalar product and of the transposed of a physical transformation. What is new in the present paper with respect to Ref. [1], is the operational deduction of an involution corresponding to the complex-conjugation for effects, whose extension to transformations allows to define the adjoint of a transformation when the extension is composition-preserving. The existence of such composition-preserving extension among possible extensions is analyzed.

D'Ariano, Giacomo Mauro [QUIT Group, Dipartimento di Fisica 'A. Volta', via Bassi 6, I-27100 Pavia (Italy); Department of Electrical and Computer Engineering, Northwestern University, Evanston, IL 60208 (United States)

2007-02-21

216

Operational Axioms for Quantum Mechanics

The mathematical formulation of Quantum Mechanics in terms of complex Hilbert space is derived for finite dimensions, starting from a general definition of "physical experiment" and from five simple Postulates concerning "experimental accessibility and simplicity". For the infinite dimensional case, on the other hand, a C*-algebra representation of physical transformations is derived, starting from just four of the five Postulates via a Gelfand-Naimark-Segal (GNS) construction. The present paper simplifies and sharpens the previous derivation in version 1. The main ingredient of the axiomatization is the postulated existence of "faithful states" that allows one to calibrate the experimental apparatus. Such notion is at the basis of the operational definitions of the scalar product and of the "transposed" of a physical transformation. What is new in the present paper with respect to quant-ph/0603011 is the operational deduction of an involution corresponding to the "complex-conjugation" for effects, whose extension to transformations allows to define the "adjoint" of a transformation when the extension is composition-preserving.

Giacomo Mauro D'Ariano

2006-11-08

217

Quantum mechanical studies of lincosamides.

Lincosamides are a class of antibiotics used both in clinical and veterinary practice for a wide range of pathogens. This group of drugs inhibits the activity of the bacterial ribosome by binding to the 23S RNA of the large ribosomal subunit and blocking protein synthesis. Currently, three X-ray structures of the ribosome in complex with clindamycin are available in the Protein Data Bank, which reveal that there are two distinct conformations of the pyrrolidinyl propyl group of the bound clindamycin. In this work, we used quantum mechanical methods to investigate the probable conformations of clindamycin in order to explain the two binding modes in the ribosomal 23S RNA. We studied three lincosamide antibiotics: clindamycin, lincomycin, and pirlimycin at the B3LYP level with the 6-31G** basis set. The focus of our work was to connect the conformational landscape and electron densities of the two clindamycin conformers found experimentally with their physicochemical properties. For both functional conformers, we applied natural bond orbital (NBO) analysis and the atoms in molecules (AIM) theory, and calculated the NMR parameters. Based on the results obtained, we were able to show that the structure with the intramolecular hydrogen bond C=O…H-O is the most stable conformer of clindamycin. The charge transfer between the pyrrolidine-derivative ring and the six-atom sugar (methylthiolincosamide), which are linked via an amide bond, was found to be the dominant factor influencing the high stability of this conformer. PMID:22116607

Kulczycka-Mierzejewska, Katarzyna; Trylska, Joanna; Sadlej, Joanna

2012-06-01

218

Comment on Consistent Interpretation of Quantum Mechanics Using Quantum Trajectories

Recently, Griffiths presented a generalization of the consistent history approach to quantum mechanics. I can easily construct all possible complete families satisfying Griffiths' "noninterference conditions". Since only trivial families exist one may conclude that Griffiths' proposal has not got farther than the ordinary theory of quantum measurement.

Lajos Diosi

1993-04-27

219

Quantum mechanical wavepacket transport in quantum cascade laser structures

We present a viewpoint of the transport process in quantum cascade laser structures in which spatial transport of charge through the structure is a property of coherent quantum mechanical wave functions. In contrast, scattering processes redistribute particles in energy and momentum but do not directly cause spatial motion of charge.

S.-C. Lee; F. Banit; M. Woerner; A. Wacker

2006-01-01

220

Canonical distribution and incompleteness of quantum mechanics

The paper discusses the physical groundlessness of the models used for the derivation of canonical distribution and provides the experimental data demonstrating the incompleteness of quantum mechanics. The possibility of using statistical ensembles is presented as a consequence of the existence of probabilistic processes which are not accounted for by quantum mechanics. The paper provides a new analytical derivation of canonical distribution for macrosystems which takes into account subquantum processes. The paper discusses the possibility of the experimental study of a probability which is beyond quantum mechanics.

V. A. Skrebnev

2014-05-05

221

Snyder noncommutativity and pseudo-Hermitian Hamiltonians from a Jordanian twist

Nonrelativistic quantum mechanics and conformal quantum mechanics are deformed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian Hamiltonians of the type discussed by Mostafazadeh. The quantization scheme makes use of the so-called 'unfolded formalism' discussed in previous works. A Hopf algebra structure, compatible with the physical interpretation of the coproduct, is introduced for the universal enveloping algebra of a suitably chosen dynamical Lie algebra (the Hamiltonian is contained among its generators). The multi-particle sector, uniquely determined by the deformed two-particle Hamiltonian, is composed of bosonic particles.

Castro, P. G. [DM/ICE/UFJF, Campus Universitario, cep 36036-330, Juiz de Fora (Brazil); Kullock, R.; Toppan, F. [TEO/CBPF, Rua Dr. Xavier Sigaud 150, cep 22290-180, Rio de Janeiro (Brazil)

2011-06-15

222

Playing Games with Quantum Mechanics

We present a perspective on quantum games that focuses on the physical aspects of the quantities that are used to implement a game. If a game is to be played, it has to be played with objects and actions that have some physical existence. We call such games playable. By focusing on the notion of playability for games we can more clearly see the distinction between classical and quantum games and tackle the thorny issue of what it means to quantize a game. The approach we take can more properly be thought of as gaming the quantum rather than quantizing a game and we find that in this perspective we can think of a complete quantum game, for a given set of preferences, as representing a single family of quantum games with many different playable versions. The versions of Quantum Prisoners Dilemma presented in the literature can therefore be thought of specific instances of the single family of Quantum Prisoner's Dilemma with respect to a particular measurement. The conditions for equilibrium are given for playable quantum games both in terms of expected outcomes and a geometric approach. We discuss how any quantum game can be simulated with a classical game played with classical coins as far as the strategy selections and expected outcomes are concerned.

Simon J. D. Phoenix; Faisal Shah Khan

2012-02-21

223

Visual Quantum Mechanics: Online Interactive Programs

NSDL National Science Digital Library

The Visual Quantum Mechanics project, from the Physics Education Group of Kansas State University's Department of Physics, develops innovative ways to "introduce quantum physics to high school and college students who do not have a background in modern physics or higher level math." Funded by the National Science Foundation, this resource for educators provides interactive computer visualizations and animations that introduce quantum mechanics. The interactive programs (which require Shockwave) include a spectroscopy lab suite, a probability illustrator, an energy band creator, quantum tunneling, a color creator (a Java version is also available), a wave function sketcher, a wave packet explorer, an energy diagram explorer, a diffraction suite, and a hydrogen spectroscopy program. These online demonstrations should prove to be excellent visual, hands-on teaching aids when introducing concepts involving quantum mechanics. Users can download Shockwave at the site.

224

On Wigner functions and a damped star product in dissipative phase-space quantum mechanics

Dito and Turrubiates recently introduced an interesting model of the dissipative quantum mechanics of a damped harmonic oscillator in phase space. Its key ingredient is a non-Hermitian deformation of the Moyal star product with the damping constant as deformation parameter. We compare the Dito-Turrubiates scheme with phase-space quantum mechanics (or deformation quantization) based on other star products, and extend it to incorporate Wigner functions. The deformed (or damped) star product is related to a complex Hamiltonian, and so necessitates a modified equation of motion involving complex conjugation. We find that with this change the Wigner function satisfies the classical equation of motion. This seems appropriate since non-dissipative systems with quadratic Hamiltonians share this property.

Belchev, B. [Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive West, Lethbridge, Alta., T1K 3M4 (Canada)], E-mail: borislav.belchev@uleth.ca; Walton, M.A. [Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive West, Lethbridge, Alta., T1K 3M4 (Canada)], E-mail: walton@uleth.ca

2009-03-15

225

Strange Bedfellows: Quantum Mechanics and Data Mining

Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.

Weinstein, Marvin; /SLAC

2009-12-16

226

Strange Bedfellows: Quantum Mechanics and Data Mining

Last year, in 2008, I gave a talk titled {\\it Quantum Calisthenics}. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.

Marvin Weinstein

2009-11-03

227

On the Gravitization of Quantum Mechanics 1: Quantum State Reduction

NASA Astrophysics Data System (ADS)

This paper argues that the case for "gravitizing" quantum theory is at least as strong as that for quantizing gravity. Accordingly, the principles of general relativity must influence, and actually change, the very formalism of quantum mechanics. Most particularly, an "Einsteinian", rather than a "Newtonian" treatment of the gravitational field should be adopted, in a quantum system, in order that the principle of equivalence be fully respected. This leads to an expectation that quantum superpositions of states involving a significant mass displacement should have a finite lifetime, in accordance with a proposal previously put forward by Diósi and the author.

Penrose, Roger

2014-05-01

228

NASA Astrophysics Data System (ADS)

We use the adaptive time-dependent density matrix renormalization group method (t-DMRG) to study the nonequilibrium dynamics of a benchmark quantum impurity system which has a time-dependent Hamiltonian. This model is a resonant-level model, obtained by a mapping from a certain Ohmic spin-boson model describing the dissipative Landau-Zener transition. We map the resonant-level model onto a Wilson chain, then calculate the time-dependent occupation nd(t) of the resonant level. We compare t-DMRG results with exact results at zero temperature and find very good agreement. We also give a physical interpretation of the numerical results.

Guo, Cheng; Weichselbaum, Andreas; Kehrein, Stefan; Xiang, Tao; von Delft, Jan

2009-03-01

229

Quantum-Mechanical Model of Spacetime

We consider a possibility to construct a quantum-mechanical model of spacetime, where Planck size quantum black holes act as the fundamental constituents of space and time. Spacetime is assumed to be a graph, where black holes lie on the vertices. Our model implies that area has a discrete spectrum with equal spacing. At macroscopic length scales our model reproduces Einstein's

Jarmo Makela

2007-01-01

230

Quantum Mechanics and the Generalized Uncertainty Principle

The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.

Jang Young Bang; Micheal S. Berger

2006-11-30

231

Quantum mechanics and the generalized uncertainty principle

The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.

Bang, Jang Young; Berger, Micheal S. [Physics Department, Indiana University, Bloomington, Indiana 47405 (United States)

2006-12-15

232

Quantum mechanics as electrodynamics of curvilinear waves

The suggested theory is the new quantum mechanics (QM) interpretation.The\\u000aresearch proves that QM represents the electrodynamics of the curvilinear\\u000aclosed (non-linear) waves. It is entirely according to the modern\\u000ainterpretation and explains the particularities and the results of the quantum\\u000afield theory.

Alexander G. Kyriakos

2002-01-01

233

Space time symmetry in quantum mechanics

New prescription to treat position and time equally in quantum mechanics is presented. Using this prescription, we could successfully derive some interesting formulae such as time-of-arrival for a free particle and quantum tunneling formula. The physical interpretation will be discussed.

Zinkoo Yun

2014-02-26

234

The Compton effect: Transition to quantum mechanics

The discovery of the Compton effect at the end of 1922 was a decisive event in the transition to the new quantum mechanics of 1925-1926 because it stimulated physicists to examine anew the fundamental problem of the interaction between radiation and matter. I first discuss Albert Einstein's light-quantum hypothesis of 1905 and why physicists greeted it with extreme skepticism, despite

R. H. Stuewer

2000-01-01

235

Quantum Semiotics: A Sign Language for Quantum Mechanics

Semiotics is the language of signs which has been used effectively in various disciplines of human scientific endeavor. It gives a beautiful and rich structure of language to express the basic tenets of any scientific discipline. In this article we attempt to develop from first principles such an axiomatic structure of semiotics for Quantum Mechanics. This would be a further enrichment to the already existing well understood mathematical structure of Quantum Mechanics but may give new insights and understanding to the theory and may help understand more lucidly the fundamentality of Nature which Quantum Theory attempts to explain.

Prashant

2006-01-01

236

The paper describes self-adjoint extensions of the operator Hâ = \\/minus\\/\\/triangle\\/ from the Hilbert space Lâ(R\\/sub n\\/) to a certain Pontryagin space generated by interactions represented by generalized functions. Hamiltonians of quantum-mechanical models are obtained by restricting such extensions to positive invariant subspaces.

Yu. G. Shondin; Yu. G

1988-01-01

237

Classical and quantum-mechanical systems of Toda lattice type. I

NASA Astrophysics Data System (ADS)

The structure of the commutant of Laplace operators in the enveloping and “Poisson algebra” of certain generalized “ ax + b” groups leads (in this article) to a determination of classical and quantum mechanical first integrals to generalized periodic and non-periodic Toda lattices. Certain new Hamiltonian systems of Toda lattice type are also shown to fit in this framework. Finite dimensional Lax forms for the (periodic) Toda lattices are given generalizing results of Flaschke.

Goodman, Roe; Wallach, Nolan R.

1982-09-01

238

Action principle for cellular automata and the linearity of quantum mechanics

We introduce an action principle for a class of integer valued cellular automata and obtain Hamiltonian equations of motion. Employing sampling theory, these discrete deterministic equations are invertibly mapped on continuum equations for a set of bandwidth limited harmonic oscillators, which encode the Schr\\"odinger equation. Thus, the linearity of quantum mechanics is related to the action principle of such cellular automata and its conservation laws to discrete ones.

Hans-Thomas Elze

2013-12-05

239

Action principle for cellular automata and the linearity of quantum mechanics

NASA Astrophysics Data System (ADS)

We introduce an action principle for a class of integer-valued cellular automata and obtain Hamiltonian equations of motion. Employing sampling theory, these discrete deterministic equations are invertibly mapped on continuum equations for a set of bandwidth-limited harmonic oscillators, which encode the Schrödinger equation. Thus, the linearity of quantum mechanics is related to the action principle of such cellular automata and its conservation laws to discrete ones.

Elze, Hans-Thomas

2014-01-01

240

Lecture Notes in Quantum Mechanics Doron Cohen

formula Â· Fermi golden rule Â· Markovian master equations Â· Cross section / Born Â· The adiabatic equation Â· Spherical geometry, phase shifts Â· Cross section, optical theorem, resonances Quantum mechanics in practice

Cohen, Doron

241

Fundamental Quantum Mechanics--A Graphic Presentation

ERIC Educational Resources Information Center

Describes a presentation of basic quantum mechanics for nonscience majors that relies on a computer-generated graphic display to circumvent the usual mathematical difficulties. It allows a detailed treatment of free-particle motion in a wave picture. (MLH)

Wise, M. N.; Kelley, T. G.

1977-01-01

242

Student Difficulties with Energy in Quantum Mechanics

NSDL National Science Digital Library

This website contains the results of a study on student difficulties in understanding energy in quantum mechanics. The most common misconceptions are listed. This content was presented to the 1997 meeting of the AAPT.

Redish, Edward F.; Bao, Lei; Jolly, Pratibha

2005-07-26

243

Spectral geometry of power-law potentials in quantum mechanics

NASA Astrophysics Data System (ADS)

It is supposed that a single particle moves in openR3 in an attractive central power-law potential V(q)(r)=sgn(q)rq, q>-2, and obeys nonrelativistic quantum mechanics. This paper is concerned with the question: How do the discrete eigenvalues Enl(q) of the Hamiltonian H=-?+V(q) depend on the power parameter q\\? Pure power-law potentials have the elementary property that, for p

Hall, Richard L.

1989-06-01

244

Quantum mechanical model for J/? suppression in the LHC era

NASA Astrophysics Data System (ADS)

We discuss the interplay of screening, absorption and regeneration effects, on the quantum mechanical evolution of quarkonia states, within a time-dependent harmonic oscillator (THO) model with complex oscillator strength. We compare the results with data for RAA/RAA(CNM) from CERN and RHIC experiments. In the absence of a measurement of cold nuclear matter (CNM) effects at LHC we estimate their role and interpret the recent data from the ALICE experiment. We also discuss the temperature dependence of the real and imaginary parts of the oscillator frequency which stand for screening and absorption/regeneration, respectively. We point out that a structure in the J/? suppression pattern for In-In collisions at SPS is possibly related to the recently found X(3872) state in the charmonium spectrum. Theoretical support for this hypothesis comes from the cluster expansion of the plasma Hamiltonian for heavy quarkonia in a strongly correlated medium.

Peńa, C.; Blaschke, D.

2014-07-01

245

Stochastic Models of Quantum Mechanics - A Perspective

A subjective survey of stochastic models of quantum mechanics is given along with a discussion of some key radiative processes, the clues they offer, and the difficulties they pose for this program. An electromagnetic basis for deriving quantum mechanics is advocated, and various possibilities are considered. It is argued that only non-local or non-causal theories are likely to be a successful basis for such a derivation.

Mark P. Davidson

2006-10-06

246

NASA Astrophysics Data System (ADS)

Within the ideas of pseudo-supersymmetry, we have studied a non-Hermitian Hamiltonian H_{-}=\\omega \\big(\\xi ^{\\dag } \\xi +\\frac{1}{2}\\big)+\\alpha \\xi ^{2}+\\beta \\xi ^{\\dag 2}, where ? ? ? and ? is a first-order differential operator, to obtain the partner potentials V+(x) and V-(x) which are new isotonic and isotonic nonlinear oscillators, respectively, as the Hermitian equivalents of the non-Hermitian partner Hamiltonians H±. We have provided an algebraic way to obtain the spectrum and wavefunctions of a nonlinear isotonic oscillator. The solutions of V-(x) which are Hermitian counterparts of Swanson Hamiltonian are obtained under some parameter restrictions that are found. Also, we have checked whether the intertwining operator satisfies ?1H- = H+?1, where \\eta _{1}=\\rho ^{-1} {A} \\rho and {A} is the first-order differential operator, which factorizes Hermitian equivalents of H±.

Ye?ilta?, Özlem

2011-07-01

247

We use quantum mechanics/molecular mechanics simulations to study the cleavage of the ribonucleic acid (RNA) backbone catalyzed by ribonuclease H. This protein is a prototypical member of a large family of enzymes that use two-metal catalysis to process nucleic acids. By combining Hamiltonian replica exchange with a finite-temperature string method, we calculate the free energy surface underlying the RNA-cleavage reaction and characterize its mechanism. We find that the reaction proceeds in two steps. In a first step, catalyzed primarily by magnesium ion A and its ligands, a water molecule attacks the scissile phosphate. Consistent with thiol-substitution experiments, a water proton is transferred to the downstream phosphate group. The transient phosphorane formed as a result of this nucleophilic attack decays by breaking the bond between the phosphate and the ribose oxygen. In the resulting intermediate, the dissociated but unprotonated leaving group forms an alkoxide coordinated to magnesium ion B. In a second step, the reaction is completed by protonation of the leaving group, with a neutral Asp132 as a likely proton donor. The overall reaction barrier of ?15 kcal mol(-1), encountered in the first step, together with the cost of protonating Asp132, is consistent with the slow measured rate of ?1-100/min. The two-step mechanism is also consistent with the bell-shaped pH dependence of the reaction rate. The nonmonotonic relative motion of the magnesium ions along the reaction pathway agrees with X-ray crystal structures. Proton-transfer reactions and changes in the metal ion coordination emerge as central factors in the RNA-cleavage reaction. PMID:21539371

Rosta, Edina; Nowotny, Marcin; Yang, Wei; Hummer, Gerhard

2011-06-15

248

Simple New Axioms for Quantum Mechanics

The space P of pure states of any physical system, classical or quantum, is identified as a Poisson space with a transition probability. The latter is a function p: PxP -> [0,1]; in addition, a Poisson bracket is defined for functions on P. These two structures are connected through unitarity. Classical and quantum mechanics are each characterized by a simple axiom on the transition probability p. Unitarity then determines the Poisson bracket of quantum mechanics up to a multiplicative constant (identified with Planck's constant). Superselection rules are naturally incorporated.

N. P. Landsman

1996-04-10

249

Testing foundations of quantum mechanics with photons

The foundational ideas of quantum mechanics continue to give rise to counterintuitive theories and physical effects that are in conflict with a classical description of Nature. Experiments with light at the single photon level have historically been at the forefront of tests of fundamental quantum theory and new developments in photonics engineering continue to enable new experiments. Here we review recent photonic experiments to test two foundational themes in quantum mechanics: wave-particle duality, central to recent complementarity and delayed-choice experiments; and Bell nonlocality where recent theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different photonics experiments.

Peter Shadbolt; Jonathan C. F. Matthews; Anthony Laing; Jeremy L. O'Brien

2015-01-15

250

Projection evolution in quantum mechanics

We propose a model of time evolution of quantum objects which unites the unitary evolution and the measurement procedures. The model allows to treat the time on equal footing with other dynamical variables.

A. Gozdz; M. Pietrow; M. Debicki

2005-08-08

251

Time-dependent {P} {T}-symmetric quantum mechanics

NASA Astrophysics Data System (ADS)

The parity-time-reversal ( {P} {T})-symmetric quantum mechanics (QM) (PTQM) has developed into a noteworthy area of research. However, to date, most known studies of PTQM focused on the spectral properties of non-Hermitian Hamiltonian operators. In this work, we propose an axiom in PTQM in order to study general time-dependent problems in PTQM, e.g., those with a time-dependent {P} {T}-symmetric Hamiltonian and with a time-dependent metric. We illuminate our proposal by examining a proper mapping from a time-dependent Schrödinger-like equation of motion for PTQM to the familiar time-dependent Schrödinger equation in conventional QM. The rich structure of the proper mapping hints that time-dependent PTQM can be a fruitful extension of conventional QM. Under our proposed framework, we further study in detail the Berry-phase generation in a class of {P} {T}-symmetric two-level systems. It is found that a closed path in the parameter space of PTQM is often associated with an open path in a properly mapped problem in conventional QM. In one interesting case, we further interpret the Berry phase as the flux of a continuously tunable fictitious magnetic monopole, thus highlighting the difference between PTQM and conventional QM despite the existence of a proper mapping between them.

