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1

Resources Students Use to Understand Quantum Mechanical Operators  

NSDL National Science Digital Library

The Paradigms team at Oregon State University has developed a quantum mechanics curriculum aimed at middle division students that begins with a strong emphasis on using operators, matrices and Dirac notation to describe quantum systems. The curriculum begins with spin systems, and this content ordering relies on students being able to understand quantum mechanical operators, eigenstates and quantum measurement without prior instruction on wave functions. We have analyzed classroom and an interview video to identify resources students use when considering these quantum ideas. Identification of such resources will inform introductory curricula that are prerequisite to the quantum Paradigms and inform the development of Paradigms materials that will guide students to use these resources productively.

Gire, Elizabeth; Manogue, Corinne A.

2008-11-04

2

Phase operator problem and macroscopic extension of quantum mechanics  

SciTech Connect

To find the Hermitian phase operator of a single-mode electromagnetic field in quantum mechanics, the Schr{umlt o}dinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis. The Hermitian phase operator is shown to exist on the extended Hilbert space. This operator is naturally considered as the controversial limit of the approximate phase operators on finite dimensional spaces proposed by Pegg and Barnett. The spectral measure of this operator is a Naimark extension of the optimal probability operator-valued measure for the phase parameter found by Helstrom. Eventually, the two promising approaches to the statistics of the phase in quantum mechanics are synthesized by means of the Hermitian phase operator in the macroscopic extension of the Schr{umlt o}dinger representation. {copyright} 1997 Academic Press, Inc.

Ozawa, M. [School of Informatics and Sciences, Nagoya University, Nagoya 464-01 (Japan)] [School of Informatics and Sciences, Nagoya University, Nagoya 464-01 (Japan)

1997-06-01

3

Duality, Mechanical Wave Theory, New Quantum Operators and Nonlinear Equations in Quantum Theory  

E-print Network

Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various mechanical equations, and may be derive some new results. It is called the mechanical wave theory. From this we derive new operators which represent more physical quantities. Further, we propose some nonlinear equations and their solutions, which may be probably applied to quantum theory.

Yi-Fang Chang

2010-08-17

4

A dynamical time operator in Dirac's relativistic quantum mechanics  

NASA Astrophysics Data System (ADS)

A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The ensuing time-energy uncertainty relation involves the uncertainty in the instant of time when the wave packet passes a particular spatial position and the energy uncertainty associated with the wave packet at the same time, as envisaged originally by Bohr. The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in electron channeling, in interference in time, in Zitterbewegung-like effects in spintronics, graphene and superconducting systems and in cosmology is noted.

Bauer, M.

2014-03-01

5

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 stationary…

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

2007-01-01

6

Quantum Operations and Measurement  

E-print Network

Quantum Operations and Measurement M.P Seevinck E-mail: M.P.Seevinck@phys.uu.nl Utrecht field in quantum physics ­ or perhaps better, a new way of doing quantum physics ­ . . . Surprisingly of these developments to the conceptual problems of quantum mechanics. In our view, the new work on quantum information

Seevinck, Michiel

7

Quantum Operations and Measurement  

E-print Network

Quantum Operations and Measurement # M.P Seevinck # E­mail: M.P.Seevinck@phys.uu.nl Utrecht in quantum physics -- or perhaps better, a new way of doing quantum physics -- . . . Surprisingly, with few to the conceptual problems of quantum mechanics. In our view, the new work on quantum information changes

Seevinck, Michiel

8

Towards a General Operational and Realistic Framework for Quantum Mechanics and Relativity Theory  

Microsoft Academic Search

We propose a general operational and realistic framework that aims at a generalization of quantum mechanics and relativity theory, such that both appear as special cases of this new theory. Our framework is operational, in the sense that all aspects are introduced with specific reference to events to be experienced, and realistic, in the sense that the hypothesis of an

Diederik Aerts; Sven Aerts

9

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

10

Ladder Operators for Some Spherically Symmetric Potentials in Quantum Mechanics  

ERIC Educational Resources Information Center

The energy levels of the free field, Coulomb potential, and the three-dimensional harmonic oscillator are found using the Dirac operator formalism by the construction of suitable ladder operators. The degeneracy of each level is also discussed. (Author/GA)

Newmarch, J. D.; Golding, R. M.

1978-01-01

11

Quantum Mechanics  

NASA Astrophysics Data System (ADS)

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

Commins, Eugene D.

2014-10-01

12

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.

De Raedt, Hans; Michielsen, Kristel

2010-03-25

13

Transforming quantum operations: quantum supermaps  

E-print Network

We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.

G. Chiribella; G. M. D'Ariano; P. Perinotti

2008-04-01

14

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

15

Quantum Mechanics  

Microsoft Academic Search

We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with respect to a uniquely defined positive scalar product in a infinite dimensional (right) quaternionic Hilbert space. According to such results we obtain two alternative descriptions of a quantum

A. L. Stewart; G. Scolarici; L. Solombrino

1963-01-01

16

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 5 problems LAST NAME FIRST NAME #12 with the effective electron mass at the band edges. #12;Applied quantum mechanics 3 (c) Write a computer program

Levi, Anthony F. J.

17

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 1 problems LAST NAME FIRST NAME #12 happens to the beat frequency if the airplane moves in an arc? #12;Applied quantum mechanics 3 Problem 1

Levi, Anthony F. J.

18

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 8 problems LAST NAME FIRST NAME #12;Applied quantum mechanics 3 (b) If the electron is in a semiconductor and has an effective mass m * 0.07 m

Levi, Anthony F. J.

19

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 10 problems LAST NAME FIRST NAME #12 ­( ) L/( )= L/ #12;Applied quantum mechanics 3 (d) Use the results of (b) an (c) to draw the electron

Levi, Anthony F. J.

20

Path-Integral Formulation of Pseudo-Hermitian Quantum Mechanics and the Role of the Metric Operator  

E-print Network

We provide a careful analysis of the generating functional in the path integral formulation of pseudo-Hermitian and in particular PT-symmetric quantum mechanics and show how the metric operator enters the expression for the generating functional.

Ali Mostafazadeh

2007-08-29

21

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 6 problems LAST NAME FIRST NAME #12 --- and that for a Poisson distribution of such photons #12; 1 2 n ---------------- Applied quantum mechanics 3 (c) Apply conditions is the quantum mechanical result m t 2 2 d d x xd d V x ­= the same Newton's second law in which

Levi, Anthony F. J.

22

Natural star-products on symplectic manifolds and related quantum mechanical operators  

E-print Network

In this paper is considered a problem of defining natural star-products on symplectic manifolds, admissible for quantization of classical Hamiltonian systems. First, a construction of a star-product on a cotangent bundle to an Euclidean configuration space is given with the use of a sequence of pair-wise commuting vector fields. The connection with a covariant representation of such a star-product is also presented. Then, an extension of the construction to symplectic manifolds over flat and non-flat pseudo-Riemannian configuration spaces is discussed. Finally, a coordinate free construction of related quantum mechanical operators from Hilbert space over respective configuration space is presented.

Maciej Blaszak; Ziemowit Domanski

2013-11-13

23

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 6 problems LAST NAME FIRST NAME #12 of the system. (b) Find . (c) Find and show that . Under what conditions is the quantum mechanical result( ) td d A t( ) t A td d A /= A B i 2 --- A^ B^,[ ] A^ B^ Et 2 --- n n 1 2 --- #12;Applied quantum

Levi, Anthony F. J.

24

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. PMID:23509390

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

2013-01-01

25

What is quantum mechanics?  

