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1

Realism, operationalism, and quantum mechanics  

Microsoft Academic Search

A comprehensive formal system is developed that amalgamates the operational and the realistic approaches to quantum mechanics. In this formalism, for example, a sharp distinction is made between events, operational propositions, and the properties of physical systems.

D. Foulis; C. Piron; C. Randall

1983-01-01

2

Tensor operators in noncommutative quantum mechanics.  

PubMed

Some consequences of promoting the object of noncommutativity theta(ij) to an operator in Hilbert space are explored. Its canonical conjugate momentum is also introduced. Consequently, a consistent algebra involving the enlarged set of canonical operators is obtained, which permits us to construct theories that are dynamically invariant under the action of the rotation group. In this framework it is also possible to give dynamics to the noncommutativity operator sector, resulting in new features. PMID:18764601

Amorim, Ricardo

2008-08-22

3

Operational dynamic modeling transcending quantum and classical mechanics.  

PubMed

We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories. PMID:23215365

Bondar, Denys I; Cabrera, Renan; Lompay, Robert R; Ivanov, Misha Yu; Rabitz, Herschel A

2012-11-08

4

Overcoming Misconceptions in Quantum Mechanics with the Time Evolution Operator  

ERIC Educational Resources Information Center

|Recently, there have been many efforts to use the research techniques developed in the field of physics education research to improve the teaching and learning of quantum mechanics. In particular, part of this research is focusing on misconceptions held by students. For instance, a set of misconceptions is associated with the concept of…

Quijas, P. C. Garcia; Aguilar, L. M. Arevalo

2007-01-01

5

The structure of Poincaré covariant tensor operators in quantum mechanical models  

Microsoft Academic Search

The structure of operators that transform covariantly in Poincare invariant quantum mechanical models is analyzed. These operators are shown to have an interaction dependence that comes from the geometry of the Poincare group. The operators can be expressed in terms of matrix elements in a complete set of eigenstates of the mass and spin operators associated with the dynamical representation

Wayne N. Polyzou; W. H. Klink

1988-01-01

6

Operational foundation of quantum logic  

Microsoft Academic Search

The logic of quantum mechanical propositions—called quantum logic—is constructed on the basis of the operational foundation of logic. Some obvious modifications of the operational method, which come from the incommensurability of the quantum mechanical propositions, lead to the effective quantum logic. It is shown in this paper that in the framework of a calculization of this effective quantum logic the

P. Mittelstaedt; E. W. Stachow

1974-01-01

7

Quantum Deformations of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Based on a deformation of the quantum mechanical phase space we study q-deformations of quantum mechanics for qk=1 and 0operators in both cases. A formulation of quantum mechanics for qk=1 is given and the dynamics for the free Hamiltonian is studied. For 0quantum mechanics and the cases of the free Hamiltonian and the one with a x2-potential are solved in terms of basic hypergeometric functions.

Ubriaco, Marcelo R.

8

Operational Quantum Physics  

Microsoft Academic Search

This tome is a formal presentation of the unsharp observable approach to quantum mechanics using the positive operator valued (POV) concept of an observable. It is intended for philosophers and mathematicians as well as physicists. This is a very formalistic book. There are, however, portions that should be read by all experimentalists performing quantum mechanical studies as well as graduate

J L Safko

1996-01-01

9

Newton Leibniz integration for ket bra operators in quantum mechanics and derivation of entangled state representations  

NASA Astrophysics Data System (ADS)

Newton Leibniz integration rule only applies to commuting functions of continuum variables, while operators made of Dirac’s symbols (ket versus bra, e.g., |q>quantum mechanics are usually not commutative. Therefore, integrations over the operators of type |><| cannot be directly performed by Newton Leibniz rule. We invented an innovative technique of integration within an ordered product (IWOP) of operators that made the integration of non-commutative operators possible. The IWOP technique thus bridges this mathematical gap between classical mechanics and quantum mechanics, and further reveals the beauty and elegance of Dirac’s symbolic method and transformation theory. Various applications of the IWOP technique, including constructing the entangled state representations and their applications, are presented.

Fan, Hong-Yi; Lu, Hai-Liang; Fan, Yue

2006-02-01

10

Quantum Mechanics  

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.

Michielsen, Kristel; De Raedt, Hans

2004-03-04

11

Renormalizing the Kinetic Energy Operator in Elementary Quantum Mechanics  

ERIC Educational Resources Information Center

|In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form [psi](r) = u(r)/r, where u(0) [is not equal to] 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly…

Coutinho, F. A. B.; Amaku, M.

2009-01-01

12

Classical optics representation of the quantum mechanical translation operator via ABCD matrices  

NASA Astrophysics Data System (ADS)

The ABCD matrix formalism describing paraxial propagation of optical beams across linear systems is generalized to arbitrary beam trajectories. As a by-product of this study, a one-to-one correspondence between the extended ABCD matrix formalism presented here and the quantum mechanical translation operator is established.

Ornigotti, Marco; Aiello, Andrea

2013-07-01

13

Invariant Eigen-Operator Method of Deriving Energy-Level Gap for Noncommutative Quantum Mechanics  

Microsoft Academic Search

We propose a new method to derive energy-level gap for Hamiltonians in the context of noncommutative quantum mechanics (NCQM). This method relies on finding invariant eigen-operators whose commutators with Hamiltonian are still the operators themselves but with some eigenvalue-like coefficients, which correspond to the energy-level gaps of the systems. Based on this method, only after some simple algebra, we derive

Si-Cong Jing; Hong-Yi Fan

2005-01-01

14

Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Quantum Mechanics aims to teach those parts of the subject which every physicist should know. The object is to display the inherent structure of quantum mechanics, concentrating on general principles and on methods of wide applicability without taking them to their full generality. This book will equip students to follow quantum-mechanical arguments in books and scientific papers, and to cope with simple cases. To bring the subject to life, the theory is applied to the all-important field of atomic physics. No prior knowledge of quantum mechanics is assumed. However, it would help most readers to have met some elementary wave mechanics before. Primarily written for students, it should also be of interest to experimental research workers who require a good grasp of quantum mechanics without the full formalism needed by the professional theorist. Quantum Mechanics features: A flow diagram allowing topics to be studied in different orders or omitted altogether. Optional "starred" and highlighted sections containing more advanced and specialized material for the more ambitious reader. Sets of problems at the end of each chapter to help student understanding. Hints and solutions to the problems are given at the end of the book.

Mandl, F.

1992-07-01

15

Quantumness beyond quantum mechanics  

NASA Astrophysics Data System (ADS)

Bohmian mechanics allows us to understand quantum systems in the light of other quantum traits than the well-known ones (coherence, diffraction, interference, tunnelling, discreteness, entanglement, etc.). Here the discussion focusses precisely on two of these interesting aspects, which arise when quantum mechanics is thought within this theoretical framework: the non-crossing property, which allows for distinguishability without erasing interference patterns, and the possibility to define quantum probability tubes, along which the probability remains constant all the way. Furthermore, taking into account this hydrodynamic-like description as a link, it is also shown how this knowledge (concepts and ideas) can be straightforwardly transferred to other fields of physics (for example, the transmission of light along waveguides).

Sanz, Ángel S.

2012-05-01

16

Quantum mechanics made transparent  

NASA Astrophysics Data System (ADS)

This article is a ``sampler,'' which shows how quantum mechanics may be presented to students in a way that makes apparent how natural quantum mechanics is as a description of the world. The mathematical machinery of Hilbert space, the idea of representing observables by operators, the Schrödinger equation, and the position-momentum uncertainty relation all follow from natural assumptions that students can readily accept. The basic ideas of quantum mechanics are developed from intuitive first principles to the point where one can connect with more traditional treatments of quantum mechanics.

Henry, Richard C.

1990-11-01

17

How to Derive the Hilbert-Space Formulation of Quantum Mechanics From Purely Operational Axioms  

NASA Astrophysics Data System (ADS)

In the present paper I show how it is possible to derive the Hilbert space formulation of Quantum Mechanics from a comprehensive definition of physical experiment and assuming experimental accessibility and simplicity as specified by five simple Postulates. This accomplishes the program presented in form of conjectures in the previous paper. Pivotal roles are played by the local observability principle, which reconciles the holism of nonlocality with the reductionism of local observation, and by the postulated existence of informationally complete observables and of a symmetric faithful state. This last notion allows one to introduce an operational definition for the real version of the ``adjoint''-i. e. the transposition-from which one can derive a real Hilbert-space structure via either the Mackey-Kakutani or the Gelfand-Naimark-Segal constructions. Here I analyze in detail only the Gelfand-Naimark-Segal construction, which leads to a real Hilbert space structure analogous to that of (classes of generally unbounded) selfadjoint operators in Quantum Mechanics. For finite dimensions, general dimensionality theorems that can be derived from a local observability principle, allow us to represent the elements of the real Hilbert space as operators over an underlying complex Hilbert space (see, however, a still open problem at the end of the paper). The route for the present operational axiomatization was suggested by novel ideas originated from Quantum Tomography.

D'Ariano, Giacomo Mauro

2006-06-01

18

Invariant Eigen-Operator Method of Deriving Energy-Level Gap for Noncommutative Quantum Mechanics  

NASA Astrophysics Data System (ADS)

We propose a new method to derive energy-level gap for Hamiltonians in the context of noncommutative quantum mechanics (NCQM). This method relies on finding invariant eigen-operators whose commutators with Hamiltonian are still the operators themselves but with some eigenvalue-like coefficients, which correspond to the energy-level gaps of the systems. Based on this method, only after some simple algebra, we derive the energy-level gaps for several important systems in NCQM, and most of these results have not been reported in literature so far.

Jing, Si-Cong; Fan, Hong-Yi

19

On two-dimensional supersymmetric quantum mechanics, pseudoanalytic functions and transmutation operators  

NASA Astrophysics Data System (ADS)

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, the 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.

Bilodeau, Alex; Tremblay, Sébastien

2013-10-01

20

Reply to ‘Comment on “Overcoming misconceptions in quantum mechanics with the time evolution operator”’  

NASA Astrophysics Data System (ADS)

We contend that the statement attributing to us the implication that the wave functions ?I(x, t) and ?II(x, t) are different cannot not be logically supported. On the contrary, throughout our paper ‘Overcoming misconceptions in quantum mechanics with the time evolution operator’ (Garcia Quijas and Arévalo Aguilar 2007 Eur. J. Phys. 28 147) we constructed an argument to give support to the statement that the two wave functions ?I(x, t) and ?II(x, t) are the same. In other words, in our paper we really did appreciate that methods I and II lead to identical results.

Arévalo Aguilar, L. M.; García Quijas, P. C.

2013-07-01

21

quantum mechanics  

PubMed Central

-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.

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

2013-01-01

22

Comment on ‘Overcoming misconceptions in quantum mechanics with the time evolution operator  

NASA Astrophysics Data System (ADS)

In their paper ‘Overcoming misconceptions in quantum mechanics with the time evolution operator’, García Quijas and Arévalo Aguilar (2007 Eur. J. Phys. 28 147) examined the time-dependent wave function of a particle in the one-dimensional harmonic oscillator potential using two different methods. The two wave functions that the authors obtained through the methods have different analytical expressions. The authors showed numerically that the two wave functions lead to the same probability density. When the real parts of the wave functions are compared, however, they are different in their details. That was puzzling because both wave functions are supposed to be solutions of the same time-dependent Schrödinger equation with the same initial condition. We point out that the two wave functions are actually identical. We show this analytically.

Toyama, F. M.; Nogami, Y.

2013-07-01

23

Supersymmetry in quantum mechanics  

SciTech Connect

An elementary introduction is given to the subject of supersymmetry in quantum mechanics which can be understood and appreciated by any one who has taken a first course in quantum mechanics. We demonstrate with explicit examples that given a solvable problem in quantum mechanics with n bound states, one can construct n new exactly solvable Hamiltonians having n - 1, n - 2,..., 0 bound states. The relationship between the eigenvalues, eigenfunctions and scattering matrix of the supersymmetric partner potentials is derived and a class of reflectionless potentials are explicitly constructed. We extend the operator method of solving the one-dimensional harmonic oscillator problem to a class of potentials called shape-invariant potentials. It is worth emphasizing that this class includes almost all the solvable problems that are found in the standard text books on quantum mechanics. Further, we show that given any potential with at least one bound state, one can very easily construct one continuous parameter family of potentials having same eigenvalues and s-matrix. The supersymmetry inspired WKB approximation (SWKB) is also discussed and it is shown that unlike the usual WKB, the lowest order SWKB approximation is exact for the shape-invariant potentials and further, this approximation is not only exact for large quantum numbers but by construction, it is also exact for the ground state. Finally, we also construct new exactly solvable periodic potentials by using the machinery of supersymmetric quantum mechanics.

Khare, Avinash [Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, Orissa (India)

2004-12-23

24

Quantum-mechanical models in R n associated with extensions of the energy operator in a Pontryagin space  

Microsoft Academic Search

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

25

Quantum logic operations with  

Microsoft Academic Search

We describe a method of performing simple quantum logic operations with trapped ions that have not been cooled to their vibrational ground state. The scheme is based on D'Helon and Milburn's measurement model for the collective vibrational motion of N ions in a linear trap, which uses quantum computation and an interaction Hamiltonian of a special form to entangle the

Sara Schneider; Daniel F. V. James; Gerard J. Milburn

1998-01-01

26

Schmidt number for quantum operations  

SciTech Connect

To understand how entangled states behave under local quantum operations is an open problem in quantum-information theory. The Jamiolkowski isomorphism provides a natural way to study this problem in terms of quantum states. We introduce the Schmidt number for quantum operations by this duality and clarify how the Schmidt number of a quantum state changes under a local quantum operation. Some characterizations of quantum operations with Schmidt number k are also provided.

Huang Siendong [Department of Applied Mathematics, National Dong Hwa University, Hualien 974, Taiwan (China)

2006-05-15

27

Quantum cosmology and quantum mechanics.  

NASA Astrophysics Data System (ADS)

The interpretative framework of quantum mechanics loosely subsumed under the name "Copenhagen interpretation" contains two central assumptions which seem incompatible with a quantum cosmology built on a covariant quantum theory of spacetime. The first is a distinguished class of classical systems. The second is a distinguished time variable and its associated notion of causality. The first assumption is incompatible with the uniform application of quantum mechanics to the universe as a whole. The second is incompatible with the general covariance of gravitational theory. This paper explores the possibility that both of these distinguished features of our world arise, not as special features of the formalism of quantum mechanics, but rather as consequences of specific initial conditions for cosmology.

Hartle, J. B.

28

Quantum mechanics and symmetries  

Microsoft Academic Search

Symmetries have always played an important role in physics. With quantum mechanics, however, the interplay between physics and symmetries has reached a new dimension. The very structure of quantum mechanics invites the application of group theoretical methods to an extent that physicists would have been led to invent various concepts of group theory, such as Lie groups, by quantum mechanics

J. Wess

2000-01-01

29

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

30

Analytical and self-consistent quantum mechanical model for a surrounding gate MOS nanowire operated in JFET mode  

Microsoft Academic Search

We derive an analytical model for the electrostatics and the drive current in a silicon nanowire operating in JFET mode. We\\u000a show that there exists a range of nanowire radii and doping densities for which the nanowire JFET satisfies reasonable device\\u000a characteristics. For thin nanowires we have developed a self-consistent quantum mechanical model to obtain the electronic\\u000a structure.

Bart Sorée; Wim Magnus; Geoffrey Pourtois

2008-01-01

31

Introduction to Quantum Mechanics  

Microsoft Academic Search

Discussed here is the mathematics of quantum mechanics at an introductory level. Hilbert spaces, the Bra-Ket notation, Fourier Transforms, the Schrodinger Wave Equation, and Quantum Computing are covered.

ROHIT TRIPATHI

1945-01-01

32

Introduction to Quantum Mechanics  

NSDL National Science Digital Library

This text is intended for junior/senior Quantum Mechanics courses. It covers the fundamentals of quantum theory in a concise manner, covering topics from the basic formalism through perturbation theory, the adiabatic approximation, and scattering.

Griffiths, David J.

2005-04-16

33

SENSIBLE QUANTUM MECHANICS: ARE ONLY PERCEPTIONS  

Microsoft Academic Search

Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so that it contains nothing probabilistic, except, in a certain frequency sense, conscious perceptions. Sets of these perceptions can be deterministi- cally realized with measures given by expectation values of positive-operator- valued awareness operators in a quantum state of the universe which never jumps or collapses. Ratios of the measures

Don N. Page

34

Operational interpretations of quantum discord  

SciTech Connect

Quantum discord quantifies nonclassical correlations beyond the standard classification of quantum states into entangled and unentangled. Although it has received considerable attention, it still lacks any precise interpretation in terms of some protocol in which quantum features are relevant. Here we give quantum discord its first information-theoretic operational meaning in terms of entanglement consumption in an extended quantum-state-merging protocol. We further relate the asymmetry of quantum discord with the performance imbalance in quantum state merging and dense coding.

Cavalcanti, D.; Modi, K. [Centre for Quantum Technologies, National University of Singapore, Singapore 117542 (Singapore); Aolita, L. [ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona) (Spain); Boixo, S. [Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States); Piani, M. [Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Winter, A. [Centre for Quantum Technologies, National University of Singapore, Singapore 117542 (Singapore); Department of Mathematics, University of Bristol, Bristol BS8 1TW (United Kingdom)

2011-03-15

35

Ph 125 Quantum Mechanics  

NSDL National Science Digital Library

This web site contains resources for a comprehensive quantum mechanics course designed for graduate and advanced undergraduate students at Cal Tech. The course has been revised to include quantum information science, and prepares students for a course in quantum computation. Lecture notes, a syllabus, homework problems with solutions, and exam solutions are available.

Mabuchi, Hideo

2011-01-21

36

Ph 125 Quantum Mechanics  

NSDL National Science Digital Library

This web site contains resources for a comprehensive quantum mechanics course designed for graduate and advanced undergraduate students at Cal Tech. The course has been revised to include quantum information science, and prepares students for a course in quantum computation. Lecture notes, a syllabus, homework problems with solutions, and exam solutions are available.

Mabuchi, Hideo

2005-12-05

37

Quantum mechanics: Entanglement goes mechanical  

Microsoft Academic Search

A neat experiment shows that the mechanical vibration of two ion pairs separated by a few hundred micrometres is entangled - their motions are intrinsically and inseparably connected in a quantum way.

Rainer Blatt

2009-01-01

38

Quantum Mechanics from Classical Logic  

NASA Astrophysics Data System (ADS)

Although quantum mechanics is generally considered to be fundamentally incompatible with classical logic, it is argued here that the gap is not as great as it seems. Any classical, discrete, time reversible system can be naturally described using a quantum Hubert space, operators, and a Schrödinger equation. The quantum states generated this way resemble the ones in the real world so much that one wonders why this could not be used to interpret all of quantum mechanics this way. Indeed, such an interpretation leads to the most natural explanation as to why a wave function appears to "collapse" when a measurement is made, and why probabilities obey the Born rule. Because it is real quantum mechanics that we generate, Bell's inequalities should not be an obstacle.

't Hooft, Gerard

2012-05-01

39

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

40

Quantum mechanics from classical statistics  

SciTech Connect

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.

Wetterich, C. [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)], E-mail: c.wetterich@thphys.uni-heidelberg.de

2010-04-15

41

Trojan wavepackets in quantum mechanics equivalent to classical mechanics  

NASA Astrophysics Data System (ADS)

We formulate the theory of wavepackets moving on classical circular orbits in Hydrogen atom in rotating electromagnetic wave within the quantum mechanics equivalent to classical mechanics [1]. Unlike within the true quantum mechanics the wavepackets spreads during the time comparable with the time of full quantum revival within true quantum mechanics. Numerical solutions of the nonlinear Schrodingers equation are provided using non-linear split operator method for this equation. [1] D. Shay, Phys. Rev A, 13, 2261 (1976).

Kalinski, Matt

2005-05-01

42

Extending quantum operations  

NASA Astrophysics Data System (ADS)

For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on quantum states are trace-preserving completely positive maps, but we also consider variants of these requirements. We generalize the definition of complete positivity to linear maps defined on arbitrary subspaces, then formulate this notion as a semidefinite program, and relate it by duality to approximative extensions of this map. This gives a characterization of the maps which can be approximated arbitrarily well as the restriction of a map that is completely positive on the whole algebra, also yielding the familiar extension theorems on operator spaces. For quantum channel extensions and extensions by probabilistic operations we obtain semidefinite characterizations, and we also elucidate the special case of Abelian inputs or outputs. Finally, revisiting a theorem by Alberti and Uhlmann, we provide simpler and more widely applicable conditions for certain extension problems on qubits, and by using a semidefinite programming formulation we exhibit counterexamples to seemingly reasonable but false generalizations of the Alberti-Uhlmann theorem.

Heinosaari, Teiko; Jivulescu, Maria A.; Reeb, David; Wolf, Michael M.

2012-10-01

43

Extending quantum operations  

SciTech Connect

For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on quantum states are trace-preserving completely positive maps, but we also consider variants of these requirements. We generalize the definition of complete positivity to linear maps defined on arbitrary subspaces, then formulate this notion as a semidefinite program, and relate it by duality to approximative extensions of this map. This gives a characterization of the maps which can be approximated arbitrarily well as the restriction of a map that is completely positive on the whole algebra, also yielding the familiar extension theorems on operator spaces. For quantum channel extensions and extensions by probabilistic operations we obtain semidefinite characterizations, and we also elucidate the special case of Abelian inputs or outputs. Finally, revisiting a theorem by Alberti and Uhlmann, we provide simpler and more widely applicable conditions for certain extension problems on qubits, and by using a semidefinite programming formulation we exhibit counterexamples to seemingly reasonable but false generalizations of the Alberti-Uhlmann theorem.

Heinosaari, Teiko [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku (Finland); Jivulescu, Maria A. [Department of Mathematics, University Politehnica Timisoara, 300006 Timisoara (Romania); Reeb, David; Wolf, Michael M. [Department of Mathematics, Technische Universitaet Muenchen, 85748 Garching (Germany)

2012-10-15

44

Quantum Mechanics Conceptual Survey  

NSDL National Science Digital Library

This web page is the home for the Quantum Mechanics Conceptual Survey (QMCS). The goal of this assessment is to provide an accurate measure of students' understanding of fundamental concepts in quantum mechanics. The QMCS is inspired by the many carefully researched and validated tests of conceptual understanding in physics. The authors developed the questions to be independent of notation unique to a specific course and avoiding jargon as much as possible. The questions in the QMCS are based on faculty interviews, textbooks and syllabi, existing assessments, research on student misconceptions in quantum mechanics, and student observations.

Mckagan, Sarah B.

2011-06-28

45

Is quantum mechanics exact?  

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

46

Visual Quantum Mechanics  

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

47

Graduate quantum mechanics reform  

NASA Astrophysics Data System (ADS)

We address four main areas in which graduate quantum mechanics education can be improved: course content, textbook, teaching methods, and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all these areas. In particular, we have modified the content of the course to reflect progress in the field of quantum mechanics over the last 50 years, used textbooks that include such content, incorporated a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey. We find that graduate students respond well to research-based techniques that have been tested mainly in introductory courses, and that they learn much of the new content introduced in each version of the course. We also find that students' ability to answer conceptual questions about graduate quantum mechanics is highly correlated with their ability to solve calculational problems on the same topics. In contrast, we find that students' understanding of basic undergraduate quantum mechanics concepts at the modern physics level is not improved by instruction at the graduate level.

Carr, L. D.; McKagan, S. B.

2009-04-01

48

Variational methods in relativistic quantum mechanics  

Microsoft Academic Search

This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to the Laplacian appearing in the equations of nonrelativistic quantum mechanics, the Dirac operator has a negative continuous spectrum which is not bounded from below.

Maria J. Esteban; Mathieu Lewin; Eric séré

2007-01-01

49

Physlets for Quantum Mechanics  

NSDL National Science Digital Library

This article presents the use of Physlet-based questions with proven pedagogical techniques to improve student conceptual understanding. Physlet problems are used in a Just-in-Time-Teaching approach. Most examples are from a senior level quantum mechanics class, although examples in introductory mechanics are also shown. Results of pre/post testing using the Quantum Mechanics Visualization Instrument (QMVI) show significant gain in understanding. Comparison is made with other QMVI results from undergraduate and graduate students. This article was cited as the best education article in the journal Computers in Science and Engineering for the American Institute of Physics' 75th anniversary. This citation is given below under Annotations.

Belloni, Mario; Christian, Wolfgang

2006-08-02

50

Self-Referential Quantum Mechanics  

NASA Astrophysics Data System (ADS)

A nonlinear quantum mechanics based upon the nonlinear logarithmic Schrodinger equation, is developed which has the property of self-reference, that is, the nonlinear term is dependent upon the square of the wavefunction. The self-referential system is examined in terms of its mathematical properties, the definition of the wavefunction, and the nonlinear system in the feedback between equation and solution. Theta operators are introduced which make possible new operations in the quantum phase. Two interpretations are presented utilizing the nonlinear quantum system: the idealistic interpretation based upon consciousness focused upon the measurement problem, and the statistical interpretation focused upon stochastic quantum fluctuations. Experimental properties are examined, beginning with a proposed analog of the Bohm-Aharonov experiment. Interference due to difference in path length for a split electron beam is effected in a region of spacetime where electromagnetic field and the vector potential are enclosed within but screened to be zero at the paths. If the wavefunction's geometrical phase contribution along the paths is different, then there should be interference induced purely by the wave-function alone. A positive result would be due to a purely wavefunction dependent effect. The spin phase of the wavefunction is postulated to be the source of the zitterbewegung of the electron. Reduction of the wavefunction in measurement is examined for self -referential quantum systems arising from consciousness and then arising from a stochastic quantum spacetime model. These results are applied to the mind-brain as a quantum processor producing a behavioral double slit experiment (ideation experiments) and nonlocal transferred potentials in an EPR-style experiment. Looking at the universe as a whole as a quantum self-referential system, leads to a modified zitterbewegung Wheeler-DeWitt equation; and, the transition from quantum-to-classical on a cosmological scale for the measurement problem is accomplished for an expanding-only deSitter quantum spacetime.

Mitchell, Mark Kenneth

1993-01-01

51

Visual Quantum Mechanics  

NSDL National Science Digital Library

The Kansas State University Visual Quantum Mechanics project is developing instructional materials about quantum physics for high school and college students. Instructional units and/or courses are being created for high school and college non-science students, pre-medical and biology students, and science and engineering majors. Each set of the teaching-learning materials integrates interactive visualizations with inexpensive materials and written documents in an activity-based environment.

Group, Kansas S.; Zollman, Dean A.

2003-10-10

52

The parity operator in quantum optical metrology  

Microsoft Academic Search

Photon number states are assigned a parity of if their photon number is even and a parity of if odd. The parity operator, which is minus one to the power of the photon number operator, is a Hermitian operator and thus a quantum mechanical observable though it has no classical analog, the concept being meaningless in the context of classical

Christopher C. Gerry; Jihane Mimih

2010-01-01

53

Decoherence in quantum mechanics  

SciTech Connect

Research Highlights: > We study decoherence in a simple quantum mechanical model using two approaches. > Following the conventional approach to decoherence we solve the master equation. > We also consider our novel correlator approach to decoherence. > The system's total entropy increase cannot reliably be calculated in the conventional approach. > This does follow correctly from our correlator approach. - Abstract: We study decoherence in a simple quantum mechanical model using two approaches. Firstly, we follow the conventional approach to decoherence where one is interested in solving the reduced density matrix from the perturbative master equation. Secondly, we consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. We show that both methods can accurately predict decoherence time scales. However, the perturbative master equation generically suffers from instabilities which prevents us to reliably calculate the system's total entropy increase. We also discuss the relevance of the results in our quantum mechanical model for interacting field theories.

Koksma, Jurjen F., E-mail: J.F.Koksma@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); Prokopec, Tomislav, E-mail: T.Prokopec@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); Schmidt, Michael G., E-mail: M.G.Schmidt@thphys.uni-heidelberg.de [Institut fuer Theoretische Physik, Heidelberg University, Philosophenweg 16, D-69120 Heidelberg (Germany)

2011-06-15

54

Eigenvalue problem for bundle of operators and the sturm expansion method in quantum mechanics  

NASA Astrophysics Data System (ADS)

Different variants of the generalized formulation of the eigenvalue problem related to a single-particle Schrödinger equation are considered. The nature of the spectrum of problems for a bundle of operators containing the Hamiltonian of the system is analyzed in relation to the form of the weighting operator. For rather general conditions, corresponding systems of eigenfunctions provide diagonal representations of the Green’s function and provide of a rather fast convergence of expansions over intermediate states. Cases of potentials with Coulomb asymptotics and short-range potentials are considered.

Nikitin, S. I.; Sherstyuk, A. I.

2009-04-01

55

Visual Quantum Mechanics  

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

56

Noncommutative quantum mechanics  

NASA Astrophysics Data System (ADS)

A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter ?, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of ? the model can be solved by using perturbation theory.

Gamboa, J.; Loewe, M.; Rojas, J. C.

2001-09-01

57

Superposition and quantum mechanics  

SciTech Connect

This work is primarily concerned with finding those statements or observations from which quantum mechanics can reasonably be said to follow. Within the context of characterizing quantum mechanics as any probability field (with bounded probability density) whose associated stochastic velocity field is governed by a differential equation of first order in time, it is shown that the single statement required is the stipulation that the superposition principle is satisfied. This is demonstrated by showing that only the Schrodinger equation is an acceptable dynamic description for such probability fields if the superposition principle is to hold.

Cohn, J.

1986-08-01

58

Time Asymmetric Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width ? and exponentially decaying states of lifetime ?=h/? should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t0?tquantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.

Bohm, Arno R.; Gadella, Manuel; Kielanowski, Piotr

2011-09-01

59

Bohmian mechanics and quantum field theory.  

PubMed

We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end. PMID:15447078

Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino

2004-08-23

60

Quantum phase and quantum phase operators: some physics and some history  

Microsoft Academic Search

After reviewing the role of phase in quantum mechanics, I discuss, with the aid of a number of unpublished documents, the development of quantum phase operators in the 1960's. Interwoven in the discussion are the critical physics questions of the field: are there (unique) quantum phase operators and are there quantum systems which can determine their nature? I conclude with

Michael Martin Nieto

1993-01-01

61

Quantum Zeno effect of general quantum operations  

NASA Astrophysics Data System (ADS)

In this paper, we show that the quantum Zeno effect can occur for generalized quantum measurements or operations. As a consequence of frequently performing nonselective measurements (or trace-preserving completely positive maps), the evolution of a certain measurement-invariant state is governed by an effective Hamiltonian defined by the measurement (or map) and the free-evolution Hamiltonian. For selective measurements, the state may change randomly with time according to measurement outcomes, but some physical quantities (operators) still evolve according to the effective Hamiltonian.

Li, Ying; Herrera-Martí, David A.; Kwek, Leong Chuan

2013-10-01

62

Quantum Mechanics, Locality and Realism.  

National Technical Information Service (NTIS)

We show that the concept of locality is independent of the postulates of quantum mechanics. In particular, we show that under the assumption that nature is local, the quantum-mechanical predictions concerning experiments on correlated systems satisfy Bell...

J. W. de Roever M. Streng

1993-01-01

63

Introduction to Biological Quantum Mechanics.  

National Technical Information Service (NTIS)

There are observables and eigenstates in biology as well as in physical quantum mechanics. Furthermore, the basic principle of quantum mechanics that 'measurement of an observable of a physical system will find the system in an eigenstate of the observabl...

S. Goldman

1969-01-01

64

Holistic Aspects of Quantum Mechanics.  

National Technical Information Service (NTIS)

Aspects of quantum mechanics irreconcilable with classical physics are outlined. Quantum mechanics started with a negative statement about reality, namely: it is impossible to determine momentum and position of a particle simultaneously. Meanwhile it has ...

H. Pietschmann

1987-01-01

65

Fidelity balance in quantum operations.  