Gong, Jiangbin; Wang, Qing-hai

2013-12-01

252

Modal Interpretations of Quantum Mechanics and Relativity: A Reconsideration

Two of the main interpretative problems in quantum mechanics are the so-called measurement problem and the question of the compatibility of quantum mechanics with relativity theory. Modal interpretations of quantum mechanics were designed to solve both of these problems. They are no-collapse (typically) indeterministic interpretations of quantum mechanics that supplement the orthodox state description of physical systems by a set

Joseph Berkovitz; Meir Hemmo

2005-01-01

253

N + 1 dimensional quantum mechanical model for a closed universe

A quantum mechanical model for an N + 1 dimensional universe arising from a quantum fluctuation is outlined. (3 + 1) dimensions are a closed infinitely-expanding universe and the remaining N - 3 dimensions are compact. The (3 + 1) non-compact dimensions are modeled by quantizing a canonical Hamiltonian description of a homogeneous isotropic universe. It is assumed gravity and the strong-electro-weak (SEW) forces had equal strength in the initial state. Inflation occurred when the compact N -3 dimensional space collapsed after a quantum transition from the initial state of the univers, during its evolution to the present state where gravity is much weaker than the SEW force. The model suggests the universe has no singularities and the large size of our present universe is determined by the relative strength of gravity and the SEW force today. A small cosmological constant, resulting from the zero point energy of the scalar field corresponding to the compact dimensions, makes the model universe expand forever.

T. R. Mongan

1999-02-10

254

Quantum mechanics as "space-time statistical mechanics"?

In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time configurations. It is argued that this could perhaps be accomplished by giving up the assumption that the objective ``state'' of a system is independent of a future measurement performed on the system. This idea is then applied in an example of quantum state estimation on a qubit system.

Anders Mĺnsson

2005-01-24

255

Weak measurements in quantum mechanics

The article recapitulates the concept of weak measurement in its broader sense encapsulating the trade between asymptotically weak measurement precision and asymptotically large measurement statistics. Essential applications in time-continuous measurement and in postselected measurement are presented both in classical and in quantum contexts. We discuss the anomalous quantum weak value in postselected measurement. We concentrate on the general mathematical and physical aspects of weak measurements and we do not expand on their interpretation. Particular applications, even most familiar ones, are not subject of the article which was written for Elsevier's Encyclopedia of Mathematical Physics.

Lajos Diosi

2005-05-10

256

Notes on Quantum Mechanics and Consciousness

There have lately been a variety of attempts to connect, or even explain, if not in fact, reduce human consciousness to quantum mechanical processes. Such attempts tend to draw a sharp and fundamental distinction between the role of consciousness in classical mechanics, and on the other hand, in quantum mechanics, with an insistence on the assumed exceptional character of the latter. What is strangely missed, however, is the role of human consciousness as such in the very discovery or creation of both of these physical theories. And this a priori role is far more important than all the possible a posteriori interplays between consciousness and the mentioned two theories of physics, interplays which may happen during one or another specific experiment, measurement, and so on. In this regard it is suggested that the specific features human consciousness may exhibit during interactions with quantum mechanical systems may as well have other explanations which do not appear to be less plausible, or less well founded.

Elemer E Rosinger

2005-08-13

257

Quantum Mechanics, Spacetime Locality, and Gravity

NASA Astrophysics Data System (ADS)

Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only one of the many, bringing an apparent arbitrariness in defining probabilities, called the measure problem. In this paper, we discuss how these two problems are related with each other, developing a picture for quantum measurement and cosmological histories in the quantum mechanical universe. In order to describe the cosmological dynamics correctly within the full quantum mechanical context, we need to identify the structure of the Hilbert space for a system with gravity. We argue that in order to keep spacetime locality, the Hilbert space for dynamical spacetime must be defined only in restricted spacetime regions: in and on the (stretched) apparent horizon as viewed from a fixed reference frame. This requirement arises from eliminating all the redundancies and overcountings in a general relativistic, global spacetime description of nature. It is responsible for horizon complementarity as well as the "observer dependence" of horizons/spacetime—these phenomena arise to represent changes of the reference frame in the relevant Hilbert space. This can be viewed as an extension of the Poincaré transformation in the quantum gravitational context. Given an initial condition, the evolution of the multiverse state obeys the laws of quantum mechanics—it evolves deterministically and unitarily. The beginning of the multiverse, however, is still an open issue.

Nomura, Yasunori

2013-08-01

258

Local Currents for a Deformed Algebra of Quantum Mechanics with a Fundamental Length Scale

We explore some explicit representations of a certain stable deformed algebra of quantum mechanics, considered by R. Vilela Mendes, having a fundamental length scale. The relation of the irreducible representations of the deformed algebra to those of the (limiting) Heisenberg algebra is discussed, and we construct the generalized harmonic oscillator Hamiltonian in this framework. To obtain local currents for this algebra, we extend the usual nonrelativistic local current algebra of vector fields and the corresponding group of diffeomorphisms, modeling the quantum configuration space as a commutative spatial manifold with one additional dimension.

Gerald A. Goldin; Sarben Sarkar

2006-01-31

259

BOOK REVIEWS: Quantum Mechanics: Fundamentals

This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried's well-known book published by Benjamin in 1966. This was written as a text

Kurt Gottfri; Tung-Mow Yan

2004-01-01

260

Quantum Mechanics and Algorithmic Randomness

A long sequence of tosses of a classical coin produces an apparently random bit string, but classical randomness is an illusion: the algorithmic information content of a classically-generated bit string lies almost entirely in the description of initial conditions. This letter presents a simple argument that, by contrast, a sequence of bits produced by tossing a quantum coin is, almost

Ulvi Yurtsever

1998-01-01

261

Zeno Dynamics in Quantum Statistical Mechanics

We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time behaviour of the dynamics. Examples of quantum spin systems show that this condition can be effectively applied to quantum statistical mechanical models. Further, we derive an explicit form of the Zeno generator, and use it to construct Gibbs equilibrium states for the Zeno dynamics. As a concrete example, we consider the X-Y model, for which we show that a frequent measurement at a microscopic level, e.g. a single lattice site, can produce a macroscopic effect in changing the global equilibrium.

Andreas U. Schmidt

2002-07-11

262

Statistical mechanics of disordered quantum optimization

NASA Astrophysics Data System (ADS)

The classical statistical mechanical approach to complexity theory proceeds from the study of ensembles of computationally intractable optimization problems as a species of unusual disordered magnetic systems. Over the last thirty years, researchers have used this approach to supplement worst-case hardness results encoded by complexity theory with detailed information about thermodynamic and dynamic phase transitions in the structure of typical cases. This exchange of ideas between classical statistical mechanics and computer science enabled the development of important heuristic algorithms such as simulated annealing and survey propagation and further refined our understanding of glassiness and critical slowing in physical disordered systems. In this thesis, we map out an analogous program in the quantum context. The question is simple: what can quantum statistical mechanics reveal about the difficulty of solving hard quantum optimization problems? Or more directly, what makes those problems hard even for quantum computers? In this pursuit, we introduce the study of ensembles of optimization problems whose complexity status is intrinsically quantum mechanical (Part I) and develop techniques to study quantum spin glasses and the transverse field adiabatic algorithm applied to classically hard random optimization problems (Part II). In particular, we introduce the study of random quantum satisfiability (QSAT) and identify the coarse aspects of its phase diagram, including a new form of entanglement transition. We generalize the cavity method to the study of quantum models and use it to study the transverse field Ising glass and frustrated AKLT models on the Bethe lattice. We further apply the cavity method to extract Griffiths-McCoy singularities in a diluted (classical) ferromagnet and finally observe that there are no Goldstone bosons on the Bethe lattice.

Laumann, Christopher Richard

263

Testing the limits of quantum mechanical superpositions

Quantum physics has intrigued scientists and philosophers alike, because it challenges our notions of reality and locality--concepts that we have grown to rely on in our macroscopic world. It is an intriguing open question whether the linearity of quantum mechanics extends into the macroscopic domain. Scientific progress over the last decades inspires hope that this debate may be decided by table-top experiments.

Markus Arndt; Klaus Hornberger

2014-10-01

264

. ?The accurate modeling of biological processes presents major computational difficulties owing to the inherent complexity\\u000a of the macromolecular systems of interest. Simulations of biochemical reactivity tend to require highly computationally intensive\\u000a quantum mechanical methods, but localized chemical effects tend to depend significantly on properties of the extended biological\\u000a environment – a regime far more readily examined with lower-level classical empirical

M. M. Hurley; J. B. Wright; G. H. Lushington; W. E. White

2003-01-01

265

On Time. 6b: Quantum Mechanical Time

The existence of small amounts of advanced radiation, or a tilt in the arrow of time, makes the basic equations of physics mixed-type functional differential equations. The novel features of such equations point to a microphysical structure of time. This corresponds to a change of logic at the microphysical level. We show that the resulting logic is a quantum logic. This provides a natural and rigorous explanation of quantum interference. This structured-time interpretation of quantum mechanics is briefly compared with various other interpretations of q.m.

C. K. Raju

2008-08-09

266

Optimal guidance law in quantum mechanics

Following de Broglie’s idea of a pilot wave, this paper treats quantum mechanics as a problem of stochastic optimal guidance law design. The guidance scenario considered in the quantum world is that an electron is the flight vehicle to be guided and its accompanying pilot wave is the guidance law to be designed so as to guide the electron to a random target driven by the Wiener process, while minimizing a cost-to-go function. After solving the stochastic optimal guidance problem by differential dynamic programming, we point out that the optimal pilot wave guiding the particle’s motion is just the wavefunction ?(t,x), a solution to the Schrödinger equation; meanwhile, the closed-loop guidance system forms a complex state–space dynamics for ?(t,x), from which quantum operators emerge naturally. Quantum trajectories under the action of the optimal guidance law are solved and their statistical distribution is shown to coincide with the prediction of the probability density function ?{sup ?}?. -- Highlights: •Treating quantum mechanics as a pursuit-evasion game. •Reveal an interesting analogy between guided flight motion and guided quantum motion. •Solve optimal quantum guidance problem by dynamic programming. •Gives a formal proof of de Broglie–Bohm’s idea of a pilot wave. •The optimal pilot wave is shown to be a wavefunction solved from Schrödinger equation.

Yang, Ciann-Dong, E-mail: cdyang@mail.ncku.edu.tw; Cheng, Lieh-Lieh, E-mail: leo8101@hotmail.com

2013-11-15

267

Multichannel framework for singular quantum mechanics

A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant (“asymptotic”) observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances. -- Highlights: •A multichannel framework is proposed for singular quantum mechanics and analogues. •The framework unifies several established approaches for singular potentials. •Singular points are treated as new scattering channels. •Nonunitary asymptotic behavior is subsumed in a unitary multichannel S-matrix. •Conformal quantum mechanics and the inverse quartic potential are highlighted.

Camblong, Horacio E., E-mail: camblong@usfca.edu [Department of Physics and Astronomy, University of San Francisco, San Francisco, CA 94117-1080 (United States); Epele, Luis N., E-mail: epele@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Fanchiotti, Huner, E-mail: huner@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina)] [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); García Canal, Carlos A., E-mail: garcia@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Ordóńez, Carlos R., E-mail: ordonez@uh.edu [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States)

2014-01-15

268

Two basic Uncertainty Relations in Quantum Mechanics

In the present article, we discuss two types of uncertainty relations in Quantum Mechanics-multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schroedinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics-Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.

Angelow, Andrey [Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko chaussee, 1784 Sofia (Bulgaria)

2011-04-07

269

First-Person Plural Quantum Mechanics

Doing justice to quantum mechanics calls for a deeper examination of the relations between our experience, its objects, and its subjects than either third-person interpretations or the first-person singular interpretation of the QBist permit. The metaphysical space opened by Bohr's employment of the "Kantian wedge" between the objective world, about which we can communicate, and the world "in itself" allows quantum mechanics to unfold its metaphysical potential. This in turn makes it possible to go a long way towards bridging the epistemological gap between the empirical and transcendental conceptions of reality.

Ulrich Mohrhoff

2014-10-22

270

Equivariant Localization for Supersymmetric Quantum Mechanics

We apply equivariant localization to supersymmetric quantum mechanics and show that the partition function localizes on the instantons of the theory. Our construction of equivariant cohomology for SUSY quantum mechanics is different than the ones that already exist in the literature. A hidden bosonic symmetry is made explicit and the supersymmetry is extended. New bosonic symmetry is the square of the new fermionic symmetry. The D term is now the parameter of the bosonic symmetry. This construction provides us with an equivariant complex together with a Cartan differential and makes the use of localization principle possible.

Levent Akant

2005-05-26

271

Several algorithms have been proposed to calculate the spatial entanglement spectrum from high order Renyi entropies. In this work we present an alternative approach for computing the entanglement spectrum with quantum Monte Carlo for both continuum and lattice Hamiltonians. This method provides direct access to the matrix elements of the spatially reduced density matrix and we determine an estimator that can be used in variational Monte Carlo as well as other Monte Carlo methods. The algorithm is based on using a generalization of the Swap operator, which can be extended to calculate a general class of density matrices that can include combinations of spin, space, particle and even momentum coordinates. We demonstrate the method by applying it to the Hydrogen and Nitrogen molecules and describe for the first time how the spatial entanglement spectrum encodes a covalent bond that includes all the many body correlations.

Norm M. Tubman; D. ChangMo Yang

2014-02-03

272

Statistical approach to quantum mechanics II: Nonrelativistic spin

In this second paper in a series, we show that the the general statistical approach to nonrelativistic quantum mechanics developed in the first paper yields a representation of quantum spin and magnetic moments based on classical nonrelativistic spinning top models, using Euler angle coordinates. The models allow half-odd-integer spin and predict supraluminal speeds only for electrons and other leptons, which must be treated relativistically. The spin operators in the space-fixed frame satisfy the usual commutation rules, while those in the rotating body-fixed frame satisfy "left-handed" rules. The commutation rules are independent of the structure of the top, so all nonrelativistic rigidly rotating objects must have integer or odd-half-integer spin. Physical boundary conditions restrict all mixed spin states to involve only half-odd-integer or only integer spin eigenstates. For spin 1/2, the theory automatically yields a modified Pauli-Schr\\"odinger equation. The Hamiltonian operator in this equation contains a rigid rotator term and a term involving the square of the magmetic field, as well as an interaction term having the usual form in spherically symmetric and some cylindrically symmetric models, valid for any magnetogyric ratio.

G. H. Goedecke

2014-08-07

273

We present a case demonstrating the connection between supersymmetric quantum mechanics (SUSYQM), reflectionless scattering, and soliton solutions of integrable partial differential equations. We show that the members of a class of reflectionless Hamiltonians, namely, Akulin's Hamiltonians, are connected via supersymmetric chains to a potential-free Hamiltonian, explaining their reflectionless nature. While the reflectionless property in question has been mentioned in the literature for over two decades, the enabling algebraic mechanism was previously unknown. Our results indicate that the multisoliton solutions of the sine-Gordon and nonlinear Schroedinger equations can be systematically generated via the supersymmetric chains connecting Akulin's Hamiltonians. Our findings also explain a well-known but little-understood effect in laser physics: when a two-level atom, initially in the ground state, is subjected to a laser pulse of the form V(t)=(n({h_bar}/2{pi})/{tau})/cosh(t/{tau}), with n being an integer and {tau} being the pulse duration, it remains in the ground state after the pulse has been applied, for any choice of the laser detuning.

Koller, Andrew; Olshanii, Maxim [Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125 (United States)

2011-12-15

274

A new introductory quantum mechanics curriculum

NASA Astrophysics Data System (ADS)

The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum-mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of the interpretive aspects of quantum mechanics and quantum information theory. This paper gives an overview of the resources available from the IOP website. The core text includes around 80 articles which are co-authored by leading experts, arranged in themes, and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is included in the resource. Solutions to activities are available to instructors. The resources can be used in a variety of ways, from being supplemental to existing courses to forming a complete programme.

Kohnle, Antje; Bozhinova, Inna; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth

2014-01-01

275

From Cbits to Qbits: Teaching computer scientists quantum mechanics

NSDL National Science Digital Library

In this article, a strategy is suggested for teaching mathematically literate students, with no background in physics, just enough quantum mechanics for them to understand and develop algorithms in quantum computation and quantum information theory.

Mermin, N. D.

2004-04-29

276

Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics

NASA Astrophysics Data System (ADS)

A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level...

Grössing, Gerhard

2015-10-01

277

Quantum statistical mechanics, L-series, Anabelian Geometry

Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Adem Lectures, Mexico City, January 2011 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12 Mechanics, L-series and Anabelian Geometry, arXiv:1009.0736 Matilde Marcolli Quantum statistical mechanics

Marcolli, Matilde

278

Open Source Physics: Quantum Mechanical Measurement

NSDL National Science Digital Library

This set of quantum mechanics java applets, part of the Open Source Physics project, provides simulations that demonstrate the effect of measurement on the time-dependence of quantum states. Exercises are available that demonstrate the results of measurement of energy, position, and momentum on states in potential wells (square well, harmonic oscillator, asymmetric well, etc). Eigenstates, superpositions of eigenstates, and wave packets can all be studied. Tutorials are also available. The material stresses the measurement of a quantum-mechanical wave function. The simulations can be delivered either through the OSP Launcher interface or embedded in html pages. The source code is available, and users are invited to contribute to the collection's development by submitting improvements. The simulations are available through the "View attached documents" link below.

Belloni, Mario; Christian, Wolfgang

2008-06-02

279

Quantum mechanics and the time travel paradox

The closed causal chains arising from backward time travel do not lead to paradoxes if they are self consistent. This raises the question as to how physics ensures that only self-consistent loops are possible. We show that, for one particular case at least, the condition of self consistency is ensured by the interference of quantum mechanical amplitudes associated with the loop. If this can be applied to all loops then we have a mechanism by which inconsistent loops eliminate themselves.

David T. Pegg

2005-06-17

280

Student Difficulties with Quantum Mechanics Formalism

NSDL National Science Digital Library

We discuss student difficulties in distinguishing between the physical space and Hilbert space and difficulties related to the Time-independent Schroedinger equation and measurements in quantum mechanics. These difficulties were identified by administering written surveys and by conducting individual interviews with students.

Singh, Chandralekha

2007-06-26

281

Quantum Mechanics Studies of Cellobiose Conformations

Technology Transfer Automated Retrieval System (TEKTRAN)

Three regions of the Phi,Psi space of cellobiose were analyzed with quantum mechanics. A central region, in which most crystal structures are found, was covered by a 9 x 9 grid of 20° increments of Phi and Psi. Besides these 81 constrained minimizations, we studied two central sub-regions and two re...

282

Is Quantum Mechanics needed to explain consciousness ?

In this short comment to a recent contribution by E. Manousakis [1] it is argued that the reported agreement between the measured time evolution of conscious states during binocular rivalry and predictions derived from quantum mechanical formalisms does not require any direct effect of QM. The recursive consumption analysis process in the Ouroboros Model can yield the same behavior.

Knud Thomsen

2007-11-13

283

Vlasov hydrodynamics of a quantum mechanical model

We derive the Vlasov hydrodynamics from the microscopic equations of a quantum mechanical model, which simulates that of an assembly of gravitating particles. In addition we show that the local microscopic dynamics of the model corresponds, on a suitable time-scale, to that of an ideal Fermi gas.

Heide Narnhofer; Geoffrey L. Sewell

1981-01-01

284

Quantum mechanical model for Maya Blue

This work is about Maya Blue (MB), a pigment developed by Mesoamerican civilizations between the 5th and 16th centuries from an aluminosilicate mineral (palygorskite) and an organic dye (indigo). Two different supramolecular quantum-mechanical models afford explanations for the unusual stability of MB based on the oxidation of the indigo molecule during the heating process and its interaction with palygorskite. A

María E. Fuentes; Brisa Peńa; César Contreras; Ana L. Montero; Russell Chianelli; Manuel Alvarado; Ramón Olivas; Luz M. Rodríguez; Héctor Camacho; Luis A. Montero-Cabrera

2008-01-01

285

A Quantum Mechanical Model of Spherical Supermembranes

We present a quantum mechanical model of spherical supermembranes. Using superfields to represent the Cartesian coordinates of the membrane, we are able to exactly determine its supersymmetric vacua. We find there are two classical vacua, one corresponding to an extended membrane and one corresponding to a point-like membrane. Instanton effects then lift these vacua to massive states. Similarities to spherical

John Conley; Ben Geller; Mark G. Jackson; Laura Pomerance; Sharad Shrivastava

2003-01-01

286

Comparison of Classical and Quantum Mechanical Uncertainties.

ERIC Educational Resources Information Center

Comparisons are made for the particle-in-a-box, the harmonic oscillator, and the one-electron atom. A classical uncertainty principle is derived and compared with its quantum-mechanical counterpart. The results are discussed in terms of the statistical interpretation of the uncertainty principle. (Author/BB)

Peslak, John, Jr.

1979-01-01

287

Neutron Interferometry: Lessons in Experimental Quantum Mechanics

The first successful operation of a perfect crystal neutron interferometer by Rauch, Treimer and Bonse (1974) in Vienna opened up new vistas; intricate quantum mechanical concepts that could only be dealt with in thought experiments during the Einstein-Bohr era, now became accessible to direct tests in the laboratory. In the following decade, Helmut Rauch and co-workers implemented interferometric verifications of

2001-01-01

288

Octonionic Quantum Mechanics and Complex Geometry

The use of complex geometry allows us to obtain a consistent formulation of octonionic quantum mechanics (OQM). In our octonionic formulation we solve the hermiticity problem and define an appropriate momentum operator within OQM. The nonextendability of the completeness relation and the norm conservation is also discussed in details.