Microsoft Academic Search

We discuss the arguments for suspecting that there exists a classical, i.e. deterministic theory underlying quantum mechanics. A difficulty is that an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in

Gerard't Hooft

2007-01-01

26

Bohmian mechanics contradicts quantum mechanics  

E-print Network

Bohmian mechanics contradicts quantum mechanics Arnold Neumaier Institut fur Mathematik, Universit and quantum mechanics predict values of opposite sign for certain time correlations. The discrepancy can no loophole for claiming that Bohmian mechanics reproduces all predictions of quantum mechanics exactly

Neumaier, Arnold

27

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 9 problems LAST NAME FIRST NAME #12 10 cm 1­ = 2 1� 0.2� µm 3 2 µm 100 µA #12;Applied quantum mechanics 3 Problem 9.4 Modify the computer

Levi, Anthony F. J.

28

Playing Games in Quantum Mechanical Settings:. Features of Quantum Games  

Microsoft Academic Search

In this lecture note, we present the implications of playing classical games in quantum mechanical settings where the quantum mechanical toolbox consisting of entanglement, quantum operations and measurement is used. After a brief introduction to the concepts of classical game theory and quantum mechanics, we study quantum games and their corresponding classical analogues to determine the novelties. In addition, we

Sahin Kaya Özdemir; Junichi Shimamura; Nobuyuki Imoto

2008-01-01

29

Principles of Fractional Quantum Mechanics  

E-print Network

A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum mechanics, hermiticity of the Hamilton operator, parity conservation law and the current density. Applications of fractional quantum mechanics cover dynamics of a free particle, new representation for a free particle quantum mechanical kernel, infinite potential well, bound state in {\\delta}-potential well, linear potential, fractional Bohr atom and fractional oscillator. We also review fundamentals of the L\\'evy path integral approach to fractional statistical mechanics.

Nick Laskin

2010-09-28

30

Quantum Mechanics in Quantum Computing  

Microsoft Academic Search

Mathew Johnson is a Ball State junior majoring in Mathematics (Option 1) with a minor in Physics. In his sophomore year, he participated in the student- faculty colloquium, where he explored quantum com- puting with several other students and faculty. Quantum mechanics is a scientific theory that seeks to describe atomic and subatomic particles (or quantum particles) as well as

Mathew Johnson

2003-01-01

31

Quantum Mechanics Measurements, Mutually  

E-print Network

Quantum Mechanics Measurements, Mutually Unbiased Bases and Finite Geometry Or why six is the first) #12;Quantum Mechanics for Dummies Finite dimensional quantum states are represented by trace one,1 -icS1,1[ ] #12;Quantum systems evolve and are measured. The evolution of a quantum system using

Gruner, Daniel S.

32

Speculation on Quantum Mechanics and the Operation of Life Giving Catalysts  

NASA Astrophysics Data System (ADS)

The origin of life necessitated the formation of catalytic functionalities in order to realize a number of those capable of supporting reactions that led to the proliferation of biologically accessible molecules and the formation of a proto-metabolic network. Here, the discussion of the significance of quantum behavior on biological systems is extended from recent hypotheses exploring brain function and DNA mutation to include origins of life considerations in light of the concept of quantum decoherence and the transition from the quantum to the classical. Current understandings of quantum systems indicate that in the context of catalysis, substrate-catalyst interaction may be considered as a quantum measurement problem. Exploration of catalytic functionality necessary for life's emergence may have been accommodated by quantum searches within metal sulfide compartments, where catalyst and substrate wave function interaction may allow for quantum based searches of catalytic phase space. Considering the degree of entanglement experienced by catalytic and non catalytic outcomes of superimposed states, quantum contributions are postulated to have played an important role in the operation of efficient catalysts that would provide for the kinetic basis for the emergence of life.

Haydon, Nathan; McGlynn, Shawn E.; Robus, Olin

2011-02-01

33

Quantum Mechanics  

NASA Astrophysics Data System (ADS)

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

Murdin, P.

2000-11-01

34

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 5 problems LAST NAME FIRST NAME #12 + --------------------------------------------- k = t 10/= t 1­= Ek 2t kxL( ) 2t 2kxL( )cos+cos= t 10/= t 1­= t 0.2­= #12;Applied quantum mechanics 3 (c) Write a computer program to plot the electron density of states for a square lat- tice

Levi, Anthony F. J.

35

Fractional quantum mechanics  

Microsoft Academic Search

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

Nikolai Laskin

2000-01-01

36

Classical integrals as quantum mechanical differential operators: a comparison with the symmetries of the Schrödinger Equation  

NASA Astrophysics Data System (ADS)

Superintegrable systems are characterised by the possession of many symmetries and integrals. We use the simple harmonic oscillator as an example and examine the relationship between the Noetherian integrals of a given Lagrangian as quantum operators and the Lie symmetries of the corresponding Schrödinger Equation.

Nucci, M. C.; Leach, P. G. L.

2014-10-01

37

Quantum Statistical Mechanics. IV. Non-Equilibrium Probability Operator and Stochastic, Dissipative Schrodinger Equation  

E-print Network

The probability operator for a generic non-equilibrium quantum system is derived. The corresponding stochastic, dissipative Schr\\"odinger equation is also given. The dissipative and stochastic propagators are linked by the fluctuation-dissipation theorem that is derived from the unitary condition on the time propagator. The dissipative propagator is derived from thermodynamic force and entropy fluctuation operators that are in general non-linear.

Attard, Phil

2014-01-01

38

Quantum Mechanics + Open Systems  

E-print Network

Quantum Mechanics + Open Systems = Thermodynamics ? Jochen Gemmer T¨ubingen, 09.02.2006 #12., World Scientific) #12;Fundamental Law or Emergent Description? Quantum Mechanics i t = (- 2 2m + V or Emergent Description? Quantum Mechanics i t = (- 2 2m + V ) "Heisenberg Cut" Classical Mechanics: m d2

Steinhoff, Heinz-Jürgen

39

Astrophysics QuantumMechanics  

E-print Network

Astrophysics Geometry QuantumMechanics Stochasticanalysis DifferentialEquations A N N U A L R E P O report 2010 6 Geometry 6 Stochastic analysis 8 Differential Equations 9 Astrophysics 11 Quantum Mechanics

Johansen, Tom Henning

40

Introduction to Quantum Mechanics  

E-print Network

The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.

Eduardo J. S. Villaseñor

2008-04-23

41

Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods  

NASA Astrophysics Data System (ADS)

In this paper we use Dirac function to construct a fractional operator called fractional corresponding operator, which is the general form of momentum corresponding operator. Then we give a judging theorem for this operator and with this judging theorem we prove that R-L, G-L, Caputo, Riesz fractional derivative operator and fractional derivative operator based on generalized functions, which are the most popular ones, coincide with the fractional corresponding operator. As a typical application, we use the fractional corresponding operator to construct a new fractional quantization scheme and then derive a uniform fractional Schrödinger equation in form. Additionally, we find that the five forms of fractional Schrödinger equation belong to the particular cases. As another main result of this paper, we use fractional corresponding operator to generalize fractional quantization scheme by using Lévy path integral and use it to derive the corresponding general form of fractional Schrödinger equation, which consequently proves that these two quantization schemes are equivalent. Meanwhile, relations between the theory in fractional quantum mechanics and that in classic quantum mechanics are also discussed. As a physical example, we consider a particle in an infinite potential well. We give its wave functions and energy spectrums in two ways and find that both results are the same.