PubMed

I derive a tight bound between the quality of estimating the state of a single copy of a d-level system, and the degree the initial state has to be altered in the course of this procedure. This result provides a complete analytical description of the quantum mechanical trade-off between the information gain and the quantum state disturbance expressed in terms of mean fidelities. I also discuss consequences of this bound for quantum teleportation using nonmaximally entangled states. PMID:11178085

Banaszek, K

2001-02-12

66

Entanglement and collective quantum operations  

Microsoft Academic Search

We show how shared entanglement, together with classical communication and local quantum operations, can be used to perform an arbitrary collective quantum operation upon N spatially-separated qubits. A simple teleportation-based protocol for achieving this, which requires 2(N?1) ebits of shared, bipartite entanglement and 4(N?1) classical bits, is proposed. In terms of the total required entanglement, this protocol is shown to

Anthony Chefles; Claire R. Gilson; Stephen M. Barnett

2000-01-01

67

Entanglement and collective quantum operations  

Microsoft Academic Search

We show how shared entanglement, together with classical communication and local quantum operations, can be used to perform an arbitrary collective quantum operation upon \\/N spatially-separated qubits. A simple teleportation-based protocol for achieving this, which requires \\/2(N-1) ebits of shared, bipartite entanglement and \\/4(N-1) classical bits, is proposed. In terms of the total required entanglement, this protocol is shown to

A. Chefles; C. R. Gilson; S. M. Barnett

2000-01-01

68

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

69

Attaching Theories of Consciousness to Bohmian Quantum Mechanics  

Microsoft Academic Search

The de Broglie-Bohm theory of quantum mechanics (here simply called Bohmian Mechanics or BM) [1-10] is an augmentation of ``bare'' quantum mechanics (the bare theory being given by an algebra of operators and a quantum state that sets the expectation values of these operators) that includes a definite history or Bohmian trajectory. This definite trajectory gives BM a somewhat more

Don N. Page

1995-01-01

70

Logical foundation of quantum mechanics  

Microsoft Academic Search

The subject of this article is the reconstruction of quantum mechanics on the basis of a formal language of quantum mechanical propositions. During recent years, research in the foundations of the language of science has given rise to adialogic semantics that is adequate in the case of a formal language for quantum physics. The system ofsequential logic which is comprised

E. W. Stachow; Theoretische Physik

1980-01-01

71

Newton Leibniz integration for ket bra operators in quantum mechanics (IV)—Integrations within Weyl ordered product of operators and their applications  

NASA Astrophysics Data System (ADS)

We show that the technique of integration within normal ordering of operators [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480 494] applied to tackling Newton Leibniz integration over ket bra projection operators, can be generalized to the technique of integration within Weyl ordered product (IWWOP) of operators. The Weyl ordering symbol ? is introduced to find the Wigner operator’s Weyl ordering form ?(p,q) = ? ?(p - P)?(q - Q) ?, and to find operators’ Weyl ordered expansion formula. A remarkable property is that Weyl ordering of operators is covariant under similarity transformation, so it has many applications in quantum statistics and signal analysis. Thus the invention of the IWWOP technique promotes the progress of Dirac’s symbolic method.

Fan, Hong-Yi

2008-02-01

72

Reality Problem in Quantum Mechanics.  

National Technical Information Service (NTIS)

A series of 12 lectures on quantum mechanics and its interpretations: The more specific part begins with chapter 8: spin and polarization measurements; the Einstein-Podolski-Rosen paradox; interpretations of quantum theory; the role of the observer and th...

D. Flamm

1988-01-01

73

Algorithms Speedup From Quantum Mechanics.  

National Technical Information Service (NTIS)

This project was concerned primarily with one central theme which is the attempt to use quantum mechanics to design algorithms that perform better than conventional (non-quantum) algorithms for solving certain problems. We looked at a variety of approache...

E. Farhi J. Goldstone

2005-01-01

74

Realist model approach to quantum mechanics  

NASA Astrophysics Data System (ADS)

The paper proves that quantum mechanics is compatible with the constructive realism of modern philosophy of science. The proof is based on the observation that properties of quantum systems that are uniquely determined by their preparations can be assumed objective without the difficulties that are encountered by the same assumption about values of observables. The resulting realist interpretation of quantum mechanics is made rigorous by studying the space of quantum states—the convex set of state operators. Prepared states are classified according to their statistical structure into indecomposable and decomposable instead of pure and mixed. Simple objective properties are defined and showed to form a Boolean lattice.

Hájí?ek, P.

2013-06-01

75

Stochastic mechanics and quantum theory  

Microsoft Academic Search

Stochastic mechanics may be regarded as both generalizing classical mechanics to processes with intrinsic randomness, as well as providing the sort of detailed description of microscopic events declared impossible under the traditional interpretation of quantum mechanics. It avoids the many conceptual difficulties which arise from the assumption that quantum mechanics, i.e., the wave function, provides a complete description of (microscopic)

Sheldon Goldstein

1987-01-01

76

Gravitomagnetism in quantum mechanics  

SciTech Connect

We give a systematic treatment of the quantum mechanics of a spin zero particle in a combined electromagnetic field and a weak gravitational field that is produced by a slow moving matter source. The analysis is based on the Klein-Gordon equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The Klein-Gordon equation is recast into Schroedinger equation form, which we then analyze in the nonrelativistic limit. We include a discussion of some rather general observable physical effects implied by the Schroedinger equation form, concentrating on gravitomagnetism. Of particular interest is the interaction of the orbital angular momentum of the particle with the gravitomagnetic field.

Adler, Ronald J.; Chen Pisin [Gravity Probe B, Hansen Laboratory for Experimental Physics, Stanford University, Stanford California 94309 (United States); Leung Center for Cosmology and Particle Astrophysics and Department of Physics and Graduate Institute of Astrophysics, National Taiwan University, Taipei, Taiwan 10617 and Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Menlo Park, California 94025 (United States)

2010-07-15

77

Supersymmetric Quantum Mechanics  

SciTech Connect

Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulae concerning SUSY QM of first second order for one-dimensional arbitrary systems, we will illustrate the method through the trigonometric Poeschl-Teller potentials. Some intrinsically related subjects, as the algebraic structure inherited by the new Hamiltonians and the corresponding coherent states will be analyzed. The technique will be as well implemented for periodic potentials, for which the corresponding spectrum is composed of allowed bands separated by energy gaps.

David, J.; Fernandez, C. [Depto. de Fisica, Cinvestav, A.P. 14-740, 07000 Mexico D.F. (Mexico)

2010-10-11

78

Thermalization Processes in Quantum Mechanics  

NASA Astrophysics Data System (ADS)

In quantum mechanics, the emergence of thermalization processes from unitary evolution has remained one of the greatest challenges. The two outstanding theories of this issue by Srednicki and Tasaki cannot address the concepts of temperature, heat, and work. Here, we present a theory using multiple quenches to examine the thermalization processes to advance thermodynamics concepts. To perform multiple quenches, one can vary one single control parameter (?) in a series of time evolutions, which create a set of density operators. The average of these density operators results into a diagonal operator with probability distribution function that can describe the emerging ensembles. Measuring probability distribution functions of key physical observables, temperature, equal to the derivative of energy with respect to entropy, can be easily measured. Therefore, simulations via multiple quenches can mimic dynamics in open quantum systems with much cheaper computational cost. They allow (1) tuning of temperature and entropy via ?, (2) measuring work distribution functions from distributions of a reaction coordinate, and (3) computing free-energy changes via Jarzynski's Equality. We hope that this approach can provide a new foundation and open up new directions for studying control of quantum systems.

Ngo, Van; Haas, Stephan

2013-03-01

79

Quantum Mechanics in Terms of Symmetric Measurements  

NASA Astrophysics Data System (ADS)

In the neo-Bayesian view of quantum mechanics that Appleby, Caves, Pitowsky, Schack, the author, and others are developing, quantum states are taken to be compendia of partial beliefs about potential measurement outcomes, rather than objective properties of quantum systems. Different observers may validly have different quantum states for a single system, and the ultimate origin of each individual state assignment is taken to be unanalyzable within physical theory---its origin, instead, comes from prior probability assignments at stages of physical investigation or laboratory practice previous to quantum theory. The objective content of quantum mechanics thus resides somewhere else than in the quantum state, and various ideas for where that ``somewhere else'' is are presently under debate. What is overwhelmingly agreed upon in this effort is only the opening statement. Still, quantum states are not Bayesian probability assignments themselves, and different representations of the theory (in terms of state vectors or Wigner functions or C*-algebras, etc.) can take one further from or closer to a Bayesian point of view. It is thus worthwhile thinking about which representation might be the most propitious for the point of view and might quell some of the remaining debate. In this talk, I will present several results regarding a representation of quantum mechanics in terms of symmetric bases of positive-semidefinite operators. I also argue why this is probably the most natural representation for a Bayesian-style quantum mechanics.

Fuchs, Christopher

2006-03-01

80

Crypto-Unitary Forms of Quantum Evolution Operators  

NASA Astrophysics Data System (ADS)

The description of quantum evolution using unitary operator {u}(t)=exp(-i{h}t) requires that the underlying self-adjoint quantum Hamiltonian {h} remains time-independent. In a way extending the so called {PT}-symmetric quantum mechanics to the models with manifestly time-dependent "charge" {C}(t) we propose and describe an extension of such an exponential-operator approach to evolution to the manifestly time-dependent self-adjoint quantum Hamiltonians {h}(t).

Znojil, Miloslav

2013-06-01

81

Quantum Mechanics as Dualism  

NASA Astrophysics Data System (ADS)

I do not agree with mind-body dualism. Today the consensus view is that thought and mind is a combination of processes like memory, generalization, comparison, deduction, organization, induction, classification, feature detection, analogy, etc. performed by computational machinery. (R. Jones, Trans. of the Kansas Acad. Sci., vol. 109, # 3/4, 2006 and www.robert-w-jones.com, philosopher, theory of thought) But I believe that quantum mechanics is a more plausible dualist theory of reality. The quantum mechanical wave function is nonphysical, it exists in a 3N space (for an N body system) not in (x,y,z,t) 4-space, and does not possess physical properties. But real physical things like energy (which do exist in our 4-space world) influence the wave function and the wave function, in its turn, influences real physical things, like where a particle can be found in 4-space. The coupling between the spirit-like wave function and things found in the real (4-space) world (like energy) is via mathematical equations like the Schrodinger equation and Born normalization.

Jones, Robert

2011-03-01

82

Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime  

Microsoft Academic Search

These are the author's lectures at the 1992 Les Houches Summer School,\\u000a``Gravitation and Quantizations''. They develop a generalized\\u000asum-over-histories quantum mechanics for quantum cosmology that does not\\u000arequire either a preferred notion of time or a definition of measurement. The\\u000a``post-Everett'' quantum mechanics of closed systems is reviewed. Generalized\\u000aquantum theories are defined by three elements (1) the set

James B. Hartle

1993-01-01

83

SEI: Quantum Mechanics I Course Materials  

NSDL National Science Digital Library

This web site provides research-based materials for junior-level quantum mechanics I courses on quantum mechanics. Topics covered include the Schroedinger equation, bound state problems, Hilbert space and operators, the hydrogen atom, and spin. The course archives include documented student difficulties, learning goals, ConcepTests (clicker questions), class activities, homework, tutorials, and a conceptual assessment tool. All may be downloaded, although the assessment tools require permission from the authors for access.

Goldhaber, Steve; Pollock, Steven J.

2010-01-29

84

Entangled state representations in noncommutative quantum mechanics  

Microsoft Academic Search

We introduce new representations to formulate quantum mechanics on\\u000anoncommutative coordinate space, which explicitly display entanglement\\u000aproperties between degrees of freedom of different coordinate components and\\u000ahence could be called entangled state representations. Furthermore, we derive\\u000aunitary transformations between the new representations and the ordinary one\\u000aused in noncommutative quantum mechanics (NCQM) and obtain eigenfunctions of\\u000asome basic operators in

Sicong Jing; Qiu-Yu Liu; Hongyi Fan

2005-01-01

85

OPERATIONAL PATTERNS IN QUANTUM STATES  

Microsoft Academic Search

A major issue for modern physics is how reality in terms of general relativity may emerge from quantum mechanics. Two observations motivate this paper: 1) General relativity (GR) with Einstein's Field equation is highly recursive in how it is formulated. The energy distribution determines spacetime geometry and vice versa spacetime geometry determines local trajectories and the evolution of the mass-energy

SIEGFRIED GENREITH

86

Quantum-Mechanical Dualities on the Torus  

NASA Astrophysics Data System (ADS)

On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal, i.e. independent of the observer on classical phase space. Such is the case in all standard applications of quantum mechanics. However, recent developments suggest that the notion of a quantum may not be universal. Transformations between observers that do not agree on the notion of an elementary quantum are called dualities. Classical phase spaces admitting more than one complex-differentiable structure thus provide a natural framework to study dualities in quantum mechanics. As an example we quantise a classical mechanics whose phase space is a torus and prove explicitly that it exhibits dualities.

Isidro, José M.

87

Nonlocality, counterfactuals, and quantum mechanics  

NASA Astrophysics Data System (ADS)

Stapp [Am. J. Phys. 65, 300 (1997)] has recently argued from a version of the Hardy-type experiments that quantum mechanics must be nonlocal, independent of any additional assumptions such as realism or hidden variables. I argue either that his conclusions do not follow from his assumptions or that his assumptions are not true of quantum mechanics and can be interpreted as assigning an unwarranted level of reality to the value of certain quantum attributes.

Unruh, W.

1999-01-01

88

The emergence of quantum mechanics  

NASA Astrophysics Data System (ADS)

It is pointed out that a mathematical relation exists between cellular automata and quantum field theories. Although the proofs are far from perfect, they do suggest a new look at the origin of quantum mechanics: quantum mechanics may be nothing but a natural way to handle the statistical correlations of a cellular automaton. An essential role for the gravitational force in these considerations is suspected.

't Hooft, Gerard

2012-06-01

89

Reversible quantum operations and their application to teleportation  

Microsoft Academic Search

Quantum operations provide a general description of the state changes allowed\\u000aby quantum mechanics. Simple necessary and sufficient conditions for an ideal\\u000aquantum operation to be reversible by a unitary operation are derived in this\\u000apaper. These results generalize recent work on reversible measurements by\\u000aMabuchi and Zoller [Phys. Rev. Lett. {\\\\bf 76}, 3108 (1996)]. Quantum\\u000ateleportation can be understood

M. A. Nielsen; Carlton M. Caves

1997-01-01

90

Probability Interpretation of Quantum Mechanics.  

ERIC Educational Resources Information Center

This paper draws attention to the frequency meaning of the probability concept and its implications for quantum mechanics. It emphasizes that the very meaning of probability implies the ensemble interpretation of both pure and mixed states. As a result some of the "paradoxical" aspects of quantum mechanics lose their counterintuitive character.…

Newton, Roger G.

1980-01-01

91

Quantum mechanics of cluster melting  

SciTech Connect

We present here prototype studies of the effects of quantum mechanics on the melting of clusters. Using equilibrium path integral methods, we examine the melting transition for small rare gas clusters. Argon and neon clusters are considered. We find the quantum-mechanical effects on the melting and coexistence properties of small neon clusters to be appreciable.

Beck, T.L.; Doll, J.D.; Freeman, D.L.

1989-05-15

92

Tensorial description of quantum mechanics  

NASA Astrophysics Data System (ADS)

Relevant algebraic structures for the description of quantum mechanics in the Heisenberg picture are replaced by tensor fields on the space of states. This replacement introduces a differential geometric point of view which allows for a covariant formulation of quantum mechanics under the full diffeomorphism group.

Clemente-Gallardo, J.; Marmo, G.

2013-03-01

93

Graph reconstruction and quantum statistical mechanics  

NASA Astrophysics Data System (ADS)

We study how far it is possible to reconstruct a graph from various Banach algebras associated to its universal covering, and extensions thereof to quantum statistical mechanical systems. It turns out that most the boundary operator algebras reconstruct only topological information, but the statistical mechanical point of view allows for complete reconstruction of multigraphs with minimal degree three.

Cornelissen, Gunther; Marcolli, Matilde

2013-10-01

94

Multiverse interpretation of quantum mechanics  

NASA Astrophysics Data System (ADS)

We argue that the many worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics. Decoherence—the modern version of wave-function collapse—is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the environment. In fact decoherence is absent in the complete description of any region larger than the future light cone of a measurement event. However, if one restricts to the causal diamond—the largest region that can be causally probed—then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment. We argue that the global multiverse is a representation of the many worlds (all possible decoherent causal diamond histories) in a single geometry. We propose that it must be possible in principle to verify quantum-mechanical predictions exactly. This requires not only the existence of exact observables but two additional postulates: a single observer within the Universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite. In causal diamonds with a finite surface area, holographic entropy bounds imply that no exact observables exist, and both postulates fail: experiments cannot be repeated infinitely many times; and decoherence is not completely irreversible, so outcomes are not definite. We argue that our postulates can be satisfied in hats (supersymmetric multiverse regions with vanishing cosmological constant). We propose a complementarity principle that relates the approximate observables associated with finite causal diamonds to exact observables in the hat.

Bousso, Raphael; Susskind, Leonard

2012-02-01

95

Quantum secret sharing schemes and reversibility of quantum operations  

SciTech Connect

Quantum secret sharing schemes encrypting a quantum state into a multipartite entangled state are treated. The lower bound on the dimension of each share given by Gottesman [Phys. Rev. A 61, 042311 (2000)] is revisited based on a relation between the reversibility of quantum operations and the Holevo information. We also propose a threshold ramp quantum secret sharing scheme and evaluate its coding efficiency.

Ogawa, Tomohiro [Graduate School of Information Science and Technology, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656 (Japan); Sasaki, Akira [Sumitomo Mitsui Banking Corporation, 1-3-2, Marunouchi, Chiyoda-ku, Tokyo 100-0005 (Japan); Iwamoto, Mitsugu [Graduate School of Information Systems, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo, 182-8585 (Japan); Yamamoto, Hirosuke [Graduate School of Frontier Sciences, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba, 277-8561 (Japan)

2005-09-15

96

Electrical bistabilities and operating mechanisms of memory devices fabricated utilizing ZnO quantum dot-multi-walled carbon nanotube nanocomposites.  

PubMed

Transmission electron microscopy images showed that the ZnO quantum dots (QDs) were conjugated with multi-walled carbon nanotubes (MWCNTs). Bistable memories utilizing an ensemble of the ZnO QD-MWCNT heterostructures were developed and the storage capability of the devices was significantly enhanced due to the conjugation of the ZnO QDs and the MWCNTs. Operating mechanisms of memory devices fabricated utilizing the ZnO QD-MWCNT heterostructures are described on the basis of the current-voltage results. The memory devices exhibited excellent environmental stability at ambient conditions. PMID:19420606

Li, Fushan; Son, Dong Ick; Cho, Sung Hwan; Kim, Tae Whan

2009-04-14

97

Newton Leibniz integration for ket-bra operators in quantum mechanics (V)—Deriving normally ordered bivariate-normal-distribution form of density operators and developing their phase space formalism  

NASA Astrophysics Data System (ADS)

We show that Newton Leibniz integration over Dirac’s ket-bra projection operators with continuum variables, which can be performed by the technique of integration within ordered product (IWOP) of operators [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480], can directly recast density operators and generalized Wigner operators into normally ordered bivariate-normal-distribution form, which has resemblance in statistics. In this way the phase space formalism of quantum mechanics can be developed. The Husimi operator, entangled Husimi operator and entangled Wigner operator for entangled particles with different masses are naturally introduced by virtue of the IWOP technique, and their physical meanings are explained.

Fan, Hong-Yi

2008-06-01

98

Unambiguous discrimination among quantum operations  

SciTech Connect

We address the problem of unambiguous discrimination among a given set of quantum operations. The necessary and sufficient condition for them to be unambiguously distinguishable is derived in the cases of single use and multiple uses, respectively. For the latter case we explicitly construct the input states and corresponding measurements that accomplish the task. It is also found that the introduction of entanglement can improve the discrimination.

Wang Guoming; Ying Mingsheng [State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing, 100084 (China)

2006-04-15

99

Decoherence in Quantum Mechanics and Quantum Cosmology.  

National Technical Information Service (NTIS)

A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work o...

J. B. Hartle

1992-01-01

100

Communication: Quantum mechanics without wavefunctions  

SciTech Connect

We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications--theoretical, computational, and interpretational--are discussed.

Schiff, Jeremy [Department of Mathematics, Bar-Ilan University, Ramat Gan 52900 (Israel); Poirier, Bill [Department of Chemistry and Biochemistry, Texas Tech University, Box 41061, Lubbock, Texas 79409-1061 (United States) and Department of Physics, Texas Tech University, Box 41051, Lubbock, Texas 79409-1051 (United States)

2012-01-21

101

Symplectic Topology and Geometric Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.

Sanborn, Barbara

102

Variational methods in relativistic quantum mechanics  

Microsoft Academic Search

This review is devoted to the study of stationary solutions of linear and\\u000anonlinear equations from relativistic quantum mechanics, involving the Dirac\\u000aoperator. The solutions are found as critical points of an energy functional.\\u000aContrary to the Laplacian appearing in the equations of nonrelativistic quantum\\u000amechanics, the Dirac operator has a negative continuous spectrum which is not\\u000abounded from below.

Maria J. Esteban; Mathieu Lewin; ERIC SERE

2008-01-01

103

Fuzzy quantum logic II. The logics of unsharp quantum mechanics  

NASA Astrophysics Data System (ADS)

A survey of the main results of the Italian group about the logics of unsharp quantum mechanics is presented. In particular partial ordered structures playing with respect to effect operators (linear bounded operators F on a Hilbert space ? such that ????, 0?????2) the role played by orthomodular posets with respect to orthogonal projections (corresponding to “sharp” effects) are analyzed. These structures are generally characterized by the splitting of standard orthocomplementation on projectors into two nonusual orthocomplementations (a fuzzy-like and an intuitionistic-like) giving rise to different kinds of Brouwer-Zadeh (BZ) posets: de Morgan BZ posets, BZ* posets, and BZ3 posets. Physically relevant generalizations of ortho-pair semantics (paraconsistent, regular paraconsistent, and minimal quantum logics) are introduced and their relevance with respect to the logic of unsharp quantum mechanics are discussed.

Cattaneo, Gianpiero

1993-10-01

104

Attaching Theories of Consciousness to Bohmian Quantum Mechanics  

Microsoft Academic Search

The de Broglie-Bohm theory of quantum mechanics (here simply called Bohmian\\u000aMechanics or BM) [1-10] is an augmentation of ``bare'' quantum mechanics (the\\u000abare theory being given by an algebra of operators and a quantum state that\\u000asets the expectation values of these operators) that includes a definite\\u000ahistory or Bohmian trajectory. This definite trajectory gives BM a somewhat\\u000amore

Don N. Page

1995-01-01

105

Commutator Anomaly in Noncommutative Quantum Mechanics  

NASA Astrophysics Data System (ADS)

In this paper, the Schrödinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space-space and space-momentum as well as momentum-momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.

Dulat, Sayipjamal; Li, Kang

106

Permutation interpretation of quantum mechanics  

NASA Astrophysics Data System (ADS)

We analyse quantum concepts in a constructive finite background. Introduction of continuum or other actual infinities into physics leads to non-constructivity without any need for them in description of empirical observations. We argue that quantum behavior is a natural consequence of symmetries of dynamical systems. It is a result of fundamental impossibility to trace identity of indistinguishable objects in their evolution — only information about invariant combinations of such objects is available. General mathematical arguments imply that any quantum dynamics can be reduced to a sequence of permutations. Quantum phenomena, such as interferences, arise in invariant subspaces of permutation representations of the symmetry group of a system. Observable quantities can be expressed in terms of the permutation invariants. We demonstrate that for description of quantum phenomena there is no need to use such non-constructive number system as complex numbers. It is sufficient to employ the cyclotomic numbers — a minimal extension of the natural numbers which is suitable for quantum mechanics.

Kornyak, V. V.

2012-02-01

107

Singular potentials in quantum mechanics.  

National Technical Information Service (NTIS)

This paper is a review of some mathematical methods as recently developed and applied to deal with singular potentials in Quantum Mechanics. Regular and singular perturbative methods as well as variational treatments are considered. (author). 25 refs. (At...

V. C. Aguilera-Navarro E. Koo

1995-01-01

108

Computing With Quantum Mechanical Oscillators.  

National Technical Information Service (NTIS)

Despite the obvious practical considerations (e.g., stability, controllability), certain quantum mechanical systems seem to naturally lend themselves in a theoretical sense to the task of performing computations. The purpose of this report is to describe ...

A. D. Parks J. L. Solka

1991-01-01

109

Yang-Mills Quantum Mechanics.  

National Technical Information Service (NTIS)

Quantum mechanical properties of the Yang-Mills space homogeneous model are considered in the Schroedinger representation. By means of compact variables the dependence of the wave function on ''rotational'' degrees of freedom is separated and effective Ha...

G. K. Savvidy

1984-01-01

110

Measurement Theory in Quantum Mechanics.  

National Technical Information Service (NTIS)

It is assumed that consciousness, memory and liberty (within the limits of the quantum mechanics indeterminism) are fundamental properties of elementary particles. Then, using this assumption it is shown how measurements and observers may be introduced in...

G. Klein

1980-01-01

111

Quantum Mechanics in Insulators  

SciTech Connect

Atomic physics is undergoing a large revival because of the possibility of trapping and cooling ions and atoms both for individual quantum control as well as collective quantum states, such as Bose-Einstein condensates. The present lectures start from the 'atomic' physics of isolated atoms in semiconductors and insulators and proceed to coupling them together to yield magnets undergoing quantum phase transitions as well as displaying novel quantum states with no classical analogs. The lectures are based on: G.-Y. Xu et al., Science 317, 1049-1052 (2007); G. Aeppli, P. Warburton, C. Renner, BT Technology Journal, 24, 163-169 (2006); H. M. Ronnow et al., Science 308, 392-395 (2005) and N. Q. Vinh et al., PNAS 105, 10649-10653 (2008).

Aeppli, G. [London Centre for Nanotechnology, 17-19 Gordon Street, London (United Kingdom); Department of Physics and Astronomy, University College of London, London (United Kingdom)

2009-08-20

112

Formulation, interpretation and application of non-commutative quantum mechanics  

NASA Astrophysics Data System (ADS)

In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the standard quantum mechanical interpretation based on positive operator valued measures, provides a sufficient framework for the consistent interpretation of this quantum system. The implications of this formalism for rotational and time reversal symmetry are discussed. The formalism is applied to the free particle and harmonic oscillator in two dimensions and the physical signatures of non-commutativity are identified.

Scholtz, F. G.; Gouba, L.; Hafver, A.; Rohwer, C. M.

2009-05-01

113

Introduction to Quantum Mechanics: Assessment  

NSDL National Science Digital Library

This resource provides an assessment for students who have just learned the basics of quantum mechanics. The accompanying interactive lesson which may be used before this assessment is given may be found here. This five question assessment covers the concept of probability, electrons and some other basic concepts related to quantum mechanics. The other educational modules in this series can be found here. Instructors and students are encouraged to sign up with the Electron Technologies site here before starting to use these materials.

2012-03-20

114

Fourier transform identities in quantum mechanics and the quantum line  

NASA Astrophysics Data System (ADS)

We give a quantum-mechanical interpretation of some modular identities (LF)3=?L2 arising in conformal field theory and the theory of quantum groups in relation to the mapping class group of a torus. The interpretation follows by evaluating the identity in the case of a non-standard group of the real line. The operation L takes the form of the Fourier transform of wave functions in L2(R) with length scale ???/m. We find that this can be factorised as ?L=exp(-i?p2/2m?) exp(-ix2/2??) P exp(-i?p2/2m?), where x, p mare the usual quantum mechanical position and momentum operators, P is the parity and ?=(1-i)/?2 is a normalization constant determined by verifying the identity on wavepackets. We understand this further in terms of the observation that the Fourier transformation is realized on the wavefunctions in quantum mechanics as the evolution by a quantum harmonic oscillator of period 2?? for 1/4 of a cycle. SERC Advanced Fellow and Drapers Fellow of Pembroke College, Cambridge.

Lyubashenko, V. V.; Majid, S.

1992-06-01

115

Noncommutative Poisson boundaries of unital quantum operations  

SciTech Connect

In this paper, Poisson boundaries of unital quantum operations (also called Markov operators) are investigated. In the case of unital quantum channels, compact operators belonging to Poisson boundaries are characterized. Using the characterization of amenable groups by the injectivity of their von Neumann algebras, we will answer negatively some conjectures appearing in the work of Arias et al. ['Fixed points of quantum operations', J. Math. Phys. 43, 5872 (2002)] about injectivity of the commuting algebra of the Kraus operators of unital quantum operations and their injective envelopes.

Lim, Bunrith Jacques [Institut de Recherche Mathematique de Rennes (IRMAR), Universite de Rennes 1 and CNRS (UMR 6625), 35042 Rennes Cedex (France)

2010-05-15

116

Generalized quantum mechanics  

Microsoft Academic Search

A convex scheme of quantum theory is outlined where the states are not necessarily the density matrices in a Hilbert space. The physical interpretation of the scheme is given in terms of generalized “impossibility principles”. The geometry of the convex set of all pure and mixed states (called a statistical figure) is conditioned by the dynamics of the system. This

Bogdan Mielnik

1974-01-01

117

Quantum Mechanics Resource Packet  

NSDL National Science Digital Library

This website contains a collection of computational resources for use in a quantum physics class. Maple files are provided to introduce students to scientific computation. This collection includes suggested problems for use with the CUPS software. Topics covered include energy levels and wave functions for various potential wells and a 1-D lattice.

Moloney, Mike; Mitra-Kirtley, Sudipa; Joenathan, Charles; Western, Arthur; Mcinerney, Michael

2005-07-25

118

Bohmian Mechanics and Quantum Information  

NASA Astrophysics Data System (ADS)

Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of quantum mechanics, Bohmian mechanics, is concerned, not with information but with the behavior of an objective microscopic reality given by particles and their positions. What I would like to do here is to examine whether, and to what extent, the importance of information, observation, and the like in quantum theory can be understood from a Bohmian perspective. I would like to explore the hypothesis that the idea that information plays a special role in physics naturally emerges in a Bohmian universe.

Goldstein, Sheldon

2010-04-01

119

PT quantum mechanics - Recent results  

NASA Astrophysics Data System (ADS)

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 = p2+ix3 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 = p2+ix3 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 = p2-x4, 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?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.

2012-09-01

120

PT quantum mechanics - Recent results  

SciTech Connect

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

121

Deduction, Ordering, and Operations in Quantum Logic  

Microsoft Academic Search

We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a substitution and arrive at operation algebras that are not lattices what proves the claim. We devise algorithms and programs which write down any

Norman D. Megill; Mladen Pavicic

2001-01-01

122

Deduction, Ordering, and Operations in Quantum Logic  

Microsoft Academic Search

We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a substitution and arrive at operation algebras that are not lattices what proves the claim. We devise algorithms and programs which write down any

Normal D. Megill; Mladen Pavi?i?

2002-01-01

123

Why Do the Quantum Observables Form a Jordan Operator Algebra?  

Microsoft Academic Search

The Jordan algebra structure of the bounded real quantum observables was recognized already in the early days of quantum mechanics. While there are plausible reasons for most parts of this structure, the existence of the distributive nonassociative multiplication operation is hard to justify from a physical or statistical point of view. Considering the non-Boolean extension of classical probabilities, presented in

Gerd Niestegge

2004-01-01

124

Commutator Anomaly in Noncommutative Quantum Mechanics  

Microsoft Academic Search

In this paper, the Schrödinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space-space and space-momentum as well as momentum-momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical

Sayipjamal Dulat; Kang Li

2006-01-01

125

Physicalism Versus Quantum Mechanics  

Microsoft Academic Search

The widely held philosophical position called “physicalism” has been described and defended in a recent book by Jaegwon Kim.\\u000a The physicalist position claims that the world is basically purely physical. However, “physical” is interpreted in a way predicated,\\u000a in effect, upon certain properties of classical physics that are contradicted by the precepts of orthodox quantum physics.\\u000a Kim’s arguments reveal two

Henry P. Stapp

126

Quantum Mechanics Tutorials  

NSDL National Science Digital Library

This website contains a collection of materials for use in a small group tutorial setting. The materials are a part of a model applied quantum physics course at the University of Maryland which is directed toward science and engineering students. This web page contains links to research and resources, such as pretests, tutorials, homework, and handouts. (A password must be obtained for access to resources)

Redish, Edward F.; Steinberg, Richard N.; Wittmann, Michael C.

2005-08-07

127

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

128

The transitions among classical mechanics, quantum mechanics, and stochastic quantum mechanics  

NASA Astrophysics Data System (ADS)

Various formalisms for recasting quantum mechanics in the framework of classical mechanics on phase space are reviewed and compared. Recent results in stochastic quantum mechanics are shown to avoid the difficulties encountered by the earlier approach of Wigner, as well as to avoid the well-known incompatibilities of relativity and ordinary quantum theory. Specific mappings among the various formalisms are given.

Schroeck, Franklin E.