Stefano De Leo; Khaled Abdel-Khalek

1996-09-03

289

The Transactional Interpretation of Quantum Mechanics

NSDL National Science Digital Library

This article introduces the interpretation of the formalism of quantum mechanics, the Transactional Interpretation (TI) which addresses some issues raised by recent tests of Bell's inequalities. TI is non-local, relativistically invariant, and fully causal. A detailed comparison is made with the Copenhagen interpretation. Also, there is a link providing articles that have cited this one.

Cramer, John

2013-11-08

290

We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation ...

Rezakhani, A. T.

291

Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D parabolic potential barrier

We show that quantum Bateman's system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy plane. It is shown that this representation is more suitable than the hyperbolic one used recently by Blasone and Jizba.

Chruscinski, Dariusz [Institute of Physics, Nicolaus Copernicus University, ul. Grudziadzka 5/7, 87-100 Torun (Poland)]. E-mail: darch@phys.uni.torun.pl

2006-04-15

292

Consistent interpretations of quantum mechanics

Within the last decade, significant progress has been made towards a consistent and complete reformulation of the Copenhagen interpretation (an interpretation consisting in a formulation of the experimental aspects of physics in terms of the basic formalism; it is consistent if free from internal contradiction and complete if it provides precise predictions for all experiments). The main steps involved decoherence (the transition from linear superpositions of macroscopic states to a mixing), Griffiths histories describing the evolution of quantum properties, a convenient logical structure for dealing with histories, and also some progress in semiclassical physics, which was made possible by new methods. The main outcome is a theory of phenomena, viz., the classically meaningful properties of a macroscopic system. It shows in particular how and when determinism is valid. This theory can be used to give a deductive form to measurement theory, which now covers some cases that were initially devised as counterexamples against the Copenhagen interpretation. These theories are described, together with their applications to some key experiments and some of their consequences concerning epistemology.

Omnes, R. (Laboratoire de Physique Theorique et Hautes Energies, Universite de Paris XI, Batiment 211, 91405 Orsay CEDEX (France))

1992-04-01

293

Riemann hypothesis and quantum mechanics

NASA Astrophysics Data System (ADS)

In their 1995 paper, Jean-Benoît Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ?(?), where ? is an inverse temperature. We formulate Riemann hypothesis (RH) as a property of the low-temperature Kubo-Martin-Schwinger (KMS) states of this theory. More precisely, the expectation value of the BC phase operator can be written as \\phi _{\\beta }(q)=N_{q-1}^{\\beta -1} \\psi _{\\beta -1}(N_q), where Nq = ?qk = 1pk is the primorial number of order q and ?b is a generalized Dedekind ? function depending on one real parameter b as \\psi _b (q)=q \\prod _{p \\in {P,}p \\vert q}\\frac{1-1/p^b}{1-1/p}. Fix a large inverse temperature ? > 2. The RH is then shown to be equivalent to the inequality N_q |\\phi _\\beta (N_q)|\\zeta (\\beta -1) \\gt e^\\gamma log log N_q, for q large enough. Under RH, extra formulas for high-temperature KMS states (1.5 < ? < 2) are derived. 'Number theory is not pure Mathematics. It is the Physics of the world of Numbers.' Alf van der Poorten

Planat, Michel; Solé, Patrick; Omar, Sami

2011-04-01

294

The Compton effect: Transition to quantum mechanics

NASA Astrophysics Data System (ADS)

The discovery of the Compton effect at the end of 1922 was a decisive event in the transition to the new quantum mechanics of 1925-1926 because it stimulated physicists to examine anew the fundamental problem of the interaction between radiation and matter. I first discuss Albert Einstein's light-quantum hypothesis of 1905 and why physicists greeted it with extreme skepticism, despite Robert A. Millikan's confirmation of Einstein's equation of the photoelectric effect in 1915. I then follow in some detail the experimental and theoretical research program that Arthur Holly Compton pursued between 1916 and 1922 at the University of Minnesota, the Westinghouse Lamp Company, the Cavendish Laboratory, and Washington University that culminated in his discovery of the Compton effect. Surprisingly, Compton was not influenced directly by Einstein's light-quantum hypothesis, in contrast to Peter Debye and H.A. Kramers, who discovered the quantum theory of scattering independently. I close by discussing the most significant response to that discovery, the Bohr-Kramers-Slater theory of 1924, its experimental refutation, and its influence on the emerging new quantum mechanics.

Stuewer, R. H.

2000-11-01

295

Quantum Mechanics, Spacetime Locality, and Gravity

Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only one of the many, bringing an apparent arbitrariness in defining probabilities, called the measure problem. In this paper, we discuss how these two problems are intimately related with each other, developing a complete picture for quantum measurement and cosmological histories in the quantum mechanical universe. On one hand, quantum mechanics eliminates the arbitrariness of defining probabilities in the multiverse, as discussed in arXiv:1104.2324. On the other hand, the multiverse allows for understanding why we observe an ordered world obeying consistent laws of physics, by providing an infinite-dimensional Hilbert space. This results in the irreversibility of quantum measurement, despite the fact that the evolution of the multiverse state is unitary. In order to describe the cosmological dynamics correctly, we need to identify the structure of the Hilbert space for a system with gravity. We argue that in order to keep spacetime locality, the Hilbert space for dynamical spacetime must be defined only in restricted spacetime regions: in and on the (stretched) apparent horizon as viewed from a fixed reference frame. This requirement arises from eliminating all the redundancies and overcountings in a general relativistic, global spacetime description of nature. It is responsible for horizon complementarity as well as the "observer dependence" of horizons/spacetime---these phenomena arise to represent changes of the reference frame in the relevant Hilbert space. This can be viewed as an extension of the Poincare transformation in the quantum gravitational context, as the Lorentz transformation is viewed as an extension of the Galilean transformation.

Yasunori Nomura

2012-05-08

296

Spectral and Quantum Dynamical Properties of the Weakly Coupled Fibonacci Hamiltonian

NASA Astrophysics Data System (ADS)

We consider the spectrum of the Fibonacci Hamiltonian for small values of the coupling constant. It is known that this set is a Cantor set of zero Lebesgue measure. Here we study the limit, as the value of the coupling constant approaches zero, of its thickness and its Hausdorff dimension. We prove that the thickness tends to infinity and, consequently, the Hausdorff dimension of the spectrum tends to one. We also show that at small coupling, all gaps allowed by the gap labeling theorem are open and the length of every gap tends to zero linearly. Moreover, for a sufficiently small coupling, the sum of the spectrum with itself is an interval. This last result provides a rigorous explanation of a phenomenon for the Fibonacci square lattice discovered numerically by Even-Dar Mandel and Lifshitz. Finally, we provide explicit upper and lower bounds for the solutions to the difference equation and use them to study the spectral measures and the transport exponents.

Damanik, David; Gorodetski, Anton

2011-07-01

297

Towards bringing Quantum Mechanics and General Relativity together

Two questions are suggested as having priority when trying to bring together Quantum Mechanics and General Relativity. Both questions have a scope which goes well beyond Physics, and in particular Quantum Mechanics and General Relativity.

Elemer E Rosinger

2005-12-16

298

A Signal Processing Model of Quantum Mechanics

This paper develops a deterministic model of quantum mechanics as an accumulation-and-threshold process. The model arises from an analogy with signal processing in wireless communications. Complex wavefunctions are interpreted as expressing the amplitude and phase information of a modulated carrier wave. Particle transmission events are modeled as the outcome of a process of signal accumulation that occurs in an extra (non-spacetime) dimension. Besides giving a natural interpretation of the wavefunction and the Born rule, the model accommodates the collapse of the wave packet and other quantum paradoxes such as EPR and the Ahanorov-Bohm effect. The model also gives a new perspective on the 'relational' nature of quantum mechanics: that is, whether the wave function of a physical system is "real" or simply reflects the observer's partial knowledge of the system. We simulate the model for a 2-slit experiment, and indicate possible deviations of the model's predictions from conventional quantum mechanics. We also indicate how the theory may be extended to a field theory.

Chris Thron; Johnny Watts

2012-05-08

299

The emergent Copenhagen interpretation of quantum mechanics

NASA Astrophysics Data System (ADS)

We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. This interpretation describes a world in which definite measurement results are obtained with probabilities that reproduce the Born rule. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint probabilities for the ergodic subsets of states of disjoint macro-systems only arise as emergent quantities. Finally we give an account of the EPR-Bohm thought experiment and show that the interpretation implies the violation of the Bell inequality characteristic of quantum mechanics but in a way that is rather novel. The final conclusion is that the Copenhagen interpretation gives a completely satisfactory phenomenology of macro-systems interacting with micro-systems.

Hollowood, Timothy J.

2014-05-01

300

PERSPECTIVE Quantum Mechanics of Black Holes

The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.

Edward Witten

301

Quantum mechanical coherence, resonance, and mind

Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in natural process, the classical character of our perceptions of the quantum universe can be seen to be a consequence of evolutionary pressures for the survival of the species.

Stapp, H.P.

1995-03-26

302

The Schrodinger Equation From a Quadratic Hamiltonian System

We regard the real and imaginary parts of the Schrodinger wave function as canonical conjugate variables.With this pair of conjugate variables and some other 2n pairs, we construct a quadratic Hamiltonian density. We then show that the Schrodinger Equation follows from the Hamilton's Equation of motion when the Planck frequency is much larger than the characteristic frequencies of the Hamiltonian system. The Hamiltonian and the normal mode solutions coincide, respectively, with the energy expectation value and the energy eigenstates of the corresponding quantum mechanical system.

Wai Bong Yeung

1999-11-02

303

Quantum Mechanics with a Momentum-Space Artificial Magnetic Field

The Berry curvature is a geometrical property of an energy band which acts as a momentum space magnetic field in the effective Hamiltonian describing single-particle quantum dynamics. We show how this perspective may be exploited to study systems directly relevant to ultracold gases and photonics. Given the exchanged roles of momentum and position, we demonstrate that the global topology of momentum space is crucially important. We propose an experiment to study the Harper-Hofstadter Hamiltonian with a harmonic trap that will illustrate the advantages of this approach and that will also constitute the first realization of magnetism on a torus.

Hannah M. Price; Tomoki Ozawa; Iacopo Carusotto

2014-11-19

304

NASA Astrophysics Data System (ADS)

Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.

Khots, Boris; Khots, Dmitriy

2014-12-01

305

Exact Parent Hamiltonian for the Quantum Hall States in a Lattice

We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.

Kapit, Eliot; Mueller, Erich [Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York (United States)

2010-11-19

306

Operational Axioms for Quantum Mechanics Giacomo Mauro D'Ariano

Operational Axioms for Quantum Mechanics Giacomo Mauro D'Ariano QUIT Group, Dipartimento di Fisica is derived. Undeniably the axioms of Quantum Mechanics are of a highly abstract and mathematical nature of Quantum Mechanics, its "physical" axioms-- if they exist--must be of very general nature: they must even

D'Ariano, Giacomo Mauro

307

Quantum statistical mechanics, L-series, Anabelian Geometry

Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Beijing, August 2013 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12;joint work with Gunther Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12;Number fields: finite

Marcolli, Matilde

308

Quantum statistical mechanics, L-series, Anabelian Geometry

Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Colloquium, Harvard University, March 24, 2011 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12 as partition functions of physical systems Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian

Marcolli, Matilde

309

The Objective Inde...niteness Interpretation of Quantum Mechanics

The Objective Inde...niteness Interpretation of Quantum Mechanics David Ellerman University of California at Riverside Draft (not for quotation) May 28, 2013 Abstract Quantum mechanics (QM models indef- inite elements that become more de...nite as distinctions are made. If quantum mechanics

WĂĽthrich, Christian

310

PHYS 530A: QUANTUM MECHANICS II SYLLABUS (2014 Spring)

PHYS 530A: QUANTUM MECHANICS II SYLLABUS (2014 Spring) Department of Physics, Southern Illinois be familiar with the contents of an undergraduate level course on Quantum mechanics, an equivalent of PHYS-430 Quantum Mechanics-I. Familiarity with the following topics will be assumed: complex variables, partial

Nickrent, Daniel L.

311

Representation of natural numbers in quantum mechanics

This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural numbers or a model of arithmetic if the set and operations satisfy the axioms of number theory or arithmetic. This paper is limited to k-ary representations of length L and to the axioms for arithmetic modulo k{sup L}. A model of the axioms is described based on an abstract L-fold tensor product Hilbert space H{sup arith}. Unitary maps of this space onto a physical parameter based product space H{sup phy} are then described. Each of these maps makes states in H{sup phy}, and the induced operators, a model of the axioms. Consequences of the existence of many of these maps are discussed along with the dependence of Grover's and Shor's algorithms on these maps. The importance of the main physical requirement, that the basic arithmetic operations are efficiently implementable, is discussed. This condition states that there exist physically realizable Hamiltonians that can implement the basic arithmetic operations and that the space-time and thermodynamic resources required are polynomial in L.

Benioff, Paul

2001-03-01

312

A Chaotic, Deterministic Model for Quantum Mechanics

With the decline of the Copenhagen interpretation of quantum mechanics and the recent experiments indicating that quantum mechanics does actually embody 'objective reality', one might ask if a 'mechanical', conceptual model for quantum mechanics could be found. We propose such a model. Vacuum energy fluctuations imply mass fluctuations and, through general relativity, curvature fluctuations. And those fluctuations are indicated by fluctuations of the metric tensor. The metric tensor fluctuations can 'explain' the uncertainty relations and non-commuting properties of conjugate variables. We argue that that the probability density is proportional to the square root of minus the determinant of the metric tensor (the differential volume element). We argue that the metric elements are not stochastic but are oscillating at a high enough frequency that measured values of same appear stochastic (i.e. crypto-stochastic). We suggest that the oscillations at the position of particles are described as torsional vibrations. A crypto-stochastic (or chaotic) oscillating metric yields, among other things, a model of super-position, photon polarization, and entanglement, and all within the confines of a 4-dimensional space-time.

Carl Frederick

2014-06-20

313

Information geometry, dynamics and discrete quantum mechanics

NASA Astrophysics Data System (ADS)

We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the picture. We do this in three steps. Our starting point is information geometry, the natural geometry of the space of probability distributions. Dynamics requires additional structure. To evolve the Pk, we introduce coordinates Sk canonically conjugate to the Pk and a symplectic structure. We then seek to extend the metric structure of information geometry, to define a geometry over the full space of the Pk and Sk. Consistency between the metric tensor and the symplectic form forces us to introduce a Kähler geometry. The construction has notable features. A complex structure is obtained in a natural way. The canonical coordinates of the ?k = ?Pk eiSk Kähler space are precisely the wave functions of quantum mechanics. The full group of unitary transformations is obtained. Finally, one may associate a Hilbert space with the Kähler space, which leads to the standard version of quantum theory. We also show that the metric that we derive here using purely geometrical arguments is precisely the one that leads to Wootters' expression for the statistical distance for quantum systems.

Reginatto, Marcel; Hall, Michael J. W.

2013-08-01

314

Beyond relativity and quantum mechanics: space physics

NASA Astrophysics Data System (ADS)

Albert Einstein imposed an observer-based epistemology upon physics. Relativity and Quantum Mechanics limit physics to describing and modeling the observer's sensations and measurements. Their "underlying reality" consists only of ideas that serve to model the observer's experience. These positivistic models cannot be used to form physical theories of Cosmic phenomena. To do this, we must again remove the observer from the center of physics. When we relate motion to Cosmic space instead of to observers and we attempt to explain the causes of Cosmic phenomena, we are forced to admit that Cosmic space is a substance. We need a new physics of space. We can begin by replacing Relativity with a modified Lorentzian-Newtonian model of spatial flow, and Quantum Mechanics with a wave-based theory of light and electrons. Space physics will require the reinterpretation of all known phenomena, concepts, and mathematical models.

Lindner, Henry H.

2011-09-01

315

Emerging interpretations of quantum mechanics and recent progress in quantum measurement

NASA Astrophysics Data System (ADS)

The focus of this paper is to provide a brief discussion on the quantum measurement process, by reviewing select examples highlighting recent progress towards its understanding. The areas explored include an outline of the measurement problem, the standard interpretation of quantum mechanics, quantum to classical transition, types of measurement (including weak and projective measurements) and newly emerging interpretations of quantum mechanics (decoherence theory, objective reality, quantum Darwinism and quantum Bayesianism).

Clarke, M. L.

2014-01-01

316

1/N expansion in noncommutative quantum mechanics

We study the 1/N expansion in noncommutative quantum mechanics for the anharmonic and Coulombian potentials. The expansion for the anharmonic oscillator presented good convergence properties, but for the Coulombian potential, we found a divergent large N expansion when using the usual noncommutative generalization of the potential. We proposed a modified version of the noncommutative Coulombian potential which provides a well-behaved 1/N expansion.

Ferrari, A. F. [Universidade Federal do ABC, Centro de Ciencias Naturais e Humanas, Rua Santa Adelia, 166, 09210-170, Santo Andre, SP (Brazil); Gomes, M.; Stechhahn, C. A. [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo - SP (Brazil)

2010-08-15

317

A tossed coin as quantum mechanical object

Comprehensive and physically consistent model of a tossed coin is presented in terms of geometric algebra. The model clearly shows that there is nothing elementary particle specific in the half-spin quantum mechanical formalism. It also demonstrates what really is behind this formalism, feasibly reveals the probabilistic meaning of wave function and shows that arithmetic of packed objects, namely wave functions and Pauli matrices, reduces the amount of available information.

Alexander M. Soiguine

2014-08-28

318

Non-Lipschitz approach to quantum mechanics

An attempt to reconcile quantum mechanics with Newton's laws represented by the non-Lipschitz formalism has been made. As a proof-of-concept, a line of equally spaced atoms was studied. It appeared that enforcement of atom incompressibility required relaxation of the Lipschitz condition at the points of contact. This, in turn, led to fractional powers and discreteness of values of the basic

Michail Zak

1998-01-01

319

Nine Formulations of Quantum Mechanics: Lecture

NSDL National Science Digital Library

In this lecture, Dr. Daniel Styer, a physics professor at Oberlin College, guides the listener through nine formulations of quantum mechanics. Styer discusses each formulation's unique abilities and challenges, then offers his perspective on the application to undergraduate education. This lecture was delivered at the Kavli Institute for Physics, as a part of the Theorists at Undergraduate Institutions mini-program. Audio, video and slides are included.

Styer, Dan

2005-08-07

320

Quantum mechanics in q-deformed calculus

Starting on the basis of q-deformed calculus and q-symmetric oscillator algebra, we introduce a generalized Schrödinger equation which admits factorized time-space solutions and the free plane wave functions can be expressed in terms of the so-called basic-hypergeometric functions. In this framework, q-deformed adjoint and q-hermitian operator properties occur i a natural way in order to satisfy the fundamental quantum mechanics

A. Lavagno; G. Gervino

2009-01-01

321

Relativistic non-Hermitian quantum mechanics

NASA Astrophysics Data System (ADS)

We develop relativistic wave equations in the framework of the new non-Hermitian PT quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of PT-symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that, in particular, the mass matrix be Hermitian also allows for models that have no counterpart in conventional quantum mechanics. For example it is well known that a quartet of Weyl spinors coupled by a Hermitian mass matrix reduces to two independent Dirac fermions; here, we show that the same quartet of Weyl spinors, when coupled by a non-Hermitian but PT-symmetric mass matrix, describes a single relativistic particle that can have massless dispersion relation even though the mass matrix is nonzero. The PT-generalized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a noninteracting theory it violates P and T individually. The relativistic wave equations are reformulated as canonical fermionic field theories to facilitate the study of interactions and are shown to maintain many of the canonical structures from Hermitian field theory, but with new and interesting possibilities permitted by the non-Hermiticity parameter m2.

Jones-Smith, Katherine; Mathur, Harsh

2014-06-01

322

Hunting for Snarks in Quantum Mechanics

NASA Astrophysics Data System (ADS)

A long-standing debate over the interpretation of quantum mechanics has centered on the meaning of Schroedinger's wave function ? for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school (led by Bohr, Heisenberg and Pauli) holds that ? provides a complete description of a single electron state; hence the probability interpretation of ??* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school (led by Einstein, de Broglie, Bohm and Jaynes) holds that ? represents a statistical ensemble of possible electron states; hence it is an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung (first noticed by Schroedinger) opens a window to particle substructure in quantum mechanics that explains the physical significance of the complex phase factor in ?. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school. I give details. The perils of research on the foundations of quantum mechanics have been foreseen by Lewis Carroll in The Hunting of the Snark!

Hestenes, David

2009-12-01

323

Hunting for Snarks in Quantum Mechanics

A long-standing debate over the interpretation of quantum mechanics has centered on the meaning of Schroedinger's wave function {psi} for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school(led by Bohr, Heisenberg and Pauli) holds that {psi} provides a complete description of a single electron state; hence the probability interpretation of {psi}{psi}* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school(led by Einstein, de Broglie, Bohm and Jaynes) holds that {psi} represents a statistical ensemble of possible electron states; hence it is an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung(first noticed by Schroedinger) opens a window to particle substructure in quantum mechanics that explains the physical significance of the complex phase factor in {psi}. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school. I give details. The perils of research on the foundations of quantum mechanics have been foreseen by Lewis Carroll in The Hunting of the Snark{exclamation_point}.