Zhang, Xiao; Wei, Chaozhen; Liu, Yingming; Luo, Maokang

2014-11-01

42

Thermodynamic and quantum chemical study of the transformations and operation mechanism of molybdenum catalysts under hydrogenation conditions  

Microsoft Academic Search

Structural transformations and the mechanism of the operation of molybdenum-containing catalysts under hydrogenation conditions\\u000a have been studied by chemical thermodynamics and quantum chemistry methods, as well as the role of sulfur compounds in this\\u000a process. It has been shown that molybdenum disulfide, an effective hydrogenation catalyst, is produced via the reaction of\\u000a molybdenum oxide with hydrogen sulfide, not elemental sulfur.

Kh. M. Kadiev; A. M. Gyul’maliev; M. Ya. Shpirt; S. N. Khadzhiev

2010-01-01

43

Making sense of quantum operators, eigenstates and quantum measurements  

NSDL National Science Digital Library

Operators play a central role in the formalism of quantum mechanics. In particular, operators corresponding to observables encode important information about the results of quantum measurements. We interviewed upper-level undergraduate physics majors about their understanding of the role of operators in quantum measurements. Previous studies have shown that many students think of measurements on quantum systems as being deterministic and that measurements mathematically correspond to operators acting on the initial quantum state. This study is consistent with and expands on those results. We report on how two students make sense of a quantum measurement problem involving sequential measurements and the role that the eigenvalue equation plays in this sense-making.

Gire, Elizabeth; Manogue, Corinne A.

2012-05-15

44

Quantum Mechanics II (Undergraduate)  

E-print Network

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

Nickrent, Daniel L.

45

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

46

Phase Space Quantum Mechanics - Direct  

E-print Network

Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of non commuting observables. Further conceptual and practical merits of the formalism are demonstrated throughout the text.

S. Nasiri; Y. Sobouti; F. Taati

2006-05-15

47

Conformal Orthosymplectic Quantum Mechanics  

E-print Network

We present the most general curvature obstruction to the deformed parabolic orthosymplectic symmetry subalgebra of the supersymmetric quantum mechanical models recently developed to describe Lichnerowicz wave operators acting on arbitrary tensors and spinors. For geometries possessing a hypersurface-orthogonal homothetic conformal Killing vector we show that the parabolic subalgebra is enhanced to a (curvature-obstructed) orthosymplectic algebra. The new symmetries correspond to time-dependent conformal symmetries of the underlying particle model. We also comment on generalizations germane to three dimensions and new Chern--Simons-like particle models.

J. Burkart; A. Waldron

2008-12-20

48

Conformal orthosymplectic quantum mechanics  

NASA Astrophysics Data System (ADS)

We present the most general curvature obstruction to the deformed parabolic orthosymplectic symmetry subalgebra of the supersymmetric quantum mechanical models recently developed to describe Lichnerowicz wave operators acting on arbitrary tensors and spinors. For geometries possessing a hypersurface-orthogonal homothetic conformal Killing vector we show that the parabolic subalgebra is enhanced to a (curvature-obstructed) orthosymplectic algebra. The new symmetries correspond to time-dependent conformal symmetries of the underlying particle model. We also comment on generalizations germane to three dimensions and new Chern-Simons-like particle models.

Burkart, Joshua; Waldron, Andrew

2009-05-01

49

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

50

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

51

Covariant quantum mechanics and quantum symmetries  

E-print Network

Covariant quantum mechanics and quantum symmetries Josef JanyŸska 1 , Marco Modugno 2 , Dirk Saller: quantum mechanics, classical mechanics, general relativity, infinitesimal symmetries. 2000 MSC: 81P99, 81Q Introduction 2 2 Covariant quantum mechanics 5 2.1 Classical background

JanyÂ?ka, Josef

52

An introduction to quantum probability, quantum mechanics, and quantum computation  

E-print Network

An introduction to quantum probability, quantum mechanics, and quantum computation Greg Kuperberg". Recently quantum computation has entered as a new reason for both mathematicians and computer scientists deterministic algorithms for some computational problems, quantum algorithms can be moderately faster

Thomases, Becca

53

What is quantum mechanics?  

NASA Astrophysics Data System (ADS)

We discuss the arguments for suspecting that there exists a classical, i.e. deterministic theory underlying quantum mechanics. A difficulty is that an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes is further elucidated, as it follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model. An example of a deterministic dissipative model producing exact quantum mechanics is provided for the case of a finite-dimensional vector space. These lecture notes have been produced partly from material published earlier, and as such contain more material than what could be presented in the talk.

't Hooft, Gerard

2007-04-01

54

Quantum Statistical Mechanics and Quantum Computation  

E-print Network

Quantum Statistical Mechanics and Quantum Computation 22-23 March 2012 Room 111, Jadwin Hall, focused meeting to explore the intersection between quantum statistical mechanics and quantum computation, specifically quantum complexity theory. Advances in complexity theory have interesting implications for physics

55

Time in quantum mechanics  

E-print Network

The role of time in quantum mechanics has been and is still very controversial. The purpose of this paper was to explore the historical interpretation of time in quantum mechanics, to determine the current status of this problem-L and to investigate...

Chapin, Kimberly R.

2012-06-07

56

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

57

Geometrization of Quantum Mechanics  

E-print Network

We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.

J. F. Carinena; J. Clemente-Gallardo; G. Marmo

2007-01-19

58

NON-COMMUTATIVE SPHERES AND NUMERICAL QUANTUM MECHANICS  

E-print Network

NON-COMMUTATIVE SPHERES AND NUMERICAL QUANTUM MECHANICS basic issues that arise when one attempts to mo* *del quantum mechanical systems on a computer, quantum mechanics. Contributed to the proceedings of a NATO conference on operator algebras, ma

Arveson, William

59

Membrane Quantum Mechanics  

E-print Network

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

Okazaki, Tadashi

2014-01-01

60

Operator Formulation of Classical Mechanics.  

ERIC Educational Resources Information Center

Discusses the construction of an operator formulation of classical mechanics which is directly concerned with wave packets in configuration space and is more similar to that of convential quantum theory than other extant operator formulations of classical mechanics. (Author/HM)

Cohn, Jack

1980-01-01

61

Pseudospectra in non-Hermitian quantum mechanics  

E-print Network

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT-symmetric quantum mechanics.

D. Krejcirik; P. Siegl; M. Tater; J. Viola

2014-02-05

62

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

SciTech Connect

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

Ritchie, A B

1998-08-01

63

Is quantum mechanics exact?  

SciTech Connect

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 [California Institute of Technology, Pasadena, California 91125 (United States)] [California Institute of Technology, Pasadena, California 91125 (United States)

2013-06-15

64

Constructibility in Quantum Mechanics  

E-print Network

We propose a set theoretical foundation including an axiom of constructibility and derive a generalized quantum mechanics by postulating symmetry of action. The Schroedinger equation proves to be a special case of a nonlinear sigma model. Quantum mechanics is obtained here without the requirement for presupposing the statistical interpretation of the wave function; thus this derivation becomes continuous with prior physics. In this theory we also see space-time as relational and the fields as free of singularities.