1982-09-01

129

Remarks on Osmosis, Quantum Mechanics, and Gravity  

NASA Astrophysics Data System (ADS)

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

2012-05-01

130

Kowalevski top in quantum mechanics  

NASA Astrophysics Data System (ADS)

The quantum mechanical Kowalevski top is studied by the direct diagonalization of the Hamiltonian. The spectra show different behaviors depending on the region divided by the bifurcation sets of the classical invariant tori. Some of these spectra are nearly degenerate due to the multiplicity of the invariant tori. The Kowalevski top has several symmetries and symmetry quantum numbers can be assigned to the eigenstates. We have also carried out the semiclassical quantization of the Kowalevski top by the EBK formulation. It is found that the semiclassical spectra are close to the exact values, thus the eigenstates can be also labeled by the integer quantum numbers. The symmetries of the system are shown to have close relations with the semiclassical quantum numbers and the near-degeneracy of the spectra.

Matsuyama, A.

2013-09-01

131

Faster than Hermitian quantum mechanics.  

PubMed

Given an initial quantum state |psi(I)> and a final quantum state |psi(F)>, there exist Hamiltonians H under which |psi(I)> evolves into |psi(F)>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time tau? For Hermitian Hamiltonians tau has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, tau can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from |psi(I)> to |psi(F)> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing. PMID:17358747

Bender, Carl M; Brody, Dorje C; Jones, Hugh F; Meister, Bernhard K

2007-01-24

132

Measurement theory and stochastic differential equations in quantum mechanics  

NASA Astrophysics Data System (ADS)

Continuous (in time) measurements can be introduced in quantum mechanics by using operation-valued measures and quantum stochastic calculus. In this paper quantum stochastic calculus is used for showing the connections between measurement theory and open-system theory. In particular, it is shown how continuous measurements are strictly related to the concept of output channels, introduced in the framework of quantum stochastic differential equations by Gardiner and Collet.

Barchielli, Alberto

1986-09-01

133

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

134

Effective equations for the quantum pendulum from momentous quantum mechanics  

SciTech Connect

In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.

Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)

2012-08-24

135

Capacity and quantum mechanical tunneling  

Microsoft Academic Search

We connect the notion of capacity of sets in the theory of symmetric Markov process and Dirichlet forms with the notion of tunneling through the boundary of sets in quantum mechanics. In particular we show that for diffusion processes the notion appropriate to a boundary without tunneling is more refined than simply capacity zero. We also discuss several examples in

S. Albeverio; M. Fukushima; W. Karwowski; L. Streit

1981-01-01

136

Self-Referential Quantum Mechanics  

Microsoft Academic Search

A nonlinear quantum mechanics based upon the nonlinear logarithmic Schrodinger equation, is developed which has the property of self-reference, that is, the nonlinear term is dependent upon the square of the wavefunction. The self-referential system is examined in terms of its mathematical properties, the definition of the wavefunction, and the nonlinear system in the feedback between equation and solution. Theta

Mark Kenneth Mitchell

1993-01-01

137

Quantum Mechanics and Physical Reality  

Microsoft Academic Search

IN a recent article by A. Einstein, B. Podolsky and N. Rosen, which appeared in the Physical Review of May 15, and was reviewed in NATURE of June 22, the question of the completeness of quantum mechanical description has been discussed on the basis of a ``criterion of physical reality'', which the authors formulate as follows : ``If, without in

N. Bohr

1935-01-01

138

Negative Observations in Quantum Mechanics  

Microsoft Academic Search

In quantum mechanics, it is possible to make observations that affect\\u000aphysical entities without there being a physical interaction between the\\u000aobserver and the physical entity measured. Epstein (1945) and Renninger (1960)\\u000adiscussed this situation, and Renninger called this type of observation a\\u000a\\

Douglas M. Snyder

1999-01-01

139

Quantum mechanics, relativity and time  

Microsoft Academic Search

A discussion on quantum mechanics, general relativity and their relations is introduced. The assumption of the absolute validity of conservation laws and the extension to a 5D-space lead to reconsider several shortcomings and paradoxes of modern physics under a new light without the necessity to take into account symmetry breakings. In this picture, starting from first principles, and after a

Giuseppe Basini; Salvatore Capozziello

2005-01-01

140

Collective Motion in Quantum Mechanics  

Microsoft Academic Search

A general method of discussing quantum-mechanical problems involving collective motion is proposed, in which the emphasis is placed on consideration of sets of states rather than single states, and in which the additional collective co-ordinates are not redundant but used to describe the sets. The method is applied to a number of relatively simple examples: plasma oscillations of an electron

T. H. R. Skyrme

1957-01-01

141

Quantum Mechanical Methods for Enzyme Kinetics  

Microsoft Academic Search

This review discusses methods for the incorporation of quantum mechanical effects into enzyme kinetics simulations in which the enzyme is an explicit part of the model. We emphasize three aspects: (a) use of quantum mechanical electronic structure methods such as molecular orbital theory and density functional theory, usually in conjunction with molecular mechanics; (b) treating vibrational motions quantum mechanically, either

Jiali Gao; Donald G. Truhlar

2002-01-01

142

Relational motivation for conformal operator ordering in quantum cosmology  

Microsoft Academic Search

Operator ordering in quantum cosmology is a major as-yet unsettled ambiguity with not only formal but also physical consequences. We determine the Lagrangian origin of the conformal invariance that underlies the conformal operator-ordering choice in quantum cosmology. This arises particularly naturally and simply from relationalist product-type actions (such as the Jacobi action for mechanics or Baierlein-Sharp-Wheeler-type actions for general relativity),

Edward Anderson

2010-01-01

143

New Potentials for Old: The Darboux Transformation in Quantum Mechanics  

ERIC Educational Resources Information Center

|The Darboux transformation in quantum mechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics

Williams, Brian Wesley; Celius, Tevye C.

2008-01-01

144

On the representation of quantum mechanics on phase space  

NASA Astrophysics Data System (ADS)

It is shown that Hilbert-space quantum mechanics can be represented on phase space in the sense that the density operators can be identified with phase-space densities and the observables can be described by functions on phase space. In particular, we consider phase-space representations of quantum mechanics which are related to certain joint position-momentum observables.

Stulpe, Werner

1992-09-01

145

Probable Inference and Quantum Mechanics  

SciTech Connect

In its current very successful interpretation the quantum theory is fundamentally statistical in nature. Although commonly viewed as a probability amplitude whose (complex) square is a probability, the wavefunction or state vector continues to defy consensus as to its exact meaning, primarily because it is not a physical observable. Rather than approach this problem directly, it is suggested that it is first necessary to clarify the precise role of probability theory in quantum mechanics, either as applied to, or as an intrinsic part of the quantum theory. When all is said and done the unsurprising conclusion is that quantum mechanics does not constitute a logic and probability unto itself, but adheres to the long-established rules of classical probability theory while providing a means within itself for calculating the relevant probabilities. In addition, the wavefunction is seen to be a description of the quantum state assigned by an observer based on definite information, such that the same state must be assigned by any other observer based on the same information, in much the same way that probabilities are assigned.

Grandy, W. T. Jr. [Department of Physics and Astronomy, University of Wyoming, Laramie, WY 82070 (United States)

2009-12-08

146

Topics in quantum mechanics  

SciTech Connect

The present paper deals with three independent subjects. I. We show how for classical canonical transformation we can pass, with the help of Wigner distribution functions, from their representation U in the configurational Hilbert space to a kernel K in phase space. The latter is a much more transparent way of looking at representations of canonical transformations, as the classical limit is reached when ({Dirac_h}/2{pi}){yields}0 and successive quantum corrections are related with powers of ({Dirac_h}/2{pi}){sup 2n}, n=1,2,... . II. We discuss the coherent states solution for a charged particle in a constant magnetic field and show that it is the appropriate one for getting the classical limit of the problem, i.e., motion in a circle around any point in the plane perpendicular to the field and with the square of the radius proportional to the energy of the particle. III. We show that it is possible to have just one equation involving n{alpha}'s and {beta} matrices to get relativistic wave equations that can have spins with values up to n/2. We then decompose the {alpha}'s and {beta}'s into direct products of ordinary spin matrices and a new type of them that we call sign spin. The problem reduces then to that of the generators of a SU(4) group, entirely similar to the one in the spin-isospin theory of nuclear physics. For a free particle of arbitrary spin the symmetry group is actually the unitary symplectic subgroup of SU(4), i.e., Sp(4). As the latter is isomorphic to O(5), we can characterize our states by the canonical chain O(5) superset of O(4) superset of O(3) superset of O(2), and from it obtain the spin and mass content of our relativistic equation.

Moshinsky, Marcos [Instituto de Fisica-UNAM. Apartado Postal 20-364, 01000 Mexico, D.F. (Mexico)

1999-03-06

147

Student understanding of quantum mechanics  

NSDL National Science Digital Library

We investigate the difficulties of advanced undergraduate students toward the end of a full year upper-level quantum mechanics course with concepts related to quantum measurements and time development. Our analysis is based upon a test administered to 89 students from six universities and interviews with 9 students. Strikingly, most students shared the same difficulties despite variations in background, teaching styles, and textbooks. Concepts related to stationary states, eigenstates, and time dependence of expectation values were found to be particularly difficult. An analysis of written tests and interviews suggests that widespread misconceptions originate from an inability to discriminate between related concepts and a tendency to overgeneralize.

Singh, Chandralekha

2005-11-23

148

On Quantum Mechanics on Noncommutative Quantum Phase Space  

Microsoft Academic Search

In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM) is showed to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this particular transformation, we firstly find that the product of the two noncommutativity parameters possesses a lower bound in direct relation with Heisenberg incertitude relations,

A. E. F. Djemai; H. Smail

2003-01-01

149

A quantum mechanical model of interference  

Microsoft Academic Search

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

150

Singular potentials in nonrelativistic quantum mechanics  

Microsoft Academic Search

Summary  The mathematical aspects of singular potentials in nonrelativistic quantum mechanics are studied in terms of the self-adjoint\\u000a transformations related to singular differential operators in the space L2(0, ?). The physical content is expressed by the spectral decompositions and for attractive potentials found to be determined\\u000a only up to a parameter denning a particular extension. In general it is not possible

K. Meetz

1964-01-01

151

Quantum Logical Operations on Encoded Qubits  

Microsoft Academic Search

We show how to carry out quantum logical operations (controlled-not and Toffoli gates) on encoded qubits for several encodings which protect against various 1-bit errors. This improves the reliability of these operations by allowing one to correct for 1-bit errors which either preexisted or occurred in the course of operation. The logical operations we consider allow one to carry out

Wojciech Hubert Zurek; Raymond Laflamme

1996-01-01

152

Quantum mechanics of black holes.  

PubMed

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. PMID:22859480

Witten, Edward

2012-08-01

153

Three-space from quantum mechanics  

SciTech Connect

We formulate a discrete quantum-mechanical precursor to spacetime geometry. The objective is to provide the foundation for a quantum mechanics that is rooted exclusively in quantum-mechanical concepts, with all classical features, including the three-dimensional spatial continuum, emerging dynamically.

Chew, G.F.; Stapp, H.P.

1988-08-01

154

Quantum mechanics and the psyche  

NASA Astrophysics Data System (ADS)

In this paper we apply the last developments of the theory of measurement in quantum mechanics to the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of measurement in quantum mechanics can be distinguished by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse of the wave function, whereas in the active aspect of consciousness—i.e., that which goes together with an act or a choice—there seems to be a collapse of the wave function. As an example of the second possibility we study in detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correlation at a distance between minds, as well as to group correlations that appear during group therapies or group training. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we propose to test the existence of such correlations during sessions of group training.

Galli Carminati, G.; Martin, F.

2008-07-01

155

Quantum Logic, Statistical Operator and the Problem of Measurement  

Microsoft Academic Search

An argument is presented that the consistent description of the evolution of a system is possible only with the statistical operator and not with the wave function. A reconstruction of the logic of quantum mechanics is proposed with the statistical operator as the basic quantity to describe the state in one-to-one correspondence. The problem of measurement is reconsidered in the

Yutaka Toyozawa

1984-01-01

156

Simulation of n-qubit quantum systems. III. Quantum operations  

NASA Astrophysics Data System (ADS)

During the last decade, several quantum information protocols, such as quantum key distribution, teleportation or quantum computation, have attracted a lot of interest. Despite the recent success and research efforts in quantum information processing, however, we are just at the beginning of understanding the role of entanglement and the behavior of quantum systems in noisy environments, i.e. for nonideal implementations. Therefore, in order to facilitate the investigation of entanglement and decoherence in n-qubit quantum registers, here we present a revised version of the FEYNMAN program for working with quantum operations and their associated (Jamio?kowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. Apart from the implementation of different noise models, the current program extension may help investigate the fragility of many quantum states, one of the main obstacles in realizing quantum information protocols today. Catalogue identifier: ADWE_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v3_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Operating systems: Any system that supports MAPLE; tested under Microsoft Windows XP, SuSe Linux 10 Program language used:MAPLE 10 Typical time and memory requirements: Most commands that act upon quantum registers with five or less qubits take ?10 seconds of processor time (on a Pentium 4 processor with ?2 GHz or equivalent) and 5 20 MB of memory. Especially when working with symbolic expressions, however, the memory and time requirements critically depend on the number of qubits in the quantum registers, owing to the exponential dimension growth of the associated Hilbert space. For example, complex (symbolic) noise models (with several Kraus operators) for multi-qubit systems often result in very large symbolic expressions that dramatically slow down the evaluation of measures or other quantities. In these cases, MAPLE's assume facility sometimes helps to reduce the complexity of symbolic expressions, but often only numerical evaluation is possible. Since the complexity of the FEYNMAN commands is very different, no general scaling law for the CPU time and memory usage can be given. No. of bytes in distributed program including test data, etc.: 799?265 No. of lines in distributed program including test data, etc.: 18?589 Distribution format: tar.gz Reasons for new version: While the previous program versions were designed mainly to create and manipulate the state of quantum registers, the present extension aims to support quantum operations as the essential ingredient for studying the effects of noisy environments. Does this version supersede the previous version: Yes Nature of the physical problem: Today, entanglement is identified as the essential resource in virtually all aspects of quantum information theory. In most practical implementations of quantum information protocols, however, decoherence typically limits the lifetime of entanglement. It is therefore necessary and highly desirable to understand the evolution of entanglement in noisy environments. Method of solution: Using the computer algebra system MAPLE, we have developed a set of procedures that support the definition and manipulation of n-qubit quantum registers as well as (unitary) logic gates and (nonunitary) quantum operations that act on the quantum registers. The provided hierarchy of commands can be used interactively in order to simulate and analyze the evolution of n-qubit quantum systems in ideal and nonideal quantum circuits.

Radtke, T.; Fritzsche, S.

2007-05-01

157

From quantum mechanics to universal structures of conceptualization and feedback on quantum mechanics  

SciTech Connect

In previous works we have established that the spacetime probabilistic organization of the quantum theory is determined by the spacetime characteristics of the operations by which the observer produces the objects to be studied (states of microsystems) and obtains qualifications of these. Guided by this first conclusion, we have then built a general syntax of relativized conceptualization where any description is explicity and systematically referred to the two basic epistemic operations by which the conceptor introduces the object to be qualified and then obtains qualifications of it. Inside this syntax there emerges a general typology of the relativized descriptions. Here we show that with respect to this typology the type of the predictive quantum mechanical descriptions acquires a precise definition. It appears that the quantum mechanical formalism has captured and has expressed directly in a mathematical language the most complex form in which can occur a first descriptional phase that lies universally at the bottom of any chain of conceptualization. The main features of the Hilbert-Dirac algorithms are decoded in terms of the general syntax of relativized conceptualiztion. This renders explicit the semantical contents of the quantum mechanical representations relating each one of these to its mathematical quantum mechanical expression. Basic insufficiencies are thus identified and, correlatively, false problems as well as answers to these, or guides towards the answers. Globally the results obtained provide a basis for the future attempts at a general mathematical representation of the processes of conceptualization.

Mugur-Schaechter, M. (Univ. of Reims (France))

1993-01-01

158

Quantum Theory of Geometry I: Area Operators  

Microsoft Academic Search

A new functional calculus, developed recently for a fully non- perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corre- sponding to areas of 2-surfaces are introduced and shown to be self-adjoint on the underlying (kinematical) Hilbert space of states. It is shown that their spectra are purely discrete

Abhay Ashtekar; Jerzy Lewandowski

1996-01-01

159

What is an Essentially Quantum Mechanical Effect?  

Microsoft Academic Search

Abstract When asking whether consciousness is an “essentially quantum effect”, one must first lay down criteria for considering an effect ,quantum ,mechanical. After a brief survey ,of the ,interpretations of quantum theory, three such sufficient criteria are proposed and examined: wave-particle duality (or collapse), entanglement (“non-locality”), and quantum condensation (involving “identical” particles). A fourth criteria could involve the use of

Osvaldo Pessoa Jr

160

Superconformal black hole quantum mechanics  

Microsoft Academic Search

In recent work, the superconformal quantum mechanics describing D0 branes in the AdS2 × S2 × CY3 attractor geometry of a Calabi-Yau black hole with D4 brane charges pA has been constructed and found to contain a large degeneracy of chiral primary bound states. In this paper it is shown that the asymptotic growth of chiral primaries for N D0

Davide Gaiotto; Andrew Strominger; Xi Yin

2005-01-01

161

Teaching quantum mechanics on an introductory level  

NSDL National Science Digital Library

We present a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. In the context of virtual laboratories, the students discover from the very beginning how quantum phenomena deviate from our classical everyday experience. The results of the evaluation of the course show that most of the students acquired appropriate quantum mechanical conceptions, and that many of the common misconceptions encountered in traditional instruction have been avoided.

Mã¼ller, Rainer; Wiesner, Hartmut

2005-10-27

162

Facets of contextual realism in quantum mechanics  

SciTech Connect

In recent times, there is an upsurge of interest in demonstrating the quantum contextuality. In this proceedings, we explore the two different forms of arguments that have been used for showing the contextual character of quantum mechanics. First line of study concerns the violations of the noncontextual realist models by quantum mechanics, where second line of study that is qualitatively distinct from the earlier one, demonstrates the contextuality within the formalism of quantum mechanics.

Pan, Alok Kumar [LPTM (CNRS Unite 8089), Universite de Cergy-Pontoise, 95302 Cergy-Pontoise cedex (France); Home, Dipankar [CAPSS, Department of Physics, Bose Institute, Salt Lake, Calcutta 700091 (India)

2011-09-23

163

Quantum logic operations in optical fibers  

Microsoft Academic Search

We have recently demonstrated several probabilistic quantum logic operations using linear optics and post selection. Here we show how the fidelity of these devices can be increased using fibers to reduce optical mode mismatch errors.

B. C. Jacobs; M. J. Fitch; T. B. Pittman; J. D. Franson

2003-01-01

164

Faster than Hermitian Quantum Mechanics  

SciTech Connect

Given an initial quantum state vertical bar {psi}{sub I}> and a final quantum state vertical bar {psi}{sub F}>, there exist Hamiltonians H under which vertical bar {psi}{sub I}> evolves into vertical bar {psi}{sub F}>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time {tau}? For Hermitian Hamiltonians {tau} has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, {tau} can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from vertical bar {psi}{sub I}> to vertical bar {psi}{sub F}> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.

Bender, Carl M. [Physics Department, Washington University, St. Louis, Missouri 63130 (United States); Department of Mathematics, Imperial College, London SW7 2BZ (United Kingdom); Brody, Dorje C. [Department of Mathematics, Imperial College, London SW7 2BZ (United Kingdom); Jones, Hugh F. [Blackett Laboratory, Imperial College, London SW7 2BZ (United Kingdom); Meister, Bernhard K. [Department of Physics, Renmin University of China, Beijing 100872 (China)

2007-01-26

165

Position-dependent noncommutativity in quantum mechanics  

SciTech Connect

The model of the position-dependent noncommutativity in quantum mechanics is proposed. We start with given commutation relations between the operators of coordinates [x-circumflex{sup i},x-circumflex{sup j}]={omega}{sup ij}(x-circumflex), and construct the complete algebra of commutation relations, including the operators of momenta. The constructed algebra is a deformation of a standard Heisenberg algebra and obeys the Jacobi identity. The key point of our construction is a proposed first-order Lagrangian, which after quantization reproduces the desired commutation relations. Also we study the possibility to localize the noncommutativity.

Gomes, M.; Kupriyanov, V. G. [Instituto de Fisica, Universidade de Sao Paulo (Brazil)

2009-06-15

166

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

167

Teaching Quantum Mechanics on an Introductory Level.  

ERIC Educational Resources Information Center

|Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)|

Muller, Rainer; Wiesner, Hartmut

2002-01-01

168

Quantum Mechanical Models of Turing Machines That Dissipate No Energy  

Microsoft Academic Search

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

169

Web-based Quantum Mechanics I Course  

NSDL National Science Digital Library

This web site is an entire web-based Quantum Mechanics I Course based at the University of Tennessee. It includes instructional materials, in-class tutorials, simulations, links to other quantum resources, homework assignments, and solutions.

Breinig, Marianne

2009-09-17

170

Fun with supersymmetric quantum mechanics  

SciTech Connect

One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup ..cap alpha../ for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpotentials to test various ideas about how to see if supersymmetry is broken in an arbitrary model. Recently, Witten proposed a topological invariant, the Witten index ..delta.. which counts the number of bosons minus the number of fermions having ground state energy zero. Since if supersymmetry is broken, the ground state energy cannot be zero, one expects if ..delta.. is not zero, SUSY is preserved and the theory is not a good candidate for a realistic model. In this study we evaluate ..delta.. for several examples, and show some unexpected peculiarities of the Witten index for certain choice of superpotentials W(x). We also discuss two other nonperturbative methods of studying supersymmetry breakdown. One involves relating supersymmetric quantum mechanics to a stochastic classical problem and the other involves considering a discrete (but not supersymmetric) version of the theory and studying its behavior as one removes the lattice cuttoff. In this survey we review the Hamiltonian and path integral approaches to supersymmetric quantum mechanics. We then discuss the related path integrals for the Witten Index and for stochastic processes and show how they are indications for supersymmetry breakdown. We then discuss a system where the superpotential W(x) has assymetrical values at +-infinity. We finally discuss nonperturbative strategies for studying supersymmetry breakdown based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed. 17 references.

Freedman, B.; Cooper, F.

1984-04-01

171

Introduction to Quantum Mechanics Activity  

NSDL National Science Digital Library

This resource provides an introductory activity on "the basic quantum mechanics concepts about electrons that are essential to understanding modern and future technology- especially nanotechnology that will be vitally important to the industry." Core concepts include probability distribution, electron waves, diffraction, interference, tunneling, bound states and excited states. The interactive module allows students to test their knowledge as they learn. The material would be best for high school AP classes and college level students. The other educational modules in this series can be found here. Instructors and students are encouraged to sign up with the Electron Technologies site here before starting to use these materials.

2012-02-24

172

Quantum mechanical polar surface area.  

PubMed

A correlation has been established between the absorbed fraction of training-set molecules after oral administration in humans and the Quantum Mechanical Polar Surface Area (QMPSA). This correlation holds for the QMPSA calculated with structures where carboxyl groups are deprotonated. The correlation of the absorbed fraction and the QMPSA calculated on the neutral gas phase optimized structures is much less pronounced. This suggests that the absorption process is mainly determined by polar interactions of the drug molecules in water solution. Rules are given to derive the optimal polar/apolar ranges of the electrostatic potential. PMID:22391921

Schaftenaar, Gijs; de Vlieg, Jakob

2012-03-04

173

Tunneling in fractional quantum mechanics  

NASA Astrophysics Data System (ADS)

We study tunneling through delta and double delta potentials in fractional quantum mechanics. After solving the fractional Schrödinger equation for these potentials, we calculate the corresponding reflection and transmission coefficients. These coefficients have a very interesting behavior. In particular, we can have zero energy tunneling when the order of the Riesz fractional derivative is different from 2. For both potentials, the zero energy limit of the transmission coefficient is given by {T}_0 = \\cos ^2{(\\pi /\\alpha )}, where ? is the order of the derivative (1 < ? <= 2).

Capelas de Oliveira, E.; Vaz, Jayme, Jr.

2011-05-01

174

Twist deformation of rotationally invariant quantum mechanics  

SciTech Connect

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

175

Operational geometric phase for mixed quantum states  

NASA Astrophysics Data System (ADS)

The geometric phase has found a broad spectrum of applications in both classical and quantum physics, such as condensed matter and quantum computation. In this paper, we introduce an operational geometric phase for mixed quantum states, based on spectral weighted traces of holonomies, and we prove that it generalizes the standard definition of the geometric phase for mixed states, which is based on quantum interferometry. We also introduce higher order geometric phases, and prove that under a fairly weak, generically satisfied, requirement, there is always a well-defined geometric phase of some order. Our approach applies to general unitary evolutions of both non-degenerate and degenerate mixed states. Moreover, since we provide an explicit formula for the geometric phase that can be easily implemented, it is particularly well suited for computations in quantum physics.

Andersson, O.; Heydari, H.

2013-05-01

176

N=4 supersymmetric multidimensional quantum mechanics, partial SUSY breaking, and superconformal quantum mechanics  

Microsoft Academic Search

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

177

Phase-space contraction and quantum operations  

SciTech Connect

We give a criterion to differentiate between dissipative and diffusive quantum operations. It is based on the classical idea that dissipative processes contract volumes in phase space. We define a quantity that can be regarded as 'quantum phase space contraction rate' and which is related to a fundamental property of quantum channels: nonunitality. We relate it to other properties of the channel and also show a simple example of dissipative noise composed with a chaotic map. The emergence of attractor-like structures is displayed.

Garcia-Mata, Ignacio; Spina, Maria Elena [Departamento de Fisica, Comision Nacional de Energia Atomica. Av del Libertador 8250 (1429), Buenos Aires (Argentina); Saraceno, Marcos [Departamento de Fisica, Comision Nacional de Energia Atomica. Av del Libertador 8250 (1429), Buenos Aires (Argentina); Escuela de Ciencia y Tecnologia, Universidad Nacional de San Martin. Alem 3901 (B1653HIM), Villa Ballester (Argentina); Carlo, Gabriel [Center for Nonlinear and Complex Systems, Universita degli Studi dell'Insubria and Instituto Nazionale per la Fisica della Materia, Unita di Como, Via Valleggio 11, 22100 Como (Italy)

2005-12-15

178

Propagators in polymer quantum mechanics  

NASA Astrophysics Data System (ADS)

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 ?0, the length scale introduced in the polymer dynamics and which plays a role analog of that of Planck length in Quantum Gravity.

Flores-González, Ernesto; Morales-Técotl, Hugo A.; Reyes, Juan D.

2013-09-01

179

Implementation of the quantum-walk step operator in lateral quantum dots  

NASA Astrophysics Data System (ADS)

We propose a physical implementation of the step operator of the discrete quantum walk for an electron in a one-dimensional chain of quantum dots. The operating principle of the step operator is based on locally enhanced Zeeman splitting and the role of the quantum coin is played by the spin of the electron. We calculate the probability of successful transfer of the electron in the presence of decoherence due to quantum charge fluctuations, modeled as a bosonic bath. We then analyze two mechanisms for creating locally enhanced Zeeman splitting based on, respectively, locally applied electric and magnetic fields and slanting magnetic fields. Our results imply that a success probability of >90% is feasible under realistic experimental conditions.

van Hoogdalem, K. A.; Blaauboer, M.

2009-09-01

180

A Modern Approach to Quantum Mechanics  

NSDL National Science Digital Library

This textbook, unlike most others in the topic, introduces the basic quantum concepts using spin, rather than starting from wave mechanics. This grounding in quantum phenomena, rather than difficult mathematics, is then used to cover all the standard topics in quantum physics. Relationships to experimental results are stressed. An instructor's manual is available.

Townsend, John

2004-03-04

181

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

182

Moyal quantum mechanics: The semiclassical Heisenberg dynamics  

SciTech Connect

The Moyal description of quantum mechanics, based on the Wigner--Weyl isomorphism between operators and symbols, provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in {h_bar} and so presents a preferred foundation for semiclassical analysis. Its semiclassical expansion ``coefficients,`` acting on symbols that represent observables, are simple, globally defined (phase space) differential operators constructed in terms of the classical flow. The first of two presented methods introduces a cluster-graph expansion for the symbol of an exponentiated operator, which extends Groenewold`s formula for the Weyl product of two symbols and has {h_bar} as its natural small parameter. This Poisson bracket based cluster expansion determines the Jacobi equations for the semiclassical expansion of ``quantum trajectories.`` Their Green function solutions construct the regular {h_bar}{down_arrow}0 asymptotic series for the Heisenberg--Weyl evolution map. The second method directly substitutes such a series into the Moyal equation of motion and determines the {h_bar} coefficients recursively. In contrast to the WKB approximation for propagators, the Heisenberg--Weyl description of evolution involves no essential singularity in {h_bar}, no Hamilton--Jacobi equation to solve for the action, and no multiple trajectories, caustics, or Maslov indices. {copyright} 1995 Academic Press, Inc.

Osborn, T.A.; Molzahn, F.H. [Department of Physics, University of Manitoba, Winnipeg, MB, R3T 2N2 (Canada)

1995-07-01

183

Probabilistic quantum logic operations using polarizing beam splitters  

Microsoft Academic Search

It has previously been shown that probabilistic quantum logic operations may be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors. Here we describe the operation of several quantum logic operations of an elementary nature, including a quantum parity check and a quantum encoder, and we show how they may be combined

T. B. Pittman; B. C. Jacobs; J. D. Franson

2001-01-01

184

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS: Preparation of Macroscopic Quantum-Interference States for a Collection of Trapped Ions Via a Single Geometric Operation  

NASA Astrophysics Data System (ADS)

We describe a scheme for the generation of macroscopic quantum-interference states for a collection of trapped ions by a single geometric phase operation. In the scheme the vibrational mode is displaced along a circle with the radius proportional to the number of ions in a certain ground electronic state. For a given interaction time, the vibrational mode returns to the original state, and the ionic system acquires a geometric phase proportional to the area of the circle, evolving from a coherent state to a superposition of two coherent states. The ions undergo no electronic transitions during the operation. Taking advantage of the inherent fault-tolerant feature of the geometric operation, our scheme is robust against decoherence.

Lin, Li-Hua

2010-05-01

185

Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators  

NASA Astrophysics Data System (ADS)

We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in Doplicher et al. (Commun Math Phys 172:187-220, 1995). The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum Spacetime; this allows us to compute their spectra. In particular, we consider operators that can be interpreted as distances, areas, 3- and 4-volumes. The Minkowski distance operator between two independent events is shown to have pure Lebesgue spectrum with infinite multiplicity. The Euclidean distance operator is shown to have spectrum bounded below by a constant of the order of the Planck length. The corresponding statement is proved also for both the space-space and space-time area operators, as well as for the Euclidean length of the vector representing the 3-volume operators. However, the space 3-volume operator (the time component of that vector) is shown to have spectrum equal to the whole complex plane. All these operators are normal, while the distance operators are also selfadjoint. The Lorentz invariant spacetime volume operator, representing the 4-volume spanned by five independent events, is shown to be normal. Its spectrum is pure point with a finite distance (of the order of the fourth power of the Planck length) away from the origin. The mathematical formalism apt to these problems is developed and its relation to a general formulation of Gauge Theories on Quantum Spaces is outlined. As a byproduct, a Hodge Duality between the absolute differential and the Hochschild boundary is pointed out.

Bahns, D.; Doplicher, S.; Fredenhagen, K.; Piacitelli, G.

2011-12-01

186

Thermodynamic integration from classical to quantum mechanics  

SciTech Connect

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

187

Relationship between quantum walks and relativistic quantum mechanics  

SciTech Connect

Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This article revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled forms of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schroedinger form. By showing the coin to be a means to make the walk reversible and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modeled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. The Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of the quantum walk, the maximum speed of walk propagation, and earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two-state system to which the study can be extended.

Chandrashekar, C. M. [Institute for Quantum Computing, University of Waterloo, Ontario N2L 3G1 (Canada); Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada); Banerjee, Subhashish [Chennai Mathematical Institute, Padur PO, Siruseri 603 103 (India); Srikanth, R. [Poornaprajna Institute of Scientific Research, Devanahalli, Bangalore 562 110 (India); Raman Research Institute, Sadashiva Nagar, Bangalore 560 080 (India)

2010-06-15

188

Weyl Geometries, Fisher Information and Quantum Entropy in Quantum Mechanics  

NASA Astrophysics Data System (ADS)

It is known that quantum mechanics can be interpreted as a non-Euclidean deformation of the space-time geometries by means Weyl geometries. We propose here a dynamical explanation of such approach by deriving Bohm potential from minimum condition of Fisher information connected to the entropy of a quantum system.