Hestenes, David [Physics Department, Arizona State University, Tempe, Arizona 85287 (United States)

2009-12-08

324

A quantum-mechanical relaxation model

NASA Astrophysics Data System (ADS)

The atomic origin of micromagnetic damping is investigated by developing and solving a quantum-mechanical relaxation model. A projection-operator technique is used to derive an analytical expression for the relaxation time as a function of the heat-bath and interaction parameters. The present findings are consistent with earlier research beyond the Landau-Lifshitz-Gilbert (LLG) equation and show that the underlying relaxation mechanism is very general. Zermelo's recurrence paradox means that there is no true irreversibility in non-interacting nanoparticles, but the corresponding recurrence times are very long and can be ignored in many cases.

Skomski, R.; Kashyap, A.; Sellmyer, D. J.

2012-04-01

325

A method of combined quantum mechanics\\/molecular mechanics has been developed to model larger organometallic and metallobiochemical systems where neither quantum mechanics nor molecular mechanics, applied separately, can solve the problem. An electronically transparent interface, which allows charge transfers between the quantum and classical fragments, is devised and realized by employing a special iterative procedure of double (intrafragment and interfragment) self-consistent

Max Kangchien Leong

1997-01-01

326

Possible corrections to quantum mechanical predictions in hidden variable model

We derive possible corrections to the statistical predictions of quantum mechanics in measurement over ensemble of identically prepared system based on a hidden variable model of quantization developed in the previous work. The corrections are characterized by a dimensionless parameter $\\sigma$ and the prediction of quantum mechanics is reproduced in the formal limit $\\sigma\\rightarrow 0$. Quantum mechanics is argued to be reliable for sufficiently low quantum number.

Agung Budiyono

2012-01-22

327

Quantum mechanics, by itself, implies perception of a classical world

Several versions of reality can simultaneously exist in the states of quantum mechanics, but we perceive only one classical version. The question is whether the mathematics of quantum mechanics, by itself, implies we perceive only one classical version. Zurek has used a method involving the environment, redundancy, decoherence and quantum Darwinism to show that quantum mechanics does indeed imply this result, but the argument is quite complex. Here we give a simpler method based on linearity.

Casey Blood

2010-09-23

328

Quantum groups, coherent states, squeezing and lattice quantum mechanics

By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg algebra, $q$-WH, into the theory of entire analytic functions. The $q$--WH algebra operators are realized in terms of finite difference operators in the $z$ plane. In order to exhibit the relevance of our study, several applications to different cases of physical interest are discussed: squeezed states and the relation between coherent states and theta functions on one side, lattice quantum mechanics and Bloch functions on the other, are shown to find a deeper mathematical understanding in terms of $q$-WH. The r\\^ole played by the finite difference operators and the relevance of the lattice structure in the completeness of the coherent states system suggest that the quantization of the WH algebra is an essential tool in the physics of discretized (periodic) systems.

E. Celeghini; S. De Martino; S. De Siena; M. Rasetti; G. Vitiello

1996-04-04

329

Quantum Groups, Coherent States, Squeezing and Lattice Quantum Mechanics

By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg ($q$-WH) algebra into the theory of entire analytic functions. The main tool is the realization of the $q$--WH algebra in terms of finite difference operators. The physical relevance of our study relies on the fact that coherent states (CS) are indeed formulated in the space of entire analytic functions where they can be rigorously expressed in terms of theta functions on the von Neumann lattice. The r\\^ole played by the finite difference operators and the relevance of the lattice structure in the completeness of the CS system suggest that the $q$--deformation of the WH algebra is an essential tool in the physics of discretized (periodic) systems. In this latter context we define a quantum mechanics formalism for lattice systems.

Celeghini; S. De Martino; S. De Siena; M. Rasetti; G. Vitiello

1993-10-20

330

Neutrino oscillations: Quantum mechanics vs. quantum field theory

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.

Akhmedov, Evgeny Kh.; Kopp, Joachim; ,

2010-01-01

331

Noncommutative quantum mechanics in a time-dependent background

NASA Astrophysics Data System (ADS)

We investigate a quantum mechanical system on a noncommutative space for which the structure constant is explicitly time dependent. Any autonomous Hamiltonian on such a space acquires a time-dependent form in terms of the conventional canonical variables. We employ the Lewis-Riesenfeld method of invariants to construct explicit analytical solutions for the corresponding time-dependent Schrödinger equation. The eigenfunctions are expressed in terms of the solutions of variants of the nonlinear Ermakov-Pinney equation and discussed in detail for various types of background fields. We utilize the solutions to verify a generalized version of Heisenberg's uncertainty relations for which the lower bound becomes a time-dependent function of the background fields. We study the variance for various states, including standard Glauber coherent states with their squeezed versions and Gaussian Klauder coherent states resembling a quasiclassical behavior. No type of coherent state appears to be optimal in general with regard to achieving minimal uncertainties, as this feature turns out to be background field dependent.

Dey, Sanjib; Fring, Andreas

2014-10-01

332

Bohmian mechanics in relativistic quantum mechanics, quantum field theory and string theory

I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle trajectories, the problem of particle creation and destruction, the Bohmian interpretation of fermionic fields and the intrinsically Bohmian quantization of fields and strings based on the De Donder-Weyl covariant canonical formalism.

H. Nikolic

2006-10-12

333

Unstable trajectories and the quantum mechanical uncertainty

There is still an ongoing discussion about various seemingly contradictory aspects of classical particle motion and its quantum mechanical counterpart. One of the best accepted viewpoints that intend to bridge the gap is the so-called Copenhagen Interpretation. A major issue there is to regard wave functions as probability amplitudes (usually for the position of a particle). However, the literature also reports on approaches that claim a trajectory for any quantum mechanical particle, Bohmian mechanics probably being the most prominent one among these ideas. We introduce a way to calculate trajectories as well, but our crucial ingredient is their well controlled local (thus also momentaneous) degree of instability. By construction, at every moment their unpredictability, i.e., their local separation rates of neighboring trajectories, is governed by the local value of the given modulus square of a wave function. We present extensive numerical simulations of the H and He atom, and for some velocity-related quantities, namely angular momentum and total energy, we inspect their agreement with the values appearing in wave mechanics. Further, we interpret the archetypal double slit interference experiment in the spirit of our findings. We also discuss many-particle problems far beyond He, which guides us to a variety of possible applications.

Moser, Hans R. [Physics Institute, University of Zuerich, Winterthurerstrasse 190, CH-8057 Zuerich (Switzerland)], E-mail: moser@physik.uzh.ch

2008-08-15

334

Quantum mechanics with coordinate dependent noncommutativity

Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.

Kupriyanov, V. G. [CMCC, Universidade Federal do ABC, Santo André, SP (Brazil)] [CMCC, Universidade Federal do ABC, Santo André, SP (Brazil)

2013-11-15

335

Comment on ``Adiabatic quantum computation with a one-dimensional projector Hamiltonian''

NASA Astrophysics Data System (ADS)

The partial adiabatic search algorithm was introduced in Tulsi's paper [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.052328 80, 052328 (2009)] as a modification of the usual adiabatic algorithm for a quantum search with the idea that most of the interesting computation only happens over a very short range of the adiabatic path. By focusing on that restricted range, one can potentially gain an advantage by reducing the control requirements on the system, enabling a uniform rate of evolution. In this Comment, we point out an oversight in Tulsi's paper [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.052328 80, 052328 (2009)] that invalidates its proof. However, the argument can be corrected, and the calculations in Tulsi's paper [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.052328 80, 052328 (2009)] are then sufficient to show that the scheme still works. Nevertheless, subsequent works [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.034304 82, 034304 (2010), Chin. Phys. BCPBHAJ1674-105610.1088/1674-1056/20/4/040309 20, 040309 (2011), Chin. Phys. BCPBHAJ1674-105610.1088/1674-1056/21/1/010306 21, 010306 (2012), AASRI Procedia 1, 5862 (2012), and Quantum Inf. Process.10.1007/s11128-013-0557-1 12, 2689 (2013)] cannot all be recovered in the same way.

Kay, Alastair

2013-10-01

336

MSE 157: Quantum Mechanics of Nanoscale Materials Course Information

there. Textbook The textbook for this course is Introduction to Quantum Mechanics by David Griffiths. We Quantum Mechanics by Walter A. Harrison An Introduction to Quantum Physics by A.P. French and Edwin F was created to describe and explain a world of atoms and electrons far removed from everyday human experience

337

A theoretical study of the molecular mechanism of the thymidylate synthase-catalyzed reaction has been carried out using hybrid quantum mechanics\\/molecular mechanics methods. We have examined all of the stationary points (reactants, intermediates, transition structures, and products) on the multidimensional potential energy surfaces for the multistep enzymatic process. The characterization of these relevant structures facilitates the gaining of insight into the

Natalia Kanaan; Sergio Martí; Vicent Moliner; Amnon Kohen

2007-01-01

338

Quantum-Mechanical Model of Spacetime

We consider a possibility to construct a quantum-mechanical model of spacetime, where Planck size quantum black holes act as the fundamental constituents of space and time. Spacetime is assumed to be a graph, where black holes lie on the vertices. Our model implies that area has a discrete spectrum with equal spacing. At macroscopic length scales our model reproduces Einstein's field equation with a vanishing cosmological constant as a sort of thermodynamical equation of state of spacetime and matter fields. In the low temperature limit, where most black holes are assumed to be in the ground state, our model implies the Unruh and the Hawking effects, whereas in the high temperature limit we find, among other things, that black hole entropy depends logarithmically on the event horizon area, instead of being proportional to the area.

Jarmo Makela

2007-06-20

339

Quantum spin Hall effect in a three-orbital tight-binding Hamiltonian.

We consider the quantum spin hall (QSH) state in a three-orbital model, with a certain spin loop current order which is induced by spin-dependent interactions. This type of order is motivated by the loop current model, which was proposed long ago to describe the pseudogap phase of cuprates. It is shown that this model has nontrivial Chern parity by directly counting the zeros of the Pfaffian of the time reversal operator. By connecting to the second Chern number, we explicitly show the property of singularities of the wave-functions, and also their dependance on the gauge choices. Also it is shown that the Berry phase of the QSH state can be mapped to a non-Abelian instanton. PMID:24979371

He, Yan; Hou, Changtao

2014-07-23

340

Quantum Transport in Crystals: Effective Mass Theorem and K·P Hamiltonians

NASA Astrophysics Data System (ADS)

In this paper the effective mass approximation and the k·p multi-band models, describing quantum evolution of electrons in a crystal lattice, are discussed. Electrons are assumed to move in both a periodic potential and a macroscopic one. The typical period {?} of the periodic potential is assumed to be very small, while the macroscopic potential acts on a much bigger length scale. Such homogenization asymptotic is investigated by using the envelope-function decomposition of the electron wave function. If the external potential is smooth enough, the k·p and effective mass models, well known in solid-state physics, are proved to be close (in the strong sense) to the exact dynamics. Moreover, the position density of the electrons is proved to converge weakly to its effective mass approximation.

Barletti, Luigi; Ben Abdallah, Naoufel

2011-11-01

341

Quantum transport in crystals: effective-mass theorem and k.p Hamiltonians

In this paper the effective mass approximation and k.p multi-band models, describing quantum evolution of electrons in a crystal lattice, are discussed. Electrons are assumed to move in both a periodic potential and a macroscopic one. The typical period of the periodic potential is assumed to be very small, while the macroscopic potential acts on a much bigger length scale. Such homogenization asymptotic is investigated by using the envelope-function decomposition of the electron wave function. If the external potential is smooth enough, the k.p and effective mass models, well known in solid-state physics, are proved to be close (in strong sense) to the exact dynamics. Moreover, the position density of the electrons is proved to converge weakly to its effective mass approximation.

Luigi Barletti; Naoufel Ben Abdallah

2014-11-14

342

5.74 Introductory Quantum Mechanics II, Spring 2005

Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...

Tokmakoff, Andrei

343

Probability Representation of Quantum Mechanics: Comments and Bibliography

The probability representation of states in standard quantum mechanics where the quantum states are associated with fair probability distributions (instead of wave function or density matrix) is shortly commented and bibliography related to the probability representation is given.

V. I. Man'ko; O. V. Pilyavets; V. G. Zborovskii

2006-10-17

344

Lecture Script: Introduction to Computational Quantum Mechanics

This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding analytical as well as numerical solutions and their visualization. Most of these calculations are too complicated to be done by hand. Even relatively simple problems, such as two interacting particles in a one-dimensional trap, do not have analytic solutions and require the use of computers for their solution and visualization. More complex problems scale exponentially with the number of degrees of freedom, and make the use of large computer simulations unavoidable. The course is taught using the Mathematica programming language; however, the concepts presented are readily translated to any other programming language.

Roman Schmied

2014-03-27

345

Euclidean Quantum Mechanics and Universal Nonlinear Filtering

An important problem in applied science is the continuous nonlinear filtering problem, i.e., the estimation of a Langevin state that is observed indirectly. In this paper, it is shown that Euclidean quantum mechanics is closely related to the continuous nonlinear filtering problem. The key is the configuration space Feynman path integral representation of the fundamental solution of a Fokker-Planck type of equation termed the Yau Equation of continuous-continuous filtering. A corollary is the equivalence between nonlinear filtering problem and a time-varying Schr\\"odinger equation.

Bhashyam Balaji

2008-09-25

346

Hidden geometric character of relativistic quantum mechanics

Geometry can be an unsuspected source of equations with physical relevance, as everybody is aware since Einstein formulated the general theory of relativity. However, efforts to extend a similar type of reasoning to other areas of physics, namely, electrodynamics, quantum mechanics, and particle physics, usually had very limited success; particularly in quantum mechanics the standard formalism is such that any possible relation to geometry is impossible to detect; other authors have previously trod the geometric path to quantum mechanics, some of that work being referred to in the text. In this presentation we will follow an alternate route to show that quantum mechanics has indeed a strong geometric character. The paper makes use of geometric algebra, also known as Clifford algebra, in five-dimensional space-time. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from such choice and their consistency with experimental results. Given a metric space of any dimension, one can define monogenic functions, the natural extension of analytic functions to higher dimensions; such functions have null vector derivative and have previously been shown by other authors to play a decisive role in lower dimensional spaces. All monogenic functions have null Laplacian by consequence; in a hyperbolic space this fact leads inevitably to a wave equation with planelike solutions. This is also true for five-dimensional space-time and we will explore those solutions, establishing a parallel with the solutions of the free particle Dirac equation. For this purpose we will invoke the isomorphism between the complex algebra of 4x4 matrices, also known as Dirac's matrices. There is one problem with this isomorphism, because the solutions to Dirac's equation are usually known as spinors (column matrices) that do not belong to the 4x4 matrix algebra and as such are excluded from the isomorphism. We will show that a solution in terms of Dirac spinors is equivalent to a plane wave solution. Just as one finds in the standard formulation, monogenic functions can be naturally split into positive/negative energy together with left/right ones. This split is provided by geometric projectors and we will show that there is a second set of projectors providing an alternate fourfold split. The possible implications of this alternate split are not yet fully understood and are presently the subject of profound research.

Almeida, Jose B. [Physics Department, Universidade do Minho, 4710-057 Braga (Portugal)

2007-01-15

347

A toy model for quantum mechanics

The toy model used by Spekkens [R. Spekkens, Phys. Rev. A 75, 032110 (2007)] to argue in favor of an epistemic view of quantum mechanics is extended by generalizing his definition of pure states (i.e. states of maximal knowledge) and by associating measurements with all pure states. The new toy model does not allow signaling but, in contrast to the Spekkens model, does violate Bell-CHSH inequalities. Negative probabilities are found to arise naturally within the model, and can be used to explain the Bell-CHSH inequality violations.

S. J. van Enk

2007-05-18

348

Topological Solution of Bohmian Quantum Mechanics

NASA Astrophysics Data System (ADS)

The topological solutions of the De Broglie-Bohm quantum mechanics are presented. Starting from the Schrödinger equation for one particle system and ?-mapping topological current theory, the trajectory of the particle is derived explicitly, and can be used as the world line of the particle. The world line is just at the zero point of the wave function and it is shown that the vorticity of the world line can be expressed by Hopf index and Brouwer degree. The evolution of the world line at the bifurcation point is given.

Shi, Xuguang; Yu, Ming; Duan, Yishi

349

A Quantum Mechanical Model of Spherical Supermembranes

We present a quantum mechanical model of spherical supermembranes. Using superfields to represent the cartesian coordinates of the membrane, we are able to exactly determine its supersymmetric vacua. We find there are two classical vacua, one corresponding to an extended membrane and one corresponding to a point-like membrane. For the ${\\mathcal N} = 2$ case, instanton effects then lift these vacua to massive states. For the ${\\mathcal N} = 4$ case, there is no instanton tunneling, and the vacua remain massless. Similarities to spherical supermembranes as giant gravitons and in Matrix theory on pp-waves is discussed.

John Conley; Ben Geller; Mark G. Jackson; Laura Pomerance; Sharad Shrivastava

2003-02-07

350

From PT-symmetric quantum mechanics to conformal field theory

One of the simplest examples of a PT-symmetric quantum system is the scaling Yang-Lee model, a quantum field theory with cubic interaction and purely imaginary coupling. We give a historical review of some facts about this model in d PT-symmetric quantum mechanics. We also discuss some more general results on PT-symmetric quantum mechanics and the ODE/IM correspondence, and mention applications to magnetic systems and cold atom physics.

Patrick Dorey; Clare Dunning; Roberto Tateo

2009-06-05

351

The authors prove that the dynamics of spin 1/2 particles in stationary gravitational fields can be described using an approach, which builds upon the formalism of pseudo-Hermitian Hamiltonians. The proof consists in the analysis of three expressions for Hamiltonians, which are derived from the Dirac equation and describe the dynamics of spin 1/2 particles in the gravitational field of the Kerr solution. The Hamiltonians correspond to different choices of tetrad vectors and differ from each other. The differences between the Hamiltonians confirm the conclusion known from many studies that the Hamiltonians derived from the Dirac equation are nonunique. Application of standard pseudo-Hermitian quantum mechanics rules to each of these Hamiltonians produces the same Hermitian Hamiltonian. The eigenvalue spectrum of the resulting Hamiltonian is the same as that of the Hamiltonians derived from the Dirac equation with any chosen system of tetrad vectors. For description of the dynamics of spin 1/2 particles in stationary gravitational fields can be used not only the formalism of pseudo-Hermitian Hamiltonians but also an alternative approach, which employs the Parker scalar product. The authors show that the alternative approach is equivalent to the formalism of pseudo-Hermitian Hamiltonians.

Gorbatenko, M. V.; Neznamov, V. P. [Russian Federal Nuclear Center - All-Russian Research Institute of Experimental Physics, Sarov, Mira 37, Nizhni Novgorod region, 607188 (Russian Federation)

2010-11-15

352

The metaphysics of quantum mechanics: Modal interpretations

NASA Astrophysics Data System (ADS)

This dissertation begins with the argument that a preferred way of doing metaphysics is through philosophy of physics. An understanding of quantum physics is vital to answering questions such as: What counts as an individual object in physical ontology? Is the universe fundamentally indeterministic? Are indiscernibles identical? This study explores how the various modal interpretations of quantum mechanics answer these sorts of questions; modal accounts are one of the two classes of interpretations along with so-called collapse accounts. This study suggests a new alternative within the class of modal views that yields a more plausible ontology, one in which the Principle of the Identity of Indisceribles is necessarily true. Next, it shows that modal interpretations can consistently deny that the universe must be fundamentally indeterministic so long as they accept certain other metaphysical commitments: either a perfect initial distribution of states in the universe or some form of primitive dispositional properties. Finally, the study sketches out a future research project for modal interpretations based on developing quantified quantum logic.

Gluck, Stuart Murray

2004-11-01

353

Hamiltonian description of the ideal fluid

Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems.

Morrison, P.J.

1994-01-01

354

Smallest Relational Mechanics Model of Quantum Cosmology

Relational particle mechanics are models in which there is, overall, no time, position, orientation (nor, sometimes, scale). They are useful for whole-universe modelling - the setting for quantum cosmology. This note concerns 3 particles in 1d in shape-scale split variables. The scale part parallels certain Friedmann equations, while in this note the shape part involves functions on the circle. The scale part is taken to be `heavy' and `slow' so the semiclassical approach applies and scale provides an approximate timestandard with repect to which the light physics runs. Relational particle mechanics moreover provide conceptual models of inhomogeneity, structure formation and nontrivial linear constraints (minisuperspace models do not and midisuperspace models only do at the cost of substantial complications).

Edward Anderson

2009-08-13

355

Ewald mesh method for quantum mechanical calculations

The Fourier transform Coulomb (FTC) method has been shown to be effective for the fast and accurate calculation of long-range Coulomb interactions between diffuse (low-energy cutoff) densities in quantum mechanical (QM) systems. In this work, we split the potential of a compact (high-energy cutoff) density into short-range and long-range components, similarly to how point charges are handled in the Ewald mesh methods in molecular mechanics simulations. With this linear scaling QM Ewald mesh method, the long-range potential of compact densities can be represented on the same grid as the diffuse densities that are treated by the FTC method. The new method is accurate and significantly reduces the amount of computational time on short-range interactions, especially when it is compared to the continuous fast multipole method. PMID:22443753

Chang, Chun-Min; Shao, Yihan; Kong, Jing

2012-01-01

356

In the paper we analyze the quantum-mechanical equivalence of the metrics of a centrally symmetric uncharged gravitational field. We consider the Schwarzschild metrics in the spherical, isotropic and harmonic coordinates, and the Eddington-Finkelstein, Painleve-Gullstrand, Lemaitre-Finkelstein, Kruskal metrics. The scope of the analysis includes domains of the wave functions of Dirac's equation, hermiticity of Hamiltonians, and the possibility of existence of stationary bound states of spin-half particles. The constraint on the domain of the wave functions of the Hamiltonian in a Schwarzschild field in spherical coordinates (r > r_{0}) resulting from the fulfillment of Hilbert's condition g_{00} > 0 also holds in other coordinates for all the metrics considered. The self-adjoint Hamiltonians for the Schwarzschild metrics in the spherical, isotropic and harmonic coordinates and also for the Eddington-Finkelstein and Painleve-Gullstrand metrics are Hermitian, and for them the existence of stationary bound states of spin-half particles is possible. The self-adjoint Hamiltonians for non-stationary Lemaitre-Finkelstein and Kruskal metrics have the explicit dependence on the temporal coordinates and stationary bound states of spin-half particles cannot be defined for these Hamiltonians. The results of this study can be useful when addressing the issues related to the evolution of the universe and interaction of collapsars with surrounding matter.