D. J. Bendaniel

2008-06-06

65

Supersymmetry in quantum mechanics  

Microsoft Academic Search

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical\\u000a problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable. In\\u000a this lecture I review the theoretical formulation of supersymmetric quantum mechanics and discuss many of its applications.\\u000a I show that the well-known exactly solvable

Avinash Khare

1997-01-01

66

Evading quantum mechanics  

E-print Network

Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement back action often limit the precision of conventional classical information-processing devices, such as sensors and atomic clocks. Here we show that by engineering the dynamics of coupled quantum systems, it is possible to construct a subsystem that evades the measurement back action of quantum mechanics, at all times of interest, and obeys any classical dynamics, linear or nonlinear, that we choose. We call such a system a quantum-mechanics-free subsystem (QMFS). All of the observables of a QMFS are quantum-nondemolition (QND) observables; moreover, they are dynamical QND observables, thus demolishing the widely held belief that QND observables are constants of motion. QMFSs point to a new strategy for designing classical information-processing devices in regimes where quantum noise is detrimental, unifying previous approaches that employ QND observables, back-action evasion, and quantum noise cancellation. Potential applications include gravitational-wave detection, optomechanical force sensing, atomic magnetometry, and classical computing. Demonstrations of dynamical QMFSs include the generation of broad-band squeezed light for use in interferometric gravitational-wave detection, experiments using entangled atomic spin ensembles, and implementations of the quantum Toffoli gate.

Mankei Tsang; Carlton M. Caves

2012-03-11

67

Graduate Quantum Mechanics Reform  

NSDL National Science Digital Library

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, Lincoln D.; Mckagan, Sam B.

2009-05-06

68

The Teaching of Quantum Mechanics  

NSDL National Science Digital Library

This website has tips and techniques for teaching quantum mechanics. It presents and outlines central ideas in quantum mechanics and includes descriptions of textbooks and software that can be helpful in quantum classes.

Styer, Dan

2003-10-10

69

I. BASICS OF STATISTICAL MECHANICS AND QUANTUM MECHANICS Markus Holzmann  

E-print Network

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

70

Quantum mechanics needs no interpretation  

E-print Network

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule, probability density current, commutation relations, momentum operator, uncertainty relations, rules for including the scalar and vector potentials and existence of antiparticles can be derived from the definition of the mean values of the space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schroedinger equation and Dirac equation are obtained from requirement of the relativistic invariance of the theory. Limit case of localized probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many particle systems are also discussed.

L. Skala; V. Kapsa

2004-12-22

71

Quantum Mechanics From the Cradle?  

ERIC Educational Resources Information Center

States that the major problem in learning quantum mechanics is often the student's ignorance of classical mechanics and that one conceptual hurdle in quantum mechanics is its statistical nature, in contrast to the determinism of classical mechanics. (MLH)

Martin, John L.

1974-01-01

72

QUANTUM MECHANICS II Physics 342  

E-print Network

QUANTUM MECHANICS II Physics 342 KPTC 103 9:00 ­ 10:20 a.m. 1 Tues., Thurs. ­ Winter Quarter 2011 quantum mechanics at the graduate level. The text for Quantum Mechanics II will be J. J. Sakurai and Jim Napolitano, Modern Quantum Mechanics, Second Edition (Addison-Wesley, San Francisco, 2011). For supplemental

Rosner, Jonathan L.

73

Quantum mechanics over sets  

E-print Network

In the tradition of toy models of quantum mechanics in vector spaces over finite fields (e.g., Schumacher and Westmoreland's "modal quantum theory"), one finite field stands out, 2, since vectors over 2 have an interpretation as natural mathematical objects, i.e., sets. This engages a sets-to-vector-spaces bridge that is part of the mathematical folklore to translate both ways between set concepts and vector space concepts. Using that bridge, the mathematical framework of (finite-dimensional) quantum mechanics can be transported down to sets resulting in quantum mechanics over sets or QM/sets. This approach leads to a different treatment of Dirac's brackets than in "modal quantum theory" (MQT), and that gives a full probability calculus (unlike MQT that only has zero-one modalities of impossible and possible). That, in turn, leads to a rather fulsome theory of QM over sets that includes "logical" models of the double-slit experiment, Bell's Theorem, quantum information theory, quantum computing, and much else. Indeed, QM/sets is proposed as the "logic" of QM in the old-fashioned sense of "logic" as giving the simplified essentials of a theory. QM/sets is also a key part of a broader research program to provide an interpretation of QM based on the notion of "objective indefiniteness," a program that grew out the recent development of the logic of partitions mathematically dual to the usual Boolean logic of subsets.

David Ellerman

2013-10-30

74

Orthodox Quantum Mechanics Free from Paradoxes  

E-print Network

A formulation of quantum mechanics based on an operational definition of state is presented. This formulation, which includes explicitly the macroscopic systems, assumes the probabilistic interpretation and is nevertheless objective. The classical paradoxes of quantum mechanics are analyzed and their origin is found to be the fictitious properties that are usually attributed to quantum-mechanical states. The hypothesis that any mixed state can always be considered as an incoherent superposition of pure states is found to contradict quantum mechanics. A solution of EPR paradox is proposed. It is shown that entanglement of quantum states is compatible with realism and locality of events, but implies non-local encoding of information.

Rodrigo Medina

2005-08-02

75

Distinguishing quantum operations having few Kraus operators  

E-print Network

Entanglement is sometimes helpful in distinguishing between quantum operations, as differences between quantum operations can become magnified when their inputs are entangled with auxiliary systems. Bounds on the dimension of the auxiliary system needed to optimally distinguish quantum operations are known in several situations. For instance, the dimension of the auxiliary space never needs to exceed the dimension of the input space of the operations for optimal distinguishability, while no auxiliary system whatsoever is needed to optimally distinguish unitary operations. Another bound, which follows from work of R. Timoney, is that optimal distinguishability is always possible when the dimension of the auxiliary system is twice the number of operators needed to express the difference between the quantum operations in Kraus form. This paper provides an alternate proof of this fact that is based on concepts and tools that are familiar to quantum information theorists.

John Watrous

2007-10-03

76

Probability in Quantum Mechanics  

Microsoft Academic Search

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

Abner Shimony

77

Algebraic Quantum Mechanics and Pregeometry  

E-print Network

We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points" we suggest an approach that may make it possible to dispense with an a priori given space manifold. In this approach the algebra itself would carry the symmetries of translation, rotation, etc. Our suggestion is illustrated in a preliminary way by using a particular generalized Clifford Algebra proposed originally by Weyl, which approaches the ordinary Heisenberg algebra in a suitable limit. We thus obtain a certain insight into how quantum mechanics may be regarded as a purely algebraic theory, provided that we further introduce a new set of "neighbourhood operators", which remove an important kind of arbitrariness that has thus far been present in the attempt to treat quantum mechanics solely in terms of a Heisenberg algebra.

D. J. Bohm; P. G. Davies; B. J. Hiley

2006-11-30

78

Supersymmetric Quantum Mechanics with Reflections  

E-print Network

We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q-> -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wave functions of extended Scarf I potentials with different parameters are presented.

S. Post; L. Vinet; A. Zhedanov

2011-07-28

79

Supersymmetric Quantum Mechanics with Reflections  

E-print Network

A novel realization of supersymmetric quantum mechanics is obtained by using as supercharges, differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q-> -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wave functions of extended Scarf I potentials with different parameters are presented.

Post, S; Zhedanov, A

2011-01-01

80

Playing Games in Quantum Mechanical Settings:. Features of Quantum Games  

NASA Astrophysics Data System (ADS)

In this lecture note, we present the implications of playing classical games in quantum mechanical settings where the quantum mechanical toolbox consisting of entanglement, quantum operations and measurement is used. After a brief introduction to the concepts of classical game theory and quantum mechanics, we study quantum games and their corresponding classical analogues to determine the novelties. In addition, we introduce a benchmark which attempts to make a fair comparison of classical games and their quantum extensions. This benchmark exploits the fact that in special settings a classical game should be reproduced as a subgame of its quantum extension. We obtained a rather surprising result that this requirement prevents the use of a large set of entangled states in quantum extension of classical games.