Fiscaletti, Davide; Licata, Ignazio

2012-11-01

189

Alternative decohering histories in quantum mechanics.  

NASA Astrophysics Data System (ADS)

The authors continue their efforts to understand, within the framework of the quantum mechanics of the universe as a whole, the quasi-classical domain of familiar experience as a feature emergent from the Hamiltonian of the elementary particles and the initial condition of the universe. Quantum mechanics assigns probabilities to exhaustive sets of alternative decoherent histories of the universe.

Gell-Mann, M.; Hartle, J. B.

190

Macroscopicity of Mechanical Quantum Superposition States  

NASA Astrophysics Data System (ADS)

We propose an experimentally accessible, objective measure for the macroscopicity of superposition states in mechanical quantum systems. Based on the observable consequences of a minimal, macrorealist extension of quantum mechanics, it allows one to quantify the degree of macroscopicity achieved in different experiments.

Nimmrichter, Stefan; Hornberger, Klaus

2013-04-01

191

On the quantum mechanics of supermembranes  

Microsoft Academic Search

We study the quantum-mechanical properties of a supermembrane and examine the nature of its ground state. A supersymmetric gauge theory of area-preserving transformations provides a convenient framework for this study. The supermembrane can be viewed as a limiting case of a class of models in supersymmetric quantum mechanics. Its mass does not depend on the zero modes and vanishes only

Bernard de Wit; J. Hoppe; H. Nicolai

1988-01-01

192

Noncommutative Quantum Mechanics with Path Integral  

Microsoft Academic Search

We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment of the usual formalism. In particular, we found explicit connections between quadratic Hamiltonians and Lagrangians, in their commutative and noncommutative regimes. In the quantum case we give

Branko Dragovich; Zoran Rakic

2005-01-01

193

Path Integral Approach to Noncommutative Quantum Mechanics  

Microsoft Academic Search

We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the another one with usual commutative coordinates and momenta. We found connection between quadratic classical Hamiltonians, as well as Lagrangians, in their commutative and noncommutative

Branko Dragovich; Zoran Rakic

2004-01-01

194

Reciprocal relativity of noninertial frames: quantum mechanics  

NASA Astrophysics Data System (ADS)

Noninertial transformations on time-position-momentum-energy space {t, q, p, e} with invariant Born-Green metric ds^{2}=-d t^{2}+\\frac{1}{c^{2}}\\,d q^{2}+\\frac{1}{b^{2}} \\big(d p^{2}-\\frac{1}{c^{2}}\\,d e^{2}\\big) and the symplectic metric -de ? dt + dp ? dq are studied. This {\\cal U}1,3) group of transformations contains the Lorentz group as the inertial special case and, in the limit of small forces and velocities, reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds2 = -dt2. The {\\cal 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. In the limit of b ? ?, spacetime is invariant. 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 representations of its central extension. The same method of projective representations for the inhomogeneous {\\cal U}( 1,3) group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous {\\cal U}( 1,3) group is the cover of the quaplectic group {\\cal Q}( 1,3) ={\\cal U}( 1,3) \\otimes _{s}{\\cal H}(4) . {\\cal H}( 4) is the Weyl-Heisenberg group. The {\\cal H}( 4) group, and the associated Heisenberg commutation relations central to quantum mechanics, results directly from requiring projective representations. A set of second-order wave equations result from the representations of the Casimir operators.

Low, Stephen G.

2007-04-01

195

Logical operator tradeoff for local quantum codes  

NASA Astrophysics Data System (ADS)

We study the structure of logical operators in local D-dimensional quantum codes, considering both subsystem codes with geometrically local gauge generators and codes defined by geometrically local commuting projectors. We show that if the code distance is d, then any logical operator can be supported on a set of specified geometry containing d qubits, where d d^1/(D-1) = O(n) and n is the code length. Our results place limitations on partially self-correcting quantum memories, in which at least some logical operators are protected by energy barriers that grow with system size. We also show that two-dimensional codes defined by local commuting projectors admit logical "string" operators and are not self correcting.

Haah, Jeongwan; Preskill, John

2011-03-01

196

Operator Calculations in Loop Quantum Gravity  

NASA Astrophysics Data System (ADS)

In canonical quantum gravity we express various geometrical and physical quantities as non-local operators based on loops. The action of these operators leads to expressions which are evaluated with the aid of a specific loop calculus. The loop calculus is closely related to the recoupling theory of colored knots and links with trivalent vertices. We introduce the basic ingredients of the loop calculus and present few examples.

Borissov, R.

1997-08-01

197

PROBABILISTIC THEORIES: WHAT IS SPECIAL ABOUT QUANTUM MECHANICS?  

Microsoft Academic Search

Quantum Mechanics (QM) is a very special probabilistic theory, yet we don't know which operational principles make it so. Here I will analyze the possibility of deriving QM as the mathematical representation of a fair operational framework, i. e. a set of rules which allows the experimenter to make predictions on future events on the basis of suitable tests, e.

GIACOMO MAURO

198

Measurement of time in nonrelativistic quantum and classical mechanics  

Microsoft Academic Search

Possible theoretical frameworks for measurement of (arrival) time in the nonrelativistic quantum mechanics are reviewed. It is argued that the ambiguity between indirect measurements by a suitably introduced time operator and direct measurements by a physical clock particle has a counterpart in the corresponding classical framework of measurement of the Newtonian time based on the Hamiltonian mechanics.

Piret Kuusk; Madis Koiv

2001-01-01

199

Distribution Functions in Classical and Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The correspondence between classical and quantum mechanics is an important subject for the better understandings of ``quantum chaos''. In particular, it is very important to investigate the correspondence between distribution functions in classical mechanics and in phase space representation of quantum mechanics. This is the review of our recent progresses in the study of distribution functions in classical and quantum mechanics, namely distribution functions in classical mechanics and in coarse-grained classical mechanics as well as the Wigner function and the Husimi function. Topics dealt with include formulations of the Wigner representation, the Husimi representation and coarse-grained classical mechanics, and their applications to the analyses of the eigenstates and time developments of the distribution functions.

Takahashi, K.

200

Quantum Mechanical Models Of The Fermi Shuttle  

SciTech Connect

The Fermi shuttle is a mechanism in which high energy electrons are produced in an atomic collision by multiple collisions with a target and a projectile atom. It is normally explained purely classically in terms of the electron's orbits prescribed in the collision. Common calculations to predict the Fermi shuttle use semi-classical methods, but these methods still rely on classical orbits. In reality such collisions belong to the realm of quantum mechanics, however. In this paper we discuss several purely quantum mechanical calculations which can produce the Fermi shuttle. Being quantum mechanical in nature, these calculations produce these features by wave interference, rather than by classical orbits.

Sternberg, James [University of Tennessee, Department of Physics and Astronomy, Knoxville TN 37996 (United States)

2011-06-01

201

Quantum operations: technical or fundamental challenge?  

NASA Astrophysics Data System (ADS)

A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined. The possibility of using the ion traps as ‘operation factories’ transforming quantum states is discussed. The non-perturbative algorithms indicate that the results of abstract ?-pulses of oscillator potentials can become real. Some of them, if empirically achieved, could be essential to examine certain atypical quantum ideas. In particular, simple dynamical manipulations might contribute to the Aharonov–Bohm criticism of the time–energy uncertainty principle, while some others may verify the existence of fundamental precision limits of the position measurements or the reality of ‘non-commutative geometries’.

Mielnik, Bogdan

2013-09-01

202

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

203

Quantum Physics Online: Wave Mechanics  

NSDL National Science Digital Library

This is a set of interactive Java applets illustrating the wave nature of quantum physics. Animations are used to illustrate propagation of wave packets, and scattering from potentials. There is also a simple illustration of a scanning tunneling microscope. These applets are part of an extensive collection of animations and simulations illustrating a large range of quantum topics, and an ongoing effort for developing a fully interactive quantum-physics class. Both French and English versions are available.

Joffre, Manuel

2004-03-28

204

Use of Quantum Mechanical Models in Studies of Reaction Mechanisms,  

National Technical Information Service (NTIS)

The problems involved in determining the mechanisms of reactions by quantum mechanical calculations are discussed. Various precautions must be taken if the results of any calculation are to be chemically meaningful. Ab initio studies of reactions must als...

M. J. Dewar

1988-01-01

205

Strange Bedfellows: Quantum Mechanics and Data Mining  

SciTech Connect

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

206

Quantum continuum mechanics made simple  

NASA Astrophysics Data System (ADS)

In this paper we further explore and develop the quantum continuum mechanics (QCM) of Tao et al. [Phys. Rev. Lett. 103, 086401 (2009)] with the aim of making it simpler to use in practice. Our simplifications relate to the non-interacting part of the QCM equations, and primarily refer to practical implementations in which the groundstate stress tensor is approximated by its Kohn-Sham (KS) version. We use the simplified approach to directly prove the exactness of QCM for one-electron systems via an orthonormal formulation. This proof sheds light on certain physical considerations contained in the QCM theory and their implication on QCM-based approximations. The one-electron proof then motivates an approximation to the QCM (exact under certain conditions) expanded on the wavefunctions of the KS equations. Particular attention is paid to the relationships between transitions from occupied to unoccupied KS orbitals and their approximations under the QCM. We also demonstrate the simplified QCM semianalytically on an example system.

Gould, Tim; Jansen, Georg; Tokatly, I. V.; Dobson, John F.

2012-05-01

207

Why space has three dimensions: A quantum mechanical explanation  

NASA Astrophysics Data System (ADS)

The theoretical physics of a quantum mechanical model of space, relativistic quantum holography, is described. It specifies three dimensions, such as is validated by the nature of our spatial experience, but where additionally, quantum non-locality, which Feynman described as the only mystery of quantum theory, is made manifest by means of observable phase relationships. For example, synchronicity between events, and other phenomena such as are described by the geometric/Berry phase, etc., which are outside the bounds of classical explanation. It can therefore be hypothesized: a) that we live in a entirely quantum mechanical world/universe and not a classical mechanical one (where quantum phenomena are confined to the microscopic scale) as is the current generally held scientific view, b) that three spatial dimensions are a fundamental consequence of quantum mechanics, c) that quantum holography is a natural candidate to explain quantum gravity, such that mass/inertia concerns not the eigenvalues of some operator, but rather the observable gauge invariant phases of a state vector, postulated to be that of the universe itself, as a whole, and d) that this model provides a natural explanation in terms of relativistic quantum signal processing of any each individual's perception and cognition will be of a three dimensional world, defined similarly in relation to each individual's quantum state vector, describing its mind/body and associated gauge invariant phases or mindset, which have observable consequences, such that mental processes and events can cause neural events and processes! These testable hypotheses, if validated, will have profound implications for our understanding, radically changing our scientific perspective on the world, as we enter the new millennium. .

Marcer, Peter; Schempp, Walter

2000-05-01

208

Quantum mechanical model for two-state jump Markovian process  

Microsoft Academic Search

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

209

A Real Ensemble Interpretation of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ensemble have microscopic states, described by beables. The probabilities of quantum theory turn out to be just ordinary relative frequencies probabilities in these ensembles. Laws for the evolution of the beables of individual systems are given such that their ensemble relative frequencies evolve in a way that reproduces the predictions of quantum mechanics. These laws are highly non-local and involve a new kind of interaction between the members of an ensemble that define a quantum state. These include a stochastic process by which individual systems copy the beables of other systems in the ensembles of which they are a member. The probabilities for these copy processes do not depend on where the systems are in space, but do depend on the distribution of beables in the ensemble. Macroscopic systems then are distinguished by being large and complex enough that they have no copies in the universe. They then cannot evolve by the copy law, and hence do not evolve stochastically according to quantum dynamics. This implies novel departures from quantum mechanics for systems in quantum states that can be expected to have few copies in the universe. At the same time, we are able to argue that the center of masses of large macroscopic systems do satisfy Newton's laws.

Smolin, Lee

2012-10-01

210

Active Quantum Mechanics: Tutorials and Writing Assignments  

NSDL National Science Digital Library

This web site contains active-learning tutorials and writing assignments for upper-level undergraduate quantum mechanics. The tutorials focus on the mathematical formalism of quantum mechanics. The writing assignments focus on the interpretation of quantum mechanics, and particularly the role of experiments. The topics cover range from introduction to the Schrodinger equation through perturbation theory. In the course using these materials, students work in small groups to complete worksheet-based tutorials during class time, and do fairly typical homework problems and writing assignments, on their own.

Timberlake, Todd

2011-08-01

211

Statistical Structures Underlying Quantum Mechanics and Social Science  

NASA Astrophysics Data System (ADS)

Common observations of the unpredictability of human behavior and the influence of one question on the answer to another suggest social science experiments are probabilistic and may be mutually incompatible with one another, characteristics attributed to quantum mechanics (as distinguished from classical mechanics). This paper examines this superficial similarity in depth using the Foulis-Randall Operational Statistics language. In contradistinction to physics, social science deals with complex, open systems for which the set of possible experiments is unknowable and outcome interference is a graded phenomenon resulting from the ways the human brain processes information. It is concluded that social science is, in some ways, “less classical” than quantum mechanics, but that generalized “quantum” structures may provide appropriate descriptions of social science experiments. Specific challenges to extending “quantum” structures to social science are identified.

Wright, Ron

2007-08-01

212

Approach to Measurement to Quantum Mechanics.  

National Technical Information Service (NTIS)

An unconventional approach to the measurement problem in quantum mechanics is considered, the apparatus is treated as a classical system, belonging to the macro-world. In order to have a measurement the apparatus must interact with the quantum system. As ...

E. C. G. Sudarshan T. N. Sherry S. R. Gautam

1977-01-01

213

Web-based Quantum Mechanics II Course  

NSDL National Science Digital Library

This web site is an entire web-based Quantum Mechanics II Course based at the University of Tennessee; it has all instructional materials, in-class tutorials, simulations, links to other quantum resources, a discussion forum, homework assignments, and solutions.

Breinig, Marianne

2005-04-16

214

Quantum-Mechanical Model of Spacetime  

Microsoft Academic Search

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

215

Test of quantum mechanics by neutron interferometry  

NASA Astrophysics Data System (ADS)

Interferometry with massive elementary particles combines particle and wave features in a direct way. In this respect, neutrons are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their magnetic moment, and they are subject to all basic interactions, and they are sensitive to topological effects, as well. They play a pionieering role in the development of interferometry with even heavier objects, like atoms, molecules and clusters. Deterministic and stochastic partial absorption experiments can be described by Bell-type inequalities. Recent neutron interferometry experiments based on postselection methods renewed the discussion about quantum nonlocality and the quantum measuring process. It has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast. This indicates persisting coupling in phase space even in cases of spatially separated Schrödinger cat-like situations. These states are extremely fragile and sensitive to any kind of fluctuations or other decoherence processes. More complete quantum experiments also show that a complete retrieval of quantum states behind an interaction region becomes impossible in principle. The transition from a quantum world to a classical one is still an open question and will be tackled by means of dedicated decoherence experiments. Recent measurements deal with quantum contextuality and quantum state reconstruction. The observed results agree with quantum mechanical laws and may stimulate further discussions about their interpretations.

Rauch, H.

2008-06-01

216

Sedeonic Generalization of Relativistic Quantum Mechanics  

NASA Astrophysics Data System (ADS)

We represent sixteen-component values "sedeons," generating associative noncommutative space-time algebra. We demonstrate a generalization of relativistic quantum mechanics using sedeonic wave functions and sedeonic space-time operators. It is shown that the sedeonic second-order equation for the sedeonic wave function, obtained from the Einstein relation for energy and momentum, describes particles with spin 1/2. We showed that the sedeonic second-order wave equation can be reformulated in the form of the system of the first-order Maxwell-like equations for the massive fields. We proposed the sedeonic first-order equations analogous to the Dirac equation, which differ in space-time properties and describe several types of massive and massless particles. In particular we proposed four different equations, which could describe four types of neutrinos.

Mironov, Victor L.; Mironov, Sergey V.

217

Relative-State Formulation of Quantum Mechanics  

NSDL National Science Digital Library

This entry in the Stanford Encyclopedia of Philosophy 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, Jeffrey A.

2010-04-12

218

Many-Worlds Interpretation of Quantum Mechanics  

NSDL National Science Digital Library

This entry in the Stanford Encyclopedia of Philosophy 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

2010-04-09

219

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

220

Quantum mechanical effects on the shock Hugoniot.  

National Technical Information Service (NTIS)

Calculations of the locus of shock Hugoniot states of aluminum, using two equations of state that either omit or include a quantum mechanical treatment for the material's electronic excitations, will be presented. The difference between the loci will be a...

B. I. Bennett D. A. Liberman

1991-01-01

221

Symmetry and symmetry breaking in quantum mechanics.  

National Technical Information Service (NTIS)

In the world of infinitely small, the world of atoms, nuclei and particles, the quantum mechanics enforces its laws. The discovery of Quanta, this unbelievable castration of the Possible in grains of matter and radiation, in discrete energy levels compels...

P. Chomaz

1998-01-01

222

Quantum mechanical stabilization of Minkowski signature wormholes  

SciTech Connect

When one attempts to construct classical wormholes in Minkowski signature Lorentzian spacetimes violations of both the weak energy hypothesis and averaged weak energy hypothesis are encountered. Since the weak energy hypothesis is experimentally known to be violated quantum mechanically, this suggests that a quantum mechanical analysis of Minkowski signature wormholes is in order. In this note I perform a minisuperspace analysis of a simple class of Minkowski signature wormholes. By solving the Wheeler-de Witt equation for pure Einstein gravity on this minisuperspace the quantum mechanical wave function of the wormhole is obtained in closed form. The wormhole is shown to be quantum mechanically stabilized with an average radius of order the Planck length. 8 refs.

Visser, M.

1989-05-19

223

Supersymmetric q-deformed quantum mechanics  

SciTech Connect

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

224

Advantages of quantum mechanics on phase space  

NASA Astrophysics Data System (ADS)

Quantum mechanics formulated in terms of (wave) functions over phase space is shown to have numerous advantages over the standard approach. These advantages arise in the contexts of discussion of the theoretical framework and of descriptions of laboratory experiments.

Schroeck, F. E.

1994-01-01

225

Quantum Mechanics: Rigid Rotator Applet  

NSDL National Science Digital Library

This simulation shows time-dependent quantum state wavefunctions for the rigid rotator, the spherical harmonic states projected on a sphere. Position, angular momentum, and energy of the states can all be viewed, with phase shown with color. Energy-eigenstate wavefunctions, and combinations of states, can be created through changes in the amplitude and phase of the basis states using spinors, or through the creation of Gaussian wavefunctions with the mouse. The quantum numbers of the states are shown.

Falstad, Paul

2004-05-17

226

Controlled exchange interaction for quantum logic operations with spin qubits in coupled quantum dots  

SciTech Connect

A two-electron system confined in two coupled semiconductor quantum dots is investigated as a candidate for performing quantum logic operations with spin qubits. We study different processes of swapping the electron spins by a controlled switching on and off of the exchange interaction. The resulting spin swap corresponds to an elementary operation in quantum-information processing. We perform direct simulations of the time evolution of the two-electron system. Our results show that, in order to obtain the full interchange of spins, the exchange interaction should change smoothly in time. The presence of jumps and spikes in the time characteristics of the confinement potential leads to a considerable increase of the spin-swap time. We propose several mechanisms to modify the exchange interaction by changing the confinement potential profile and discuss their advantages and disadvantages.

Moskal, S.; Bednarek, S.; Adamowski, J. [Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Cracow (Poland)

2007-09-15

227

Macroscopic quantum mechanics in a classical spacetime.  

PubMed

We apply the many-particle Schrödinger-Newton equation, which describes the coevolution of a many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency-with a difference that depends on the internal structure of the object-and can be observable using current technology. For several objects, the Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another. PMID:23679686

Yang, Huan; Miao, Haixing; Lee, Da-Shin; Helou, Bassam; Chen, Yanbei

2013-04-22

228

Operator method in the problem of quantum anharmonic oscillator  

SciTech Connect

The problem of quantum anharmonic oscillator is considered as a test for a new non-perturbative method of the Schroedinger equation solution-the operator method (OM). It is shown that the OM zeroth-order approximation permits us to find such analytical inter-polation for eigenfunctions and eigenvalues of the Hamiltonian which ensures high accuracy within the entire range of the anharmonicity constant changing and for any quantum numbers. The OM subsequent approximations converge quickly to the exact solutions of the Schroedinger equation. These results are justified for the different types of anharmonicity (double-well potential, quasistationary states, etc.) and can be generalized for more complicated quantum-mechanical problems. 87 refs., 10 figs., 14 tabs.

Feranchuk, I.D.; Komarov, L.I.; Nichipor, I.V. [Byelorussian State Univ., Minsk (Russian Federation)] [and others

1995-03-01

229

The Strange World of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction; 2. Classical magnetic needles; 3. The Stern-Gerlach experiment; 4. The conundrum of projections; repeated measurements; 5. Probability; 6. The Einstein-Podolsky-Rosen paradox; 7. Variations on a theme by Einstein; 8. Optical interference; 9. Quantal interference; 10. Amplitudes; 11. Working with amplitudes; 12. Two slit inventions; 13. Quantum cryptography; 14. Quantum mechanics of a bouncing ball; 15. The wavefunction; Appendix A: a brief history of quantum mechanics; Appendix B: putting weirdness to work; Appendix C: sources; Appendix D: general questions; Appendix E: bibliography; Appendix F: skeleton answers for selected problems; Index.

Styer, Daniel F.

2000-02-01

230

Optimization of a Quantum Cascade Laser Operating in the Terahertz Frequency Range Using a Multiobjective Evolutionary Algorithm.  

National Technical Information Service (NTIS)

A quantum cascade (QC) laser is a specific type of semiconductor laser that operates through principles of quantum mechanics. In less than a decade QC lasers are already able to outperform previously designed double heterostructure semiconductor lasers. B...

T. A. Keller

2004-01-01

231

Probabilistic quantum logic operations using polarizing beam splitters  

Microsoft Academic Search

It has previously been shown that probabilistic quantum logic operations can\\u000abe performed using linear optical elements, additional photons (ancilla), and\\u000apost-selection based on the output of single-photon detectors. Here we describe\\u000athe operation of several quantum logic operations of an elementary nature,\\u000aincluding a quantum parity check and a quantum encoder, and we show how they\\u000acan be combined

T. B. Pittman; B. C. Jacobs; J. D. Franson

2001-01-01

232

GENERAL: Recapitulating Quantum Phase Space Representation by Virtue of Normally Ordered Gaussian Form of Wigner Operator  

NASA Astrophysics Data System (ADS)

Using the normally ordered Gaussian form of the Wigner operator we recapitulate the quantum phase space representation, we derive a new formula for searching for the classical correspondence of quantum mechanical operators; we also show that if there exists the eigenvector |qrangle?,? of linear combination of the coordinate and momentum operator, (?Q + ?P), where ?, ? are real numbers, and |qrangle?? is complete, then the projector |qrangle??langleq| must be the Radon transform of Wigner operator. This approach seems concise and physical appealing.

Fan, Hong-Yi; Xu, Xing-Lei; Li, Hong-Qi

2010-02-01

233

On reconciling quantum mechanics and local realism  

NASA Astrophysics Data System (ADS)

Accepting nonlocal quantum correlations requires us to reject special relativity and/or probability theory. We can retain both by revising our interpretation of quantum mechanics regarding the handling of separated systems, as quantum mechanics conflicts with local realism only in its treatment of separated systems. We cannot use the joint probability formula for cases of separated measurements. We use the marginals (partial traces) together with whatever priors we have from an understanding of the system. This program can reconcile quantum mechanics with local realism. An apparent obstacle to this program is the experimental evidence, but we argue that the experiments have been misinterpreted, and that when correctly interpreted they confirm local realism. We describe a local realistic account of one important Einstein-Poldosky-Rosen-Bohm (EPRB) experiment (Weihs et al6) that claims to demonstrate nonlocal entanglement. We present a local realistic system (experiment) that can be calibrated into both quantum and classical correlation domains via adjustment of parameters (`hidden variables') of the apparatus. Weihs incorrectly dismisses these parameters as uncritical. Nonlocal entanglement is seen to be an error. The rest of quantum mechanics remains intact, and remains highly valued as a powerful probability calculus for observables. Freed from the incoherent idea of nonlocal entanglement, we can leverage powerful classical ideas, such as semiclassical radiation theory, stochastic dynamics, classical noncommutativity/contextuality, measurement effects on state, etc., to augment or complement quantum mechanics. When properly interpreted and applied, quantum mechanics lives in peaceful harmony with the local realist conception, and both perspectives offer useful paradigms for describing systems.

Graft, Donald A.

2013-10-01

234

On the Classical Limit of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results of the standard approach, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper, we shall formulate the classical limit as a scaling limit in terms of an adimensional parameter ?. We shall take the first steps toward a comprehensive understanding of the classical limit, analyzing special cases of classical behavior in the framework of a precise formulation of quantum mechanics called Bohmian mechanics which contains in its own structure the possibility of describing real objects in an observer-independent way.

Allori, Valia; Zanghì, Nino

2009-01-01

235

Mind, matter, and quantum mechanics  

SciTech Connect

A theory of psychophysical phenomena is proposed. It resolves simultaneously four basic problems of science, namely the problems of the connections between: (1) mind and matter, (2), quantum theory and reality, (3) relativity theory and ''becoming,'' and (4) relativity theory and Bell's theorem.

Stapp, H.P.

1982-04-01

236

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

237

New methods for quantum mechanical reaction dynamics  

SciTech Connect

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

238

High-fidelity quantum logic operations and entangled ancilla states  

Microsoft Academic Search

We describe a high-fidelity approach to linear optics quantum computing in which the quantum logic operations always produce an output. A method for generating the required entangled states is also described.

J. D. Franson; M. M. Donegan; M. J. Fitch; B. C. Jacobs; T. B. Pittman

2003-01-01

239

Photon Quantum Mechanics in the Undergraduate Curriculum  

NASA Astrophysics Data System (ADS)

Although it has been discussed for centuries, the true nature of light is still being debated. In fact, the quantum mechanical aspects of light have only been observed within the past 30 years. Recent advances in technology have decreased the complexity of such tests, and the Department of Physics and Astronomy at Dickinson College has worked to infuse various quantum optics experiments throughout our curriculum. We describe a set of experiments that includes the existence of photons, single-photon interference, the quantum eraser, and tests of Bell's theorem. A primary motivation is bringing undergraduate students face to face with some of the fascinating and subtle aspects of quantum mechanics in a hands-on setting.

Pearson, Brett; Carson, Zack; Jackson, David

2011-06-01

240

Levitated Quantum Nano-Magneto-Mechanical Systems  

NASA Astrophysics Data System (ADS)

Quantum nanomechanical sysems have attracted much attention as they provide new macroscopic platforms for the study of quantum mechanics but may also have applications in ultra-sensitive sensing, high precision measurements and in quantum computing. In this work we study the control and cooling of a quantum nanomechanical system which is magnetically levitated via the Meissner effect. Supercurrents in nano-sized superconducting loops give rise to a motional restoring force (trap), when placed in an highly inhomogenous magnetic field and can yield complete trapping of all translational and rotational motions of the levitated nano-object with motional oscillation frequencies ?˜10-100MHz. As the supercurrents experience little damping this system will possess unprecendented motional quality factors, with Qmotion˜10^9-10^13, and motional superposition states may remain coherent for days. We describe how to execute sideband cooling through inductive coupling to a nearby flux qubit, cooling the mechanical motion close to the ground state.

Cirio, Mauro; Twamley, Jason; Brennen, Gavin K.; Milburn, Gerard J.

2011-03-01

241

Quantum opto-mechanics: Quantum optical control of massive mechanical resonators  

Microsoft Academic Search

The toolbox of quantum optics allows to achieve coherent quantum control over massive mechanical resonators by using radiation pressure of light inside optical cavities. Only recently, cavity-assisted ground state cooling of mechanical motion has been achieved both in the micro- and in the nanomechanical domain [1, 2]. Together with the strong coupling regime [3], this opens up a new parameter

Markus Aspelmeyer

2011-01-01

242

Quantum Mechanics Based Multiscale Modeling of Materials  

NASA Astrophysics Data System (ADS)

We present two quantum mechanics based multiscale approaches that can simulate extended defects in metals accurately and efficiently. The first approach (QCDFT) can treat multimillion atoms effectively via density functional theory (DFT). The method is an extension of the original quasicontinuum approach with DFT as its sole energetic formulation. The second method (QM/MM) has to do with quantum mechanics/molecular mechanics coupling based on the constrained density functional theory, which provides an exact framework for a self-consistent quantum mechanical embedding. Several important materials problems will be addressed using the multiscale modeling approaches, including hydrogen-assisted cracking in Al, magnetism-controlled dislocation properties in Fe and Si pipe diffusion along Al dislocation core.

Lu, Gang

2013-03-01

243

Quantum Mechanical Methods for Biomolecular Simulations  

Microsoft Academic Search

We discuss quantum mechanical methods for the description of the potential energy surface and for the treatment of nuclear\\u000a quantum effects in chemical and biological applications. Two novel electronic structure methods are described, including an\\u000a electronic structure-based explicit polarization (X-Pol) force field and an effective Hamiltonian molecular orbital and valence\\u000a bond (EH-MOVB) theory. In addition, we present two path integral

Kin-Yiu Wong; Lingchun Song; Wangshen Xie; Dan T. Major; Yen-Lin Lin; Alessandro Cembran; Jiali Gao

2009-01-01

244

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

245

Quantum-mechanical theory of the organic-dye laser  

Microsoft Academic Search

We develop a fully quantum-mechanical theory for the organic-dye-solution laser, obtain density-matrix equations of motion for the single-mode radiation-density operator and the matter-density operator, and solve and investigate the steady-state case. We generalize the usual Born-Markoff approximation master equation for two matter states to include four matter states, each one of which interacts with the laser radiation field. This allows

R. B. Schaefer; C. R. Willis

1976-01-01

246

Gaussian-Wigner distributions in quantum mechanics and optics  

Microsoft Academic Search

Gaussian kernels representing operators on the Hilbert space scrH=L2(openRn) are studied. Necessary and sufficient conditions on such a kernel in order that the corresponding operator be positive semidefinite, corresponding to a density matrix (cross-spectral density) in quantum mechanics (optics), are derived. The Wigner distribution method is shown to be a convenient framework for characterizing Gaussian kernels and their unitary evolution

R. Simon; E. C. G. Sudarshan; N. Mukunda

1987-01-01

247

Quantum-Opto-Mechanics: Towards quantum optical control of micromechanical resonators  

NASA Astrophysics Data System (ADS)

Current experiments aim to achieve coherent quantum control over massive mechanical resonators. Quantum optics provides a rich toolbox to prepare and detect mechanical quantum states, in particular by combining nano- and micromechanical resonators with high-finesse cavities. To realize the full potential of mechanical systems for quantum experiments eventually requires the conjunction of strongly coupled mechanical resonators with the preparation of quantum ground states. I will report our latest progress in Vienna towards these goals. I will also discuss the prospect of generating optomechanical quantum entanglement, which is at the heart of Schrödinger's cat paradox, and the possibility of mechanical quantum transducers as a new technology for quantum information processing.

Cole, Garrett

2009-05-01

248

Nonstandard extension of quantum logic and Dirac's bra-ket formalism of quantum mechanics  

Microsoft Academic Search

An extension of the quantum logical approach to the axiomatization of quantum mechanics usingnonstandard analysis methods is proposed. The physical meaning of a quantum logic as a lattice of propositions is conserved by its nonstandard extension. But not only the usual Hubert space formalism of quantum mechanics can be derived from the nonstandard extended quantum logic. Also the Dirac bra-ket

Arye Friedman

1994-01-01

249

Quantum Model of Classical Mechanics: Maximum Entropy Packets  

NASA Astrophysics Data System (ADS)

In a previous paper, a statistical method of constructing quantum models of classical properties has been described. The present paper concludes the description by turning to classical mechanics. The quantum states that maximize entropy for given averages and variances of coordinates and momenta are called ME packets. They generalize the Gaussian wave packets. A non-trivial extension of the partition-function method of probability calculus to quantum mechanics is given. Non-commutativity of quantum variables limits its usefulness. Still, the general form of the state operators of ME packets is obtained with its help. The diagonal representation of the operators is found. A general way of calculating averages that can replace the partition function method is described. Classical mechanics is reinterpreted as a statistical theory. Classical trajectories are replaced by classical ME packets. Quantum states approximate classical ones if the product of the coordinate and momentum variances is much larger than Planck constant. Thus, ME packets with large variances follow their classical counterparts better than Gaussian wave packets.