M. V. Gorbatenko; V. P. Neznamov

2014-11-08

357

INTRODUCTION TO RELATIVISTIC QUANTUM MECHANICS AND THE DIRAC EQUATION

The development of quantum mechanics is presented from a his- torical perspective. The principles of special relativity are reviewed. Relativis- tic quantum mechanics is developed, including the Klein-Gordon equation and up to the Dirac equation. Near the end of the 19th century, physicists were confident in their view of the world. Newton's mechanics had explained the dynamics of everything from

JACOB E. SONE

358

A note on the Landauer principle in quantum statistical mechanics

A note on the Landauer principle in quantum statistical mechanics Vojkan JaksiÂ´c1 and Claude results concerning the derivation of the Landauer bound from the first principles of statistical mechanics and proof of the Landauer principle in the context of quantum statistical mechanics has led to a number

Boyer, Edmond

359

NASA Astrophysics Data System (ADS)

SUSY quantum mechanics can be applied to solve Schrodinger equation for high dimensional system that can be reduced into one dimensional system and represented in lowering and raising operators. Lowering and raising operators can be obtained using relationship between original Hamiltonian equation and the (super) potential equation. In this paper SUSY quantum mechanics is used as a method to obtain the wave function and the energy level of the Modified Poschl Teller potential. The graph of wave function equation and probability density is simulated by using Delphi 7.0 programming language. Finally, the expectation value of quantum mechanics operator could be calculated analytically using integral form or probability density graph resulted by the programming.

Angraini, Lily Maysari; Suparmi, Variani, Viska Inda

2010-12-01

360

SUSY quantum mechanics can be applied to solve Schrodinger equation for high dimensional system that can be reduced into one dimensional system and represented in lowering and raising operators. Lowering and raising operators can be obtained using relationship between original Hamiltonian equation and the (super) potential equation. In this paper SUSY quantum mechanics is used as a method to obtain the wave function and the energy level of the Modified Poschl Teller potential. The graph of wave function equation and probability density is simulated by using Delphi 7.0 programming language. Finally, the expectation value of quantum mechanics operator could be calculated analytically using integral form or probability density graph resulted by the programming.

Angraini, Lily Maysari [STKIP Hamzanwadi Selong East Lombok, NTB, PostGraduate student at Physics Department UNS, Jl. Ir. Sutami 36 A, Surakarta (Indonesia); Suparmi,; Variani, Viska Inda [Physics Department UNS, Jl. Ir. Sutami 36 A, Surakarta (Indonesia)

2010-12-23

361

A fully 3D atomistic quantum mechanical study on random dopant induced effects in 25nm MOSFETs

We present a fully 3D atomistic quantum mechanical simulation for nanometered MOSFET using a coupled Schroedinger equation and Poisson equation approach. Empirical pseudopotential is used to represent the single particle Hamiltonian and linear combination of bulk band (LCBB) method is used to solve the million atom Schroedinger's equation. We studied gate threshold fluctuations and threshold lowering due to the discrete dopant configurations. We compared our results with semiclassical simulation results. We found quantum mechanical effects increase the threshold fluctuation while decreases the threshold lowering. The increase of threshold fluctuation is in agreement with previous study based on approximated density gradient approach to represent the quantum mechanical effect. However, the decrease in threshold lowering is in contrast with the previous density gradient calculations.

Wang, Lin-Wang; Jiang, Xiang-Wei; Deng, Hui-Xiong; Luo, Jun-Wei; Li, Shu-Shen; Wang, Lin-Wang; Xia, Jian-Bai

2008-07-11

362

Quantum Mechanical Study of Nanoscale MOSFET

NASA Technical Reports Server (NTRS)

The steady state characteristics of MOSFETS that are of practical Interest are the drive current, off-current, dope of drain current versus drain voltage, and threshold voltage. In this section, we show that quantum mechanical simulations yield significantly different results from drift-diffusion based methods. These differences arise because of the following quantum mechanical features: (I) polysilicon gate depletion in a manner opposite to the classical case (II) dependence of the resonant levels in the channel on the gate voltage, (III) tunneling of charge across the gate oxide and from source to drain, (IV) quasi-ballistic flow of electrons. Conclusions dI/dV versus V does not increase in a manner commensurate with the increase in number of subbands. - The increase in dI/dV with bias is much smaller then the increase in the number of subbands - a consequence of bragg reflection. Our calculations show an increase in transmission with length of contact, as seen in experiments. It is desirable for molecular electronics applications to have a small contact area, yet large coupling. In this case, the circumferential dependence of the nanotube wave function dictates: - Transmission in armchair tubes saturates around unity - Transmission in zigzag tubes saturates at two.

Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan

2001-01-01

363

Supersymmetric quantum mechanics and the Korteweg--de Vries hierarchy

The connection between supersymmetric quantum mechanics and the Korteweg--de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the [tau] function by means of supersymmetric quantum mechanics is discussed.

Grant, A.K.; Rosner, J.L. (Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637 (United States))

1994-05-01

364

Biological applications of hybrid quantum mechanics/molecular mechanics calculation.

Since in most cases biological macromolecular systems including solvent water molecules are remarkably large, the computational costs of performing ab initio calculations for the entire structures are prohibitive. Accordingly, QM calculations that are jointed with MM calculations are crucial to evaluate the long-range electrostatic interactions, which significantly affect the electronic structures of biological macromolecules. A UNIX-shell-based interface program connecting the quantum mechanics (QMs) and molecular mechanics (MMs) calculation engines, GAMESS and AMBER, was developed in our lab. The system was applied to a metalloenzyme, azurin, and PU.1-DNA complex; thereby, the significance of the environmental effects on the electronic structures of the site of interest was elucidated. Subsequently, hybrid QM/MM molecular dynamics (MD) simulation using the calculation system was employed for investigation of mechanisms of hydrolysis (editing reaction) in leucyl-tRNA synthetase complexed with the misaminoacylated tRNA(Leu), and a novel mechanism of the enzymatic reaction was revealed. Thus, our interface program can play a critical role as a powerful tool for state-of-the-art sophisticated hybrid ab initio QM/MM MD simulations of large systems, such as biological macromolecules. PMID:22536015

Kang, Jiyoung; Hagiwara, Yohsuke; Tateno, Masaru

2012-01-01

365

The Many-Worlds Interpretation of Quantum Mechanics

NSDL National Science Digital Library

This encyclopedia entry contains a comprehensive introduction to the many-worlds interpretation of quantum mechanics. It includes discussions of the probability, tests, and objections to this interpretation.

Vaidman, Lev

2005-04-16

366

Three attempts at two axioms for quantum mechanics

The axioms of nonrelativistic quantum mechanics lack clear physical meaning. In particular, they say nothing about nonlocality. Yet quantum mechanics is not only nonlocal, it is twice nonlocal: there are nonlocal quantum correlations, and there is the Aharonov-Bohm effect, which implies that an electric or magnetic field h e r e may act on an electron t h e r e. Can we invert the logical hierarchy? That is, can we adopt nonlocality as an axiom for quantum mechanics and derive quantum mechanics from this axiom and an additional axiom of causality? Three versions of these two axioms lead to three different theories, characterized by "maximal nonlocal correlations", "jamming" and "modular energy". Where is quantum mechanics in these theories?

Daniel Rohrlich

2010-11-24

367

Action with Acceleration I: Euclidean Hamiltonian and Path Integral

An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity, and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity transformation; the matrix elements of this unbounded transformation is explicitly evaluated. The mapping fails for a critical value of the coupling constants.

Belal E. Baaquie

2012-11-30

368

Reciprocal relativity of noninertial frames: quantum mechanics

Noninertial transformations on time-position-momentum-energy space {t,q,p,e} with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and the symplectic metric -de/\\dt+dp/\\dq are studied. This U(1,3) group of transformations contains the Lorentz group as the inertial special case. In the limit of small forces and velocities, it reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds^2=dt^2. The U(1,3) transformations bound relative velocities by c and relative forces by b. Spacetime is no longer an invariant subspace but is relative to noninertial observer frames. Born was lead to the metric by a concept of reciprocity between position and momentum degrees of freedom and for this reason we call this reciprocal relativity. For large b, such effects will almost certainly only manifest in a quantum regime. Wigner showed that special relativistic quantum mechanics follows from the projective representations of the inhomogeneous Lorentz group. Projective representations of a Lie group are equivalent to the unitary reprentations of its central extension. The same method of projective representations of the inhomogeneous U(1,3) group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous U(1,3) group is the cover of the quaplectic group Q(1,3)=U(1,3)*s H(4). H(4) is the Weyl-Heisenberg group. A set of second order wave equations results from the representations of the Casimir operators.

Stephen G. Low

2007-03-23

369

Quantum Mechanical Model for Information Transfer from DNA to Protein

A model for the information transfer from DNA to protein using quantum information and computation techniques is presented. DNA is modeled as the sender and proteins are modeled as the receiver of this information. On the DNA side, a 64-dimensional Hilbert space is used to describe the information stored in DNA triplets (codons). A Hamiltonian matrix is constructed for this space, using the 64 possible codons as base states. The eigenvalues of this matrix are not degenerate. The genetic code is degenerate and proteins comprise only 20 different amino acids. Since information is conserved, the information on the protein side is also described by a 64-dimensional Hilbert space, but the eigenvalues of the corresponding Hamiltonian matrix are degenerate. Each amino acid is described by a Hilbert subspace. This change in Hilbert space structure reflects the nature of the processes involved in information transfer from DNA to protein.

Ioannis G. Karafyllidis

2008-01-18

370

Exponential complexity and ontological theories of quantum mechanics

Ontological theories of quantum mechanics describe a single system by means of well-defined classical variables and attribute the quantum uncertainties to our ignorance about the underlying reality represented by these variables. We consider the general class of ontological theories describing a quantum system by a set of variables with Markovian (either deterministic or stochastic) evolution. We provide proof that the number of continuous variables cannot be smaller than 2N-2, N being the Hilbert-space dimension. Thus, any ontological Markovian theory of quantum mechanics requires a number of variables which grows exponentially with the physical size. This result is relevant also in the framework of quantum Monte Carlo methods.

Montina, A. [Dipartimento di Fisica, Universita di Firenze, Via Sansone 1, 50019 Sesto Fiorentino (Italy)

2008-02-15

371

Supersymmetric quantum mechanics and Painlevé equations

NASA Astrophysics Data System (ADS)

In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order the potential is determined by solutions to Painlevé IV (PIV) and Painlevé V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.

Bermudez, David; Fernández C., David J.

2014-01-01

372

Quantum-mechanical suppression of bremsstrahlung

We have studied quantum-mechanical suppression of bremsstrahlung of low-energy 1-500 MeV photons from high-energy 25 GeV electrons. We measured the LPM effect, where multiple scattering of the radiating electron destroys coherence required for the emission of low-energy photons, and the dielectric effect, where the emitted photon traveling in the radiator medium interferes with itself. For the experiment, the collaboration developed a novel method of extracting a parasitic low-intensity high-energy electron beam into the fixed target area during normal SLC operation of the accelerator. The results agree quantitatively with Migdal`s calculation of the LPM effect. Surface effects, for which there is no satisfactory theoretical prediction, are visible at low photon energies. For very thin targets, the suppression disappears, as expected. Preliminary results on dielectric suppression of bremsstrahlung are in qualitative agreement with the expectation.

Becker-Szendy, R. [Stanford Linear Accelerator Center, Menlo Park, CA (United States); Anthony, P. [Stanford Linear Accelerator Center, Menlo Park, CA (United States)]|[Lawrence Livermore National Lab., CA (United States); Bosted, P. [American Univ., Washington, DC (United States)] [and others

1993-12-01

373

Supersymmetric quantum mechanics and Painlevé equations

In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order the potential is determined by solutions to Painlevé IV (PIV) and Painlevé V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.

Bermudez, David; Fernández C, David J. [Departamento de Física, Cinvestav, A.P. 14-740, 07000 México D.F. (Mexico)

2014-01-08

374

Is Quantum Mechanics the Whole Truth?

Quantum mechanics has been enormously successful in describing nature at the atomic level and most physicists believe it is, in principle, the 'whole truth' about the world even at the everyday level. However, such a view, at first glance, leads to a severe problem. In certain circumstances, the most natural interpretation of the theory implies that no definite outcome of an experiment occurs until the act of observation. For many decades this problem was regarded as merely philosophical-it was thought it had no consequences that could be tested in experiment. However, in the last dozen years or so, the situation has changed dramatically in this respect. The problem, some popular resolutions of it, the current experimental situation and prospects for the future are discussed.

Leggett, Anthony J. [University of Illinois at Urbana-Champaign (United States)

2008-05-29

375

Quantum mechanical systems exhibit an inherently probabilistic nature upon\\u000ameasurement which excludes in principle the singular direct observability\\u000acontinual case. Quantum theory of time continuous measurements and quantum\\u000aprediction theory, developed by the author on the basis of an\\u000aindependent-increment model for quantum noise and nondemolition causality\\u000aprinciple in the 80's, solves this problem allowing continual quantum\\u000apredictions and reducing

VIACHESLAV P BELAVKIN

2007-01-01

376

New methods for quantum mechanical reaction dynamics

Quantum mechanical methods are developed to describe the dynamics of bimolecular chemical reactions. We focus on developing approaches for directly calculating the desired quantity of interest. Methods for the calculation of single matrix elements of the scattering matrix (S-matrix) and initial state-selected reaction probabilities are presented. This is accomplished by the use of absorbing boundary conditions (ABC) to obtain a localized (L{sup 2}) representation of the outgoing wave scattering Green`s function. This approach enables the efficient calculation of only a single column of the S-matrix with a proportionate savings in effort over the calculation of the entire S-matrix. Applying this method to the calculation of the initial (or final) state-selected reaction probability, a more averaged quantity, requires even less effort than the state-to-state S-matrix elements. It is shown how the same representation of the Green`s function can be effectively applied to the calculation of negative ion photodetachment intensities. Photodetachment spectroscopy of the anion ABC{sup -} can be a very useful method for obtaining detailed information about the neutral ABC potential energy surface, particularly if the ABC{sup -} geometry is similar to the transition state of the neutral ABC. Total and arrangement-selected photodetachment spectra are calculated for the H{sub 3}O{sup -} system, providing information about the potential energy surface for the OH + H{sub 2} reaction when compared with experimental results. Finally, we present methods for the direct calculation of the thermal rate constant from the flux-position and flux-flux correlation functions. The spirit of transition state theory is invoked by concentrating on the short time dynamics in the area around the transition state that determine reactivity. These methods are made efficient by evaluating the required quantum mechanical trace in the basis of eigenstates of the Boltzmannized flux operator.

Thompson, W.H. [Univ. of California, Berkeley, CA (United States). Dept. of Chemistry; [Lawrence Berkeley Lab., CA (United States)

1996-12-01

377

Tampering detection system using quantum-mechanical systems

The use of quantum-mechanically entangled photons for monitoring the integrity of a physical border or a communication link is described. The no-cloning principle of quantum information science is used as protection against an intruder's ability to spoof a sensor receiver using a `classical` intercept-resend attack. Correlated measurement outcomes from polarization-entangled photons are used to protect against quantum intercept-resend attacks, i.e., attacks using quantum teleportation.

Humble, Travis S. (Knoxville, TN); Bennink, Ryan S. (Knoxville, TN); Grice, Warren P. (Oak Ridge, TN)

2011-12-13

378

Quantum Information Theory Quantum mechanics makes probabilistic predictions about experiments lead to the development of a theory of quantum information that generalises previous notions allow us to build unbreakable cryptosystems based on quantum communication, and how our intuitive

Burton, Geoffrey R.

379

NASA Astrophysics Data System (ADS)

We propose mutant versions of quantum mechanics constructed on vector spaces over the finite Galois fields GF(3) and GF(9). The mutation we consider here is distinct from what we proposed in previous papers on Galois field quantum mechanics. In this new mutation, the canonical expression for expectation values is retained instead of that for probabilities. In fact, probabilities are indeterminate. Furthermore, it is shown that the mutant quantum mechanics over the finite field GF(9) exhibits super-quantum correlations (i.e. the Bell-Clauser-Horne-Shimony-Holt bound is 4). We comment on the fundamental physical importance of these results in the context of quantum gravity.

Chang, Lay Nam; Lewis, Zachary; Minic, Djordje; Takeuchi, Tatsu

2013-12-01

380

Vortex Line Fluctuations in Superconductors from Elementary Quantum Mechanics

Concepts from elementary quantum mechanics can be used to understand vortex line fluctuations in high-temperature superconductors. Flux lines are essentially classical objects, described by a string tension, their mutual repulsion, and interactions with pinning centers. The classical partition function, however, is isomorphic to the imaginary time path integral description of quantum mechanics. This observation is used to determine the thermal

David R. Nelson

1993-01-01

381

Quantum mechanical retrocausation? Call for nonlocal causal models!

A new possible version of multisimultaneous causality is proposed, and real experiments allowing us to decide between this view and quantum mechanical retrocausation are further discussed. The interest of testing quantum mechanics against as many nonlocal causal models as possible is stressed.

Antoine Suarez

1998-02-12

382

Quantum mechanical features of optically pumped CW FIR lasers

NASA Technical Reports Server (NTRS)

Quantum mechanical predictions for the gain of an optically pumped CW FIR laser are presented for cases in which one or both of the pump and FIR transitions are pressure or Doppler broadened. The results are compared to those based on the rate equation model. Some of the quantum mechanical predictions are verified in CH3OH.

Seligson, D.; Leite, J. R. R.; Sanchez, A.; Feld, M. S.; Ducloy, M.

1977-01-01

383

Using a Computer-Rich Curriculum to Teach Quantum Mechanics

NSDL National Science Digital Library

This site is the notes for a seminar on the use of java applets in quantum mechanics pedagogy. Applets are included that cover basic quantum mechanics, hydrogenic and two-particle systems, and some simulation techniques. Time dependent results are stressed.

Belloni, Mario; Carroll, Meghan

2004-03-10

384

An overview of the transactional interpretation of quantum mechanics

We summarize the transactional interpretation of quantum mechanics (TI) and consider various points concerning the TI and its relation to the Copenhagen interpretation (CI). Questions concerning mapping the TI onto the CI, of advanced waves as solutions to proper wave equations, of collapse and the QM formalism, and of the relation of quantum mechanical interpretations to experimental tests and results are discussed. 12 refs.

Cramer, J.G.

1987-01-01

385

Hidden-Variables Models of Quantum Mechanics (Noncontextual and Contextual)

In the following discussion of hidden variables models of quantum mechanics the ? Hilbert space formulation of quantum mechanics\\u000a and the standard interpretation of its notation and concepts will be taken to be initially understood, even though challenges\\u000a to the standard interpretation are implicit in the proposals of ? hidden variables.\\u000a \\u000a Very soon after the formulation of the new quantum

Abner Shimony

386

Two-dimensional quantum mechanical modeling of nanotransistors

Quantization in the inversion layer and phase coherent transport are anticipated to have significant impact on device performance in ``ballistic'' nanoscale transistors. While the role of some quantum effects have been analyzed qualitatively using simple one-dimensional ballistic models, two-dimensional (2D) quantum mechanical simulation is important for quantitative results. In this paper, we present a framework for 2D quantum mechanical simulation

A. Svizhenko; M. P. Anantram; T. R. Govindan; B. Biegel; R. Venugopal

2002-01-01

387

Quantum Mechanical Black Holes: Towards a Unification of Quantum Mechanics and General Relativity

In this paper, starting from vortices we are finally lead to a treatment of\\u000aFermions as Kerr-Newman type Black Holes wherein we identify the horizon at the\\u000aparticle's Compton wavelength periphery. A naked singularity is avoided and the\\u000asingular processes inside the horizon of the Black Hole are identified with\\u000aQuantum Mechanical effects within the Compton wavelength. Inertial mass,\\u000agravitation,

B. G. Sidharth; B. M. Birla; Adarsh Nagar

1998-01-01

388

Depicting qudit quantum mechanics and mutually unbiased qudit theories

We generalize the ZX calculus to quantum systems of dimension higher than two. The resulting calculus is sound and universal for quantum mechanics. We define the notion of a mutually unbiased qudit theory and study two particular instances of these theories in detail: qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits. The calculus allows us to analyze the structure of qudit stabilizer quantum mechanics and provides a geometrical picture of qudit stabilizer theory using D-toruses, which generalizes the Bloch sphere picture for qubit stabilizer quantum mechanics. We also use our framework to describe generalizations of Spekkens toy theory to higher dimensional systems. This gives a novel proof that qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits are operationally equivalent in three dimensions. The qudit pictorial calculus is a useful tool to study quantum foundations, understand the relationship between qubit and qudit quantum mechanics, and provide a novel, high level description of quantum information protocols.

André Ranchin

2014-12-30

389

A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with two p electrons or a single d electron have been derived and implemented. The Hamiltonian used in the approach was obtained by rigorously separating the center-of-mass motion and it explicitly depends on the finite mass of the nucleus. The approach was employed to perform test calculations on the isotopes of the carbon atom in their ground electronic states and to determine the finite-nuclear-mass corrections for these states.