Özdemir, ?ahin Kaya; Shimamura, Junichi; Imoto, Nobuyuki

2008-04-01

81

Dual Quantum Mechanics  

E-print Network

We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position or in the momentum representation. As a way to support this complementation, starting from the action that describes conformal gravity in the world-line formalism, we show that there are duality transformations that relate the dynamics in the presence of position dependent vector and tensor fields to the dynamics in the presence of momentum dependent vector and tensor fields.

W. Chagas-Filho

2009-05-11

82

Relational Quantum Mechanics  

E-print Network

We suggest that the inner syntax of Quantum Mechanics is relational logic, a form of logic developed by C. S. Peirce during the years 1870 - 1880. The Peircean logic has the structure of category theory, with relation serving as an arrow (or morphism). At the core of the relational logical system is the law of composition of relations. This law leads to the fundamental quantum rule of probability as the square of an amplitude. Our study of a simple discrete model, extended to the continuum, indicates that a finite number of degrees of freedom can live in phase space. This "granularity" of phase space is determined by Planck's constant h. We indicate also the broader philosophical ramifications of a relational quantum mechanics.

Nicolaidis, Argyris

2012-01-01

83

Relational Quantum Mechanics  

E-print Network

We suggest that the inner syntax of Quantum Mechanics is relational logic, a form of logic developed by C. S. Peirce during the years 1870 - 1880. The Peircean logic has the structure of category theory, with relation serving as an arrow (or morphism). At the core of the relational logical system is the law of composition of relations. This law leads to the fundamental quantum rule of probability as the square of an amplitude. Our study of a simple discrete model, extended to the continuum, indicates that a finite number of degrees of freedom can live in phase space. This "granularity" of phase space is determined by Planck's constant h. We indicate also the broader philosophical ramifications of a relational quantum mechanics.

Argyris Nicolaidis

2012-11-09

84

QUANTUM MECHANICS I Physics 341  

E-print Network

QUANTUM MECHANICS I Physics 341 KPTC 103 9:00 ­ 10:20 a.m. 1 Tues., Thurs. ­ Fall Quarter 1999 mechanics at the graduate level. The text for Quantum mechanics I and II will be J. J. Sakurai and Jim Napolitano, Modern Quantum Mechanics, Second Edition (Addison- Wesley, 2011). We will cover the first three

Rosner, Jonathan L.

85

Quantum Mechanics and Gravitation  

E-print Network

In summer 1999 an experiment at ILL, Grenoble was conducted. So-called ultra-cold neutrons (UCN) were trapped in the vertical direction between the Fermi-potential of a smooth mirror below and the gravitational potential of the earth above [Ne00, Ru00]. If quantum mechanics turns out to be a sufficiently correct description of the phenomena in the regime of classical, weak gravitation, one should observe the forming of quantized bound states in the vertical direction above a mirror. Already in a simplified view, the data of the experiment provides strong evidence for the existence of such gravitationally bound quantized states. A successful quantum-mechanical description would then provide a convincing argument, that the socalled first quantization can be used for gravitation as an interaction potential, as this is widely expected. Furthermore, looking at the characteristic length scales of about 10 mikron of such bound states formed by UCN, one sees, that a complete quantum mechanical description of this experiment additionally would enable one to check for possible modifications of Newtonian gravitation on distance scales being one order of magnitude below currently available tests [Ad00]. The work presented here deals mainly with the development of a quantum mechanical description of the experiment.

A. Westphal

2002-08-21

86

Interpretation of quantum mechanics  

Microsoft Academic Search

New axioms are proposed for the interpretation of quantum mechanics. They rest on a kind of calculus allowing to select meaningful physical statements and giving rules to check a given physical reasoning containing implications. Measurement theory is reformulated. Laboratoire associé au Centre National de la Recherche Scientifique.

Roland Omnès

1987-01-01

87

Supersymmetry and quantum mechanics  

Microsoft Academic Search

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of

Fred Cooper; Avinash Khare; Uday Sukhatme

1995-01-01

88

Many physical properties of a molecule can be calculated as expectation values of a corresponding quantum mechanical operator. The evaluation of other properties can be  

E-print Network

Chapter 20 Many physical properties of a molecule can be calculated as expectation values of a corresponding quantum mechanical operator. The evaluation of other properties can be formulated in terms perturbation. I. Calculations of Properties Other Than the Energy There are, of course, properties other than

Simons, Jack

89

Physicalism versus quantum mechanics  

E-print Network

In the context of theories of the connection between mind and brain, physicalism is the demand that all is basically purely physical. But the concept of "physical" embodied in this demand is characterized essentially by the properties of the physical that hold in classical physical theories. Certain of these properties contradict the character of the physical in quantum mechanics, which provides a better, more comprehensive, and more fundamental account of phenomena. It is argued that the difficulties that have plaged physicalists for half a century, and that continue to do so, dissolve when the classical idea of the physical is replaced by its quantum successor. The argument is concretized in a way that makes it accessible to non-physicists by exploiting the recent evidence connecting our conscious experiences to macroscopic measurable synchronous oscillations occurring in well-separated parts of the brain. A specific new model of the mind-brain connection that is fundamentally quantum mechanical but that ties conscious experiences to these macroscopic synchronous oscillations is used to illustrate the essential disparities between the classical and quantum notions of the physical, and in particular to demonstrate the failure in the quantum world of the principle of the causal closure of the physical, a failure that goes beyond what is entailed by the randomness in the outcomes of observations, and that accommodates the efficacy in the brain of conscious intent.

Henry P. Stapp

2008-03-11

90

Fields and Quantum Mechanics  

E-print Network

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

Glenn Eric Johnson

2013-12-09

91

Epigenetics: Biology's Quantum Mechanics  

PubMed Central

The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene – the molecular biological view and the epigenetic view – are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider. PMID:22639577

Jorgensen, Richard A.

2011-01-01

92

On Randomness in Quantum Mechanics  

E-print Network

The quantum mechanical probability densities are compared with the probability densities treated by the theory of random variables. The relevance of their difference for the interpretation of quantum mechanics is commented.

Alberto C. de la Torre

2007-07-19

93

Does Quantum Mechanics Need Interpretation?  

E-print Network

Since the beginning, quantum mechanics has raised major foundational and interpretative problems. Foundational research has been an important factor in the development of quantum cryptography, quantum information theory and, perhaps one day, practical quantum computers. Many believe that, in turn, quantum information theory has bearing on foundational research. This is largely related to the so-called epistemic view of quantum states, which maintains that the state vector represents information on a system and has led to the suggestion that quantum theory needs no interpretation. I will argue that this and related approaches fail to take into consideration two different explanatory functions of quantum mechanics, namely that of accounting for classically unexplainable correlations between classical phenomena and that of explaining the microscopic structure of classical objects. If interpreting quantum mechanics means answering the question, "How can the world be for quantum mechanics to be true?", there seems to be no way around it.

Louis Marchildon

2009-02-17

94

Bohmian quantum mechanics with quantum trajectories  

NASA Astrophysics Data System (ADS)

The quantum trajectory method in the hydrodynamical formulation of Madelung-Bohm-Takabayasi quantum mechanics is an example of showing the cognitive importance of scientific illustrations and metaphors, especially, in this case, in computational quantum chemistry and electrical engineering. The method involves several numerical schemes of solving a set of hydrodynamical equations of motion for probability density fluids, based on the propagation of those probability density trajectories. The quantum trajectory method gives rise to, for example, an authentic quantum electron transport theory of motion to, among others, classically-minded applied scientists who probably have less of a commitment to traditional quantum mechanics. They were not the usual audience of quantum mechanics and simply choose to use a non-Copenhagen type interpretation to their advantage. Thus, the metaphysical issues physicists had a trouble with are not the main concern of the scientists. With the advantages of a visual and illustrative trajectory, the quantum theory of motion by Bohm effectively bridges quantum and classical physics, especially, in the mesoscale domain. Without having an abrupt shift in actions and beliefs from the classical to the quantum world, scientists and engineers are able to enjoy human cognitive capacities extended into the quantum mechanical domain.