Hájí?ek, P.

2009-09-01

250

Space and time from quantum mechanics  

SciTech Connect

Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over collapse of the quantum-mechanical state vector when measurement is performed. Additionally, pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.

Chew, G.F.

1992-09-16

251

Space and time from quantum mechanics  

NASA Astrophysics Data System (ADS)

Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over the collapse of the quantum-mechanical state vector when measurement is performed. Additionally, the pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as a coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.

Chew, G. F.

1992-09-01

252

Remarks on Dersarkissian's cosmic quantum mechanics  

NASA Astrophysics Data System (ADS)

Dersarkissian (1984) has proposed a cosmic quantum mechanics (CQM) characterized by the constant hg approximately equal to 10 to the 75th ergs approximately equal to 10 to the 102nd h, where h is Planck's constant of ordinary quantum mechanics; galaxies are the elementary particles of CQM. Uncertainty arguments in CQM give a number of constraints on the masses of galaxies and thus a concrete way to test CQM. A condition that has to be satisfied for a massive body to be subject to CQM is proposed.

Massa, C.

1985-12-01

253

Atomic physics tests of nonlinear quantum mechanics  

NASA Astrophysics Data System (ADS)

Atomic physics experiments which test a nonlinear generalization of quantum mechanics recently formulated by Weinberg are described. The experiments search for a dependence of hyperfine transition frequencies or nuclear spin precession frequencies on the relative populations of the hyperfine or nuclear spin states. The experiments set limits less than 10 ?Hz on the size of the possible nonlinear contributions to these frequencies. In some cases this can be interpreted as a limit of less than ~10-26 on the fraction of binding energy per nucleon that could be due to a nonlinear correction to a nuclear Hamiltonian. The possibility that a nonlinear addition to quantum mechanics violates causality is discussed.

Bollinger, J. J.; Heinzen, D. J.; Itano, Wayne M.; Gilbert, S. L.; Wineland, D. J.

1991-08-01

254

Two basic Uncertainty Relations in Quantum Mechanics  

SciTech Connect

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

255

Remote implementations of partially unknown quantum operations of multiqubits  

SciTech Connect

We propose and prove the protocol of remote implementations of partially unknown quantum operations of multiqubits belonging to the restricted sets. Moreover, we obtain the general and explicit forms of restricted sets and present evidence of their uniqueness and optimization. In addition, our protocol has universal recovery operations that can enhance the power of remote implementations of quantum operations.

Wang Anmin [Quantum Theory Group, Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China)

2006-09-15

256

Generation of quantum logic operations from physical Hamiltonians  

Microsoft Academic Search

We provide a systematic analysis of the physical generation of single- and two-qubit quantum operations from Hamiltonians available in various quantum systems for scalable quantum information processing. We show that generation of single-qubit operations can be transformed into a steering problem on the Bloch sphere, which represents all Rz -equivalence classes of single-qubit operations, whereas the two-qubit problem can be

Jun Zhang; K. Birgitta Whaley

2005-01-01

257

Noncommutative unification of general relativity and quantum mechanics  

SciTech Connect

We present a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry is developed in terms of a noncommutative algebra A which is defined on a transformation groupoid {gamma} given by the action of a noncompact group G on the total space E of a principal fiber bundle over space-time M. The case is important since to obtain physical effects predicted by the model we should assume that G is a Lorentz group or some of its representations. We show that the generalized Einstein equation of the model has the form of the eigenvalue equation for the generalized Ricci operator, and all relevant operators in the quantum sector of the model are random operators; we study their dynamics. We also show that the model correctly reproduces general relativity and the usual quantum mechanics. It is interesting that the latter is recovered by performing the measurement of any observable. In the act of such a measurement the model 'collapses' to the usual quantum mechanics.

Heller, Michael; Pysiak, Leszek; Sasin, Wieslaw [Vatican Observatory, Vatican City, V-00120 Vatican City, Rome (Italy); Department of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw (Poland)

2005-12-15

258

Controlled exchange interaction for quantum logic operations with spin qubits in coupled quantum dots  

Microsoft Academic Search

A two-electron system confined in two coupled semiconductor quantum dots is investigated as a candidate for performing quantum logic operations with spin qubits. We study different processes of swapping the electron spins by a controlled switching on and off of the exchange interaction. The resulting spin swap corresponds to an elementary operation in quantum-information processing. We perform direct simulations of

S. Moskal; S. Bednarek; J. Adamowski

2007-01-01

259

Quantum mechanics and mixed quantum mechanics\\/molecular mechanics simulations of model nerve agents with acetylcholinesterase  

Microsoft Academic Search

.  ?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

260

Macroscopic Quantum Mechanics in a Classical Spacetime  

NASA Astrophysics Data System (ADS)

We apply the many-particle Schr"odinger-Newton equation, which describes the co-evolution of an many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schr"odinger-Newton equation for their centers of mass, which are degrees of freedom that can be monitored and manipulated at the quantum mechanical levels by state-of-the-art optoemchanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, we find that its quantum uncertainty evolves in a different frequency from its classical eigenfrequency --- with a difference that depends on the internal structure of the object, and can be observable using current technology. For several objects, the Schr"odinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet it is not allowed that quantum uncertainty to be transferred from one object to another through semiclassical gravity.

Yang, Huan

2013-04-01

261

Generalized coherent states under deformed quantum mechanics with maximum momentum  

NASA Astrophysics Data System (ADS)

Following the Gazeau-Klauder approach, we construct generalized coherent states (GCS) as the quantum simulator to examine the deformed quantum mechanics, which exhibits an intrinsic maximum momentum. We study deformed harmonic oscillators and compute their probability distribution and entropy of states exactly. Also, a particle in an infinite potential box is studied perturbatively. In particular, unlike usual quantum mechanics, the present deformed case increases the entropy of the Planck scale quantum optical system. Furthermore, for simplicity, we obtain the modified uncertainty principle (MUP) with the perturbative treatment up to leading order. MUP turns out to increase generally. However, for certain values of ? (a parameter of GCS), it is possible that the MUP will vanish and hence will exhibit the classical characteristic. This is interpreted as the manifestation of the intrinsic high-momentum cutoff at lower momentum in a perturbative treatment. Although the GCS saturates the minimal uncertainty in a simultaneous measurement of physical position and momentum operators, thus constituting the squeezed states, complete coherency is impossible in quantum gravitational physics. The Mandel Q number is calculated, and it is shown that the statistics can be Poissonian and super-/sub-Poissonian depending on ?. The equation of motion is studied, and both Ehrenfest’s theorem and the correspondence principle are recovered. Fractional revival times are obtained through the autocorrelation, and they indicate that the superposition of a classical-like subwave packet is natural in GCS. We also contrast our results with the string-motivated (Snyder) type of deformed quantum mechanics, which incorporates a minimum position uncertainty rather than a maximum momentum. With the advances of quantum optics technology, it might be possible to realize some of these distinguishing quantum-gravitational features within the domain of future experiments.

Ching, Chee Leong; Ng, Wei Khim

2013-10-01

262

States in the Hilbert space formulation and in the phase space formulation of quantum mechanics  

NASA Astrophysics Data System (ADS)

We consider the problem of testing whether a given matrix in the Hilbert space formulation of quantum mechanics or a function considered in the phase space formulation of quantum theory represents a quantum state. We propose several practical criteria for recognising states in these two versions of quantum physics. After minor modifications, they can be applied to check positivity of any operators acting in a Hilbert space or positivity of any functions from an algebra with a ?-product of Weyl type.

Tosiek, J.; Brzykcy, P.

2013-05-01

263

Operator quantum Zeno effect: protecting quantum information with noisy two-qubit interactions.  

PubMed

The time evolution of some quantum states can be slowed down or even stopped under frequent measurements. This is the usual quantum Zeno effect. Here, we report an operator quantum Zeno effect, in which the evolution of some physical observables is slowed down through measurements even though the quantum state changes randomly with time. Based on the operator quantum Zeno effect, we show how we can protect quantum information from decoherence with two-qubit measurements, realizable with noisy two-qubit interactions. PMID:23521242

Wang, Shu-Chao; Li, Ying; Wang, Xiang-Bin; Kwek, Leong Chuan

2013-03-08

264

Quantum mechanics is compatible with realism  

SciTech Connect

A new paradox of quantum mechanics has recently been proposed by an author claiming that any attempt to inject realism in physical theory is bound to lead to inconsistencies. In this paper the author shows that the mentioned paradox is not such a one and that at present there are no reasons to reject realism.

Burgos, M.E.

1987-08-01

265

Quantum mechanics and elements of reality  

Microsoft Academic Search

It is widely accepted that a Born probability of 1 is sufficient for the existence of a corresponding element of reality. Recently Vaidman has extended this idea to the ABL probabilities of the time-symmetrized version of quantum mechanics originated by Aharonov, Bergmann, and Lebowitz. Several authors have objected to Vaidman's time-symmetrized elements of reality without casting doubt on the widely

Ulrich Mohrhoff; Sri Aurobindo Ashram

1999-01-01

266

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

267

Mona Lisa - ineffable smile of quantum mechanics  

Microsoft Academic Search

The portrait of Mona Lisa is scrutinized with reference to quantum mechanics. The elements of different expressions are firstly recognized on her face. The contradictory details are then classified in two pictures that, undoubtedly representing distinct moods, confirm dichotomous character of the original. Consecutive discussion has lead to conclusion that the mysterious state Mona Lisa is in actually is coherent

Slobodan Prvanovic

2003-01-01

268

No time asymmetry from quantum mechanics  

NASA Astrophysics Data System (ADS)

With CPT-invariant initial conditions that commute with CPT-invariant final conditions, the respective probabilities (when defined) of a set of histories and its CPT reverse are equal, giving a CPT-symmetric universe. This leads me to question whether the asymmetry of the Gell-Mann-Hartle decoherence functional for ordinary quantum mechanics should be interpreted as an asymmetry of time.

Page, Don N.

1993-06-01

269

Quantum Mechanical Effects in Gravitational Collapse  

NASA Astrophysics Data System (ADS)

In this thesis we investigate quantum mechanical effects to various aspects of gravitational collapse. These quantum mechanical effects are implemented in the context of the Functional Schrödinger formalism. The Functional Schrödinger formalism allows us to investigate the time-dependent evolutions of the quantum mechanical effects, which is beyond the scope of the usual methods used to investigate the quantum mechanical corrections of gravitational collapse. Utilizing the time-dependent nature of the Functional Schrödinger formalism, we study the quantization of a spherically symmetric domain wall from the view point of an asymptotic and infalling observer, in the absence of radiation. To build a more realistic picture, we then study the time-dependent nature of the induced radiation during the collapse using a semi-classical approach. Using the domain wall and the induced radiation, we then study the time-dependent evolution of the entropy of the domain wall. Finally we make some remarks about the possible inclusion of backreaction into the system.

Greenwood, Eric

2010-01-01

270

Vlasov hydrodynamics of a quantum mechanical model  

Microsoft Academic Search

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

271

Quantum mechanical model for Maya Blue  

Microsoft Academic Search

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 Peña; César Contreras; Ana L. Montero; Russell Chianelli; Manuel Alvarado; Ramón Olivas; Luz M. Rodríguez; Héctor Camacho; Luis A. Montero-Cabrera

2008-01-01

272

A Quantum Mechanical Model of Spherical Supermembranes  

Microsoft Academic Search

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

273

Quantum mechanical Liouville model with attractive potential.  

National Technical Information Service (NTIS)

We study the quantum mechanical Liouville model with attractive potential which is obtained by Hamiltonian symmetry reduction from the system of a free particle on SL(2,R). The classical reduced system consists of a pair of Liouville subsystems which are ...

H. Kobayashi I. Tsutsui

1995-01-01

274

The Importance of Causality in Quantum Mechanics  

Microsoft Academic Search

Christian theology preferentially favors some philosophical interpretations of quantum mechanics. By using a case study of stationary states of atoms this paper examines the various interpretations. The preferred interpretation is that all localized events in space- time are part of chains of contiguous events traversing space-time at a rate limited by the speed of light. This is the process of

William R. Wharton

275

The Quantum Mechanical Basis of Conceptual Chemistry  

Microsoft Academic Search

Summary.  An experimentalist approaching theory for an understanding of conceptual chemistry that can be related to measurable properties, focuses on the electron density distribution. One finds in the topology of the electron density the definition of an atom, of the bonding between atoms, and of the boundary condition for the extension of quantum mechanics to an open system – to an

Richard F. W. Bader

2005-01-01

276

Subjective and objective probabilities in quantum mechanics  

SciTech Connect

We discuss how the apparently objective probabilities predicted by quantum mechanics can be treated in the framework of Bayesian probability theory, in which all probabilities are subjective. Our results are in accord with earlier work by Caves, Fuchs, and Schack, but our approach and emphasis are different. We also discuss the problem of choosing a noninformative prior for a density matrix.

Srednicki, Mark [Department of Physics, University of California, Santa Barbara, California 93106 (United States)

2005-05-15

277

Dissipation in Quantum Mechanics. The Harmonic Oscillator  

Microsoft Academic Search

The need for a quantum-mechanical formalism for systems with dissipation which is applicable to the radiation field of a cavity is discussed. Two methods that have been used in this connection are described. The first, which starts with the classical Newtonian equation of motion for a damped oscillator and applies the conventional formal quantization techniques, leads to an exact solution;

I. R. Senitzky

1960-01-01

278

Can quantum mechanics fool the cosmic censor?  

SciTech Connect

We revisit the mechanism for violating the weak cosmic-censorship conjecture (WCCC) by overspinning a nearly-extreme charged black hole. The mechanism consists of an incoming massless neutral scalar particle, with low energy and large angular momentum, tunneling into the hole. We investigate the effect of the large angular momentum of the incoming particle on the background geometry and address recent claims that such a backreaction would invalidate the mechanism. We show that the large angular momentum of the incident particle does not constitute an obvious impediment to the success of the overspinning quantum mechanism, although the induced backreaction turns out to be essential to restoring the validity of the WCCC in the classical regime. These results seem to endorse the view that the 'cosmic censor' may be oblivious to processes involving quantum effects.

Matsas, G. E. A.; Silva, A. R. R. da [Instituto de Fisica Teorica, Universidade Estadual Paulista, Rua Pamplona 145, 01405-900, Sao Paulo, SP (Brazil); Richartz, M. [Instituto de Fisica Gleb Wataghin, UNICAMP, C. P. 6165, 13083-970, Campinas, SP (Brazil); Saa, A. [Departamento de Matematica Aplicada, UNICAMP, C. P. 6065, 13083-859, Campinas, SP (Brazil); Vanzella, D. A. T. [Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, Avenida Trabalhador Sao-carlense, 400, C. P. 369, 13560-970, Sao Carlos, SP (Brazil)

2009-05-15

279

Electrical characteristics and operating mechanisms of nonvolatile memory devices fabricated utilizing core-shell CuInS2-ZnS quantum dots embedded in a poly(methyl methacrylate) layer  

NASA Astrophysics Data System (ADS)

Nonvolatile memory devices were fabricated with core-shell CuInS2-ZnS quantum dots (QDs) embedded in poly(methyl methacrylate) (PMMA). Capacitance-voltage (C-V) measurements at 300 K on the Al/CuInS2-ZnS QDs embedded in PMMA layer/p-Si device showed capacitance hysteresis behaviors with a flatband voltage shift. The memory window of the device increased with increasing applied sweep voltage and saturated at high electric fields due to the current leakage. Capacitance-time measurements showed that the retention time was larger than 1 × 105 s that was more than 10 years. The operating mechanisms for the devices are described on the basis of the C-V curves.

Wan Han, Kyu; Ho Lee, Min; Whan Kim, Tae; Yeol Yun, Dong; Woo Kim, Sung; Wook Kim, Sang

2011-11-01

280

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

281

A quantum mechanics lab on a chip.  

PubMed

Chip technology has evolved from the desire to further shrink the size of semiconductor devices. The high sensitivity of the electronic properties of nanostructured semiconductors can be used to detect humidity, temperature, magnetic fields and other fundamental quantities. This in turn can be used to use electronic devices for fluidic or biophysical measurements and drastically reduce the volume of such measurements. Small semiconductor devices on the other hand, if measured at low enough temperatures and other appropriate boundary conditions, clearly display quantum effects. The quantum mechanical properties of such small charged islands, also called artificial atoms, can be measured by transport experiments and an energy spectrum similar to the one of real atoms can be detected. A variety of other quantum systems, such as tunnel barriers or phase-coherent rings can also be realized with such techniques. By coupling different quantum circuits on a chip the charge flow can be monitored in a time-resolved fashion on the level of individual electrons. The perfection of such systems has advanced to a degree where basic quantum mechanical properties can be probed on a semiconductor chip. PMID:20664881

Ensslin, Klaus; Gustavsson, Simon; Gasser, Urszula; Küng, Bruno; Ihn, Thomas

2010-07-28

282

Quantum mechanical tunneling in methylamine dehydrogenase  

Microsoft Academic Search

We report a calculation for a trideuteration kinetic isotope effect (KIE) for the proton transfer step in the oxidation of methylamine by the quinoprotein methylamine dehydrogenase (MADH). The potential field includes 11025 atoms, and the dynamics are based on a quantum mechanical\\/molecular mechanical (QM\\/MM) direct dynamics simulation and canonical variational transition state theory with small-curvature multidimensional tunneling contributions. About 1%

Cristóbal Alhambra; Maria Luz Sánchez; José Corchado; Jiali Gao; Donald G. Truhlar

2001-01-01

283

Simplified quantum mechanics of light detection for quantum cryptography  

NASA Astrophysics Data System (ADS)

Strong light signals are detected reliably on a time scale of a nanosecond; however, known detectors of weak light signals used in quantum key distribution (QKD) are much slower; they involve pulse-shaping arbiters based on flip-flops that take many nanoseconds to produce a stable output. Based on a recently shown logical independence of quantum particles from the devices that they are employed to explain, we make use of quantum mechanics fine-tuned so that particles serve not as rigid foundations but as improvised hypotheses useful in models that describe the recorded behavior of devices. On the experimental side, we augment the arbitrating flip-flop of a detector so that it fans out to a matched pair of auxiliary flip-flops, and show how this imparts to a detector a "self-awareness" of its own teetering, as announced by disagreements between the auxiliary flip-flops. We introduce a quantum model of this arrangement, invoking a pair of probe particles, and show this model corresponds well to an experiment. The matched pair of auxiliary flip-flops not only confirms the model of hesitation in a detector, but serves as an instrument, both conceptual and practical, that gives an added dimension to the characterization of signal sources.

Myers, John M.; Madjid, F. Hadi

2004-08-01

284

The Quantum Mechanics of the Universe  

NASA Astrophysics Data System (ADS)

Classical general relativity predicts that the universe had a singular origin. The author shows that the singularity can be removed by quantum mechanics, just as in the case of the classical model of the atom. It is proposed that the quantum state of the universe is defined by a path integral over compact positive definite metrics. In a simple model this boundary condition leads to a wave function which can be regarded as a superposition of wave functions peaked around classical oscillating solutions with a long inflationary period.

Hawking, S. W.

285

The quantum mechanics of the universe  

NASA Astrophysics Data System (ADS)

Classical general relativity predicts that the universe had a singular origin. The author shows that the singularity can be removed by quantum mechanics, just as in the case of the classical model of the atom. He proposes that the quantum state of the universe is defined by a path integral over compact positive definite metrics. It is shown that in a simple model this boundary condition leads to a wave function which can be regarded as a superposition of wave functions peaked around classical oscillating solutions with a long inflationary period.

Hawking, S. W.

286

Quantum Logic Operations Using Single Photons and the Zeno Effect  

Microsoft Academic Search

We show that the quantum Zeno effect can be used to implement several quantum logic gates for photonic qubits, including a gate that is similar to the square-root of SWAP operation. The operation of these devices depends on the fact that photons can behave as if they were non-interacting fermions instead of bosons in the presence of a strong Zeno

J. D. Franson; B. C. Jacobs; T. B. Pittman

2004-01-01

287

Novel symmetries in N=2 supersymmetric quantum mechanical models  

NASA Astrophysics Data System (ADS)

We demonstrate the existence of a novel set of discrete symmetries in the context of the N=2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the X-Y plane under the influence of a magnetic field in the Z-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We show that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary N=2 SUSY quantum mechanical system can be shown to be a tractable model for the Hodge theory.

Malik, R. P.; Khare, Avinash

2013-07-01

288

F-theory Yukawa couplings and supersymmetric quantum mechanics  

NASA Astrophysics Data System (ADS)

The localized fermions on the intersection curve ? of D7-branes, are connected to a N=2 supersymmetric quantum mechanics algebra. Due to this algebra the fields obey a global U(1) symmetry. This symmetry restricts the proton decay operators and the neutrino mass terms. Particularly, we find that several proton decay operators are forbidden and the Majorana mass term is the only one allowed in the theory. A special SUSY QM algebra is studied at the end of the paper. In addition we study the impact of a non-trivial holomorphic metric perturbation on the localized solutions along each matter curve. Moreover, we study the connection of the localized solutions to an N=2 supersymmetric quantum mechanics algebra when background fluxes are turned on.

Oikonomou, V. K.

2012-03-01

289

Nano, Quantum, and Statistical Mechanics and Thermodynamics: Educational Sites  

NSDL National Science Digital Library

This collection of links provides access to web sites associated with nano, quantum, and statistical mechanics and thermodynamics. The links are arranged by type: basic principles (including classical thermodynamics), nano, quantum, and statistical mechanics, mathematical techniques, applications, and references.

290

Quantum Optics Networks, Unitary Operators and Computer Algebra  

Microsoft Academic Search

In linear quantum optics we consider phase shifters, beam splitters, displacement operations, squeezing operations etc. The evolution can be described by unitary operators using Bose creation and annihilation operators. This evolution can be reduced to matrix multiplication using unitary matrices. We derive these evolutions for the different unitary operators. Finally a computer algebra implementation is provided.

Willi-Hans Steeb; Yorick Hardy

2008-01-01

291

Noncommutative Chern-Simons quantum mechanics  

SciTech Connect

Chern-Simons quantum mechanics is generalized to the noncommutative plane in this paper. Compared with the commutative counterpart, we find that in addition to the mass of the charged particle, there is a dimensionless parameter which behaves interestingly when it takes zero value. We study this model from both classical and quantum aspects. We show that the classical theory has continuous limits when both the parameters tend to zero while the quantum aspect (energy spectra) does not have. We must regularize the spectra of the full theory properly when these parameters tend to zero in order to get the finite results. We resort to the Dirac theory and the Faddeev-Jackiw reduction, respectively, to show that the regularization we made is proper.

Jing Jian [Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029 (China); Department of Physics and Electronic, School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Liu Fenghua [Department of Physics and Electronic, School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Chen Jianfeng [Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029 (China)

2008-12-15

292

Quantum mechanics on Laakso spaces  

NASA Astrophysics Data System (ADS)

We first review the spectrum of the Laplacian operator on a general Laakso space before considering modified Hamiltonians for the infinite square well, parabola, and Coulomb potentials. Additionally, we compute the spectrum for the Laplacian and its multiplicities when certain regions of a Laakso space are compressed or stretched and calculate the Casimir force experienced by two uncharged conducting plates by imposing physically relevant boundary conditions and then analytically regularizing the resulting zeta function. Lastly, we derive a general formula for the spectral zeta function and its derivative for Laakso spaces with strict self-similar structure before listing explicit spectral values for some special cases

Kauffman, Christopher J.; Kesler, Robert M.; Parshall, Amanda G.; Stamey, Evelyn A.; Steinhurst, Benjamin A.

2012-04-01

293

Neutrino oscillations: Quantum mechanics vs. quantum field theory  

SciTech Connect

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

294

Calculus for Functions of Noncommuting Operators and General Phase-Space Methods in Quantum Mechanics. III. A Generalized Wick Theorem and Multitime Mapping  

Microsoft Academic Search

The new c-number calculus for functions of noncommuting operators, developed in Paper I and employed in Paper II to formulate a general phase-space description of boson systems, deals with situations involving equal-time operators only. In the present paper extensions are presented for the treatment of problems involving boson operators at two or more instants of time. The mapping of time-ordered

G. S. Agarwal; E. Wolf

1970-01-01

295

The Double Rotation as Invariant of Motion in Quantum Mechanics  

Microsoft Academic Search

Quantum mechanics may loose its weirdness if systematically geometric algebra methods would be used more. Crucial aspect is to find laws of quantum mechanics be present in macroworld in form of description of motions rather than objects. To help to reach this goal we suggest to use double rotation as one of base invariants in quantum mechanics. We suggest to

Dainis Zeps

2009-01-01

296

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 = PkeiSk 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

297

The ‘time of occurrence’ in quantum mechanics  

Microsoft Academic Search

Apart from serving as a parameter in describing the evolution of a system, time appears also as an observable property of\\u000a a system in experiments where one measures ‘the time of occurrence’ of an event associated with the system. However, while\\u000a the observables normally encountered in quantum theory (and characterized by self-adjoint operators or projection-valued measures)\\u000a correspond to instantaneous measurements,

M D Srinivas; R. Vijayalakshmi

1981-01-01

298

Quantum KAM technique and Yang{endash}Mills quantum mechanics  

SciTech Connect

We study a quantum analogue of the iterative perturbation theory by Kolmogorov used in the proof of the Kolmogorov{endash}Arnold{endash}Moser (KAM) theorem. The method is based on sequent canonical transformations with a {open_quote}{open_quote}running{close_quote}{close_quote} coupling constant {lambda}, {lambda}{sup 2}, {lambda}{sup 4}, etc. The proposed scheme, as its classical predecessor, is {open_quote}{open_quote}superconvergent{close_quote}{close_quote} in the sense that after the {ital n}th step, a theory is solved to the accuracy of order {lambda}{sup 2{ital n}{minus}1}. It is shown that the Kolmogorov technique corresponds to an infinite resummation of the usual perturbative series. The corresponding expansion is convergent for the quantum anharmonic oscillator due to the fact that it turns out to be identical to the Pade series. The method is easily generalizable to many-dimensional cases. The Kolmogorov technique is further applied to a non-perturbative treatment of Yang{endash}Mills quantum mechanics. A controllable expansion for the wave function near the origin is constructed. For large fields, we build an asymptotic adiabatic expansion in inverse powers of the field. This asymptotic solution contains arbitrary constants which are not fixed by the boundary conditions at infinity. To find them, we approximately match the two expansions in an intermediate region. We also discuss some analogies between this problem and the method of QCD sum rules. Copyright {copyright} 1995 Academic Press, Inc.

Halperin, I. [Department of Physics, Technion-Israel Institute of Technology, Haifa 32000 (Israel)

1995-12-01

299

Quantum Controlled-Not Gate Operation and Complete Bell-State Analysis Using Hybrid Quantum Circuits  

NASA Astrophysics Data System (ADS)

Here we propose a hybrid quantum circuit for achieving the quantum controlled-not (CNOT) gate operation on a photon-spin hybrid state. The hybrid quantum circuit consists of a nitrogen-vacancy (N-V) center and microtoroidal resonator coupling system, and a single photon waveguide. We implement the complete Bell state analysis using the proposed circuit. This proposed hybrid quantum circuit could enable a high fidelity of qubit manipulation and allows the feasible with the current experimental technologies.

He, Ling-yan; Cao, Cong; Tong, Xin; Wang, Chuan

2013-09-01

300

Quantum Mechanics, Gravity, and the Multiverse  

NASA Astrophysics Data System (ADS)

The discovery of accelerating expansion of the universe has led us to take the dramatic view that our universe may be one of the many universes in which low energy physical laws take different forms: the multiverse. I explain why/how this view is supported both observationally and theoretically, especially by string theory and eternal inflation. I then describe how quantum mechanics plays a crucial role in understanding the multiverse, even at the largest distance scales. The resulting picture leads to a revolutionary change of our view of spacetime and gravity, and completely unifies the paradigm of the eternally inflating multiverse with the many worlds interpretation of quantum mechanics. The picture also provides a solution to a long-standing problem in eternal inflation, called the measure problem, which I briefly describe.

Nomura, Yasunori

2012-04-01

301

Expectation values, experimental predictions, events and entropy in quantum gravitationally decohered quantum mechanics  

Microsoft Academic Search

We restate Kay's 1998 hypothesis which simultaneously offers an objective definition for the entropy of a closed system, a microscopic foundation for the Second Law, a resolution of the Information Loss (and other) Black-Hole Puzzle(s) and an objective mechanism for decoherence. Presupposing a conventional unitary theory of low-energy quantum gravity, it offers all this by taking the physical density operator

Bernard S. Kay; Varqa Abyaneh

2007-01-01

302

Supersymmetry in problems of quantum mechanics  

SciTech Connect

A connection is discussed between the group SU(2) and supersymmetry for a series of quantum mechanical problems. It is pointed out that the impossibility of factorizing Hamiltonians obtained based on representations of the group SU(2) indicates that the sypersymmetry of the system is broken. The authors consider a solution of the anharmonic oscillator problem, and they study properties of solutions for a series of problems for which supersymmetry is possible. They further construct a supersymmetric matrix Hamiltonian and determine supercharges.

Bagrov, V.G.; Vshivtsev, A.S.

1989-01-01

303

Auxiliary nRules of Quantum Mechanics  

Microsoft Academic Search

Standard quantum mechanics makes use of four auxiliary rules that allow the\\u000aSchrodinger solutions to be related to laboratory experience, such as the Born\\u000arule that connects square modulus to probability. These rules (here called the\\u000asRules) lead to some unacceptable results. They do not allow the primary\\u000aobserver to be part of the system. They do not allow individual

Richard A Mould

2005-01-01

304

Grounding quantum probability in psychological mechanism.  

PubMed

Pothos & Busemeyer (P&B) provide a compelling case that quantum probability (QP) theory is a better match to human judgment than is classical probability (CP) theory. However, any theory (QP, CP, or other) phrased solely at the computational level runs the risk of being underconstrained. One suggestion is to ground QP accounts in mechanism, to leverage a wide range of process-level data. PMID:23673043

Love, Bradley C

2013-06-01

305

Nonlinear Lattice Within Supersymmetric Quantum Mechanics Formalism  

NASA Astrophysics Data System (ADS)

In the last decades, the study of nonlinear one dimensional lattices has attracted much attention of the scientific community. One of these lattices is related to a simplified model for the DNA molecule, allowing to recover experimental results, such as the denaturation of DNA double helix. Inspired by this model we construct a Hamiltonian for a reflectionless potential through the Supersymmetric Quantum Mechanics formalism, SQM. Thermodynamical properties of such one dimensional lattice are evaluated aming possible biological applications.

Drigo Filho, E.; Ricotta, R. M.

2012-02-01

306

Quantum-mechanical noise in an interferometer  

Microsoft Academic Search

The interferometers now being developed to detect gravitational waves work by measuring the relative positions of widely separated masses. Two fundamental sources of quantum-mechanical noise determine the sensitivity of such an interferometer: (i) fluctuations in number of output photons (photon-counting error) and (ii) fluctuations in radiation pressure on the masses (radiation-pressure error). Because of the low power of available continuous-wave

Carlton Caves

1981-01-01

307

Collocation method for fractional quantum mechanics  

SciTech Connect

We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on little sinc functions, which discretizes the Schroedinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a Wentzel-Kramers-Brillouin analysis is performed.

Amore, Paolo; Hofmann, Christoph P.; Saenz, Ricardo A. [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico); Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Division Quimica Teorica, Diagonal 113 y 64 S/N, Sucursal 4, Casilla de correo 16, 1900 La Plata (Argentina)

2010-12-15

308

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

309

Deformation quantization of noncommutative quantum mechanics  

Microsoft Academic Search

The Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantization. In this paper, we investigate the basic aspects of deformation quantization for noncommutative quantum mechanics (NCQM). We first prove some general relations of the Weyl correspondence in non-commuting phase-space. Then we derive explicit form of the Wigner

Sicong Jing; Fen Zuo; Taihua Heng

2004-01-01

310

Landau problem in noncommutative quantum mechanics  

Microsoft Academic Search

The Landau problem in non-commutative quantum mechanics (NCQM) is studied. First by solving the Schrödinger equations on noncommutative (NC) space we obtain the Landau energy levels and the energy correction that is caused by space-space noncommutativity. Then we discuss the noncommutative phase space case, namely, space-space and momentum-momentum non-commutative case, and we get the explicit expression of the Hamiltonian as

Dulat Sayipjamal; Kang Li

2008-01-01

311

1/N expansion in noncommutative quantum mechanics  

SciTech Connect

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

312

The 1925 Born and Jordan paper ``On quantum mechanics''  

NASA Astrophysics Data System (ADS)

The 1925 paper ``On quantum mechanics'' by M. Born and P. Jordan, and the sequel ``On quantum mechanics II'' by M. Born, W. Heisenberg, and P. Jordan, developed Heisenberg's pioneering theory into the first complete formulation of quantum mechanics. The Born and Jordan paper is the subject of the present article. This paper introduced matrices to physicists. We discuss the original postulates of quantum mechanics, present the two-part discovery of the law of commutation, and clarify the origin of Heisenberg's equation. We show how the 1925 proof of energy conservation and Bohr's frequency condition served as the gold standard with which to measure the validity of the new quantum mechanics.