Sharkey, Keeper L.; Pavanello, Michele [Department of Chemistry, University of Arizona, Tucson, Arizona 85721 (United States); Bubin, Sergiy [Quantum Chemistry Research Institute, Kyodai Katsura Venture Plaza 106, Goryo Oohara 1-36, Nishikyo-ku, Kyoto 615-8245 (Japan); Department of Chemistry, University of Arizona, Tucson, Arizona 85721 (United States); Adamowicz, Ludwik [Department of Chemistry, University of Arizona, Tucson, Arizona 85721 (United States); Department of Physics, University of Arizona, Tucson, Arizona 85721 (United States)

2009-12-15

390

Highlighting the mechanism of the quantum speedup by time-symmetric and relational quantum mechanics

Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. We explain it by extending the usual representation of the quantum algorithm, limited to the process of solving the problem, to the process of setting the problem. The number of the drawer with the ball becomes a unitary transformation of the random outcome of the preparation measurement. This brings in relational quantum mechanics: the extension is with respect to Bob and cannot be with respect to Alice. It would tell her the drawer number before she opens any drawer. To Alice, the projection of the quantum state due to the preparation measurement should be retarded at the end of her search; in the input state of the search, the drawer number is determined to Bob and undetermined to Alice. A second consequence is the emergence of an ambiguity. Either the preparation measurement or the final one required to read the solution selects the solution. For reasons of symmetry, we assume that the selection shares evenly between the two measurements. All is as if Alice, by reading the solution, selected half of the information that specifies the drawer number. This selection leaves the input state to Bob unaltered and projects that to Alice on a state of lower entropy where she knows that half in advance. The quantum algorithm is a sum over histories in each of which Alice knows in advance that the ball is in a pair of drawers and locates it by opening one of the two. More in general, given an oracle problem, this explanation of the speedup predicts the number of queries required to solve it in an optimal quantum way.

Giuseppe Castagnoli

2014-12-11

391

BYU PHYS 731 Statistical Mechanics Chapter 7: Sethna Professor Manuel Berrondo Quantum Statistical #12;BYU PHYS 731 Statistical Mechanics Chapter 7: Sethna Professor Manuel Berrondo Quantum ensembles: = n pn |n n| density matrix 2 #12;BYU PHYS 731 Statistical Mechanics Chapter 7: Sethna Professor

Hart, Gus

392

A quantum mechanical version of Price's theorem for Gaussian states

This paper is concerned with integro-differential identities which are known in statistical signal processing as Price's theorem for expectations of nonlinear functions of jointly Gaussian random variables. We revisit these relations for classical variables by using the Frechet differentiation with respect to covariance matrices, and then show that Price's theorem carries over to a quantum mechanical setting. The quantum counterpart of the theorem is established for Gaussian quantum states in the framework of the Weyl functional calculus for quantum variables satisfying the Heisenberg canonical commutation relations. The quantum mechanical version of Price's theorem relates the Frechet derivative of the generalized moment of such variables with respect to the real part of their quantum covariance matrix with other moments. As an illustrative example, we consider these relations for quadratic-exponential moments which are relevant to risk-sensitive quantum control.

Igor G. Vladimirov

2014-09-15

393

Lectures on Black Hole Quantum Mechanics

NASA Astrophysics Data System (ADS)

The lectures that follow were originally given in 1992, and written up only slightly later. Since then there have been dramatic developments in the quantum theory of black holes, especially in the context of string theory. None of these are reflected here. The concept of quantum hair, which is discussed at length in the lectures, is certainly of permanent interest, and I continue to believe that in some generalized form it will prove central to the whole question of how information is stored in black holes. The discussion of scattering and emission modes from various classes of black holes could be substantially simplified using modern techniques, and from currently popular perspectives the choice of examples might look eccentric. On the other hand fashions have changed rapidly in the field, and the big questions as stated and addressed here, especially as formulated for "real" black holes (nonextremal, in four-dimensional, asymptotically flat space-time, with supersymmetry broken), remain pertinent even as the tools to address them may evolve. The four lectures I gave at the school were based on two lengthy papers that have now been published, "Black Holes as Elementary Particles," Nuclear Physics B380, 447 (1992) and "Quantum Hair on Black Holes," Nuclear Physics B378, 175 (1992). The unifying theme of this work is to help make plausible the possibility that black holes, although they are certainly unusual and extreme states of matter, may be susceptible to a description using concepts that are not fundamentally different from those we use in describing other sorts of quantum-mechanical matter. In the first two lectures I discussed dilaton black holes. The fact that apparently innocuous changes in the "matter" action can drastically change the properties of a black hole is already very significant: it indicates that the physical properties of small black holes cannot be discussed reliably in the abstract, but must be considered with due regard to the rest of physics. (The macroscopic properties of large black holes, in particular those of astrophysical interest, are presumably well described by the familiar Einstein-Maxwell action which governs the massless fields. Heavy fields will at most provide Yukawa tails to the field surrounding the hole.) I will show how perturbations may be set up and analyzed completely, and why doing this is crucial for understanding the semiclassical physics of the hole including the Hawking radiation quantitatively. It will emerge that there is a class of dilaton black holes which behave as rather straightforward elementary particles. In the other two lectures I discussed the issue of hair on black holes, in particular the existence of hair associated with discrete gauge charges and its physical consequences. This hair is particularly interesting to analyze because it is invisible classically and to all order in ?. Its existence shows that black holes can have some "internal" quantum numbers in addition to their traditional classification by mass, charge, and angular momentum. The text that follows, follows the original papers closely.

Wilczek, Frank

394

The Born Rule in Quantum and Classical Mechanics

Considerable effort has been devoted to deriving the Born rule (e.g. that $|\\psi(x)|^2 dx$ is the probability of finding a system, described by $\\psi$, between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert space formulation of {\\it classical} mechanics as well. These results provide new insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.

Paul Brumer; Jiangbin Gong

2006-04-24

395

Quantum Mechanics as a Classical Theory III: Epistemology

The two previous papers developed quantum mechanical formalism from classical mechanics and two additional postulates. In the first paper it was also shown that the uncertainty relations possess no ontological validity and only reflect the formalism's limitations. In this paper, a Realist Interpretation of quantum mechanics based on these results is elaborated and compared to the Copenhagen Interpretation. We demonstrate that von Neumann's proof of the impossibility of a hidden variable theory is not correct, independently of Bell's argumentation. A local hidden variable theory is found for non-relativistic quantum mechanics, which is nothing else than newtonian mechanics itself. We prove that Bell's theorem does not imply in a non-locality of quantum mechanics, and also demonstrate that Bohm's theory cannot be considered a true hidden variable theory.

L. S. F. Olavo

1995-03-31

396

QUANTUM STATISTICAL MECHANICS OVER FUNCTION FIELDS CATERINA CONSANI AND MATILDE MARCOLLI

QUANTUM STATISTICAL MECHANICS OVER FUNCTION FIELDS CATERINA CONSANI AND MATILDE MARCOLLI 1 interplay between quantum statistical mechanics and arithmetic. In the case of number fields, the symmetries]. Moreover, very recently Benoit Jacob constructed an interesting quantum statistical mechanical system

Marcolli, Matilde

397

EEE 434 Quantum Mechanics for Engineers (3) [F] Course (Catalog) Description

EEE 434 Quantum Mechanics for Engineers (3) [F] Course (Catalog) Description: Angular momentum. Ferry, Quantum Mechanics: An Introduction for Device Physicists and Electrical Engineers, Institute Objective: Students are conversant with the concepts of quantum mechanics as they apply to semiconductors

Zhang, Junshan

398

Information flow in quantum mechanics: The Quantum Maxwell Demon

Quantum information can be lost only when a quantum system is placed in contact with a heat bath, and then only in proportion to the entropy generated. Applied to the universe as a whole this suggests that the universe is in an algorithmically simple nearly pure quantum state. This could be verified by squeezing'' the vacuum state, and it is quite plausible that this is exactly what is happening inside black holes. 14 refs.

Chapline, G.F.

1990-08-09

399

Is string interaction the origin of quantum mechanics?

NASA Astrophysics Data System (ADS)

String theory was developed by demanding consistency with quantum mechanics. In this paper we wish to reverse the reasoning. We pretend that open string field theory is a fully consistent definition of the theory - it is at least a self-consistent sector. Then we find in its structure that the rules of quantum mechanics emerge from the non-commutative nature of the basic string joining/splitting interactions. Thus, rather than assuming the quantum commutation rules among the usual canonical variables we derive them from the physical process of string interactions. Morally we could apply such an argument to M-theory to cover quantum mechanics for all physics. If string or M-theory really underlies all physics, it seems that the door has been opened to an explanation of the origins of quantum mechanics from the physical processes point of view.

Bars, Itzhak; Rychkov, Dmitry

2014-12-01

400

Is Holographic Entropy and Gravity the result of Quantum Mechanics?

In this paper we suggest a connection between quantum mechanics and Verlinde's recently proposed entropic force theory for the laws of Newton. We propose an entropy based on the quantum mechanical probability density distribution. With the assumption that the holographic principle holds we propose that our suggested quantum entropy generalizes the Bekenstein entropy used by Verlinde in his approach. Based on this assumption we suggest that Verlinde's entropic theory of gravity has a quantum mechanical origin. We establish a reformulation of the Newtonian potential for gravity based on this quantum mechanical entropy. We also discuss the notion of observation and the correspondence to classical physics. Finally we give a discussion, a number of open problems and some concluding remarks.

Joakim Munkhammar

2010-03-05

401

Statistical Mechanics of Quantum-Classical Systems with Holonomic Constraints

The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained system arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear response function of constrained quantum-classical systems contains non-trivial additional terms which are absent in the response of unconstrained systems.

Alessandro Sergi

2005-11-15

402

Are quantum-mechanical-like models possible, or necessary, outside quantum physics?

NASA Astrophysics Data System (ADS)

This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.

Plotnitsky, Arkady

2014-12-01

403

Supersymmetric Quantum Mechanics and Painlevé IV Equation

NASA Astrophysics Data System (ADS)

As it has been proven, the determination of general one-dimensional Schrödinger Hamiltonians having third-order differential ladder operators requires to solve the Painlevé IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmonic oscillator possess third-order differential ladder operators. This allows us to introduce a simple technique for generating solutions of the Painlevé IV equation. Finally, we classify these solutions into three relevant hierarchies.

Bermúdez, David; Fernández C., David J.

2011-03-01

404

Potentiality and Contradiction in Quantum Mechanics

Following J.-Y.B\\'eziau in his pioneer work on non-standard interpretations of the traditional square of opposition, we have applied the abstract structure of the square to study the relation of opposition between states in superposition in orthodox quantum mechanics in \\cite{are14}. Our conclusion was that such states are \\ita{contraries} (\\ita{i.e.} both can be false, but both cannot be true), contradicting previous analyzes that have led to different results, such as those claiming that those states represent \\ita{contradictory} properties (\\ita{i. e.} they must have opposite truth values). In this chapter we bring the issue once again into the center of the stage, but now discussing the metaphysical presuppositions which underlie each kind of analysis and which lead to each kind of result, discussing in particular the idea that superpositions represent potential contradictions. We shall argue that the analysis according to which states in superposition are contrary rather than contradictory is still more plausible.

Jonas R. B. Arenhart; Décio Krause

2014-06-07

405

A Process Algebra Approach to Quantum Mechanics

The process approach to NRQM offers a fourth framework for the quantization of physical systems. Unlike the standard approaches (Schrodinger-Heisenberg, Feynman, Wigner-Gronewald-Moyal), the process approach is not merely equivalent to NRQM and is not merely a re-interpretation. The process approach provides a dynamical completion of NRQM. Standard NRQM arises as a asymptotic quotient by means of a set-valued process covering map, which links the process algebra to the usual space of wave functions and operators on Hilbert space. The process approach offers an emergentist, discrete, finite, quasi-non-local and quasi-non-contextual realist interpretation which appears to resolve many of the paradoxes and is free of divergences. Nevertheless, it retains the computational power of NRQM and possesses an emergent probability structure which agrees with NRQM in the asymptotic quotient. The paper describes the process algebra, the process covering map for single systems and the configuration process covering map for multiple systems. It demonstrates the link to NRQM through a toy model. Applications of the process algebra to various quantum mechanical situations - superpositions, two-slit experiments, entanglement, Schrodinger's cat - are presented along with an approach to the paradoxes and the issue of classicality.

William H. Sulis

2014-09-07

406

The representation of numbers in quantum mechanics.

Earlier work on modular arithmetic of k-ary representations of length L of the natural numbers in quantum mechanics is extended here to k-ary representations of all natural numbers, and to integers and rational numbers. Since the length L is indeterminate, representations of states and operators using creation and annihilation operators for bosons and fermions are defined. Emphasis is on definitions and properties of operators corresponding to the basic operations whose properties are given by the axioms for each type of number. The importance of the requirement of efficient implementability for physical models of the axioms is emphasized. Based on this, successor operations for each value of j corresponding to addition of k {l_brace}j-1{r_brace} if j>0 and k {l_brace}j{r_brace} if j<0 are defined. It follows from the efficient implementability of these successors, which is the case for all computers, that implementation of the addition and multiplication operators, which are defined in terms of polynomially many iterations of the successors, should be efficient. This is not the case for definitions based on the successor for j=1 only. This is the only successor defined in the usual axioms of arithmetic.

Benioff, P.; Physics

2002-12-01

407

Quantum mechanical studies of DNA and LNA.

Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies of the electrostatic potentials were compared among model oligonucleotides, and it was observed that small structural modifications induce global changes in the molecular structure and surface potentials. Since ligand structure and electrostatic potential complementarity with a receptor is a determinant for the bonding pattern between molecules, minor chemical modifications may have profound changes in the interaction profiles of oligonucleotides, possibly leading to changes in pharmacological properties. The QM modeling data can be used to understand earlier observations of antisense oligonucleotide properties, that is, the observation that small structural changes in oligonucleotide composition may lead to dramatic shifts in phenotypes. These observations should be taken into account in future oligonucleotide drug discovery, and by focusing more on non RNA target interactions it should be possible to utilize the exhibited property diversity of oligonucleotides to produce improved antisense drugs. PMID:24491259

Koch, Troels; Shim, Irene; Lindow, Morten; Řrum, Henrik; Bohr, Henrik G

2014-04-01

408

PT-Symmetric Matrix Quantum Mechanics

Recently developed methods for PT-symmetric models are applied to quantum-mechanical matrix models. We consider in detail the case of potentials of the form $V=-(g/N^{p/2-1})Tr(iM)^{p}$ and show how the calculation of all singlet wave functions can be reduced to solving a one-dimensional PT-symmetric model. The large-N limit of this class of models exists, and properties of the lowest-lying singlet state can be computed using WKB. For $p=3,4$, the energy of this state for small values of $N$ appears to show rapid convergence to the large-N limit. For the special case of $p=4$, we extend recent work on the $-gx^{4}$ potential to the matrix model: we show that the PT-symmetric matrix model is equivalent to a hermitian matrix model with a potential proportional to $+(4g/N)Tr\\Pi^{4}$. However, this hermitian equivalent model includes an anomaly term $\\hbar\\sqrt{2g/N}Tr\\Pi$. In the large-N limit, the anomaly term does not contribute at leading order to the properties of singlet states.

Peter N. Meisinger; Michael C. Ogilvie

2007-01-23

409

A Novel Radiation to Test Foundations of Quantum Mechanics

We point out that a new mechanism for radiation should exist if the Bohm theory of quantum mechanics is taken seriously. By traversing a quantum potential, an electron will necessarily be accelerated and radiate. For an illustration, we show that in the double-slit experiment this radiation yields a characteristic spectrum and a distinct pattern on the screen that is complementary to the pattern of the electrons. Experimentally, either the existence or the nonexistence of such a radiation would have important implications for the foundations of quantum mechanics.

Pisin Chen

2014-03-05

410

Numerical Classical and Quantum Mechanical simulations of Charge Density wave models

We first present how to do a computer simulation of Charge Density Waves using a driven harmonic oscillator model by a numerical scheme as initially formulated by Littlewood, and then afterwards use this to present how the dielectric model as presented by this proceedure leads to a blow up at the initialization of a threshold field ET. We find that this is highly unphysical and this initiated our inquiry as to alternative models. Afterwards, we then investigate hwo to present this transport problem of CDW quantum mechanically, threough a numerical simulation of the massive Schwinger model. We find that this single chaing quantum mechanical simulation uwed to formulate solutions to CDW transport in itself is insufficient for transport of solitons(anti-solitons) through a pinning gap model of CDW. We show that a model Hamiltonian with Peierls condensation energy used to couple adjacent chains (or transverse wave vectors) permits formation of solitons (anti- solitons) which can be used to transport CDW through a potential barrier. This addition of the Peierls condensation energy term is essential for any quantum model of Charge Density Waves to give tunneling behavior as seen via a numerical simulation.

A. W. Beckwith

2004-10-28

411

Quantum-mechanical analysis of ion motion in a rotating-radio-frequency (rrf) trap or in a Penning trap with a quadrupole rotating field is carried out. Rrf traps were introduced by Hasegawa and Bollinger [Phys. Rev. A 72, 043404 (2005)]. The classical motion of a single ion in this trap is described by only trigonometric functions, whereas in the conventional linear radio-frequency (rf) traps it is by the Mathieu functions. Because of the simple classical motion in the rrf trap, it is expected that the quantum-mechanical analysis of the rrf traps is also simple compared to that of the linear rf traps. The analysis of Penning traps with a quadrupole rotating field is also possible in a way similar to the rrf traps. As a result, the Hamiltonian in these traps is the same as the two-dimensional harmonic oscillator, and energy levels and wave functions are derived as exact results. In these traps, it is found that one of the vibrational modes in the rotating frame can have negative energy levels, which means that the zero-quantum-number state (''ground'' state) is the highest energy state.

Abe, K.; Hasegawa, T. [Department of Physics, Keio University, Kanagawa 223-8522 (Japan)

2010-03-15

412

NASA Astrophysics Data System (ADS)

Quantum-mechanical analysis of ion motion in a rotating-radio-frequency (rrf) trap or in a Penning trap with a quadrupole rotating field is carried out. Rrf traps were introduced by Hasegawa and Bollinger [Phys. Rev. A 72, 043404 (2005)]. The classical motion of a single ion in this trap is described by only trigonometric functions, whereas in the conventional linear radio-frequency (rf) traps it is by the Mathieu functions. Because of the simple classical motion in the rrf trap, it is expected that the quantum-mechanical analysis of the rrf traps is also simple compared to that of the linear rf traps. The analysis of Penning traps with a quadrupole rotating field is also possible in a way similar to the rrf traps. As a result, the Hamiltonian in these traps is the same as the two-dimensional harmonic oscillator, and energy levels and wave functions are derived as exact results. In these traps, it is found that one of the vibrational modes in the rotating frame can have negative energy levels, which means that the zero-quantum-number state (“ground” state) is the highest energy state.

Abe, K.; Hasegawa, T.

2010-03-01

413

Entanglement swapping in the transactional interpretation of quantum mechanics

NASA Astrophysics Data System (ADS)

The transactional interpretation (TI) of quantum mechanics, which uses retarded and advanced solutions of the Schrödinger equation and its complex conjugate, offers an original way to visualize and understand quantum processes. After a brief review, we show how it can be applied to different quantum situations, emphasizing the importance of specifying a complete configuration of absorbers. We consider in more detail the phenomenon of entanglement swapping, and see how the apparent retroactive enforcement of entanglement can be understood in the TI.

Marchildon, Louis

2014-12-01

414

Lectures on Black Hole Quantum Mechanics

The lectures that follow were originally given in 1992, and written up only slightly later. Since then there have been dramatic developments in the quantum theory of black holes, especially in the context of string theory. None of these are reflected here. The concept of quantum hair, which is discussed at length in the lectures, is certainly of permanent interest,

Frank Wilczek

1998-01-01

415

Quantum statistical mechanics of vortices in high-temperature superconductors

Starting from the vortex equation of motion, we construct an effective Euclidean action and formulate the quantum statistical mechanics of the vortex system. The formalism is applied to the calculation of various thermodynamic quantities such as the specific heat and the magnetic susceptibility of the vortex lattice. Furthermore, we investigate the effect of quantum fluctuations on the vortex-lattice melting transition.

G. Blatter; B. I. Ivlev

1994-01-01

416

Quantum statistical mechanics of vortices in high-temperature superconductors

NASA Astrophysics Data System (ADS)

Starting from the vortex equation of motion, we construct an effective Euclidean action and formulate the quantum statistical mechanics of the vortex system. The formalism is applied to the calculation of various thermodynamic quantities such as the specific heat and the magnetic susceptibility of the vortex lattice. Furthermore, we investigate the effect of quantum fluctuations on the vortex-lattice melting transition.

Blatter, G.; Ivlev, B. I.

1994-10-01

417

NARST 1999: Research on Teaching and Learning Quantum Mechanics

NSDL National Science Digital Library

This is a collection of nine papers from a session at the 1999 NARST conference on teaching and learning in quantum mechanics. Topics covered include conceptual understanding of students, computers and visualization, curriculum, and the relations between classical and quantum understanding.

2004-03-10

418

QUANTUM MECHANICS When German physicist Max Planck became the

QUANTUM MECHANICS When German physicist Max Planck became the father of quantum theory in 1900, he and recentlyofGermany'sMaxPlanckInstitute.Ateam of computational scientists led by Dr. Roscilde is using the Oak under your arm. Planck had a much more modest and immediate need

Haas, Stephan

419

Interpretation of Quantum Mechanics. A view of our universe

of bright young scientists, Werner Heisenberg, Wolfgang Pauli and others (Fig. 2). THE COPENHAGEN the foundation of quantum mechanics at the Bohr Institute with Werner Heisenberg (middle) and Wolfgang Pauli

Lindgren, Ingvar

420

The Thermodynamic Arrow-of-time and Quantum Mechanics

I give an explanation of the thermodynamic arrow-of-time (namely entropy increases with time) within a quantum mechanical framework. This entails giving a solution to the Loschmidt paradox, i.e. showing how an irreversible ...