Jeong, Yeuncheol

95

Can Quantum Cryptography Imply Quantum Mechanics?  

E-print Network

It has been suggested that the ability of quantum mechanics to allow secure distribution of secret key together with its inability to allow bit commitment or communicate superluminally might be sufficient to imply the rest of quantum mechanics. I argue using a toy theory as a counterexample that this is not the case. I further discuss whether an additional axiom (key storage) brings back the quantum nature of the theory.

John A. Smolin

2003-10-10

96

Relativity and quantum mechanics  

Microsoft Academic Search

Conditions under which quantum mechanics can be made compatible with the curved space-time of gravitation theories is investigated. A postulate is imposed in the formv=vg wherev is the kinematical Hamilton-Jacobi (geometric optic limit) velocity andvg is the group velocity of the waves. This imposes a severe condition on the possible coordinates in which the Schrödinger form (the coordinate realization) of

Hüseyin Yilmaz

1982-01-01

97

Quantum information processing, operational quantum logic, convexity, and the foundations of physics  

Microsoft Academic Search

Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes of possible operations we may perform a system: ``operational states.'' I discuss general frameworks for ``operational theories'' (sets of possible operational states of a system), in which

Howard Barnum

2003-01-01

98

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

99

Quantum transfer operators and quantum scattering  

E-print Network

These notes describe a new method to investigate the spectral properties if quantum scattering Hamiltonians, developed in collaboration with J. Sj\\"ostrand and M.Zworski. This method consists in constructing a family of "quantized transfer operators" $\\{M(z,h)\\}$ associated with a classical Poincar\\'e section near some fixed classical energy E. These operators are finite dimensional, and have the structure of "open quantum maps". In the semiclassical limit, the family $\\{M(z,h)\\}$ encode the quantum dynamics near the energy E. In particular, the quantum resonances of the form $E+z$, for $z=O(h)$, are obtained as the roots of $\\det(1-M(z,h))=0$.

Stéphane Nonnenmacher

2010-01-22

100

Quantum Mechanics and Representation Theory Columbia University  

E-print Network

Quantum Mechanics and Representation Theory Peter Woit Columbia University Texas Tech, November 21 2013 Peter Woit (Columbia University) Quantum Mechanics and Representation Theory November 2013 1 / 30 #12;Does Anyone Understand Quantum Mechanics? "No One Understands Quantum Mechanics" "I think

Woit, Peter

101

Nonlinear friction in quantum mechanics  

E-print Network

The effect of nonlinear friction forces in quantum mechanics is studied via dissipative Madelung hydrodynamics. A new thermo-quantum diffusion equation is derived, which is solved for the particular case of quantum Brownian motion with a cubic friction. It is extended also by a chemical reaction term to describe quantum reaction-diffusion systems with nonlinear friction as well.

Roumen Tsekov

2010-03-01

102

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

103

Quantum Computation by Quantum Operations on Mixed States  

E-print Network

Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum systems is considered as an element of $4^{n}$-dimensional operator Hilbert space. Unitary quantum gates and nonunitary quantum operations for n-qubit system are considered as generalized quantum gates acting on mixed state. In this paper we study universality for quantum computations by quantum operations on mixed states.

Vasily E. Tarasov

2002-01-09

104

Octonic relativistic quantum mechanics  

E-print Network

In this paper we represent the generalization of relativistic quantum mechanics on the base of eght-component values "octons", generating associative noncommutative spatial algebra. It is shown that the octonic second-order equation for the eight-component octonic wave function, obtained from the Einshtein relation for energy and momentum, describes particles with spin of 1/2. It is established that the octonic wave function of a particle in the state with defined spin projection has the specific spatial structure in the form of octonic oscillator with two spatial polarizations: longitudinal linear and transversal circular. The relations between bispinor and octonic descriptions of relativistic particles are established. We propose the eight-component spinors, which are octonic generalisation of two-component Pauli spinors and four-component Dirac bispinors. It is shown that proposed eight-component spinors separate the states with different spin projection, different particle-antiparticle state as well as different polarization of the octonic oscillator. We demonstrate that in the frames of octonic relativistic quantum mechanics the second-order equation for octonic wave function can be reformulated in the form of the system of first-order equations for quantum fields, which is analogous to the system of Maxwell equations for the electromagnetic field. It is established that for the special type of wave functions the second-order equation can be reduced to the single first-order equation, which is analogous to the Dirac equation. At the same time it is shown that this first-order equation describes particles, which do not create quantum fields.

V. L. Mironov; S. V. Mironov

2008-03-04

105

Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics-II  

E-print Network

The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of probability in Quantum Mechanics and its interpretations. We give yet another interpretation to the notion of Faraday lines and loops as the locus of probability flow. Also, the possibilities of visualization of spectra of area operators by means of classical geometric forms and conventional Quantum Mechanics are explored.

Aalok Pandya

2009-01-19

106

Can Quantum Mechanics Heal Classical Singularities?  

NASA Astrophysics Data System (ADS)

We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. We show that a large subset of classically singular spacetimes is nevertheless nonsingular quantum mechanically, in that the Hamiltonian operator is essentially self-adjoint so the evolution of quantum wave packets lacks the ambiguity associated with scattering off singularities.

Helliwell, T. M.; Konkowski, D. A.

2008-09-01

107

Quantum Mechanics and the Generalized Uncertainty Principle  

E-print Network

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

Jang Young Bang; Micheal S. Berger

2006-10-11

108

Quantum Mechanics and Multiply Connected Spaces  

E-print Network

t is well known that the difference between Quantum Mechanics and Classical Theory appears most crucially in the non Classical spin half of the former theory and the Wilson-Sommerfelt quantization rule. We argue that this is symptomatic of the fact that Quantum Theory is actually a theory in multiply connected space while Classical Theory operates in simply connected space.

B. G. Sidharth

2006-05-16

109

From Quantum Mechanics to Thermodynamics?  

E-print Network

From Quantum Mechanics to Thermodynamics? Dresden, 22.11.2004 Jochen Gemmer Universit¨at Osnabr Description? Quantum Mechanics i¯h t = (- ¯h2 2m + V ) Classical Mechanics: m d2 dt2 x = - V Thermodynamics: dU = TdS - pdV dS dt > 0 #12;Fundamental Law or Emergent Description? Quantum Mechanics i

Steinhoff, Heinz-Jürgen

110

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

111

Diffusion-Schrödinger Quantum Mechanics  

NASA Astrophysics Data System (ADS)

A quantum solution of a nonlinear differential equation of diffusion type with a potential term has been found. Diffusion-Schrödinger quantum mechanics can find wide application in quantum biology, biological electronics, synthetic biology, nanomedicine, the quantum theory of consciousness, cosmology, and other fields of science and technology. One consequence of the macroscopic nature of diffusion-Schrödinger quantum mechanics is the possibility of generation of hard photons. The dust plasma in the Universe can generate cosmic rays with ultra-relativistic energies in a galactic magnetic field via a diffusion mechanism.