Fedak, William A.; Prentis, Jeffrey J.

2009-02-01

313

Suppression of quantum-mechanical reflection by environmental decoherence  

NASA Astrophysics Data System (ADS)

In quantum mechanics an incoming particle wave packet with sufficient energy will undergo both transmission and reflection when encountering a barrier of lower energy, but in classical mechanics there is no reflection, only transmission. In this paper we seek to explain the disappearance of quantum-mechanical reflection in the quasiclassical limit, using the standard machinery of decoherence through environmental interaction. We consider two models. In the first, the incoming particle is classicalized by coupling to an environment and modeled using a standard master equation of Lindblad form with Lindblad operator proportional to position (the simplest version of quantum Brownian motion). We find, however, that suppression of reflection is achieved only for environmental interaction so strong that large fluctuations in momentum are generated, which blurs the distinction between incoming and reflected wave packets. This negative conclusion also holds for a complex potential which has similar implications for attempts to understand the suppression of the Zeno effect using the same mechanism (discussed in more detail elsewhere). A different master equation with Lindblad operator proportional to momentum is shown to be successful in suppressing reflection without large fluctuations but such a master equation is unphysical. We consider a second model in which the barrier is modeled quantum mechanically by a massive target particle coupled to an environment to maintain it in a quasiclassical state. This avoids the fluctuations problem since the incoming particle is not coupled to the environment directly. We find that reflection is significantly suppressed as long as the decoherence time scale of the target particle is much smaller than certain characteristic scattering time scales of the incoming particle, or equivalently, as long as the velocity fluctuations in the target are larger than the velocity of the incoming particle.

Bedingham, D. J.; Halliwell, J. J.

2013-08-01

314

Experimental demonstration of quantum logic operations using linear optical elements  

Microsoft Academic Search

Probabilistic quantum logic operations can be implemented using linear optical elements, additional photons (ancilla), and post-selection based on the results of measurements made on the ancilla photons. Here we describe the experimental demonstration of several quantum logic devices of that kind, including a quantum parity check and a destructive controlled-NOT (CNOT) gate. An experimental demonstration of feed-forward control for use

J. D. Franson; B. C. Jacobs; T. B. Pittman

2003-01-01

315

Invariant, non-invariant operators and quantum fluctuations in tunneling  

NASA Astrophysics Data System (ADS)

Quantum fluctuations occurring in tunneling processes are studied via the operator Hamilton-Jacobi (HJ) formalism, generated from the principles of Feynman and Schwinger. It is shown that due to these quantum fluctuations and the ordering procedure, the operator HJ equation does not transform likewise its classical counterpart, and that two kinds of quantum operators (one invariant and the other non-invariant), associated to a classical invariant, can be unambiguously distinguished within this formalism. Useful discussions with Professor R.J. Finkelstein, B. Haeri, F.L.A. Machado and H. Romero on the contents of this paper and financial support for this research from CNPq-Brazil are gratefully acknowledged.

Nassar, Antônio B.

1988-05-01

316

Bayesian predictive density operators for exchangeable quantum-statistical models  

SciTech Connect

Quantum state estimation has been widely investigated and there are mainly two approaches proposed: One is based on the point estimation of an unknown parameter and the other is based on the Bayesian method. We adopt the relative entropy from the true state to a predictive density operator as a loss function. We consider exchangeable quantum models with an arbitrary chosen measurement and show that Bayesian predictive density operators are the best predictive density operators when we evaluate them by using the average relative entropy based on a prior. This result is a quantum version of Aitchison's result in classical statistics.

Tanaka, Fuyuhiko; Komaki, Fumiyasu [Department of Mathematical Informatics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656 (Japan)

2005-05-15

317

Generation of quantum logic operations from physical Hamiltonians  

SciTech Connect

We provide a systematic analysis of the physical generation of single- and two-qubit quantum operations from Hamiltonians available in various quantum systems for scalable quantum information processing. We show that generation of single-qubit operations can be transformed into a steering problem on the Bloch sphere, which represents all R{sub z}-equivalence classes of single-qubit operations, whereas the two-qubit problem can be generally transformed into a steering problem in a tetrahedron representing all the local-equivalence classes of two-qubit operations (the Weyl chamber). We use this approach to investigate several physical examples for the generation of two-qubit operations. The steering approach provides useful guidance for the realization of various quantum computation schemes.

Zhang Jun [Department of Chemistry and Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720 (United States); Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720 (United States); Whaley, K. Birgitta [Department of Chemistry and Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720 (United States)

2005-05-15

318

Representations for a spins-first approach to quantum mechanics  

NASA Astrophysics Data System (ADS)

In the Paradigms in Physics Curriculum at Oregon State University, we take a spins-first approach to quantum mechanics using a java simulation of successive Stern-Gerlach experiments to explore the postulates. The experimental schematic is a diagrammatic representation that we use throughout our discussion of quantum measurements. With a spins-first approach, it is natural to start with Dirac bra-ket language for states, observables, and projection operators. We also use explicit matrix representations of operators and ask students to translate between the Dirac and matrix languages. The projection of the state onto a basis is represented with a histogram. When we subsequently introduce wave functions, the wave function attains a natural interpretation as the continuous limit of these discrete histograms or a projection of a Dirac ket onto position or momentum eigenstates. We are able to test the students' facility with moving between these representations in later modules.

Manogue, Corinne; Gire, Elizabeth; McIntyre, David; Tate, Janet

2012-02-01

319

Continuous quantum error correction through local operations  

NASA Astrophysics Data System (ADS)

We propose local strategies to protect global quantum information. The protocols, which are quantum error-correcting codes for dissipative systems, are based on environment measurements, direct feedback control, and simple encoding of the logical qubits into physical qutrits whose decaying transitions are indistinguishable and equally probable. The simple addition of one extra level in the description of the subsystems allows for local actions to fully and deterministically protect global resources such as entanglement. We present codes for both quantum jump and quantum state diffusion measurement strategies and test them against several sources of inefficiency. The use of qutrits in information protocols suggests further characterization of qutrit-qutrit disentanglement dynamics, which we also give together with simple local environment measurement schemes able to prevent distillability sudden death and even enhance entanglement in situations in which our feedback error correction is not possible.

Mascarenhas, Eduardo; Marques, Breno; Cunha, Marcelo Terra; Santos, Marcelo França

2010-09-01

320

Demonstration of Nondeterministic Quantum Logic Operations Using Linear Optical Elements  

Microsoft Academic Search

Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)] recently showed that nondeterministic quantum logic operations could be performed using linear optical elements, additional photons (ancilla), and postselection based on the output of single-photon detectors. Here we report the experimental demonstration of two logic devices of this kind, a destructive controlled-NOT (CNOT) gate and a quantum parity check. These two

T. B. Pittman; B. C. Jacobs; J. D. Franson

2002-01-01

321

Implementation of a simple operator-quantum-error-correction scheme  

NASA Astrophysics Data System (ADS)

We provide a simple yet interesting example of operator quantum error correction avoiding fully correlated noise. Our scheme requires no initialization of ancillae, which can thus be in the uniformly mixed state. We demonstrate our scheme experimentally by making use of a three-qubit NMR quantum computer.

Kondo, Yasushi; Bagnasco, Chiara; Nakahara, Mikio

2013-08-01

322

Connecting Spin and Statistics in Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor (-1)2 s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required.

Jabs, Arthur

2010-07-01

323

Adaptive Perturbation Theory I: Quantum Mechanics  

SciTech Connect

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

324

Bohmian Mechanics In A Macroscopic Quantum System  

NASA Astrophysics Data System (ADS)

In the so called `causal' interpretation of quantum mechanics, an electron is considered as a particle and such particle is influenced not only by a classical but also by a so called quantum potential. This idea was developed by Professor Bohm in an important paper. In this paper we use some of the basics of this interpretation in a financial option pricing environment. The causal interpretation allows for trajectories. Path breaking work by Professors Bohm and Hiley and Khrennikov and Choustova have made that the causal interpretation is a step closer to potential applications in social science. In this paper we consider the wave function as a wave of information. We consider the gradient of the phase of this wave function and show how the option price could be influenced by this gradient.

Haven, Emmanuel

2006-01-01

325

Unstable trajectories and the quantum mechanical uncertainty  

SciTech Connect

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

326

Unstable trajectories and the quantum mechanical uncertainty  

NASA Astrophysics Data System (ADS)

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.

2008-08-01

327

Direct Quantum Mechanical Simulations of Shocked Energetic Materials.  

National Technical Information Service (NTIS)

Quantum mechanical calculations based on density functional theory (DFT) are used to study dynamic behavior of shocked energetic materials (EM). In this work, we present results of quantum molecular dynamics (QMD) simulations of shocked pentaerythritol te...

B. M. Rice R. Balu W. D. Mattson

2008-01-01

328

Spectral triplets, statistical mechanics and emergent geometry in non-commutative quantum mechanics  

NASA Astrophysics Data System (ADS)

We show that when non-commutative quantum mechanics is formulated on the Hilbert space of Hilbert-Schmidt operators acting on a classical configuration space, spectral triplets as introduced by Connes in the context of non-commutative geometry arise naturally. A distance function as defined by Connes can therefore also be introduced. We proceed to give a simple algorithm to compute this function in generic situations. Using this we compute the distance between pure and mixed states on the quantum Hilbert space and demonstrate a tantalizing link between statistics and geometry.

Scholtz, F. G.; Chakraborty, B.

2013-03-01

329

QUANTUM MECHANICS: Enhanced: Schrodinger's Cat Is Out of the Hat.  

PubMed

In 1935, Erwin Schrödinger suggested his famous gedanken experiment of the cat that is simultaneously "dead" and "alive" inside its box until the box is opened. But as Tesche explains in her Perspective, such a macroscopic manifestation of quantum mechanics has remained elusive until recently. The experiments by van der Wal et al. are an important step toward demonstrating that quantum mechanics can describe macroscopic phenomena. The approach may be exploited in quantum computing and quantum cryptography. PMID:17780511

Tesche, C

2000-10-27

330

Combined quantum mechanical\\/molecular mechanics modeling for large organometallic and metallobiochemical systems  

Microsoft Academic Search

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

331

Quantum Logic Operations Using Single Photons and the Zeno Effect  

Microsoft Academic Search

We show that the quantum Zeno effect can be used to implement several quantum\\u000alogic gates for photonic qubits, including a gate that is similar to the\\u000asquare-root of SWAP operation. The operation of these devices depends on the\\u000afact that photons can behave as if they were non-interacting fermions instead\\u000aof bosons in the presence of a strong Zeno

J. D. Franson; B. C. Jacobs; T. B. Pittman

2004-01-01

332

Hybrid protocol of remote implementations of quantum operations  

SciTech Connect

We propose a protocol of remote implementations of quantum operations by hybridizing bidirectional quantum-state teleportation (BQST) [Huelga et al., Phys. Rev. A 63, 042303 (2001)] and the Wang protocol [Wang, Phys. Rev. A 74, 032317 (2006)]. The protocol is available for remote implementations of quantum operations in the restricted sets specified in the paper. We also give a proof of the protocol and point out its optimization. As an extension, this hybrid protocol can be reduced to the BQST and Wang protocols.

Zhao Ningbo; Wang Anmin [Quantum Theory Group, Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China)

2007-12-15

333

Statistical Mechanics of Quantum Integrable Systems  

NASA Astrophysics Data System (ADS)

Recent developments in statistical mechanics of quantum integrable systems are reviewed. Those studies are fundamental and have a renewed interest related to newly developing fields such as atomic Bose-Einstein condensations, photonic crystals and quantum computations. After a brief summary of the basic concepts and methods, the following three topics are discussed. First, by the thermal Bethe ansatz (TBA), a hard-core Bose gas is exactly solved. The model includes fully the effect of excluded volume and is identified to be a c=1 conformal field theory. Second, the cluster expansion method based on the periodic boundary condition for the Bethe wave function, which we call the Bethe ansatz cluster expansion (BACE) method, is developed for a ?-function gas and the XXX Heisenberg chain. This directly proves the TBA and reveals intrinsic properties of quantum integrable systems. Third, for a ?-function gas, the integral equations for the distribution functions of the quasi-momentum and the quasi-particle energy are solved in the form of power series. In the weak coupling case, the results reproduce those of Bogoliubov theory.

Wadati, Miki; Kato, Go; Iida, Toshiaki

334

Supersymmetric quantum mechanics and its applications  

SciTech Connect

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

335

BiHermitian supersymmetric quantum mechanics  

NASA Astrophysics Data System (ADS)

BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2, 2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kähler manifolds recently developed by Gualtieri in [33]. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li in [9].

Zucchini, Roberto

2007-04-01

336

Hidden geometric character of relativistic quantum mechanics  

NASA Astrophysics Data System (ADS)

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 4×4 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 4×4 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, José B.

2007-01-01

337

Landau Problem in Noncommutative Quantum Mechanics  

Microsoft Academic Search

The Landau problem in non-commutative quantum mechanics (NCQM) is studied.\\u000aFirst by solving the Schr$\\\\ddot{o}$dinger equations on noncommutative(NC) space\\u000awe obtain the Landau energy levels and the energy correction that is caused by\\u000aspace-space noncommutativity. Then we discuss the noncommutative phase space\\u000acase, namely, space-space and momentum-momentum non-commutative case, and we\\u000aget the explicit expression of the Hamiltonian as well

Sayipjamal Dulat; Kang Li

2008-01-01

338

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

339

Perspectives: Quantum Mechanics on Phase Space  

NASA Astrophysics Data System (ADS)

The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical particle model descriptions exhibiting either Galileian or Lorentzian symmetry. The structures of fundamental importance are the relevant (Lie) groups of symmetries and their homogeneous (and associated) spaces that, in the situations of interest, also possess Hamiltonian structures. Comments are made on the relation between the theory outlined and a recent paper by Carmeli, Cassinelli, Toigo, and Vacchini.

Brooke, J. A.; Schroeck, F. E.

2005-11-01

340

High-fidelity continuous-variable quantum teleportation toward multistep quantum operations  

SciTech Connect

The progress in quantum operations of continuous-variable (CV) schemes can be reduced to that in CV quantum teleportation. The fidelity of quantum teleportation of an optical setup is limited by the finite degree of quantum correlation that can be prepared with a pair of finitely squeezed states. Reports of improvement of squeezing level have appeared recently, and we adopted the improved methods in our experimental system of quantum teleportation. As a result, we teleported a coherent state with a fidelity F=0.83{+-}0.01, which is better than any other figures reported to date, to our knowledge. In this paper, we introduce a measure n{sub s}, the number of teleportations expected to be carried out sequentially. Our result corresponds to n{sub s}=5.0{+-}0.4. It suggests that our improvement would enable us to proceed toward more advanced quantum operations involving multiple steps.

Yukawa, Mitsuyoshi; Furusawa, Akira [Department of Applied Physics, School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656 (Japan); CREST, Japan Science and Technology (JST) Agency, 1-9-9 Yaesu, Chuo-ku, Tokyo 103-0028 (Japan); Benichi, Hugo [Department of Applied Physics, School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656 (Japan); Department of Physics, Ecole Polytechnique, 91128 Palaiseau Cedex (France)

2008-02-15

341

Universal programmable quantum circuit schemes to emulate an operator.  

PubMed

Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we present a new quantum circuit design technique resulting in two general programmable circuit schemes. The circuit schemes can be used to simulate any given operator by setting the angle values in the circuit. This provides a fixed circuit design whose angles are determined from the elements of the given matrix-which can be non-unitary-in an efficient way. We also give both the classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations. For the electronic structure simulation on a quantum computer, one has to perform the following steps: prepare the initial wave function of the system; present the evolution operator U = e(-iHt) for a given atomic and molecular Hamiltonian H in terms of quantum gates array and apply the phase estimation algorithm to find the energy eigenvalues. Thus, in the circuit model of quantum computing for quantum chemistry, a crucial step is presenting the evolution operator for the atomic and molecular Hamiltonians in terms of quantum gate arrays. Since the presented circuit designs are independent from the matrix decomposition techniques and the global optimization processes used to find quantum circuits for a given operator, high accuracy simulations can be done for the unitary propagators of molecular Hamiltonians on quantum computers. As an example, we show how to build the circuit design for the hydrogen molecule. PMID:23267476

Daskin, Anmer; Grama, Ananth; Kollias, Giorgos; Kais, Sabre

2012-12-21

342

Universal programmable quantum circuit schemes to emulate an operator  

SciTech Connect

Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we present a new quantum circuit design technique resulting in two general programmable circuit schemes. The circuit schemes can be used to simulate any given operator by setting the angle values in the circuit. This provides a fixed circuit design whose angles are determined from the elements of the given matrix-which can be non-unitary-in an efficient way. We also give both the classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations. For the electronic structure simulation on a quantum computer, one has to perform the following steps: prepare the initial wave function of the system; present the evolution operator U=e{sup -iHt} for a given atomic and molecular Hamiltonian H in terms of quantum gates array and apply the phase estimation algorithm to find the energy eigenvalues. Thus, in the circuit model of quantum computing for quantum chemistry, a crucial step is presenting the evolution operator for the atomic and molecular Hamiltonians in terms of quantum gate arrays. Since the presented circuit designs are independent from the matrix decomposition techniques and the global optimization processes used to find quantum circuits for a given operator, high accuracy simulations can be done for the unitary propagators of molecular Hamiltonians on quantum computers. As an example, we show how to build the circuit design for the hydrogen molecule.

Daskin, Anmer; Grama, Ananth; Kollias, Giorgos [Department of Computer Science, Purdue University, West Lafayette, Indiana 47907 (United States); Kais, Sabre [Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 (United States); Qatar Environment and Energy Research Institute, Doha (Qatar)

2012-12-21

343

Efficient Synthesis of Quantum Logic Circuits by Rotation-based Quantum Operators and Unitary Functional Bi-decomposition  

Microsoft Academic Search

1. Abstract Quantum information processing technology is in its pioneering stage and no efficient method for synthesizing quantum circuits has been introduced so far. This paper introduces an efficient analysis and synthesis framework for quantum logic circuits. The proposed synthesis algorithm and flow can generate a quantum circuit using the most basic quantum operators, i.e., the rotation and controlled-rotation primitives.

Afshin Abdollahi; Massoud Pedram

344

Super classical quantum mechanics: The best interpretation of nonrelativistic quantum mechanics  

NASA Astrophysics Data System (ADS)

It has been shown that Newtonian classical mechanics (NCM) suffers from several kinds of chaotic indeterminacies. That means, a large set of problems treated with NCM gives results which are in wild disagreement with observation. In the present paper, these shortcomings are repaired in a simple, obvious, and essentially unique manner. The NCM theory is thereby transformed into a new theory which is fully equivalent to the Heisenberg, Schrödinger, and Dirac nonrelativistic quantum mechanics, with the vital addition of Born's probabilistic interpretation of the wave function built in from the start. I call this new theory ``super classical quantum mechanics'' (SCQM). Using Ehrenfest's theorem of 1927, the classical limit of the new theory, SCQM, is seen to give exactly the results expected of the repaired Newtonian theory of classical mechanics.

Lamb, Willis E.

2001-04-01

345

Loop transfer matrix and loop quantum mechanics  

NASA Astrophysics Data System (ADS)

The gonihedric model of random surfaces on a 3d euclidean lattice has equivalent representation in terms of transfer matrix K(Qi,Qf) which describes the propagation of loops Q. We extend the previous construction of loop transfer matrix to the case of non-zero self-intersection coupling constant kappa. We introduce loop generalization of Fourier transformation which allows to diagonalize transfer matrices depending on symmetric difference of loops and express all eigenvalues of 3d loop transfer matrix through the correlation functions of the corresponding 2d statistical system. The loop Fourier transformation allows to carry out analogy with quantum mechanics of point particles, to introduce conjugate momentum loop P and to define loop quantum mechanics. We also consider transfer matrix on 4d lattice which describes propagation of memebranes. This transfer matrix can also be diagonalized by using generalized Fourier transformation, and all its eigenvalues are equal to the correlation functions of the corresponding 3d statistical system. Particularly the free energy of the 4d membrane system is equal to the free energy of 3d gonihedric system of loops.

Savvidy, George K.

2000-09-01

346

Molecular model with quantum mechanical bonding information.  

PubMed

The molecular structure can be defined quantum mechanically thanks to the theory of atoms in molecules. Here, we report a new molecular model that reflects quantum mechanical properties of the chemical bonds. This graphical representation of molecules is based on the topology of the electron density at the critical points. The eigenvalues of the Hessian are used for depicting the critical points three-dimensionally. The bond path linking two atoms has a thickness that is proportional to the electron density at the bond critical point. The nuclei are represented according to the experimentally determined atomic radii. The resulting molecular structures are similar to the traditional ball and stick ones, with the difference that in this model each object included in the plot provides topological information about the atoms and bonding interactions. As a result, the character and intensity of any given interatomic interaction can be identified by visual inspection, including the noncovalent ones. Because similar bonding interactions have similar plots, this tool permits the visualization of chemical bond transferability, revealing the presence of functional groups in large molecules. PMID:21894893

Bohórquez, Hugo J; Boyd, Russell J; Matta, Chérif F

2011-09-06

347

Probability in the formalism of quantum mechanics on phase space  

NASA Astrophysics Data System (ADS)

The methods of Born and Einstein are used to obtain the probability density in the formalism of quantum mechanics on phase space. The resulting probability leads to a contextual measurement scheme. The Wigner representation, the Husimi representation and the mass shell representation are discussed from the point of view of quantum mechanics on phase space. We also give ramifications for paradoxes in standard quantum mechanics.

Schroeck, Franklin E., Jr.

2012-02-01

348

Mind, Matter and Quantum Mechanics (2nd edition)  

Microsoft Academic Search

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

G Mahler

2004-01-01

349

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

Microsoft Academic Search

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

H. P. Stapp

2004-01-01

350

INTRODUCTION TO RELATIVISTIC QUANTUM MECHANICS AND THE DIRAC EQUATION  

Microsoft Academic Search

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

351

Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics  

NASA Astrophysics Data System (ADS)

We extend the mathematical theory of quantum hypothesis testing to the general W*-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.

Jakši?, V.; Ogata, Y.; Pillet, C.-A.; Seiringer, R.

2012-07-01

352

Multiplication of distributions and Dirac formalism of quantum mechanics  

SciTech Connect

We define multiplication and convolution of distributions and ultradistributions by introducing the notions of evaluation of distributions and integration of ultradistributions. An application is made to an interpretation of the Dirac formalism of quantum mechanics. The role of the Hilbert space of states is played by what is termed a Hermitian orthonormal system, and operators are replaced by the generalized matrices. We describe a simple example of one dimensional free particle and construct explicitly a representation of the Weyl algebra as the generalized matrices.

Kim, Namhoon [Department of Mathematics Education, Hongik University, 72-1 Sangsu-dong, Mapo-gu, Seoul 121-791 (Korea, Republic of)

2010-02-15

353

Twisting all the way: From classical mechanics to quantum fields  

SciTech Connect

We discuss the effects that a noncommutative geometry induced by a Drinfeld twist has on physical theories. We systematically deform all products and symmetries of the theory. We discuss noncommutative classical mechanics, in particular its deformed Poisson bracket and hence time evolution and symmetries. The twisting is then extended to classical fields, and then to the main interest of this work: quantum fields. This leads to a geometric formulation of quantization on noncommutative space-time, i.e., we establish a noncommutative correspondence principle from *-Poisson brackets to * commutators. In particular commutation relations among creation and annihilation operators are deduced.

Aschieri, Paolo [Centro Studi e Ricerche 'Enrico Fermi' Compendio Viminale, 00184 Rome (Italy); Dipartimento di Scienze e Tecnologie Avanzate, Universita del Piemonte Orientale, and INFN, Sezione di Torino Via Bellini 25/G 15100 Alessandria (Italy); Lizzi, Fedele; Vitale, Patrizia [Dipartimento di Scienze Fisiche, Universita di Napoli Federico II and INFN, Sezione di Napoli Monte S. Angelo, Via Cintia, 80126 Naples (Italy)

2008-01-15

354

On phase-space representations of quantum mechanics  

NASA Astrophysics Data System (ADS)

We discuss a class of representations of quantum mechanics which uses functions defined on a parameter space to represent observable quantities. We show that infinitesimal canonical transformations could be used to introduce a phase-space-like structure consistent with the requirements of quantum mechanics. The resulting family of phase-space representations of quantum mechanics contains many well-known representations as special cases, e.g., the Weyl-Wigner-Moyal, normal and antinormal one. It is also flexible enough to represent, e.g., /PT-symmetric theories, introduced recently within the context of non-Hermitian quantum mechanics.

Wlodarz, J. J.

2001-07-01

355

Lyapunov exponent in quantum mechanics. A phase-space approach  

NASA Astrophysics Data System (ADS)

Using the symplectic tomography map, both for the probability distributions in classical phase-space and for the Wigner functions of its quantum counterpart, we discuss a notion of Lyapunov exponent for quantum dynamics. Because the marginal distributions, obtained by the tomography map, are always well-defined probabilities, the correspondence between classical and quantum notions is very clear. Then we also obtain the corresponding expressions in Hilbert space. Some examples are worked out. Classical and quantum exponents are seen to coincide for local and non-local time-dependent quadratic potentials. For non-quadratic potentials classical and quantum exponents are different and some insight is obtained on the taming effect of quantum mechanics on classical chaos. A detailed analysis is made for the standard map. Providing an unambiguous extension of the notion of Lyapunov exponent to quantum mechanics, the method that is developed is also computationally efficient in obtaining analytical results for the Lyapunov exponent, both classical and quantum.

Man'ko, V. I.; Vilela Mendes, R.

2000-11-01

356

Quantum cavity opto-mechanics with cold atoms: measuring and controlling a mechanical oscillator with light  

NASA Astrophysics Data System (ADS)

In cavity opto-mechanical systems, the motion of a mechanical element is sensed by its influence on the field within an electromagnetic resonator. While their experimental realizations are quite diverse, with mechanical elements ranging from picogram-scale nanofabricated metallic filament to the kilogram-scale mirrors of the LIGO detector and optical systems ranging from microfabricated stripline resonators to kilometers-long optical cavities, such systems are converging on the common goal of realizing quantum limited operation. In this talk, I will discuss the use of ensembles of ultracold trapped atoms, with atom numbers ranging presently from 10^3 to 10^5, as mechanical elements within a high-finesse optical cavity. With this system, my colleagues and I realize cavity opto-mechanics in the quantum regime, with opto-mechanical coupling parameters that may be readily tuned and extended into a distinct granular, or strong-coupling, regime. We have also begun exploring cavity optical interactions with internal quantum variables of these atoms (their spin), and the possibilities arising from interfacing their motional and spin degrees of freedom.

Stamper-Kurn, Dan

2010-03-01

357

Realization of vector fields for quantum groups as pseudodifferential operators on quantum spaces  

SciTech Connect

The vector fields of the quantum Lie algebra are described for the quantum groups GL{sub q}(n), SL{sub q}(N) and SO{sub q}(N) as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their expressions are simple and compact. It is pointed out that these vector fields satisfy certain characteristic polynomial identities. The real forms SU{sub q}(N) and SO{sub q}(N,R) are discussed in detail.

Chu, Chong-Sun; Zumino, B.

1995-01-24

358

Exponential complexity and ontological theories of quantum mechanics  

SciTech Connect

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

359

Paul A.M. Dirac's The Principles of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Paul A.M. Dirac’s book, The Principles of Quantum Mechanics, summarized the foundations of a new science, much of which was his own creation. It expressed the spirit of the new quantum mechanics, creating a descriptive language that we still use. I discuss the successive editions of Dirac’s book and their critical reception, noting changes, especially in the formulation of the general theory and in its treatment of relativistic quantum theory and quantum electrodynamics. In the case of the later editions, I discuss Dirac’s negative attitude toward renormalized quantum electrodynamics.

Brown, Laurie M.

2006-12-01

360

High-Temperature Operation of Terahertz Quantum Cascade Laser Sources  

Microsoft Academic Search

Terahertz (THz) quantum cascade lasers (QCLs) are currently the most advanced electrically pumped semiconductor lasers in the spectral range 1-5 THz. However, their operation at room temperature is still an unresolved challenge. In this paper, we discuss our efforts to improve the temperature performance of these devices. In particular, we present THz QCLs that approach thermoelectric cooled operation and discuss

Mikhail A. Belkin; Qi Jie Wang; C. Pflugl; A. Belyanin; S. P. Khanna; A. G. Davies; E. H. Linfield; F. Capasso

2009-01-01

361

Quantum estimation of states and operations from incomplete data  

NASA Astrophysics Data System (ADS)

We review minimum Kullback entropy principle for estimation of quantum states and operations and discuss its application to qubit and harmonic oscillator systems. In particular, we address the estimation of displacement and squeezing operations from incomplete data and show how to estimate the displacement or squeezing amplitude starting from photon-number resolving or on/off photodetection.

Olivares, S.; Paris, M. G. A.

2012-04-01

362

Causal Quantum Mechanics Treating Position and Momentum Symmetrically  

NASA Astrophysics Data System (ADS)

De Broglie and Bohm formulated a causal quantum mechanics with a phase space density whose integral over momentum reproduces the position probability density of the usual statistical quantum theory. We propose a causal quantum theory with a joint probability distribution such that the separate probability distributions for position and momentum agree with the usual quantum theory. Unlike the Wigner distribution the suggested distribution is positive-definite and obeys the Liouville condition.

Roy, S. M.; Singh, Virendra

363

Scheduling physical operations in a quantum information processor  

NASA Astrophysics Data System (ADS)

Irrespective of the underlying technology used to implement a large-scale quantum architecture system, one of the central challenges of accurately modeling the architecture is the ability to map and schedule a quantum application onto a physical grid while taking into account the cost of communication, the classical resources, and the maximum exploitable parallelism. In this paper we introduce and evaluate a physical operations scheduler for arbitrary quantum circuits. Our scheduler accepts a description of a circuit together with a description of a specific physical layout and outputs a sequence of operations that expose the required communication and available parallelism in the circuit. The output of the scheduler is a quantum assembly language file that can directly be simulated on a set of available tools.

Metodi, Tzvetan S.; Thaker, Darshan D.; Cross, Andrew W.; Chong, Frederic T.; Chuang, Isaac L.

2006-06-01

364

Demonstration of Nondeterministic Quantum Logic Operations Using Linear Optical Elements  

Microsoft Academic Search

Knill, Laflamme, and Milburn recently showed that non-deterministic quantum\\u000alogic operations could be performed using linear optical elements, additional\\u000aphotons (ancilla), and post-selection based on the output of single-photon\\u000adetectors [Nature 409, 46 (2001)]. Here we report the experimental\\u000ademonstration of two logic devices of this kind, a destructive controlled-NOT\\u000a(CNOT) gate and a quantum parity check. These two devices

T. B. Pittman; B. C. Jacobs; J. D. Franson

2002-01-01

365

Hilbert space for quantum mechanics on superspace  

NASA Astrophysics Data System (ADS)

In superspace a realization of sl2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie, and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, Proc. London Math. Soc. (accepted) arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl2-representation is proven. Finally, the Heisenberg uncertainty principle for the super Fourier transform is constructed.

Coulembier, K.; de Bie, H.

2011-06-01

366

Hilbert space for quantum mechanics on superspace  

SciTech Connect

In superspace a realization of sl{sub 2} is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie, and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, Proc. London Math. Soc. (accepted) arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl{sub 2}-representation is proven. Finally, the Heisenberg uncertainty principle for the super Fourier transform is constructed.