Maccone, Lorenzo

421

Quantum mechanics helps in learning for more intelligent robot

A learning algorithm based on state superposition principle is presented. The physical implementation analysis and simulated experiment results show that quantum mechanics can give helps in learning for more intelligent robot.

Dao-Yi Dong; Chun-Lin Chen; Zong-Hai Chen; Chen-Bin Zhang

2005-06-18

422

Interference with correlated photons: Five quantum mechanics experiments for undergraduates

setting. The experiments use correlated photons produced by parametric down conversion to generate for doing experiments with single photons have stimulated studies of the fundamen- tals of quantum mechanics

Galvez, Enrique J. "Kiko"

423

A Simplified Quantum Mechanical Model of Diatomic Molecules

ERIC Educational Resources Information Center

Introduces a simple one-dimensional model of a diatomic molecule that can explain all the essential features of a real two particle quantum mechanical system and gives quantitative results in fair agreement with those of a hydrogen molecule. (GA)

Nielsen, Lars Drud

1978-01-01

424

A Computational Model for Observation in Quantum Mechanics

A computational model of observation in quantum mechanics is presented. The model provides a clean and simple computational paradigm which can be used to illustrate and possibly explain some of the unintuitive and ...

Rozas, Guillermo Juan

1987-03-01

425

Everett's Relative-State Formulation of Quantum Mechanics

NSDL National Science Digital Library

This encyclopedia entry contains a comprehensive introduction of Everett's relative-state formulation of quantum mechanics. It explores the many attempts to reconstruct and interpret this no-collapse theory.

Barrett, Jeff

2005-04-16

426

QUANTUM MECHANICAL CARRIER OF THE IMPRINTS OF GRAVITATION a

QUANTUM MECHANICAL CARRIER OF THE IMPRINTS OF GRAVITATION invariance of spacetime in the absence of gravitation* *. This car- rier consists of the phase Einstein actually started o* *n the path which led towards his formulation of gravitation (general

Gerlach, Ulrich

427

Some Novel Thought Experiments Involving Foundations of Quantum Mechanics and Quantum Information

NASA Astrophysics Data System (ADS)

In this thesis, we have proposed some novel thought experiments involving foundations of quantum mechanics and quantum information theory, using quantum entanglement property. Concerning foundations of quantum mechanics, we have suggested some typical systems including two correlated particles which can distinguish between the two famous theories of quantum mechanics, i.e. the standard and Bohmian quantum mechanics, at the individual level of pair of particles. Meantime, the two theories present the same predictions at the ensemble level of particles. Regarding quantum information theory, two theoretical quantum communication schemes including quantum dense coding and quantum teleportation schemes have been proposed by using entangled spatial states of two EPR particles shared between two parties. It is shown that the rate of classical information gain in our dense coding scheme is greater than some previously proposed multi-qubit protocols by a logarithmic factor dependent on the dimension of Hilbert space. The proposed teleportation scheme can provide a complete wave function teleportation of an object having other degrees of freedom in our three-dimensional space, for the first time. All required unitary operators which are necessary in our state preparation and Bell state measurement processes are designed using symmetric normalized Hadamard matrix, some basic gates and one typical conditional gate, which are introduced here for the first time.

Akhavan, Omid

2004-02-01

428

Four dimensional supersymmetric Yang-Mills quantum mechanics with three colors

The $D=4$ supersymmetric Yang-Mills quantum mechanics with $SU(2)$ and $SU(3)$ gauge symmetry groups is studied. A numerical method to find finite matrix representation of the Hamiltonian is presented in detail. It is used to find spectrum of the theory. In the $SU(2)$ case there are bound states in all channels with definite total number of fermions and angular momentum. For 2,3,4 fermions continuous and discrete spectra coexist in the same range of energies. These results are confirmation of earlier studies. With $SU(3)$ gauge group, the continuous spectrum is moved to sectors with more fermions. Supersymmetry generators are used to identify supermultiplets and determine the level of restoration of supersymmetry for a finite cutoff. For both theories, with $SU(2)$ and $SU(3)$ symmetry, wavefunctions are studied and different behavior of bound and scattering states is observed.

Zbigniew Ambrozinski

2014-08-12

429

Vortex Line Fluctuations in Superconductors from Elementary Quantum Mechanics

Concepts from elementary quantum mechanics can be used to understand vortex\\u000aline fluctuations in high-temperature superconductors. Flux lines are\\u000aessentially classical objects, described by a string tension, their mutual\\u000arepulsion, and interactions with pinning centers. The classical partition\\u000afunction, however, is isomorphic to the imaginary time path integral\\u000adescription of quantum mechanics. This observation is used to determine the\\u000athermal

David R. Nelson

1993-01-01

430

On the geometry of the energy operator in quantum mechanics

We analyze the different ways to define the energy operator in geometric theories of quantum mechanics. In some formulations the operator contains the scalar curvature as a multiplicative term. We show that such term can be canceled or added with an arbitrary constant factor, both in the mainstream Geometric Quantization and in the Covariant Quantum Mechanics, developed by Jadczyk and Modugno with several contributions from many authors.

Carlos Tejero Prieto; Raffaele Vitolo

2014-08-26

431

Combined quantum and molecular mechanics (QM/MM).

We describe the current state of the art of mixed quantum mechanics/molecular mechanics (QM/MM) methodology, with a particular focus on modeling of enzymatic reactions. Over the past decade, the effectiveness of these methods has increased dramatically, based on improved quantum chemical methods, advances in the description of the QM/MM interface, and reductions in the cost/performance of computing hardware. Two examples of pharmaceutically relevant applications, cytochrome P450 and class C ?-lactamase, are presented.: PMID:24981493

Friesner, Richard A

2004-12-01

432

Exactly solvable quantum mechanical models with Stückelberg divergences

We consider an exactly solvable quantum mechanical model with an infinite number of degrees of freedom that is an analogue\\u000a of the model of N scalar fields (?\\/N)(?a\\u000a a)2 in the leading order in 1\\/N. The model involves vacuum and S-matrix divergences and also the Stckelberg divergences, which\\u000a are absent in other known renormalizable quantum mechanical models with, divergences (such

O. Yu. Shvedov; Shvedov I

2000-01-01

433

Three Essential Reasons Why Nature Chose Quantum Mechanics

We discuss the reason why quantum mechanics is chosen as the most basic law of nature. Probability amplitude, which becomes a probability density after square it, is considered as one of the most essential ingredient of quantum mechanics. Code transfer experiments based on the probability amplitude is proved to be i) error of code transfer is minimum, ii) that error is independent of coding parameters and iii) non-trivial and non-local correlation is possible.

Yoshimasa Kurihara

2013-04-21

434

Contribution to understanding the mathematical structure of quantum mechanics

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed.\\u000a It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, the Born rule, commutation\\u000a and uncertainty relations, probability density current, momentum operator, and rules for including the scalar and vector potentials\\u000a and antiparticles can be obtained from the probabilistic description

L. Skála; V. Kapsa

2007-01-01

435

Scalable quantum mechanical simulation of large polymer systems

We describe a program for quantum mechanical calculations of very large hydrocarbon polymer systems. It is based on a new algorithmic approach to the quantum mechanical tight binding equations that naturally leads to a very efficient parallel implementation and that scales linearly with respect to the number of atoms. We get both very high single node performance as well as a significant parallel speedup on the SGI Origin 2000 parallel computer.

Goedecker, S. [Max-Planck Institute for Solid State Research, Stuttgart (Germany); Hoisie, A.; Kress, J.; Lubeck, O.; Wasserman, H. [Los Alamos National Lab., NM (United States)

1997-08-01

436

Nonlinear Phenomenology from Quantum Mechanics: Soliton in a Lattice

We study a soliton in an optical lattice holding bosonic atoms quantum mechanically using both an exact numerical solution and quantum Monte Carlo simulations. The computation of the state is combined with an explicit account of the measurements of the numbers of the atoms at the lattice sites. In particular, importance sampling in the quantum Monte Carlo method arguably produces faithful simulations of individual experiments. Even though the quantum state is invariant under lattice translations, an experiment may show a noisy version of the localized classical soliton.

Juha Javanainen; Uttam Shrestha

2009-03-29

437

Quantum fragile matter: mechanical excitations of a Reggeon ion chain

This paper proposes to study quantum fragile materials with small linear elasticity and a strong response to zero-point fluctuations. As a first model, we consider a non-unitary (but PT-symmetric) massive quantum chain with a Reggeon-type cubic nonlinearity. At the critical point, the chain supports neither the ordinary quantum phonons of a Luttinger liquid, nor the supersonic solitons that arise in classical fragile critical points in the absence of fluctuations. Quantum fluctuations, approximately captured within a one-loop renormalization group, give rise to mechanical excitations with a nonlinear dispersion relation and dissipative spectral behavior. Models of similar complexity should be realizable with trapped ions.

Strack, Philipp

2013-01-01

438

Is Quantum Mechanics Incompatible with Newton's First Law of Motion

Quantum mechanics (QM)clearly violates Newton's First Law of Motion (NFLM) in the quantum domain. This paper examines an apparent incompatibility between the predictions of QM in the classical limit, and that of classical mechanics (CM) with respect to NFLM. In the process, a general argument is made that such a disparity may be found commonly for a wide variety of quantum predictions in the classical limit. The meaning of the classical limit is examined. Critical views regarding QM by Schrodinger, Bohm, Bell, Clauser, and others are presented as a perspective for the motivation of the present work.

Rabinowitz, Mario

2007-01-01

439

Characterizing mixing and measurement in quantum mechanics

What fundamental constraints characterize the relationship between a mixture $\\rho = \\sum_i p_i \\rho_i$ of quantum states, the states $\\rho_i$ being mixed, and the probabilities $p_i$? What fundamental constraints characterize the relationship between prior and posterior states in a quantum measurement? In this paper we show that there are many surprisingly strong constraints on these mixing and measurement processes that can be expressed simply in terms of the eigenvalues of the quantum states involved. These constraints capture in a succinct fashion what it means to say that a quantum measurement acquires information about the system being measured, and considerably simplify the proofs of many results about entanglement transformation.

M. A. Nielsen

2000-08-16

440

Assessing the Montevideo Interpretation of Quantum Mechanics

This paper gives a philosophical assessment of the Montevideo interpretation of quantum theory, advocated by Gambini, Pullin and co-authors. This interpretation has the merit of linking its proposal about how to solve the measurement problem to the search for quantum gravity: namely by suggesting that quantum gravity makes for fundamental limitations on the accuracy of clocks, which imply a type of decoherence that "collapses the wave-packet". I begin (Section 2) by sketching the topics of decoherence, and quantum clocks, on which the interpretation depends. Then I expound the interpretation, from a philosopher's perspective (Sections 3, 4 and 5). Finally, in Section 6, I argue that the interpretation, at least as developed so far, is best seen as a form of the Everett interpretation: namely with an effective or approximate branching, that is induced by environmental decoherence of the familiar kind, and by the Montevideans' "temporal decoherence".

Jeremy Butterfield

2014-06-17

441

Quantum mechanical version of the classical Liouville theorem

NASA Astrophysics Data System (ADS)

In terms of the coherent state evolution in phase space, we present a quantum mechanical version of the classical Liouville theorem. The evolution of the coherent state from |z> to |sz - rz*> corresponds to the motion from a point z (q,p) to another point sz - rz* with |s|2 - |r|2 = 1. The evolution is governed by the so-called Fresnel operator U(s,r) that was recently proposed in quantum optics theory, which classically corresponds to the matrix optics law and the optical Fresnel transformation, and obeys group product rules. In other words, we can recapitulate the Liouville theorem in the context of quantum mechanics by virtue of coherent state evolution in phase space, which seems to be a combination of quantum statistics and quantum optics.

Xie, Chuan-Mei; Fan, Hong-Yi

2013-03-01

442

From Quantum Mechanics to Quantum Field Theory: The Hopf route

NASA Astrophysics Data System (ADS)

We show that the combinatorial numbers known as Bell numbers are generic in quantum physics. This is because they arise in the procedure known as Normal ordering of bosons, a procedure which is involved in the evaluation of quantum functions such as the canonical partition function of quantum statistical physics, inter alia. In fact, we shall show that an evaluation of the non-interacting partition function for a single boson system is identical to integrating the exponential generating function of the Bell numbers, which is a device for encapsulating a combinatorial sequence in a single function. We then introduce a remarkable equality, the Dobinski relation, and use it to indicate why renormalisation is necessary in even the simplest of perturbation expansions for a partition function. Finally we introduce a global algebraic description of this simple model, giving a Hopf algebra, which provides a starting point for extensions to more complex physical systems.

Solomon, A. I.; Duchamp, G. H. E.; Blasiak, P.; Horzela, A.; Penson, K. A.

2011-03-01

443

Whether quantum mechanics can be almighty even in information science

We discuss that there is a crucial contradiction within quantum mechanics. We derive a proposition concerning a quantum expectation value under the assumption of the existence of the directions in a spin-1/2 system. The quantum predictions within the formalism of von Neumann's projective measurement cannot coexist with the proposition concerning the existence of the directions. Therefore, we have to give up either the existence of the directions or the formalism of von Neumann's projective measurement. Hence there is a crucial contradiction within the Hilbert space formalism of the quantum theory. This implies that there is no axiomatic system for the quantum theory. This also reveals that we need new physical theories in order to explain the handing of raw experimental data. We discuss that this crucial contradiction makes the quantum-theoretical formulation of Deutsch's algorithm questionable.

Koji Nagata; Tadao Nakamura

2008-11-28

444

Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaotic nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover`s and Kubo-Fox-Keizer`s approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty.

Lee, Sang-Bong

1993-09-01

445

NASA Astrophysics Data System (ADS)

Using the tight-binding method in combination with first-principles calculations, we systematically derive a low-energy effective Hilbert subspace and Hamiltonian with spin-orbit coupling for two-dimensional hydrogenated and halogenated group-V monolayers. These materials are proposed to be giant-gap quantum spin Hall insulators with record huge bulk band gaps opened by the spin-orbit coupling at the Dirac points, e.g., from 0.74 to 1.08 eV in BiX (X =H, F, Cl, and Br) monolayers. We find that the low-energy Hilbert subspace mainly consists of px and py orbitals from the group-V elements, and the giant first-order effective intrinsic spin-orbit coupling is from the on-site spin-orbit interaction. These features are quite distinct from those of group-IV monolayers such as graphene and silicene. There, the relevant orbital is pz and the effective intrinsic spin-orbit coupling is from the next-nearest-neighbor spin-orbit interaction processes. These systems represent the first real 2D honeycomb lattice materials in which the low-energy physics is associated with px and py orbitals. A spinful lattice Hamiltonian with an on-site spin-orbit coupling term is also derived, which could facilitate further investigations of these intriguing topological materials.

Liu, Cheng-Cheng; Guan, Shan; Song, Zhigang; Yang, Shengyuan A.; Yang, Jinbo; Yao, Yugui

2014-08-01

446

A Practical Quantum Mechanism for the Public Goods Game

Quantum generalizations of conventional games broaden the range of available strategies, which can help improve outcomes for the participants. With many players, such quantum games can involve entanglement among many states which is difficult to implement, especially if the states must be communicated over some distance. This paper describes a quantum mechanism for the economically significant $n$-player public goods game that requires only two-particle entanglement and is thus much easier to implement than more general quantum mechanisms. In spite of the large temptation to free ride on the efforts of others in this game, two-particle entanglement is sufficient to give near optimal expected payoff when players use a simple mixed strategy for which no player can benefit by making different choices. This mechanism can also address some heterogeneous preferences among the players.

Kay-Yut Chen; Tad Hogg; Raymond Beausoleil

2003-01-06

447

BOOK REVIEW: Mind, Matter and Quantum Mechanics (2nd edition)

NASA Astrophysics Data System (ADS)

Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried to expel the non-classical nature of quantum mechanics. More recent proposals intend to complete quantum mechanics not within mechanics proper but on a `higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). I think it is fair to say that in each case the combination is with a subject that, per se, suffers from a very limited understanding that is even more severe than that of quantum mechanics. This was acceptable, though, if it could convincingly be argued that scientific progress desperately needs to join forces. Quantum mechanics of a closed system was a beautiful and well understood theory with its respective state being presented as a point on a deterministic trajectory in Liouville space---not unlike the motion of a classical N-particle system in its 6N-dimensional phase-space. Unfortunately, we need an inside and an outside view, we need an external reference frame, we need an observer. This unavoidable partition is the origin of most of the troubles we have with quantum mechanics. A pragmatic solution is introduced in the form of so-called measurement postulates: one of the various incompatible properties of the system under consideration is supposed to be realized (i.e. to become a fact, to be defined without fundamental dispersion) based on `instantaneous' projections within some externally selected measurement basis. As a result, the theory becomes essentially statistical rather than deterministic; furthermore there is an asymmetry between the observed and the observing. This is the point where consciousness may come in. Complemented by an introduction and several appendices, Henry Stapp's book consists essentially of three parts: theory, implications, and new developments. The theory part gives a very readable account of the Copenhagen interpretation, some aspects of a psychophysical theory, and, eventually, hints towards a quantum foundation of the brain--mind connection. The next part, `implications', summarizes some previous attempts to bridge the gap between the working rules of quantum mechanics and their possible consequences for our understanding of this world (Pauli, Everett, Bohm, Heisenberg). The last section, `new developments', dwells on some ideas about the conscious brain and its possible foundation on quantum mechanics. The book is an interesting and, in part, fascinating contribution to a field that continues to be a companion to `practical' quantum mechanics since its very beginning. It is doubtful whether such types of `quantum ontologies' will ever become (empirically) testable; right now one can hardly expect more than to be offered some consistent `grand picture', which the reader may find more or less acceptable or even rewarding. Many practicing quantum physicists, though, will remain unimpressed. The shift from synthetic ontology to analytic ontology is the foundation of the present work. This means that fundamental wholes are being partitioned into their ontologically subordinate components by means of `events'. The actual event, in turn, is an abrupt change in the Heisenberg state describing the quantum universe. The new state then defines the tendencies associated with the next actual event. To avoid infinite regression in terms of going from one state of tendencies to the next, consciousness is there to give these events a special `feel', to provide a status of `intrinsic actuality'. The brain of an alert human observer is similar in an important way to a quantum detection device: it can amplify small signals to large macroscopic ef

Mahler, G.

2004-07-01

448

Quantum mechanics and reality: An interpretation of Everett's theory

NASA Astrophysics Data System (ADS)

The central part of Everett's formulation of quantum mechanics is a quantum mechanical model of memory and of observation as the recording of information in a memory. To use this model as an answer to the measurement problem, Everett has to assume that a conscious observer can be in a superposition of such memory states and be unaware of it. This assumption has puzzled generations of readers. The fundamental aim of this dissertation is to find a set of simpler assumptions which are sufficient to show that Everett's model is empirically adequate. I argue that Everett's model needs three assumptions to account for the process of observation: an assumption of decoherence of observers as quantum mechanical systems; an assumption of supervenience of mental states (qualities) over quantum mechanical properties; and an assumption about the interpretation of quantum mechanical states in general: quantum mechanical states describe ensembles of states of affairs coexisting in the same system. I argue that the only plausible understanding of such ensembles is as ensembles of possibilities, and that all standard no-collapse interpretations agree in this reading of quantum mechanical states. Their differences can be understood as different theories about what marks the real state within this ensemble, and Everett's theory as the claim that no additional 'mark of reality' is necessary. Using the three assumptions, I argue that introspection cannot determine the objective quantum mechanical state of an observer. Rather, the introspective qualities of a quantum mechanical state can be represented by a (classical) statistical ensemble of subjective states. An analysis of these subjective states and their dynamics leads to the conclusion that they suffice to give empirically correct predictions. The argument for the empirical adequacy of the subjective state entails that knowledge of the objective quantum mechanical state is impossible in principle. Empirical reality for a conscious observer is not described by the objective state, but by a Everettian relative state conditional on the subjective state, and no theoretical 'mark of reality' is necessary for this concept of reality. I compare the resulting concept of reality to Kant's distinction between empirical and transcendental reality.

Lehner, Christoph Albert

449

The mechanism of hydrolysis of deprotonated methyl triphosphate (MTP) to methyl diphosphate (MDP) and inorganic phosphate\\u000a (Pi) in water clusters in the presence and absence of magnesium cations has been modeled. Modeling has been performed by the\\u000a effective fragment potential-based quantum mechanical\\/molecular mechanical method. The energies and energy derivatives in\\u000a the quantum subsystem including MTP, reacting water molecules, and Mg2+

A. V. Rogov; B. L. Grigorenko; A. V. Bochenkova; A. A. Granovskii; A. V. Nemukhin

2007-01-01

450

Electronic structure methods based on density functional theory are used to construct a reaction path Hamiltonian for CH{sub 4} dissociation on the Ni(100) and Ni(111) surfaces. Both quantum and quasi-classical trajectory approaches are used to compute dissociative sticking probabilities, including all molecular degrees of freedom and the effects of lattice motion. Both approaches show a large enhancement in sticking when the incident molecule is vibrationally excited, and both can reproduce the mode specificity observed in experiments. However, the quasi-classical calculations significantly overestimate the ground state dissociative sticking at all energies, and the magnitude of the enhancement in sticking with vibrational excitation is much smaller than that computed using the quantum approach or observed in the experiments. The origin of this behavior is an unphysical flow of zero point energy from the nine normal vibrational modes into the reaction coordinate, giving large values for reaction at energies below the activation energy. Perturbative assumptions made in the quantum studies are shown to be accurate at all energies studied.