Lasukov, V. V.; Lasukova, T. V.; Lasukova, O. V.; Novoselov, V. V.

2014-08-01

112

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

113

Quantum Mechanics of Proca Fields  

E-print Network

We construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time-translations with the Hamiltonian, we obtain a unitary quantum system that describes first-quantized Proca fields and does not involve the conventional restriction to the positive-frequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity ($\\cP$), generalized time-reversal ...

Zamani, Farhad

2008-01-01

114

Optimizing adiabaticity in quantum mechanics  

E-print Network

A condition on the Hamiltonian of a time-dependent quantum mechanical system is derived which, if satisfied, implies optimal adiabaticity (defined below). The condition is expressed in terms of the Hamiltonian and in terms of the evolution operator related to it. Since the latter depends in a complicated way on the Hamiltonian, it is not yet clear how the condition can be used to extract useful information about the optimal Hamiltonian. The condition is tested on an exactly-soluble time-dependent problem (a spin in a magnetic field), where perfectly adiabatic evolution can be easily identified.

MacKenzie, R; Renaud-Desjardins, L

2011-01-01

115

Optimizing adiabaticity in quantum mechanics  

E-print Network

A condition on the Hamiltonian of a time-dependent quantum mechanical system is derived which, if satisfied, implies optimal adiabaticity (defined below). The condition is expressed in terms of the Hamiltonian and in terms of the evolution operator related to it. Since the latter depends in a complicated way on the Hamiltonian, it is not yet clear how the condition can be used to extract useful information about the optimal Hamiltonian. The condition is tested on an exactly-soluble time-dependent problem (a spin in a magnetic field), where perfectly adiabatic evolution can be easily identified.

R. MacKenzie; M. Pineault; L. Renaud-Desjardins

2011-09-12

116

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

117

Kindergarten Quantum Mechanics  

E-print Network

These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in quant-ph/0402130 and [4]) which subsumes my Logic of Entanglement quant-ph/0402014. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes quant-ph/0506132. In a last section we provide some pointers to the body of technical literature on the subject.

Bob Coecke

2005-10-04

118

Extremal covariant quantum operations and positive operator valued measures  

E-print Network

Extremal covariant quantum operations and positive operator valued measures Giacomo Mauro D August 2004) We consider the convex sets of QO's (quantum operations) and POVM's (positive operator quantum information technology1 has recently motivated a search for new quantum devices with maximum

D'Ariano, Giacomo Mauro

119

PT quantum mechanics.  

PubMed

PT-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 PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. 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 PT-synthetic materials are being developed, and the PT 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 PT-symmetric quantum mechanics. PMID:23509390

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

2013-04-28

120

On Finite $J$-Hermitian Quantum Mechanics  

E-print Network

In his recent paper arXiv:1312.7738, the author discussed $J$-Hermitian quantum mechanics and showed that $PT$-symmetric quantum mechanics is essentially $J$-Hermitian quantum mechanics. In this paper, the author discusses finite $J$-Hermitian quantum mechanics which is derived naturally from its continuum one and its relationship with finite $PT$-symmetric quantum mechanics.

Sungwook Lee

2014-01-21

121

Invariance in adelic quantum mechanics  

E-print Network

Adelic quantum mechanics is form invariant under an interchange of real and p-adic number fields as well as rings of p-adic integers. We also show that in adelic quantum mechanics Feynman's path integrals for quadratic actions with rational coefficients are invariant under changes of their entries within nonzero rational numbers.

Branko Dragovich

2006-12-07

122

Decoherence in quantum mechanics and quantum cosmology  

NASA Technical Reports Server (NTRS)

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 of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.

Hartle, James B.

1992-01-01

123

What is Time in Quantum Mechanics?  

E-print Network

Time of arrival in quantum mechanics is discussed in two versions: the classical axiomatic "time of arrival operator" introduced by J. Kijowski and the EEQT method. It is suggested that for free particles the two methods may lead to the same result. On the other hand the EEQT method can be easily geometrized within the framework of Galilei-Newton general relativistic quantum mechanics developed by M. Modugno and collaborators, and it can be applied to non-free evolutions. The way of geometrization of irreversible quantum dynamics based on dissipative Liouville equation is suggested.

Arkadiusz Jadczyk

2014-02-25

124

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

125

Quantum Mechanics 1 for graduate students  

E-print Network

Course 606 Quantum Mechanics 1 for graduate students Fall 2010 Instructor Valery Pokrovsky 1 electromagnetic field. Gauge invariance. Landau levels. 7. Semiclassical approximation. 8. Quantum mechanics. Scattering. The main textbook is E. Merzbacher, Quantum Mechanics, third edition, Wiley. Additional

126

Classical and Quantum Mechanical Waves  

NSDL National Science Digital Library

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

Riley, Lewis

2006-07-22

127

Quantum Mechanics as Classical Physics  

E-print Network

Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds.

Charles Sebens

2014-02-27

128

Noninertial quantum mechanical fluctuations  

E-print Network

Zero point quantum fluctuations as seen from non-inertial reference frames are of interest for several reasons. In particular, because phenomena such as Unruh radiation (acceleration radiation) and Hawking radiation (quantum leakage from a black hole) depend intrinsically on both quantum zero-point fluctuations and some appropriate notion of an accelerating vacuum state, any experimental test of zero-point fluctuations in non-inertial frames is implicitly a test of the foundations of quantum field theory, and the Unruh and Hawking effects

H. C. Rosu

2000-12-20

129

Quantum Mechanics Of Consciousness  

E-print Network

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

Rajat Kumar Pradhan

2009-07-28

130

A Quantum Mechanical Travelling Salesman  

E-print Network

A quantum simulation of a travelling salesman is described. A vector space for a graph is defined together with a sequence of operators which transform a special initial state into a superposition states representing Hamiltonian tours. The quantum amplitude for any tour is a function of the classical cost of travelling along the edges in that tour. Tours with the largest quantum amplitude may be different than those with the smallest classically-computed cost.

Ravindra N. Rao

2011-08-23

131

Bananaworld: Quantum Mechanics for Primates  

E-print Network

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

Jeffrey Bub

2012-11-13

132

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

133

Scattering Relativity in Quantum Mechanics  

E-print Network

Transforming from one reference frame to another yields an equivalent physical description. If quantum fields are transformed one way and quantum states transformed a different way then the physics changes. We show how to use the resulting changed physical description to obtain the equations of motion of charged, massive particles in electromagnetic and gravitational fields. The derivation is based entirely on special relativity and quantum mechanics.

Richard Shurtleff

2011-08-09

134

Topological quantum mechanics  

SciTech Connect

The quantum theory of a type of generally covariant field theory, that has no local degrees of freedom, is described. Physical observables that capture topological properties of the manifold are identified and a representation of their Poisson algebra is constructed to obtain the quantum theory. A non-Abelian generalization to SU(2) is also discussed in a similar way.

Husain, V. (Department of Physics, University of Utah, Salt Lake City, Utah 84112 (US))

1991-03-15

135

Quantum transfer operators and chaotic scattering Stephane Nonnenmacher  

E-print Network

in the recent lecture notes of C.Evans & M.Zworski [1]. We are using these operators as nice models for "quantum of such operators in quantum mechanics. The operator M(T, h) (understood as a family (M(T, h))h(0,1]) can be inter chaos", that is the study of quantum systems, the classical limits of which are "chaotic

Boyer, Edmond

136

Quantum Phase and Quantum Phase Operators: Some Physics and Some History  

E-print Network

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 a critique of recent proposals which have shed new light on the problem.