Coulembier, K.; De Bie, H. [Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Krijgslaan 281, 9000 Gent (Belgium)

2011-06-15

367

Momentum diffusion of the quantum kicked rotor: Comparison of Bohmian and standard quantum mechanics  

Microsoft Academic Search

Momentum diffusion of the quantum kicked rotor is studied with both de Broglie–Bohm and standard approach to quantum mechanics. The Schrödinger equation is solved exactly for the case of quantum resonance and an analytical expression is given for the momentum diffusion. Numerical solutions for both resonance and nonresonance are obtained. We obtain agreement between the two approaches only when the

Yindong Zheng; Donald H. Kobe

2007-01-01

368

Quantum physics with non-Hermitian operators Quantum physics with non-Hermitian operators  

NASA Astrophysics Data System (ADS)

The main motivation behind the call for this special issue was to gather recent results, developments and open problems in quantum physics with non-Hermitian operators. There have been previous special issues in this journal [1, 2] and elsewhere on this subject. The intention of this issue is to reflect the current state of this rapidly-developing field. It has therefore been open to all contributions containing new results on non-Hermitian theories that are explicitly PT-symmetric and/or pseudo-Hermitian or quasi-Hermitian. In the last decade these types of systems have proved to be viable self-consistent physical theories with well defined unitary time-evolution and real spectra. As the large number of responses demonstrates, this is a rapidly evolving field of research. A consensus has been reached regarding most of the fundamental problems, and the general ideas and techniques are now readily being employed in many areas of physics. Nonetheless, this issue still contains some treatments of a more general nature regarding the spectral analysis of these models, in particular, the physics of the exceptional points, the breaking of the PT-symmetry, an interpretation of negative energies and the consistent implementation of the WKB analysis. This issue also contains a treatment of a scattering theory associated with these types of systems, weak measurements, coherent states, decoherence, unbounded metric operators and the inclusion of domain issues to obtain well defined self-adjoint theories. Contributions in the form of applications of the general ideas include: studies of classical shock-waves and tunnelling, supersymmetric models, spin chain models, models with ring structure, random matrix models, the Pauli equation, the nonlinear Schrödinger equation, quasi-exactly solvable models, integrable models such as the Calogero model, Bose-Einstein condensates, thermodynamics, nonlinear oligomers, quantum catastrophes, the Landau-Zener problem and pseudo-Fermions. Applications close to experimental realization are proposed in optics, including short light pulse models, waveguides and laser systems, and also in electronics. We hope that this issue will become a valuable reference and inspiration for the broader scientific community working in mathematical and theoretical physics. References [1] Fring A, Jones H F and Znojil M (ed) 2008 J. Phys. A: Math. Theor. 41 240301 [2] Geyer H, Heiss D and Znojil M (ed) 2006 J. Phys. A: Math. Gen. 39 9963

Bender, Carl; Fring, Andreas; Günther, Uwe; Jones, Hugh

2012-11-01

369

Auxiliary nRules of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Standard quantum mechanics makes use of four auxiliary rules that allow the Schrödinger solutions to be related to laboratory experience - such as the Born rule that connects square modulus to probability. These rules (here called the sRules) lead to some unacceptable results. They do not allow the primary observer to be part of the system. They do not allow individual observations (as opposed to ensembles) to be part of the system. They make a fundamental distinction between microscopic and macroscopic things, and they are ambiguous in their description of secondary observers such as Schrödinger's cat. The nRules are an alternative set of auxiliary rules that avoid the above difficulties. In this paper we look at a wide range of representative experiments showing that the nRules adequately relate the Schrödinger solutions to empirical experience.

Mould, Richard A.

2006-01-01

370

Quantum mechanics without an equation of motion  

SciTech Connect

We propose a formulation of quantum mechanics for a finite level system whose potential function is not realizable and/or analytic solution of the wave equation is not feasible. The system's wavefunction is written as an infinite sum in a complete set of square integrable functions. Interaction in the theory is introduced in function space by a real finite tridiagonal symmetric matrix. The expansion coefficients of the wavefunction satisfy a three-term recursion relation incorporating the parameters of the interaction. Information about the structure and dynamics of the system is contained in the scattering matrix, which is defined in the usual way. The bound state energy spectrum (system's structure) is finite. Apart from the 2M- 1 dimensionless parameters of the interaction matrix, whose rank is M, the theory has one additional scale parameter. In the development, we utilize the kinematic tools of the J-matrix method.

Alhaidari, A. D. [Saudi Center for Theoretical Physics, Jeddah 21438 (Saudi Arabia)

2011-06-15

371

Supersymmetric quantum mechanics for string-bits  

SciTech Connect

The authors develop possible versions of supersymmetric single particle quantum mechanics, with application to superstring-bit models in view. The authors focus principally on space dimensions d = 1,2,4,8, the transverse dimensionalities of superstring in 3, 4, 7, 10 space-time dimensions. These are the cases for which classical superstring makes sense, and also the values of d for which Hooke`s force law is compatible with the simplest superparticle dynamics. The basic question they address is: when is it possible to replace such harmonic force laws with more general ones, including forces which vanish at large distances? This is an important question because forces between string-bits that do not fall off with distance will almost certainly destroy cluster decomposition. They show that the answer is affirmative for d = 1,2, negative for d = 8, and so far inconclusive for d = 4.

Thorn, C.B. [Univ. of Florida, Gainesville, FL (United States). Dept. of Physics

1997-08-01

372

Deformation quantization of noncommutative quantum mechanics  

NASA Astrophysics Data System (ADS)

The Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantization. In this paper, we investigate the basic aspects of deformation quantization for noncommutative quantum mechanics (NCQM). We first prove some general relations of the Weyl correspondence in non-commuting phase-space. Then we derive explicit form of the Wigner Function (WF) for NCQM starting from fundamental principle of the Weyl correspondence, and show that it satisfies a generalized lowast-genvalue equation. We also demonstrate that the new WFs possess orthonormality and completeness, so they can be used as a basis to expand all phase-space functions. Some example is discussed to support our results.

Jing, Sicong; Zuo, Fen; Heng, Taihua

2004-10-01

373

Quantum logic gate operation between different ions in a trap  

Microsoft Academic Search

We suggest a scheme for realizing a universal two-quantum-bit (qubit) operation. The scheme uses two laser beams with different intensities to illuminate two different ions in a harmonic trap. Both beams are tuned to the red motional sideband. We find that, under certain conditions, the interaction will realize a universal two-qubit operation, the controlled-rotation operation, which is to rotate the

Li-Xiang Li; Guang-Can Guo

1999-01-01

374

Two-dimensional quantum mechanical modeling of nanotransistors  

Microsoft Academic Search

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

375

Property Definiteness in Quantum Mechanics: Modal Interpretations.  

NASA Astrophysics Data System (ADS)

Recently, several writers have independently proposed similar solutions to the quantum-mechanical measurement problem. This dissertation examines the conception of physical properties implicit in these proposals, which are known as modal interpretations of quantum mechanics. The dissertation focuses on Richard Healey's interpretation, which I regard as the most promising of the proposals. Chapter One reviews the measurement problem and the way in which modal interpretations address the problem. Chapter Two discusses certain mathematical theorems that impose strict limits on the number of properties that a system can possess at any instant. I examine a number of inferences that interpreters have drawn from these theorems, and argue that some of these inferences are misguided. This discussion leads to the recognition that, despite overarching similarities between Healey's interpretations and several of the other modal interpretations, the interpretations differ in fundamental respects. Chapter Three presents several desiderata on the set of properties possessed by a quantum system at an instant. One of these desiderata concerns the relation between a system's properties and the properties of that system's subsystems. To borrow Frank Arntzenius's illustration, the desideratum demands, for instance, that the left-hand leaf of a table be green if and only if the table has a green left-hand leaf. Unfortunately, most modal interpretations fail to satisfy this demand. Using mathematical arguments, I show that Healey's interpretation satisfies the demand. Chapter Four turns to a problematic feature of Healey's interpretation, namely its violation of a desideratum called Property Intersection. Property Intersection demands that if a variable's value is restricted to a set Delta and is also restricted to a set Gamma, then the value is restricted to the intersection of Delta and Gamma. I propose two strategies for amending Healey's interpretation so that it respects Property Intersection, but I find both of these strategies unsatisfactory, since each creates new problems. I then consider several possible reasons for imposing Property Intersection as a requirement, and I argue that none of these reasons is compelling; thus, I claim, Healey's violation of Property Intersection is defensible.

Reeder, Nicholas Lee

376

Born in an infinite universe: A cosmological interpretation of quantum mechanics  

NASA Astrophysics Data System (ADS)

We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist, the standard projection operators and Born rule method for calculating probabilities must be supplemented by estimates of relative frequencies of observers. We argue that an infinite space actually renders the Born rule redundant, by physically realizing all outcomes of a quantum measurement in different regions, with relative frequencies given by the square of the wave-function amplitudes. Our formal argument hinges on properties of what we term the quantum confusion operator, which projects onto the Hilbert subspace where the Born rule fails, and we comment on its relation to the oft-discussed quantum frequency operator. This analysis unifies the classical and quantum levels of parallel universes that have been discussed in the literature, and has implications for several issues in quantum measurement theory. Replacing the standard hypothetical ensemble of measurements repeated ad infinitum by a concrete decohered spatial collection of experiments carried out in different distant regions of space provides a natural context for a statistical interpretation of quantum mechanics. It also shows how, even for a single measurement, probabilities may be interpreted as relative frequencies in unitary (Everettian) quantum mechanics. We also argue that after discarding a zero-norm part of the wave function, the remainder consists of a superposition of indistinguishable terms, so that arguably “collapse” of the wave function is irrelevant, and the “many worlds” of Everett’s interpretation are unified into one. Finally, the analysis suggests a “cosmological interpretation” of quantum theory in which the wave function describes the actual spatial collection of identical quantum systems, and quantum uncertainty is attributable to the observer’s inability to self-locate in this collection.

Aguirre, Anthony; Tegmark, Max

2011-11-01

377

Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems  

ERIC Educational Resources Information Center

|In this study, students' conceptual difficulties about some basic concepts in quantum mechanics like one-dimensional potential well problems and probability density of tunneling particles were identified. For this aim, a multiple choice instrument named Quantum Mechanics Conceptual Test has been developed by one of the researchers of this study…

Ozcan, Ozgur; Didis, Nilufer; Tasar, Mehmet Fatih

2009-01-01

378

In Defense of a Heuristic Interpretation of Quantum Mechanics  

ERIC Educational Resources Information Center

Although the presentation of quantum mechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantum mechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift…

Healy, Eamonn F.

2010-01-01

379

On the End of a Quantum Mechanical Romance  

Microsoft Academic Search

Comparatively recent advances in quantum measurement theory suggest that the decades-old flirtation between quantum mechanics and the philosophy of mind is about to end. Various approaches to what I have elsewhere dubbed 'interactive decoherence' promise to remove the conscious observer from the phenomenon of state vector reduction. The mechanisms whereby decoherence occurs suggest, on the one hand, that consciousness per

Gregory R. Mulhauser

1995-01-01

380

Quantum mechanics needs no consciousness (and the other way around)  

Microsoft Academic Search

It has been suggested that consciousness plays an important role in quantum mechanics as it is necessary for the collapse of wave function during the measurement. Furthermore, this idea has spawned a symmetrical proposal: a possibility that quantum mechanics explains the emergence of consciousness in the brain. Here we formulated several predictions that follow from this hypothetical relationship and that

Shan Yu; Danko Nikolic

2010-01-01

381

Quantum Mechanics and Consciousness: A Causal Correspondence Theory  

Microsoft Academic Search

We may suspect that quantum mechanics and consciousness are re- lated, but the details are not at all clear. In this paper, I suggest how the mind and brain might fit together intimately while still maintaining dis- tinct identities. The connection is based on the correspondence of similar functions in both the mind and the quantum-mechanical brain.

I. J. Thompson

382

On a generalization of quantum mechanics of biquaternions  

SciTech Connect

A generalization of the quantum mechanical formalism by biquaternions is proposed. By a direct example, it is evidenced that such a generalization explains in an algebraic manner the {open_quotes}wave packet reduction{close_quotes} of quantum mechanics. 8 refs.

Conte, E. [Inst. of Cybernetics, San Marino (Italy)

1993-06-01

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

Categorization of Quantum Mechanics Problems by Professors and Students  

ERIC Educational Resources Information Center

|We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…

Lin, Shih-Yin; Singh, Chandralekha

2010-01-01

385

Design and Validation of the Quantum Mechanics Conceptual Survey  

ERIC Educational Resources Information Center

|The Quantum Mechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantum mechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper, we describe the design and validation of the survey, a process that included…

McKagan, S. B.; Perkins, K. K.; Wieman, C. E.

2010-01-01

386

Developing and Evaluating Animations for Teaching Quantum Mechanics Concepts  

ERIC Educational Resources Information Center

|In this paper, we describe animations and animated visualizations for introductory and intermediate-level quantum mechanics instruction developed at the University of St Andrews. The animations aim to help students build mental representations of quantum mechanics concepts. They focus on known areas of student difficulty and misconceptions by…

Kohnle, Antje; Douglass, Margaret; Edwards, Tom J.; Gillies, Alastair D.; Hooley, Christopher A.; Sinclair, Bruce D.

2010-01-01

387

In Defense of a Heuristic Interpretation of Quantum Mechanics  

ERIC Educational Resources Information Center

|Although the presentation of quantum mechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantum mechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift…

Healy, Eamonn F.

2010-01-01

388

Phase Space Correspondence between Classical Optics and Quantum Mechanics  

Microsoft Academic Search

The paper scrutinizes both the similarities and the differences between the classical optics and quantum mechanical theories in phase space, especially between the Wigner distribution functions defined in the respective phase spaces. Classical optics is able to provide an understanding of either the corpuscular or wave aspects of quantum mechanics, reflected in phase space through the classical limit of the

Daniela Dragoman

2004-01-01

389

Predicting crystal structure by merging data mining with quantum mechanics  

Microsoft Academic Search

Modern methods of quantum mechanics have proved to be effective tools to understand and even predict materials properties. An essential element of the materials design process, relevant to both new materials and the optimization of existing ones, is knowing which crystal structures will form in an alloy system. Crystal structure can only be predicted effectively with quantum mechanics if an

Christopher C. Fischer; Kevin J. Tibbetts; Dane Morgan; Gerbrand Ceder

2006-01-01

390

Quantum Mechanics from Periodic Dynamics: the bosonic case  

SciTech Connect

Enforcing the periodicity hypothesis of the 'old' formulation of Quantum Mechanics we show the possibility for a new scenario where Special Relativity and Quantum Mechanics are unified in a deterministic field theory. A novel interpretation of the AdS/CFT conjecture is discussed.

Dolce, Donatello [Johannes-Gutenberg Universitaet, D-55099 Mainz (Germany)

2010-05-04

391

Linear Logic for Generalized Quantum Mechanics  

Microsoft Academic Search

Quantum logic is static, describing automata having uncertain states but no state transitions and no Heisenberg uncertainty tradeo. We cast Girard's linear logic in the role of a dynamic quantum logic, regarded as an extension of quantum logic with time nonstandardly interpreted over a domain of linear automata and their dual linear schedules. In this extension the uncertainty tradeo emerges

Vaughan Pratt

1993-01-01

392

Quantum Operator Design for Lattice Baryon Spectroscopy  

SciTech Connect

A previously-proposed method of constructing spatially-extended gauge-invariant three-quark operators for use in Monte Carlo lattice QCD calculations is tested, and a methodology for using these operators to extract the energies of a large number of baryon states is developed. This work is part of a long-term project undertaken by the Lattice Hadron Physics Collaboration to carry out a first-principles calculation of the low-lying spectrum of QCD. The operators are assemblages of smeared and gauge-covariantly-displaced quark fields having a definite flavor structure. The importance of using smeared fields is dramatically demonstrated. It is found that quark field smearing greatly reduces the couplings to the unwanted high-lying short-wavelength modes, while gauge field smearing drastically reduces the statistical noise in the extended operators.

Adam Lichtl

2007-09-06

393

Amplitude Phase-Space Model for Quantum Mechanics  

NASA Astrophysics Data System (ADS)

We show that there is a close relationship between quantum mechanics and ordinary probability theory. The main difference is that in quantum mechanics the probability is computed in terms of an amplitude function, while in probability theory a probability distribution is used. Applying this idea, we then construct an amplitude model for quantum mechanics on phase space. In this model, states are represented by amplitude functions and observables are represented by functions on phase space. If we now postulate a conjugation condition, the model provides the same predictions as conventional quantum mechanics. In particular, we obtain the usual quantum marginal probabilities, conditional probabilities and expectations. The commutation relations and uncertainty principle also follow. Moreover Schrödinger's equation is shown to be an averaged version of Hamilton's equation in classical mechanics.

Gudder, Stanley P.

1985-04-01

394

Logical-operator tradeoff for local quantum codes  

NASA Astrophysics Data System (ADS)

We study the structure of logical operators in local D-dimensional quantum codes, considering both subsystem codes with geometrically local gauge generators and codes defined by geometrically local commuting projectors. We show that if the code distance is d, then any logical operator can be supported on a set of specified geometry containing d˜ qubits, where d˜d1/(D-1)=O(n) and n is the code length. Our results place limitations on partially self-correcting quantum memories, in which at least some logical operators are protected by energy barriers that grow with system size. We also show that for any two-dimensional local commuting projector code there is a nontrivial logical “string” operator supported on a narrow strip, where the operator is only slightly entangling across any cut through the strip.

Haah, Jeongwan; Preskill, John

2012-09-01

395

Biological Applications of Hybrid Quantum Mechanics/Molecular Mechanics Calculation  

PubMed Central

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 tRNALeu, 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.

Kang, Jiyoung; Hagiwara, Yohsuke; Tateno, Masaru

2012-01-01

396

Entropic trade-off relations for quantum operations  

NASA Astrophysics Data System (ADS)

Spectral properties of an arbitrary matrix can be characterized by the entropy of its rescaled singular values. Any quantum operation can be described by the associated dynamical matrix or by the corresponding superoperator. The entropy of the dynamical matrix describes the degree of decoherence introduced by the map, while the entropy of the superoperator characterizes the a priori knowledge of the receiver of the outcome of a quantum channel ?. We prove that for any map acting on an N-dimensional quantum system the sum of both entropies is not smaller than lnN. For any bistochastic map this lower bound reads 2lnN. We investigate also the corresponding Rényi entropies, providing an upper bound for their sum, and analyze the entanglement of the bi-partite quantum state associated with the channel.

Roga, Wojciech; Pucha?a, Zbigniew; Rudnicki, ?ukasz; ?yczkowski, Karol

2013-03-01

397

Quantifying quantum correlations in fermionic systems using witness operators  

NASA Astrophysics Data System (ADS)

We present a method to quantify quantum correlations in arbitrary systems of indistinguishable fermions using witness operators. The method associates the problem of finding the optimal entanglement witness of a state with a class of problems known as semidefinite programs, which can be solved efficiently with arbitrary accuracy. Based on these optimal witnesses, we introduce a measure of quantum correlations which has an interpretation analogous to the Generalized Robustness of entanglement. We also extend the notion of quantum discord to the case of indistinguishable fermions, and propose a geometric quantifier, which is compared to our entanglement measure. Our numerical results show a remarkable equivalence between the proposed Generalized Robustness and the Schliemann concurrence, which are equal for pure states. For mixed states, the Schliemann concurrence presents itself as an upper bound for the Generalized Robustness. The quantum discord is also found to be an upper bound for the entanglement.

Iemini, Fernando; Maciel, Thiago O.; Debarba, Tiago; Vianna, Reinaldo O.

2013-02-01

398

Frame transforms, star products and quantum mechanics on phase space  

NASA Astrophysics Data System (ADS)

Using the notions of frame transform and of square integrable projective representation of a locally compact group G, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier Hilbert space of the representation into the space of square integrable functions on the direct product group G × G. These transforms have remarkable properties. In particular, their ranges are reproducing kernel Hilbert spaces endowed with a suitable 'star product' which mimics, at the level of functions, the original product of operators. A 'phase space formulation' of quantum mechanics relying on the frame transforms introduced in the present paper, and the link of these maps with both the Wigner transform and the wavelet transform are discussed.

Aniello, P.; Man'ko, V. I.; Marmo, G.

2008-07-01

399

Quantum Mechanics as Quantum Information (and only a little more)  

Microsoft Academic Search

In this paper, I try once again to cause some good-natured trouble. The issue\\u000aremains, when will we ever stop burdening the taxpayer with conferences devoted\\u000ato the quantum foundations? The suspicion is expressed that no end will be in\\u000asight until a means is found to reduce quantum theory to two or three\\u000astatements of crisp physical (rather than

Christopher A. Fuchs

2002-01-01

400

A pedestrian approach to the measurement problem in quantum mechanics  

NASA Astrophysics Data System (ADS)

The quantum theory of measurement has been a matter of debate for over eighty years. Most of the discussion has focused on theoretical issues with the consequence that other aspects (such as the operational prescriptions that are an integral part of experimental physics) have been largely ignored. This has undoubtedly exacerbated attempts to find a solution to the "measurement problem". How the measurement problem is defined depends to some extent on how the theoretical concepts introduced by the theory are interpreted. In this paper, we fully embrace the minimalist statistical (ensemble) interpretation of quantum mechanics espoused by Einstein, Ballentine, and others. According to this interpretation, the quantum state description applies only to a statistical ensemble of similarly prepared systems rather than representing an individual system. Thus, the statistical interpretation obviates the need to entertain reduction of the state vector, one of the primary dilemmas of the measurement problem. The other major aspect of the measurement problem, the necessity of describing measurements in terms of classical concepts that lay outside of quantum theory, remains. A consistent formalism for interacting quantum and classical systems, like the one based on ensembles on configuration space that we refer to in this paper, might seem to eliminate this facet of the measurement problem; however, we argue that the ultimate interface with experiments is described by operational prescriptions and not in terms of the concepts of classical theory. There is no doubt that attempts to address the measurement problem have yielded important advances in fundamental physics; however, it is also very clear that the measurement problem is still far from being resolved. The pedestrian approach presented here suggests that this state of affairs is in part the result of searching for a theoretical/mathematical solution to what is fundamentally an experimental/observational question. It suggests also that the measurement problem is, in some sense, ill-posed and might never be resolved. This point of view is tenable so long as one is willing to view physical theories as providing models of nature rather than complete descriptions of reality. Among other things, these considerations lead us to suggest that the Copenhagen interpretation's insistence on the classicality of the measurement apparatus should be replaced by the requirement that a measurement, which is specified operationally, should simply be of sufficient precision.

Boughn, Stephen; Reginatto, Marcel

2013-07-01

401

A pedestrian approach to the measurement problem in quantum mechanics  

NASA Astrophysics Data System (ADS)

The quantum theory of measurement has been a matter of debate for over eighty years. Most of the discussion has focused on theoretical issues with the consequence that other aspects (such as the operational prescriptions that are an integral part of experimental physics) have been largely ignored. This has undoubtedly exacerbated attempts to find a solution to the "measurement problem". How the measurement problem is defined depends to some extent on how the theoretical concepts introduced by the theory are interpreted. In this paper, we fully embrace the minimalist statistical (ensemble) interpretation of quantum mechanics espoused by Einstein, Ballentine, and others. According to this interpretation, the quantum state description applies only to a statistical ensemble of similarly prepared systems rather than representing an individual system. Thus, the statistical interpretation obviates the need to entertain reduction of the state vector, one of the primary dilemmas of the measurement problem. The other major aspect of the measurement problem, the necessity of describing measurements in terms of classical concepts that lay outside of quantum theory, remains. A consistent formalism for interacting quantum and classical systems, like the one based on ensembles on configuration space that we refer to in this paper, might seem to eliminate this facet of the measurement problem; however, we argue that the ultimate interface with experiments is described by operational prescriptions and not in terms of the concepts of classical theory. There is no doubt that attempts to address the measurement problem have yielded important advances in fundamental physics; however, it is also very clear that the measurement problem is still far from being resolved. The pedestrian approach presented here suggests that this state of affairs is in part the result of searching for a theoretical/mathematical solution to what is fundamentally an experimental/observational question. It suggests also that the measurement problem is, in some sense, ill-posed and might never be resolved. This point of view is tenable so long as one is willing to view physical theories as providing models of nature rather than complete descriptions of reality. Among other things, these considerations lead us to suggest that the Copenhagen interpretation's insistence on the classicality of the measurement apparatus should be replaced by the requirement that a measurement, which is specified operationally, should simply be of sufficient precision.

Boughn, Stephen; Reginatto, Marcel

2013-09-01

402

Quantum logical gates operating on stored light  

Microsoft Academic Search

An implementation is proposed of single qubit gates, e.g., phase, NOT, \\\\sqrt{NOT} and Hadamard, operating on polarized photons and based on light storage. Instead of processing photons themselves, qubit transformations are performed on atomic excitations due to photon storage in a medium of atoms in the tripod configuration.

K. Slowik; A. Raczynski; J. Zaremba; S. Zielinska-Kaniasty

2011-01-01

403

Calendar effects in quantum mechanics in view of interactive holography  

NASA Astrophysics Data System (ADS)

Quantum mechanics in terms of interactive holography appears as `normal' science [1]. With the holography quantum behavior is determined by the interplay of material formations and their conjugate images. To begin with, this effortlessly elucidates the nonlocality in quantum entanglements. Then, it has been shown that Schr"odinger's dynamics for a single particle arises from Bi-Fragmental random walks of the particle itself and its holographic image. For many particles this picture blurs with fragments merging as bosons or fermions. In biomolecules, swapping of particles and their holographic placeholders leads to self-replication of the living matter. Because of broad interpretations of quantum formalism direct experiments attributing it to holography may not be very compelling. The holographic mechanism better reveals as an absolute frame of reference. A number of physical and biological events exhibit annual variations when Earth orbital position changes with respect to the universal holographic mechanism. The well established calendar variations of heart attacks can be regarded as a positive outcome of a generalization of the Michelson experiment, where holography is interferometry and ailing hearts are detectors of pathologically replicated proteins. Also, there have been already observed calendar changes in radioactive decay rates. The same could be expected for various fine quantum experiences, like, e.g., Josephson tunneling. In other words, Quantum Mechanics (February) Quantum Mechanics (August). [1] S. Berkovich, ``A comprehensive explanation of quantum mechanics,'' www.cs.gwu.edu/research/technical-report/170 .

Berkovich, Simon

2013-04-01

404

Simulations of quantum-logic operations in a quantum computer with a large number of qubits  

SciTech Connect

We report the simulations of the dynamics of quantum-logic operations with large number of qubits (up to 1000). A nuclear-spin chain in which selective excitations of spins are provided by the gradient of the external magnetic field is considered. The spins interact with their nearest neighbors. We simulate the quantum controlled-NOT (CN) gate implementation for remote qubits, which provides the long-distance entanglement. Our approach can be applied to any implementation of quantum-logic gates involving a large number of qubits. (c) 2000 The American Physical Society.

Berman, G. P. [Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Doolen, G. D. [Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Lopez, G. V. [Departmento de Fisica, Universidad de Guadalajara, Guadalajara, Jalisco, (Mexico); Tsifrinovich, V. I. [IDS Department, Polytechnic University, Six Metrotech Center, Brooklyn, New York 11201 (United States)

2000-06-01

405

Quantum logical operations for spin 3\\/2 quadrupolar nuclei monitored by quantum state tomography  

Microsoft Academic Search

This article presents the realization of many self-reversible quantum logic gates using two-qubit quadrupolar spin 3\\/2 systems. Such operations are theoretically described using propagation matrices for the RF pulses that include the effect of the quadrupolar evolution during the pulses. Experimental demonstrations are performed using a generalized form of the recently developed method for quantum state tomography in spin 3\\/2

F. A. Bonk; E. R. Deazevedo; R. S. Sarthour; J. D. Bulnes; J. C. C. Freitas; A. P. Guimarães; I. S. Oliveira; T. J. Bonagamba

2005-01-01

406

Simulations of quantum-logic operations in a quantum computer with a large number of qubits  

Microsoft Academic Search

We report the simulations of the dynamics of quantum-logic operations with large number of qubits (up to 1000). A nuclear-spin chain in which selective excitations of spins are provided by the gradient of the external magnetic field is considered. The spins interact with their nearest neighbors. We simulate the quantum controlled-NOT (CN) gate implementation for remote qubits, which provides the

G. P. Berman; G. D. Doolen; G. V. López; V. I. Tsifrinovich

2000-01-01

407

Two-qubit conditional quantum-logic operation in a single self-assembled quantum dot  

Microsoft Academic Search

The four-level exciton\\/biexciton system of a single semiconductor quantum dot acts as a two-qubit register. We experimentally demonstrate an exciton-biexciton Rabi rotation conditional on the initial exciton spin in a single InGaAs\\/GaAs dot. This forms the basis of an optically gated two-qubit controlled rotation (CROT) quantum-logic operation where an arbitrary exciton spin is selected as the target qubit using the

S. J. Boyle; A. J. Ramsay; F. Bello; H. Y. Liu; M. Hopkinson; A. M. Fox; M. S. Skolnick

2008-01-01

408

Operator Method in the Problem of Quantum Anharmonic Oscillator  

Microsoft Academic Search

The problem of quantum anharmonic oscillator is considered as a test for a new nonperturbative method of the Schrödinger equation solution-the operator method (OM). It is shown that the OM zeroth-order approximation permits us to find such analytical interpolation for eigenfunctions and eigenvalues of the Hamiltonian which ensures high accuracy within the entire range of the anharmonicity constant changing and

I. D. Feranchuk; I. L. Komarov; V. I. Nichipor; P. A. Ulyanenkov

1995-01-01

409

Time-optimal control of SU(2) quantum operations  

NASA Astrophysics Data System (ADS)

We propose an analysis of the time-optimal control of SU(2) quantum operations. By using the Pontryagin maximum principle, we show how to determine the optimal trajectory for reaching a given target state. Explicit analytical solutions are given for two specific examples. We discuss the role of the detuning in the construction of the optimal synthesis.

Garon, A.; Glaser, S. J.; Sugny, D.

2013-10-01

410

Quantum Fields as Operator Valued Distributions and Causality  

Microsoft Academic Search

Quantum Field Theory with fields as Operator Valued Distributions with adequate test functions, -the basis of Epstein-Glaser approach known now as Causal Perturbation Theory-, is recalled. Its recent revival is due to new developments in understanding its renormalization structure, which was a major and somehow fatal disease to its widespread use in the seventies. In keeping with the usual way

Pierre Ca Grange; Ernst Werner

2006-01-01

411

Quantum Physics  

Microsoft Academic Search

In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum algebra operators is suggested by extending the definition of matrix el- ements of a physical observable, including the eventual projection on the appro- priate

E. Celeghini; M. A. del Olmo

1969-01-01

412

The Discovery of Quantum Structure and Quantum Mechanic Reinterpretation  

NASA Astrophysics Data System (ADS)

My recent interdisciplinary researches lead me to re-visit the quantum wave-particle duality property. By comparing many of the quantum physics results in scientific literatures I concluded the structure of quantum particle and formulated a new explanation of the wave effect. This discovery is further confirmed by many of the results in other fields. Evident also suggested inside quantum has a not-continuous multi-dimensional space. With this light I formed a hypostasis of space as a not-continuous infinite dimensional space. To proof or disproof this hypostasis I found strong evidences in literature supporting my hypostasis. By evaluating space properties it lead me to the same conclusion of Special Relativity and Uncertainty Principle. Evidence also support quantum is part of space itself and space carries electrical charges on both sides of its dimensional boundaries therefore we can detect the electromagnetic energy in vacuum. These discoveries also give good answers to many of the big questions in science such as gravity, dark energy and space travel.

Zhang, Meggie

2012-10-01

413

Quantum mechanics and the principle of equivalence  

NASA Astrophysics Data System (ADS)

Einstein's principle of equivalence is based on the notion of classical trajectories in spacetime, and the question arises of how this principle applies to quantum particles, especially those in delocalized, highly-non-classical states. I shall describe a quantum version of Galileo's classic experiment, using a model quantum clock to measure the time of flight of a quantum particle in a background gravitational field. Because the particle's mass does not scale out of Schrodinger's equation, unlike in the Newtonian case, conformity with the principle of equivalence is far from obvious and involves some interesting subtleties. It also suggests some new experiments.

Davies, Paul

2007-10-01

414

Quantum molecular dynamics: Propagating wavepackets and density operators using the  

Microsoft Academic Search

Quantum molecular dynamics describe the time-evolution of a chem- ical system at the atomic level by directly solving the Schrodinger equation. Time-dependent methods, exemplied by wavepacket prop- agation, are by now developed to a point where they provide an impor- tant insight into the mechanism of many fundamental processes. Of these methods, the most versatile and ecien t is probably

Hans-Dieter Meyer; Graham A. Worthy

415

Valve operating mechanism for internal combustion engine  

SciTech Connect

This patent describes a valve operating mechanism for operating valves of a particular cylinder of an internal combustion engine, comprising: a camshaft rotatable in synchronism with rotation of the internal combustion engine and having at least one cam; cam followers, one of which slidably engages with the cam for selectively operating the valves according to a cam profile of the cam; and means for selectively interconnecting and disconnecting the cam followers to operate the valves differently in different speed ranges of the internal combustion engine, the speed ranges including a range in which all of the valves remain inoperative.