Mastromatteo, Michael; Jackson, Bret, E-mail: jackson@chem.umass.edu [Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003 (United States)] [Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01003 (United States)

2013-11-21

451

Deformation quantization: Quantum mechanics lives and works in phase space

NASA Astrophysics Data System (ADS)

Wigner's 1932 quasi-probability Distribution Function in phase-space, his first paper in English, is a special (Weyl) representation of the density matrix. It has been useful in describing quantum flows in semiclassical limits; quantum optics; nuclear and physics; decoherence (eg, quantum computing); quantum chaos; "Welcher Weg" puzzles; molecular Talbot-Lau interferometry; atomic measurements. It is further of great importance in signal processing (time-frequency analysis). Nevertheless, a remarkable aspect of its internal logic, pioneered by H. Groenewold and J. Moyal, has only blossomed in the last quarter-century: It furnishes a third, alternate, formulation of Quantum Mechanics, independent of the conventional Hilbert Space (the gold medal), or Path Integral (the silver medal) formulations, and perhaps more intuitive, since it shares language with classical mechanics: one need not choose sides between coordinate or momentum space variables, since it is formulated simultaneously in terms of position and momentum. This bronze medal formulation is logically complete and self-standing, and accommodates the uncertainty principle in an unexpected manner, so that it offers unique insights into the classical limit of quantum theory. The observables in this formulation are cnumber functions in phase space instead of operators, with the same interpretation as their classical counterparts, only now composed together in novel algebraic ways using star products. One might then envision an imaginary world in which this formulation of quantum mechanics had preceded the conventional Hilbert-space formulation, and its own techniques and methods had arisen independently, perhaps out of generalizations of classical mechanics and statistical mechanics. A sampling of such intriguing techniques and methods has already been published in C. K. Zachos, Int Jou Mod Phys A17 297-316 (2002), and T. L. Curtright, D. B. Fairlie, and C. K. Zachos, A Concise Treatise on Quantum Mechanics in Phase Space, (Imperial Press & World Scientific, 2014).

Zachos, Cosmas K.

2014-09-01

452

We develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers. Here we derive upper bounds for non-time averaged outside probabilities and moments of the position operator from lower bounds for transfer matrices at complex energies. Moreover, for the time-averaged transport exponents, we present improved lower bounds in the special case of the Fibonacci Hamiltonian. These bounds lead to an optimal description of the time-averaged spreading rate of the fast part of the wavepacket in the large coupling limit. This provides the first example which demonstrates that the time-averaged spreading rates may exceed the upper box-counting dimension of the spectrum.

David Damanik; Serguei Tcheremchantsev

2008-01-22

453

Quantum tic-tac-toe: A teaching metaphor for superposition in quantum mechanics

NASA Astrophysics Data System (ADS)

Quantum tic-tac-toe was developed as a metaphor for the counterintuitive nature of superposition exhibited by quantum systems. It offers a way of introducing quantum physics without advanced mathematics, provides a conceptual foundation for understanding the meaning of quantum mechanics, and is fun to play. A single superposition rule is added to the child's game of classical tic-tac-toe. Each move consists of a pair of marks subscripted by the number of the move ("spooky" marks) that must be placed in different squares. When a measurement occurs, one spooky mark becomes real and the other disappears. Quantum tic-tac-toe illustrates a number of quantum principles including states, superposition, collapse, nonlocality, entanglement, the correspondence principle, interference, and decoherence. The game can be played on paper or on a white board. A Web-based version provides a refereed playing board to facilitate the mechanics of play, making it ideal for classrooms with a computer projector.

Goff, Allan

2006-11-01

454

Quantum mechanics of hyperbolic orbits in the Kepler problem

The problem of deriving macroscopic properties from the Hamiltonian of the hydrogen atom is resumed by extending previous results in the literature, which predicted elliptic orbits, into the region of hyperbolic orbits. As a main tool, coherent states of the harmonic oscillator are used which are continued to imaginary frequencies. The Kustaanheimo-Stiefel (KS) map is applied to transform the original configuration space into the product space of four harmonic oscillators with a constraint. The relation derived between real time and oscillator (pseudo) time includes quantum corrections. In the limit ({h_bar}/2{pi}){yields}0, the time-dependent mean values of position and velocity describe the classical motion on a hyperbola and a circular hodograph, respectively. Moreover, the connection between pseudotime and real time comes out in analogy to Kepler's equation for elliptic orbits. The mean-square-root deviations of position and velocity components behave similarly in time to the corresponding ones of a spreading Gaussian wave packet in free space. To check the approximate treatment of the constraint, its contribution to the mean energy is determined with the result that it is negligible except for energy values close to the parabolic orbit with eccentricity equal to 1. It is inevitable to introduce a suitable scalar product in R{sup 4} which makes both the transformed Hamiltonian and the velocity operators Hermitian. An elementary necessary criterion is given for the energy interval where the constraint can be approximated by averaging.

Rauh, Alexander; Parisi, Juergen [Institute of Physics, Carl von Ossietzky University Oldenburg, D-26111 Oldenburg (Germany)

2011-04-15

455

Anomalous capacitance-voltage profiles in quantum wells explained by a quantum mechanical model

We have developed a quantum mechanical model for understanding and explaining the capacitance–voltage (C–V) carrier profiles observed in quantum wells (QW). The external field imposed on the QW during C–V profiling changes the carrier distribution of the system. This model considers the effects of field and quantum confinement of the carriers in the well. The results obtained by iterative solutions

Sudakshina Kundu; Dipankar Biswas; Reshmi Datta

1997-01-01

456

Electron exchange-correlation in quantum mechanics

It is shown that Fermi-Dirac statistics is guaranteed by the Dirac current, from which spin-dependent quantum velocity fields and spin-dependent quantum trajectories can be inferred. Pauli's exclusion principle is demonstrated using the spin-dependent quantum trajectories. The Dirac current, unlike the Schroedinger current, is nonzero for stationary bound states due to the permanent magnetic moment of the electron. It is of order c{sup 0} in agreement with observation that Fermi-Dirac statistics is independent of electronic velocity. In summary the physical basis for exchange-correlation is found in Dirac's equation, although Schroedinger's equation may be used to evaluate the Dirac current in the nonrelativistic regime of electronic velocity.

Ritchie, B

2009-01-30

457

Multiple-event probability in general-relativistic quantum mechanics

We discuss the definition of quantum probability in the context of 'timeless' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the 'wave function collapse' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse.

Hellmann, Frank [Fakultaet fuer Physik, Ludwig-Maximilians-Universitaet, D-80799 Munich (Germany); Centre de Physique Theorique de Luminy, Universite de la Mediterranee, F-13288 Marseille (France); Mondragon, Mauricio; Perez, Alejandro; Rovelli, Carlo [Centre de Physique Theorique de Luminy, Universite de la Mediterranee, F-13288 Marseille (France)

2007-04-15

458

Fault Models for Quantum Mechanical Switching Networks

The difference between faults and errors is that, unlike faults, errors can be corrected using control codes. In classical test and verification one develops a test set separating a correct circuit from a circuit containing any considered fault. Classical faults are modelled at the logical level by fault models that act on classical states. The stuck fault model, thought of as a lead connected to a power rail or to a ground, is most typically considered. A classical test set complete for the stuck fault model propagates both binary basis states, 0 and 1, through all nodes in a network and is known to detect many physical faults. A classical test set complete for the stuck fault model allows all circuit nodes to be completely tested and verifies the function of many gates. It is natural to ask if one may adapt any of the known classical methods to test quantum circuits. Of course, classical fault models do not capture all the logical failures found in quantum circuits. The first obstacle faced when using methods from classical test is developing a set of realistic quantum-logical fault models. Developing fault models to abstract the test problem away from the device level motivated our study. Several results are established. First, we describe typical modes of failure present in the physical design of quantum circuits. From this we develop fault models for quantum binary circuits that enable testing at the logical level. The application of these fault models is shown by adapting the classical test set generation technique known as constructing a fault table to generate quantum test sets. A test set developed using this method is shown to detect each of the considered faults.

Jacob Biamonte; Jeff S. Allen; Marek A. Perkowski

2010-01-19

459

Scattering and reflection positivity in relativistic Euclidean quantum mechanics

Scattering and reflection positivity in relativistic Euclidean quantum mechanics W. N. Polyzou The University of Iowa, Iowa City, IA 52242 Abstract In this paper I exhibit a class of reflection positive mechanics where the dynamics is introduced through a collection of reflection positive Euclidean "Green

Polyzou, Wayne

460

Scattering and reflection positivity in relativistic Euclidean quantum mechanics

Scattering and reflection positivity in relativistic Euclidean quantum mechanics W. N. Polyzou The University of Iowa, Iowa City, IA 52242 Abstract In this paper I exhibit a class of reflection positive mechanics where the dynamics is introduced through a collection of reflection positive Euclidean ``Green

Polyzou, Wayne

461

Hamiltonian engineering via invariants and dynamical algebra

We use the dynamical algebra of a quantum system and its dynamical invariants to inverse engineer feasible Hamiltonians for implementing shortcuts to adiabaticity. These are speeded up processes that end up with the same populations than slow, adiabatic ones. As application examples we design families of shortcut Hamiltonians that drive two and a three-level systems between initial and final configurations imposing physically motivated constraints on the terms (generators) allowed in the Hamiltonian.

E. Torrontegui; S. Martínez-Garaot; J. G. Muga

2014-02-24

462

Quantum Mechanics for the Swimming of Micro-Organism in Two Dimensions

In two dimensional fluid, there are only two classes of swimming ways of micro-organisms, {\\it i.e.}, ciliated and flagellated motions. Towards understanding of this fact, we analyze the swimming problem by using $w_{1+\\infty}$ and/or $W_{1+\\infty}$ algebras. In the study of the relationship between these two algebras, there appear the wave functions expressing the shape of micro-organisms. In order to construct the well-defined quantum mechanics based on $W_{1+\\infty}$ algebra and the wave functions, essentially only two different kinds of the definitions are allowed on the hermitian conjugate and the inner products of the wave functions. These two definitions are related with the shapes of ciliates and flagellates. The formulation proposed in this paper using $W_{1+\\infty}$ algebra and the wave functions is the quantum mechanics of the fluid dynamics where the stream function plays the role of the Hamiltonian. We also consider the area-preserving algebras which arise in the swimming problem of micro-organisms in the two dimensional fluid. These algebras are larger than the usual $w_{1+\\infty}$ and $W_{1+\\infty}$ algebras. We give a free field representation of this extended $W_{1+\\infty}$ algebra.

Shin'ichi Nojiri; Masako Kawamura; Akio Sugamoto

1994-09-27

463

Comments on continuous observation in quantum mechanics

It is shown that in open quantum systems the so-called Zeno paradox is not valid. The equations of ideal continuous measurement for Markovian open systems are elaborated and applied to Pauli's simple open system, the actual energy level of which is shown to be monitorable by a continuous nondemolition measurement.

L. Diósi

1986-01-01

464

A quantum mechanical model of adaptive mutation

The principle that mutations occur randomly with respect to the direction of evolutionary change has been challenged by the phenomenon of adaptive mutations. There is currently no entirely satisfactory theory to account for how a cell can selectively mutate certain genes in response to environmental signals. However, spontaneous mutations are initiated by quantum events such as the shift of a

Johnjoe McFadden; Jim Al-Khalili

1999-01-01

465

Noncommutative quantum mechanics of a test particle under linearized gravitational waves

We consider the quantum dynamics of a test particle in noncommutative space under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. A prescription for quantizing the classical Hamiltonian for the interaction of gravitational wave with matter in noncommutative space is proposed. The Hamiltonian (and hence the system) is then exactly solved by using standard algebraic methods. The solutions show prominent signatures of the noncommutative nature of space. Computation of the expectation value of the particle's position reveals the inherent quantum nature of spacetime noncommutativity.

Anirban Saha; Sunandan Gangopadhyay

2009-08-29

466

Accurate Energy Spectrum for the Quantum Yang-Mills Mechanics with Nonlinear Color Oscillations

NASA Astrophysics Data System (ADS)

Yang-Mills theory as the foundation for quantum chromodynamics is a non-Abelian gauge theory with self-interactions between vector particles. Here, we study the Yang-Mills Hamiltonian with nonlinear color oscillations in the absence of external sources corresponding to the group SU(2). In the quantum domain, we diagonalize the Hamiltonian using the optimized trigonometric basis expansion method and find accurate energy eigenvalues and eigenfunctions for one and two degrees of freedom. We also compare our results with the semiclassical solutions.

Pedram, Pouria

2014-06-01

467

NASA Astrophysics Data System (ADS)

The last five years have witnessed an amazing development in the field of nano- and micromechanics. What was widely considered fantasy ten years ago is about to become an experimental reality: the quantum regime of mechanical systems is within reach of current experiments. Two factors (among many) have contributed significantly to this situation. As part of the widespread effort into nanoscience and nanofabrication, it is now possible to produce high-quality nanomechanical and micromechanical resonators, spanning length scales of millimetres to nanometres, and frequencies from kilohertz to gigahertz. Researchers coupled these mechanical elements to high-sensitivity actuation and readout systems such as single-electron transistors, quantum dots, atomic point contacts, SQUID loops, high-finesse optical or microwave-cavities etc. Some of these ultra-sensitive readout schemes are in principle capable of detection at the quantum limit and a large part of the experimental effort is at present devoted to achieving this. On the other hand, the fact that the groups working in the field come from various different physics backgrounds—the authors of this editorial are a representative sample—has been a constant source of inspiration for helpful theoretical and experimental tools that have been adapted from other fields to the mechanical realm. To name just one example: ideas from quantum optics have led to the recent demonstration (both in theory and experiment) that coupling a mechanical resonator to a high-finesse optical cavity can be fully analogous to the well-known sideband-resolved laser cooling of ions and hence is capable in principle of cooling a mechanical mode into its quantum ground state. There is no doubt that such interdisciplinarity has been a crucial element for the development of the field. It is interesting to note that a very similar sociological phenomenon occurred earlier in the quantum information community, an area which is deeply enriched by the diverse backgrounds and approaches of the researchers. As diverse as the approaches are the manifold of goals and perspectives for operating mechanical systems close to or within the quantum regime. Already now, nanomechanical sensors achieve single-molecule mass detection and magnetic resonance force detection from single-electron spins although they are operated far from quantum. Quantum-limited mechanical devices promise a new technology with hitherto unachieved performance for high-resolution sensing. This is also of high relevance for macroscopic mechanical resonators used in gravitational wave detectors. Furthermore, the increasing capability to couple mechanical modes to individual quantum systems raises the interesting question of whether mechanics can serve as a quantum bus in hybrid implementations of quantum information processing. Finally, the possibility of generating quantum superposition states that involve displacements of a massive macroscopic object (such as the center of mass of a mechanical beam) provides a completely new parameter regime for testing quantum theory over the amazing range from nanomechanical objects of several picograms up to gram-scale mirrors used in gravitational wave interferometers. We are looking forward to these fascinating developments! This Focus Issue is intended to highlight the present status of the field and to provide both introduction and motivation for students and researchers who want to get familiar with this exciting area or even want to join it. It also complements the conference activities of our community during the last year, where a series of dedicated invited sessions at several international conferences (APS March Meeting 2008, CLEO/QELS 2008, OSA Frontiers in Optics 2008, PQE 2008/2009 etc) culminated in the first Gordon Conference on 'Mechanical Systems at the Quantum Limit'. Given the fast development of the field it was not surprising to see that during the collection of the following contributions new progress was reported almost on a monthly basis and new groups entered the field. We intend to

Aspelmeyer, Markus; Schwab, Keith

2008-09-01

468

Non-hermitian Hamiltonians and the Painlevé IV equation with real parameters

NASA Astrophysics Data System (ADS)

In this Letter we will use higher-order supersymmetric quantum mechanics to obtain several families of complex solutions g(x;a,b) of the Painlevé IV equation with real parameters a,b. We shall also study the algebraic structure, the eigenfunctions and the energy spectra of the corresponding non-hermitian Hamiltonians.

Bermúdez, David; Fernández C., David J.

2011-08-01

469

The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

NASA Technical Reports Server (NTRS)

The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

Yeon, Kyu Hwang; Um, Chung IN; George, T. F.

1994-01-01

470

New Understandings of Quantum Mechanics Based on Interaction

The interaction between two parts in a compound quantum system may be reconsidered more completely than before and some new understandings and conclusions different from current quantum mechanics are obtained, including the conservation law in the evolution in an isolated quantum system, new understandings of duality of particle and wave and the superposition principle of states, three laws corresponding to Newton's laws, new understandings of measurement and the uncertainty relation, arguments against the non-locality of any entangled state and a simple criterion of coherence which is obtained for the experimenter to examine the correctness of the non-locality. These may make quantum mechanics be easily understood intuitively and some strange properties will not appear.

Tian-Hai Zeng

2010-08-10

471

Quantum mechanics problems in observer's mathematics

This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. Certain results and communications pertaining to solutions of these problems are provided. In particular, we prove the following theorems: Theorem I (Two-slit interference). Let {Psi}{sub 1} be a wave from slit 1, {Psi}{sub 2} - from slit 2, and {Psi} = {Psi}{sub 1}+{Psi}{sub 2}. Then the probability of {Psi} being a wave equals to 0.5. Theorem II (k-bodies solution). For W{sub n} from m-observer point of view with m>log{sub 10}((2 Multiplication-Sign 10{sup 2n}-1){sup 2k}+1), the probability of standard expression of Hamiltonian variation is less than 1 and depends on n,m,k.

Khots, Boris; Khots, Dmitriy [Compressor Controls Corp, Des Moines, Iowa (United States); iMath Consulting LLC, Omaha, Nebraska (United States)

2012-11-06

472

Quantum mechanics problems in observer's mathematics

NASA Astrophysics Data System (ADS)

This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see

Khots, Boris; Khots, Dmitriy

2012-11-01

473

From principles of mechanics to quantum mechanics - a survey on fuzziness in scientific theories

In this paper we discuss the principles of two fundamental theories of physics: mechanics and quantum mechanics. First, we consider two philosophical positions of the German physicist Heinrich Hertz. He established one of the both in the introduction of his well known Principles of Mechanics. This view - Hertz's \\

Rudolf Seising

2008-01-01

474

Hybrid quantum mechanical\\/molecular mechanical potentials have proved to be powerful tools for the simulation of many processes in condensed phase systems and, as a result, there is much current research into how they can be improved. An area of recent attention has been the inclusion of polarization effects on the atoms in the molecular mechanical region which have been shown

Martin J. Field

1997-01-01

475

Quantum mechanical model for two-state jump Markovian process

A quantum mechanical model is given which is equivalent to the stochastic dephasing subject to the two-state jump Markovian process. The stochastic variable corresponds to a Hermitian operator of a spin-1\\/2 system which is embedded in a thermal reservoir, where the time-evolution of the spin-1\\/2 system is described by the quantum master equation of the Lindblad form.

Masashi Ban; Sachiko Kitajima; Kishiko Maruyama; Fumiaki Shibata

2008-01-01

476

Quantum mechanical signature in exclusive coherent pion production

NASA Technical Reports Server (NTRS)

We calculate the coherent production of pions from subthreshold to relativistic energies in heavy-ion collisions using a quantum, microscopic, many-body model. For the first time, in this approach, we use harmonic oscillator wave functions to describe shell-model information. The theoretical quantum mechanical results obtained for the pion spectra represent an important improvement over our previous microscopic, many-body calculations.

Deutchman, P. A.; Buvel, R. L.; Maung, K. M.; Norbury, J. W.; Townsend, L. W.

1986-01-01

477

Supersymmetric Quantum Mechanics for Bianchi Class A models

In this work we present cosmological quantum solutions for all Bianchi Class A cosmological models obtained by means of supersymmetric quantum mechanics . We are able to write one general expression for all bosonic components occuring in the Grassmann expansion of the wave function of the Universe for this class of models. These solutions are obtained by means of a more general ansatz for the so-called master equations.

J. Socorro; E. R. Medina

1999-12-13

478

Quantum mechanics emerges from information theory applied to causal horizons

It is suggested that quantum mechanics is not fundamental but emerges from classical information theory applied to causal horizons. The path integral quantization and quantum randomness can be derived by considering information loss of fields or particles crossing Rindler horizons for accelerating observers. This implies that information is one of the fundamental roots of all physical phenomena. The connection between this theory and Verlinde's entropic gravity theory is also investigated.

Jae-Weon Lee

2010-05-16

479

Quantum Mechanics Emerges from Information Theory Applied to Causal Horizons

It is suggested that quantum mechanics is not fundamental but emerges from classical information theory applied to causal\\u000a horizons. The path integral quantization and quantum randomness can be derived by considering information loss of fields or\\u000a particles crossing Rindler horizons for accelerating observers. This implies that information is one of the fundamental roots\\u000a of all physical phenomena. The connection between

Jae-Weon Lee

2011-01-01

480

Imitating quantum mechanics: qubit-based model for simulation

We present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations of different frequencies results in exponential growth of the state space similar to the tensor-product composition of qubit spaces in quantum mechanics. Individual qubits remain accessible in a composite system, which is represented as a complex function of a single variable, though entanglement imposes a demand on resources that scales exponentially with the number of entangled qubits. We carry out a simulation of Shor's algorithm and discuss a simpler implementation in this classical model.

Steven Peil

2009-06-29

481

Aspects of the Decoherent Histories Approach to Quantum Mechanics

I give an informal overview of the decoherent histories approach to quantum mechanics, due to Griffiths, to Omn\\`es, and to Gell-Mann and Hartle is given. Results on the connections between decoherence, records, correlation and entropy are described. The emphasis of the presentation is on understanding the broader meaning of the conditions of consistency and decoherence, and in particular, the extent to which they permit one to assign definite properties to the system. The quantum Brownian motion model is briefly discussed. (To appear in proceedings of the workshop, "Stochastic Evolution of Quantum States in Open Systems and Measurement Processes", Budapest, March, 1993, edited by L.Diosi).