Inoue, K.; Nagahiro, K.; Ajiki, Y.; Katoh, M.

1988-12-13

416

Valve operating mechanism for internal combustion engine  

SciTech Connect

A valve operating mechanism for operating a single valve of a particular cylinder of an internal combustion engine is described comprising: a camshaft rotatable in synchronism with rotation of the internal combustion engine; a plurality of cams on the camshaft with each of the cams bearing a different cam profile; a plurality of cam followers, each of which slidably engages one of the cams for selectively operating the valve according to the profile of the selected cam and one of which engages the valve; and means for selectively interconnecting and disconnecting the respective cam followers to operate the valve differently in different speed ranges of the internal combustion engine.

Inoue, K.; Nagahiro, K.; Ajiki, Y.; Katoh, M.

1988-12-27

417

Testing Quantum Mechanics in High-Energy Physics  

Microsoft Academic Search

In this set of lectures we show that particle physics can also contribute to fundamental questions about quantum mechanics\\u000a (QM) and even shine new light in the fine workings of quantum physics and this at scales of energies which are not available\\u000a for usual quantum systems. In particular the massive meson–antimeson systems are specially suitable as they offer a unique

Beatrix C. Hiesmayr

418

Can you do quantum mechanics without Einstein?  

SciTech Connect

The present form of quantum mechanics is based on the Copenhagen school of interpretation. Einstein did not belong to the Copenhagen school, because he did not believe in probabilistic interpretation of fundamental physical laws. This is the reason why we are still debating whether there is a more deterministic theory. One cause of this separation between Einstein and the Copenhagen school could have been that the Copenhagen physicists thoroughly ignored Einstein's main concern: the principle of relativity. Paul A. M. Dirac was the first one to realize this problem. Indeed, from 1927 to 1963, Paul A. M. Dirac published at least four papers to study the problem of making the uncertainty relation consistent with Einstein's Lorentz covariance. It is interesting to combine those papers by Dirac to make the uncertainty relation consistent with relativity. It is shown that the mathematics of two coupled oscillators enables us to carry out this job. We are then led to the question of whether the concept of localized probability distribution is consistent with Lorentz covariance.

Kim, Y. S. [Department of Physics, University of Maryland, College Park, Maryland 20742 (United States); Noz, Marilyn E. [Department of Radiology, New York University, New York, New York 10016 (United States)

2007-02-21

419

Quantum mechanical studies on model ?-pleated sheets  

PubMed Central

Pauling and Corey proposed a pleated-sheet configuration, now called ?-sheet, as one of the protein secondary structures in addition to ?-helix and ?-sheet. Recently, it has been suggested that ?-sheet is a common feature of amyloidogenic intermediates. We have investigated the stability of anti-parallel ?-sheet and two conformations of ?-sheet in solution phase using the density functional theoretical method. The peptides are modeled as two-strand Acetyl-(Ala)2-N-methylamine. Using stages of geometry optimization and single point energy calculation at B3LYP/cc-pVTZ//B3LYP/6-31G* level and including zero-point energies, thermal, and entropic contribution, we have found that ?-sheet is the most stable conformation, while the ?-sheet proposed by Pauling and Corey has 13.6 kcal/mol higher free energy than the ?-sheet. The ?-sheet that resembles the structure observed in molecular dynamics simulations of amyloidogenic proteins at low pH becomes distorted after stages of geometry optimization in solution. Whether the ?-sheets with longer chains would be increasingly favorable in water relative to the increase in internal energy of the chain needs further investigation. Different from the quantum mechanics results, AMBER parm94 force field gives small difference in solution phase energy between ?-sheet and ?-sheet. The predicted amide I IR spectra of ?-sheet shows the main band at higher frequency than ?-sheet.

Wu, Hao; Canfield, Alana; Adhikari, Jhashanath; Huo, Shuanghong

2009-01-01

420

Quantum mechanical model for Maya Blue  

NASA Astrophysics Data System (ADS)

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 model considering indigo derivatives attached to several aluminates shows the principal features of the experimental visible spectrum of MB within the TD-DFT methodology. Another model of an indigo oxidized species confined within an inorganic supramolecular cavity system, that involves about 170 atoms, was calculated after a large configuration interaction of single excited determinants within the NDOL approximation (Montero-Cabrera et al., J Chem Phys, 2007, 127, 145102). It allows a correct reproduction and interpretation of the corresponding spectrum. This second methodology provides the most satisfactory results, being able to manage very big molecular systems at a QM level. Structural explanation for the unusual stability of MB is also provided.

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

421

Supersymmetric quantum mechanics for string bits  

SciTech Connect

We develop possible versions of supersymmetric single-particle quantum mechanics, with application to superstring-bit models in view. We focus principally on space dimensions d=1,2,4,8, the transverse dimensionalities of superstring in 3, 4, 6, and 10 space-time dimensions. These are the cases for which {open_quotes}classical{close_quotes} superstring makes sense, and also the values of d for which Hooke{close_quote}s force law is compatible with the simplest superparticle dynamics. The basic question we address is the following: When is it possible to replace such harmonic force laws with more general ones, including forces which vanish at large distances? This is an important question because forces between string bits that do not fall off with distance will almost certainly destroy cluster decomposition. We show that the answer is affirmative for d=1,2, negative for d=8, and so far inconclusive for d=4. {copyright} {ital 1997} {ital The American Physical Society}

Thorn, C.B. [Institute for Fundamental Theory, Department of Physics, University of Florida, Gainesville, Florida 32611 (United States)

1997-11-01

422

Scopes and limits of modality in quantum mechanics  

Microsoft Academic Search

We develop an algebraic frame for the simultaneous treatment of actual and possible properties of quantum systems. We show that, in spite of the fact that the language is enriched with the addition of a modal operator to the orthomodular structure, contextuality remains a central feature of quantum systems.

Graciela Domenech; Hector Freytes; C. de Ronde

2006-01-01

423

Implications of quantum theory in the foundations of statistical mechanics  

Microsoft Academic Search

An investigation is made into how the foundations of statistical mechanics are aected once we treat classical mechanics as an approximation to quantum mechanics in certain domains rather than as a theory in its own right; this is necessary if we are to understand statistical-mechanical systems in our own world. Relevant structural and dynamical dierences are identified between classical and

David Wallace

424

Operator algebras in statistical mechanics and noncommutative probability theory  

SciTech Connect

The fundamental notions of statistical mechanics of quantum spin systems are introduced. A survey of the main properties of the states satisfying the Kubo-Martin-Schwinger boundary conditions is given. The problem of describing the invariant states and the first integrals for the multidimensional Heisenberg model is solved. A central limit theorem of noncommutative probability theory and a noncommutative analog of the individual ergodic theorem are formulated and proved. The asymptotics of the distribution of the eigenvalues of the multiparticle Schrodinger operator is studied.

Anshelevich, V.V.; Gol'dshtein, M.S.

1987-06-20

425

What Is a Quantum-Mechanical "Weak Value" the Value of?  

NASA Astrophysics Data System (ADS)

A so called "weak value" of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM paradoxes (e.g., the so called Three-Box Paradox and Hardy's Paradox). This requires the weak value to be interpreted as a bona fide property of the system considered, a par with entities like operator mean values and eigenvalues. I question such an interpretation; it has no support in the basic axioms of quantum mechanics and it leads to unreasonable results in concrete situations.

Svensson, Bengt E. Y.

2013-09-01

426

What Is a Quantum-Mechanical "Weak Value" the Value of?  

NASA Astrophysics Data System (ADS)

A so called "weak value" of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM paradoxes ( e.g., the so called Three-Box Paradox and Hardy's Paradox). This requires the weak value to be interpreted as a bona fide property of the system considered, a par with entities like operator mean values and eigenvalues. I question such an interpretation; it has no support in the basic axioms of quantum mechanics and it leads to unreasonable results in concrete situations.

Svensson, Bengt E. Y.

2013-10-01

427

"Mysticism" in Quantum Mechanics: The Forgotten Controversy  

ERIC Educational Resources Information Center

This paper argues that a European controversy over a "mystical" hypothesis, one assigning the mind a role to play at the material level of reality, shaped much of the debate over the interpretation of the quantum equations. It traces back the controversy to the past two decades, beginning in the late 1920s--birth of quantum theory--and concluding…

Marin, Juan Miguel

2009-01-01

428

"Mysticism" in Quantum Mechanics: The Forgotten Controversy  

ERIC Educational Resources Information Center

|This paper argues that a European controversy over a "mystical" hypothesis, one assigning the mind a role to play at the material level of reality, shaped much of the debate over the interpretation of the quantum equations. It traces back the controversy to the past two decades, beginning in the late 1920s--birth of quantum theory--and concluding…

Marin, Juan Miguel

2009-01-01

429

Demonstration of nondeterministic quantum logic operations using linear optical elements.  

PubMed

Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)] recently showed that nondeterministic quantum logic operations could be performed using linear optical elements, additional photons (ancilla), and postselection based on the output of single-photon detectors. Here we report the experimental demonstration of two logic devices of this kind, a destructive controlled-NOT (CNOT) gate and a quantum parity check. These two devices can be combined with a pair of entangled photons to implement a conventional (nondestructive) CNOT that succeeds with a probability of 1/4. PMID:12097131

Pittman, T B; Jacobs, B C; Franson, J D

2002-06-06

430

Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation  

NASA Astrophysics Data System (ADS)

The dual Hamiltonian free energy perturbation (DH-FEP) method is designed for accurate and efficient evaluation of the free energy profile of chemical reactions in quantum mechanical/molecular mechanical (QM/MM) calculations. In contrast to existing QM/MM FEP variants, the QM region is not kept frozen during sampling, but all degrees of freedom except for the reaction coordinate are sampled. In the DH-FEP scheme, the sampling is done by semiempirical QM/MM molecular dynamics (MD), while the perturbation energy differences are evaluated from high-level QM/MM single-point calculations at regular intervals, skipping a pre-defined number of MD sampling steps. After validating our method using an analytic model potential with an exactly known solution, we report a QM/MM DH-FEP study of the enzymatic reaction catalyzed by chorismate mutase. We suggest guidelines for QM/MM DH-FEP calculations and default values for the required computational parameters. In the case of chorismate mutase, we apply the DH-FEP approach in combination with a single one-dimensional reaction coordinate and with a two-dimensional collective coordinate (two individual distances), with superior results for the latter choice.

Polyak, Iakov; Benighaus, Tobias; Boulanger, Eliot; Thiel, Walter

2013-08-01

431

Quantum optical test of observation and complementarity in quantum mechanics  

Microsoft Academic Search

Experiments to probe the way in which the measurement process (the presence of a detector) influences the investigated system are proposed and analyzed. These experiments are based on the fact that number states of the radiation field can be generated by the use of a micromaser and cavity quantum electrodynamics. It is shown that which-path (particle) information rules out interference

Marlan O. Scully; Herbert Walther

1989-01-01

432

Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.  

PubMed

We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom. PMID:23531015

Chou, Chia-Chun; Kouri, Donald J

2013-04-15

433

On the existence of complex spacetime in relativistic quantum mechanics  

Microsoft Academic Search

The infinite dimensional E(?) space, when viewed at large scales, mimics the appearance of a 4-dimensional complex spacetime. The aim of this paper is to prove the existence of such a complex spacetime in our physical world and to show that what the current relativistic quantum mechanics describes is just the quantum phenomena appeared in this 4-dimensional complex spacetime. We

Ciann-Dong Yang

2008-01-01

434

Decoherence, the measurement problem, and interpretations of quantum mechanics  

Microsoft Academic Search

Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most notably the quantum measurement problem, have remained a matter of great controversy. This paper is intended to clarify key features of the decoherence program, including its more recent results, and to investigate their

Maximilian Schlosshauer

2004-01-01

435

Excitation transfer through open quantum networks: a few basic mechanisms  

Microsoft Academic Search

A variety of open quantum networks are currently under intense examination to model energy transport in photosynthetic systems. Here we study the coherent transfer of a quantum excitation over a network incoherently coupled with a structured and small environment that effectively models the photosynthetic reaction center. Our goal is to distill a few basic, possibly universal, mechanisms or \\

Lorenzo Campos Venuti; Paolo Zanardi

2011-01-01

436

Generalized Lippmann-Schwinger equation in the fractional quantum mechanics  

NASA Astrophysics Data System (ADS)

From the three-dimensional space fractional Schrödinger equation, a generalized Lippmann-Schwinger equation for the fractional quantum mechanics is obtained for both scattering and bound states. We apply the generalized integral equation to study the fractional quantum scattering problem and give the approximate scattering wavefunction of first order and higher orders.

Dong, Jianping

2011-05-01

437

CXXXVI. On the quantum mechanics of helium II  

Microsoft Academic Search

The quantum mechanics of a system of identical interacting particles must lead to the classical hydrodynamic equations of motion at high temperatures, because of the correspondence principle. On the other hand, the behaviour of helium II shows that this is not always the case at low temperatures. In this paperit is shown that' in certain cases the quantum description requires

O. Penrose

1951-01-01

438

OSP Quantum Mechanics: Single Measurments of Spin States Worksheet  

NSDL National Science Digital Library

This set of tutorial worksheets, based on the OSP Quantum Mechanics Simulations, help students explore the measurement of quantum spins. The tutorial starts with an introduction of the physics of spins, and then presents the results of a single measurement on pure, mixed, and superposition states.

Christian, Wolfgang; Belloni, Mario

2010-01-11

439

Rotations et moments angulaires en mecanique quantique (2eme partie). (Rotations and angular momentum in quantum mechanics (2nd part)).  

National Technical Information Service (NTIS)

In this second part about rotations and angular momentum in quantum mechanics, the author explains the method of angular momentum addition and gives some properties of irreducible tensorial operators. (Atomindex citation 24:024334)

J. Van de Wiele

1992-01-01

440

Quantum circuits for measuring Levin-Wen operators  

NASA Astrophysics Data System (ADS)

We construct quantum circuits for measuring the commuting set of vertex and plaquette operators that appear in the Levin-Wen model for doubled Fibonacci anyons. Such measurements can be viewed as syndrome measurements for the quantum error-correcting code defined by the ground states of this model (the Fibonacci code). We quantify the complexity of these circuits with gate counts using different universal gate sets and find these measurements become significantly easier to perform if n-qubit Toffoli gates with n=3,4, and 5 can be carried out directly. In addition to measurement circuits, we construct simplified quantum circuits requiring only a few qubits that can be used to verify that certain self-consistency conditions, including the pentagon equation, are satisfied by the Fibonacci code.

Bonesteel, N. E.; DiVincenzo, D. P.

2012-10-01

441

Testing Quantum Mechanics in High-Energy Physics  

NASA Astrophysics Data System (ADS)

In this set of lectures we show that particle physics can also contribute to fundamental questions about quantum mechanics (QM) and even shine new light in the fine workings of quantum physics and this at scales of energies which are not available for usual quantum systems. In particular the massive meson-antimeson systems are specially suitable as they offer a unique laboratory to test various aspects of particle physics (CP violation, CPT violation, etc.) as well as to test the foundations of QM (local realistic theories versus QM, Bell inequalities, decoherence effects, quantum marking and erasure concepts, Bohr's complementary relation, etc.).

Hiesmayr, Beatrix C.

442

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

Microsoft Academic Search

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

443

The diffeomorphism constraint operator in loop quantum gravity  

NASA Astrophysics Data System (ADS)

We construct the smeared diffeomorphism constraint operator at finite triangulation from the basic holonomy-flux operators of loop quantum gravity (LQG), evaluate its continuum limit on the Lewandowski-Marolf habitat and show that the action of the continuum operator provides an anomaly-free representation of the Lie algebra of diffeomorphisms of the 3-manifold. Key features of our analysis include (i) finite triangulation approximants to the curvature, Fiab, of the Ashtekar-Barbero connection which involve not only small loop holonomies but also small surface fluxes as well as an explicit dependence on the edge labels of the spin network being acted on (ii) the dependence of the small loop underlying the holonomy on both the direction and magnitude of the shift vector field, (iii) continuum constraint operators which do not have finite action on the kinematic Hilbert space, thus implementing a key lesson from recent studies of parameterized field theory by the authors. Features (i) and (ii) provide the first hints in LQG of a conceptual similarity with the so-called mu-bar scheme of loop quantum cosmology. We expect our work to be of use in the construction of an anomaly-free quantum dynamics for LQG.

Laddha, Alok; Varadarajan, Madhavan

2011-10-01

444

Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians  

NASA Astrophysics Data System (ADS)

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.

Al-Hashimi, M. H.; Salman, M.; Shalaby, A.; Wiese, U.-J.

2013-10-01

445

Superluminality and the equivalence postulate of quantum mechanics  

NASA Astrophysics Data System (ADS)

An interpretation of the recent results reported by the OPERA collaboration is that neutrinos propagation in vacuum exceeds the speed of light. It has been further been suggested that this interpretation can be attributed to the variation of the particle average speed arising from the Relativistic Quantum Hamilton-Jacobi Equation. I derive an expression for the quantum correction to the instantaneous relativistic velocity in the framework of the relativistic quantum Hamilton-Jacobi equation, which is derived from the equivalence postulate of quantum mechanics. While the quantum correction does indicate deviations from the classical energy-momentum relation, it does not necessarily lead to superluminal speeds. The quantum correction found herein has a non-trivial dependence on the energy and mass of the particle, as well as on distance travelled. I speculate on other possible observational consequences of the equivalence postulate approach.

Faraggi, Alon E.

2012-03-01

446

Adaptive Perturbation Theory: Quantum Mechanics and Field Theory.  

National Technical Information Service (NTIS)

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...

M. Weinstein

2005-01-01

447

Particles, Waves, and the Interpretation of Quantum Mechanics  

ERIC Educational Resources Information Center

Presents an explanation, without mathematical equations, of the basic principles of quantum mechanics. Includes wave-particle duality, the probability character of the wavefunction, and the uncertainty relations. (MLH)

Christoudouleas, N. D.

1975-01-01

448

On the Origin of Probability in Quantum Mechanics  

NASA Astrophysics Data System (ADS)

I give a brief introduction to many worlds or "no wave function collapse" quantum mechanics, suitable for non-specialists. I then discuss the origin of probability in such formulations, distinguishing between objective and subjective notions of probability.

Hsu, Stephen D. H.

449

Why are probabilistic laws governing quantum mechanics and neurobiology?  

NASA Astrophysics Data System (ADS)

We address the question: Why are dynamical laws governing in quantum mechanics and in neuroscience of probabilistic nature instead of being deterministic? We discuss some ideas showing that the probabilistic option offers advantages over the deterministic one.

Kröger, Helmut

2005-08-01

450

Quantum dressed classical mechanics: application to non-adiabatic processes  

Microsoft Academic Search

A newly formulated theory for time-dependent molecular quantum mechanics is used to study processes involving more than one potential energy surface. Good agreement with exact numbers is obtained using one trajectory and just two grid points.

Gert D. Billing

2001-01-01

451

Natural cutoffs and Hilbert space representation of quantum mechanics  

NASA Astrophysics Data System (ADS)

We construct a Hilbert space representation of quantum mechanics in the presence of all natural cutoffs encoded in a generalized uncertainty principle (GUP) that admits a minimal measurable length, a minimal measurable momentum and a maximal momentum.

Nozari, Kourosh; Soleymani, Z.

2013-02-01

452

Quantum mechanics helps in learning for more intelligent robot  

Microsoft Academic Search

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

453

Quantum Circuits for Measuring Levin-Wen Operators  

NASA Astrophysics Data System (ADS)

We give explicit quantum circuits (expressed in terms of Toffoli gates, CNOTs and single qubit rotations) which can be used to perform quantum non-demolition measurements of the commuting set of vertex and plaquette operators that appear in the Levin-Wen model [1] for the case of doubled Fibonacci anyons. Such measurements can be viewed as syndrome measurements for the quantum error correcting code defined by the ground states of the Levin-Wen model --- a scenario envisioned in [2]. A key component in our construction is a quantum circuit F that acts on 5 qubits at a time and carries out a so-called F-move, a unitary operation whose form is essentially fixed by a self-consistency condition known as the pentagon equation. In addition to our measurement circuits we also give an explicit 7 qubit circuit which can be used to verify that F satisfies the full pentagon equation as well as a simpler 2 qubit circuit which verifies the essential nontrivial content of this equation. [1] M.A. Levin and X.-G. Wen, Phys. Rev. B 71 045110 (2005). [2] R. Koenig, G. Kuperberg, and B.W. Reichardt, Ann. Phys 325, 2707 (2010).

Bonesteel, Nick; Divincenzo, David

2012-02-01

454

Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics  

NASA Astrophysics Data System (ADS)

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10-7 calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.

Goldfarb, Yair; Degani, Ilan; Tannor, David J.

2006-12-01

455

Bohmian mechanics with complex action: a new trajectory-based formulation of quantum mechanics.  

PubMed

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10(-7) calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity. PMID:17190540

Goldfarb, Yair; Degani, Ilan; Tannor, David J

2006-12-21

456

Quantum Mechanics in Biology: Photoexcitations in DNA  

NASA Astrophysics Data System (ADS)

We consider here the theoretical and quantum chemical description of the photoexcitated states in DNA duplexes. We discuss the motivation and limitations of an exciton model and use this as the starting point for more detailed excited state quantum chemical evaluations. In particular, we focus upon the role of interbase proton transfer between Watson/Crick pairs in localizing an excitation and then quenching it through intersystem crossing and charge transfer.

Bittner, Eric R.; Czader, Arkadiusz

457

Probability in the Many-Worlds Interpretation of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

It is argued that, although in the Many-Worlds Interpretation of quantum mechanics there is no "probability" for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: (a) A "sleeping pill" gedanken experiment which makes correspondence between an illegitimate question: "What is the probability of an outcome of a quantum measurement?" with a legitimate question: "What is the probability that `I' am in the world corresponding to that outcome?"; (b) A gedanken experiment which splits the world into several worlds which are identical according to some symmetry condition; and (c) Relativistic causality, which together with (b) explain the Born rule of standard quantum mechanics. The Quantum Sleeping Beauty controversy and "caring measure" replacing probability measure are discussed.

Vaidman, Lev

458

The instrumentalist aspects of quantum mechanics stem from probability theory  

NASA Astrophysics Data System (ADS)

The aim of the article is to argue that the interpretations of quantum mechanics and of probability are much closer than usually thought. Indeed, a detailed analysis of the concept of probability (within the standard frequency interpretation of R. von Mises) reveals that this notion always refers to an observing system. Therefore the instrumentalist aspects of quantum mechanics, and in particular the enigmatic role of the observer in the Copenhagen interpretation, derive from a precise understanding of probability.

Vervoort, Louis

2012-03-01

459

A primer on quantum mechanics and its interpretations  

Microsoft Academic Search

All the concepts and principles necessary to understand quantum mechanics on an initial level are given in a form suitable for the non-expert. The concepts explained include visualizing the wave function, wave-particle duality, the implications of Schrodinger's cat, probability, the uncertainty principle, collapse of the wave function, and others. However, because of the peculiar, non-intuitive nature of quantum mechanics, one

Casey Blood

2010-01-01

460

Interpreting Quantum Mechanics according to a Pragmatist Approach  

NASA Astrophysics Data System (ADS)

The aim of this paper is to show that quantum mechanics can be interpreted according to a pragmatist approach. The latter consists, first, in giving a pragmatic definition to each term used in microphysics, second, in making explicit the functions any theory must fulfil so as to ensure the success of the research activity in microphysics, and third, in showing that quantum mechanics is the only theory which fulfils exactly these functions.

Bächtold, Manuel

2008-09-01

461

Scalable quantum mechanical simulation of large polymer systems  

SciTech Connect

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

462

Quantum mechanics and the social sciences: After hermeneutics  

NASA Astrophysics Data System (ADS)

Quantum mechanics is interpreted, in the spirit of Niels Bohr and Werner Heisenberg, as about physical objects in so far as these are revealed by and within the local, social, and historical process of measurement. An analysis of the hermeneutical aspect of quantum mechanical measurement reveals close analogues with the hermeneutical social/historical sciences. The hermeneutical analysis of science requires the move from the epistemological attitude to an ontological one.

Heelan, Patrick A.

1995-04-01

463

Exactly solvable quantum mechanical models with Stückelberg divergences  

Microsoft Academic Search

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

464

Interagency mechanical operations group numerical systems group  

SciTech Connect

This report consists of the minutes of the May 20-21, 1971 meeting of the Interagency Mechanical Operations Group (IMOG) Numerical Systems Group. This group looks at issues related to numerical control in the machining industry. Items discussed related to the use of CAD and CAM, EIA standards, data links, and numerical control.

NONE

1997-09-01

465

Standard forms of noisy quantum operations via depolarization  

SciTech Connect

We consider completely positive maps that describe noisy, multiparticle unitary operations. We show that by random single-particle operations the completely positive maps can be depolarized to a standard form with a reduced number of parameters describing the noise process in such a way that the noiseless (unitary) part of the evolution is not altered. A further reduction of the parameters, in many cases even to a single one (i.e., global white noise), is possible by tailoring the decoherence process and increasing the amount of noise. We generalize these results to the dynamical case where the noisy evolution is described by a master equation of Lindblad form, and the noiseless evolution is specified by an interaction Hamiltonian. The resulting standard forms may be used to compute lower bounds on channel capacities, to simplify quantum process tomography or to derive error thresholds for entanglement purification and quantum computation.

Duer, W.; Briegel, H.-J. [Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria); Institut fuer Quantenoptik und Quanteninformation der Oesterreichischen Akademie der Wissenschaften, Innsbruck (Austria); Hein, M. [Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria); Cirac, J. I. [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching (Germany)

2005-11-15

466

Acoustic Analog to Quantum Mechanical Level-Splitting  

NASA Astrophysics Data System (ADS)

One difficulty in teaching quantum mechanics is the lack of classroom demonstrations. To sidestep this issue, analogies can provide an enlightening alternative. Acoustics governance by the same time-independent wave equation as quantum mechanics supports it use in such analogies. This presentation examines one such analogy for an infinite potential well with a delta potential perturbation. The physical acoustic system consists of continuous sounds waves traveling in a pair of tubes which are separated by a variable diaphragm. The level-splitting nature of the quantum system can be mimicked in the acoustic system.

Hilbert, Shawn

2010-03-01

467

Aspects of relativistic quantum mechanics on phase space  

NASA Astrophysics Data System (ADS)

Recent work on formulating relativistic quantum mechanics on stochastic phase spaces is described. Starting with a brief introduction to the mathematical theory of stochastic spaces, an account is given of non-relativistic quantum mechanics on stochastic phase space. The relativistic theory is introduced by constructing certain classes of representations of the Poincaré group on phase space, obtaining thereby both the classical and the quantum dynamics. Applications to the Dirac equation are discussed, and an alternative 2-component equation for a charged spin-1/2 particle, interacting with an external electromagnetic field is studied.

Twareque Ali, S.

468

High-Fidelity Quantum Logic Operations Using Linear Optical Elements  

Microsoft Academic Search

Knill, Laflamme, and Milburn [Nature (London)NATUAS0028-0836 409, 46 (2001)] have shown that quantum logic operations can be performed using linear optical elements and additional ancilla photons. Their approach is probabilistic in the sense that the logic devices fail to produce an output with a failure rate that scales as 1\\/n, where n is the number of ancilla. Here we present

J. D. Franson; M. M. Donegan; M. J. Fitch; B. C. Jacobs; T. B. Pittman

2002-01-01

469

High-Fidelity Quantum Logic Operations Using Linear Optical Elements  

Microsoft Academic Search

Knill, Laflamme, and Milburn [Nature 409, 46 (2001)] have shown that quantum\\u000alogic operations can be performed using linear optical elements and additional\\u000aancilla photons. Their approach is probabilistic in the sense that the logic\\u000adevices fail to produce an output with a failure rate that scales as 1\\/n, where\\u000an is the number of ancilla. Here we present an

J. D. Franson; M. M. Donegan; M. J. Fitch; B. C. Jacobs; T. B. Pittman

2002-01-01

470

Relativistic quantum mechanics of spin-0 and spin-1 bosons  

NASA Astrophysics Data System (ADS)

It is shown that below the threshold of pair creation, a consistent quantum mechanical interpretation of relativistic spin-0 and spin-1 particles (both massive and mussless) is possible based an the Hamiltonian-Schrödinger form of the firstorder Kemmer equation together with a first-class constraint. The crucial element is the identification of a conserved four-vector current associated with the equation of motion, whose time component is proportional to the energy density which is constrained to be positive definite for all solutions. Consequently, the antiparticles must be interpreted as positive-energy states traveling backward in time. This also makes it possible to define hermitian position operators with localized eigensolutions (?-functions) as well as Bohmian trajectories for bosons. The exact theory is obtained by “second quantization” and is mathematically completely equivalent to conventional quantum field theory. The classical field emerges in the high mean number limit of coherent states of the exact theory. The formalism provides a new basis for computing tunneling times for photons and chaotic phenomena in optics.

Ghose, Partha

1996-11-01

471

The diffeomorphism constraint operator in loop quantum gravity  

NASA Astrophysics Data System (ADS)

We construct the diffeomorphism constraint operator at finite triangulation from the basic holonomy- flux operators of Loop Quantum Gravity, and show that the action of its continuum limit provides an anomaly free representation of the Lie algebra of diffeomorphisms of the 3- manifold. Key features of our analysis include: (i) finite triangulation approximants to the curvature, Fiab of the Ashtekar- Barbero connection which involve not only small loop holonomies but also small surface fluxes as well as an explicit dependence on the edge labels of the spin network being acted on (ii) the dependence of the small loop underlying the holonomy on both the direction and magnitude of the shift vector field (iii) continuum constraint operators which do not have finite action on the kinematic Hilbert space, thus implementing a key lesson from recent studies of parameterised field theory by the authors. Features (i) and (ii) provide the first hints in LQG of a conceptual similarity with the so called "mu- bar" scheme of Loop Quantum Cosmology. We expect our work to be of use in the construction of an anomaly free quantum dynamics for LQG. We highlight the main steps and results of our construction while suppressing most of the technical details. This work was done jointly with Alok Laddha.

Varadarajan, M.

2012-05-01

472

Foundations of quantum mechanics: The Langevin equations for QM  

NASA Astrophysics Data System (ADS)

Stochastic derivations of the Schrödinger equation are always developed on very general and abstract grounds. Thus, one is never enlightened which specific stochastic process corresponds to some particular quantum mechanical system, that is, given the physical system—expressed by the potential function, which fluctuation structure one should impose on a Langevin equation in order to arrive at results identical to those comming from the solutions of the Schrödinger equation. We show, from first principles, how to write the Langevin stochastic equations for any particular quantum system. We also show the relation between these Langevin equations and those proposed by Bohm in 1952. We present numerical simulations of the Langevin equations for some quantum mechanical problems and compare them with the usual analytic solutions to show the adequacy of our approach. The model also allows us to address important topics on the interpretation of quantum mechanics.

Olavo, L. S. F.; Lapas, L. C.; Figueiredo, A.

2012-05-01

473

Quantum mechanical states as attractors for Nelson processes  

NASA Astrophysics Data System (ADS)

In this paper we reconsider, in the light of the Nelson stochastic mechanics, the idea originally proposed by Bohm and Vigier that arbitrary solutions of the evolution equation for the probability densities always relax in time toward the quantum mechanical density ¦?¦2 derived from the Schrödinger equation. The analysis of a few general propositions and of some physical examples show that the choice of the L1 metrics and of the Nelson stochastic flux is correct for a particular class of quantum states, but cannot be adopted in general. This indicates that the question if the quantum mechanical densities attract other solution of the classical Fokker-Planck equations associated to the Schrödinger equation is physically meaningful, even if a classical probabilistic model good for every quantum stale is still not available. A few suggestion in this direction are finally discussed.

Petroni, Nicola Cufaro; Guerra, Francesco

1995-02-01

474

Quantum logic gate operation and entanglement with superconducting quantum interference devices in a cavity via a Raman transition  

Microsoft Academic Search

In the system with superconducting quantum interference devices (SQUIDs) in cavity, the quantum logic gates operation and entanglement can be achieved by using a quantized cavity field and classical microwave pluses, via Raman transition. In this scheme, no transfer of quantum information between the SQUIDs and cavity is required, the cavity field is only virtually excited and thus the cavity

Ke-Hui Song; Zheng-Wei Zhou; Guang-Can Guo

2005-01-01

475

Multiple-event probability in general-relativistic quantum mechanics  

SciTech Connect

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 multieve