Michael Martin Nieto

1993-04-08

137

Quantum mechanics as applied mathematical statistics  

SciTech Connect

Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.

Skala, L., E-mail: Lubomir.Skala@mff.cuni.cz [Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2 (Czech Republic); University of Waterloo, Department of Applied Mathematics, Waterloo, Ontario, Canada N2L 3G1 (Canada); Cizek, J. [Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2 (Czech Republic); University of Waterloo, Department of Applied Mathematics, Waterloo, Ontario, Canada N2L 3G1 (Canada); Kapsa, V. [Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2 (Czech Republic)

2011-05-15

138

Quantum mechanical description of waveguides  

E-print Network

In this paper, applying the spinor representation of the electromagnetic field, we present a quantum-mechanical description of waveguides. As an example of application, a potential qubit generated via photon tunneling is discussed.

Zhi-Yong Wang; Cai-Dong Xiong; Bing He

2006-11-02

139

Free will and quantum mechanics  

E-print Network

A simple example is provided showing that violation of free will allows to reproduce the quantum mechanical predictions, and that the Clauser-Horne parameter can take the maximum value 4 for a proper choice.

Antonio Di Lorenzo

2011-05-05

140

Quantum mechanics writ large  

E-print Network

Some two centuries before the quantum revolution, Newton (1) suggested that corpuscles of light generate waves in an aethereal medium like skipping stones generate waves in water, with their motion then being affected by ...

Bush, John W. M.

141

Quantum electro-mechanical systems (QEMS)  

NASA Astrophysics Data System (ADS)

We give a quantum description of a Quantum Electro-Mechanical System (QEMS) comprising a single quantum dot harmonically bound between two electrodes and facilitating a tunnelling current between them. An example of such a system is a fullerene molecule between two metal electrodes. The description is based on a quantum master equation for the density operator of the electronic and vibrational degrees of freedom and thus incorporates the dynamics of both diagonal (population) and off diagonal (coherence) terms. We derive coupled equations of motion for the electron occupation number of the dot and the vibrational degrees of freedom, including damping of the vibration and thermo-mechanical noise, and give a semiclassical description of the dynamics under a variety of bias conditions. This dynamical description is related to observable features of the system including the stationary conductance as a function of bias voltage.

Utami, Dian W.; Goan, Hsi-Sheng; Milburn, Gerard J.

2004-04-01

142

Pseudo-Hermitian Representation of Quantum Mechanics  

E-print Network

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review of the basic ideas and techniques responsible for the recent developments in this subject. We provide a critical assessment of the role of the geometry of the Hilbert space in conventional quantum mechanics to reveal the basic physical principle motivating our study. We then offer a survey of the necessary mathematical tools and elaborate on a number of relevant issues of fundamental importance. In particular, we discuss the role of the antilinear symmetries such as PT, the true meaning and significance of the charge operators C and the CPT-inner products, the nature of the physical observables, the equivalent description of such models using ordinary Hermitian quantum mechanics, the pertaining duality between local-non-Hermitian versus nonlocal-Hermitian descriptions of their dynamics, the corresponding classical systems, the pseudo-Hermitian canonical quantization scheme, various methods of calculating the (pseudo-) metric operators, subtleties of dealing with time-dependent quasi-Hermitian Hamiltonians and the path-integral formulation of the theory, and the structure of the state space and its ramifications for the quantum Brachistochrone problem. We also explore some concrete physical applications of the abstract concepts and tools that have been developed in the course of this investigation. These include applications in nuclear physics, condensed matter physics, relativistic quantum mechanics and quantum field theory, quantum cosmology, electromagnetic wave propagation, open quantum systems, magnetohydrodynamics, quantum chaos, and biophysics.

Ali Mostafazadeh

2008-10-31

143

From Quantum Mechanics to String Theory  

E-print Network

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics) New Particles anti-particles (combining special relativity and quantum mechanics pions (mediator/momentum/mass discrepancy must fit inside the quantum mechanical uncertainty p, E E2 - p2 c2 = 0 Thursday, May 7, 2009 #12

144

Chem 793 Quantum Mechanics I Chemistry 793  

E-print Network

Chem 793 Quantum Mechanics I Chemistry 793 Quantum Mechanics I Fall 2000 Course outline 1 formulation. · Constants of the motion. 2. Probability in classical and quantum mechanics · Probability University #12;Chem 793 Quantum Mechanics I 7. Separable problems in 2D and 3D · Direct product functions

145

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

146

Topological Strings from Quantum Mechanics  

E-print Network

We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized theta function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P2, local P1xP1 and local F1. In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Phys...

Grassi, Alba; Marino, Marcos

2014-01-01

147

Sampling with quantum mechanics  

E-print Network

A new algorithm for estimating the fraction of numbers that is present in a superpositional state which satisfies a given condition,is introduced.This algorithm is conceptually simple and does not require quantum Fourier transform.Also the number of steps required does not depend on the size of the data base to be searched.

M. P John

2003-06-26

148

A Euclidean formulation of relativistic quantum mechanics  

E-print Network

In this paper we discuss a formulation of relativistic quantum mechanics that uses Euclidean Green functions or generating functionals as input. This formalism has a close relation to quantum field theory, but as a theory of linear operators on a Hilbert space, it has many of the advantages of quantum mechanics. One interesting feature of this approach is that matrix elements of operators in normalizable states on the physical Hilbert space can be calculated directly using the Euclidean Green functions without performing an analytic continuation. The formalism is summarized in this paper. We discuss the motivation, advantages and difficulties in using this formalism. We discuss how to compute bound states, scattering cross sections, and finite Poincare transformations without using analytic continuation. A toy model is used to demonstrate how matrix elements of exp(-beta H) in normalizable states can be used to construct-sharp momentum transition matrix elements.

Philip Kopp; Wayne Polyzou

2011-06-21

149

Canonical Transformations in Quantum Mechanics  

E-print Network

Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can, in principle, be realized quantum mechanically as a product of these transformations. It is found that the intertwining of two super-Hamiltonians is equivalent to there being a canonical transformation between them. A consequence is that the procedure for solving a differential equation can be viewed as a sequence of elementary canonical transformations trivializing the super-Hamiltonian associated to the equation. It is proposed that the quantum integrability of a system is equivalent to the existence of such a sequence.

Arlen Anderson

1992-05-22

150

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

151

Quantum Mechanics (QM) Measurement Package  

NSDL National Science Digital Library

This set of tutorial worksheets, based on the OSP Quantum Mechanics Simulations, help students explore the effects of position, momentum, and energy measurements on quantum state wavepackets. The probabilistic change in the wavefunction upon measurements and the time propagation of the states are illustrated. Similar worksheets are available for measurements of single and superpositions of energy eigenstates. The worksheets can be run online or downloaded as a pdf (attached).

Belloni, Mario; Christian, Wolfgang

2010-01-07

152

Kowalevski top in quantum mechanics  

SciTech Connect

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. -- Highlights: •Quantum spectra of the Kowalevski top are calculated. •Semiclassical quantization is carried out by the EBK formulation. •Quantum states are labeled by the semiclassical integer quantum numbers. •Multiplicity of the classical torus makes the spectra nearly degenerate. •Symmetries, quantum numbers and near-degenerate spectra are closely related.

Matsuyama, A., E-mail: spamatu@ipc.shizuoka.ac.jp

2013-09-15

153

Optimal guidance law in quantum mechanics  

SciTech Connect

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

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

2013-11-15

154

Quantum Statistical Mechanics and Quantum Computation Thursday, 22 March 2012  

E-print Network

Quantum Statistical Mechanics and Quantum Computation Thursday, 22 March 2012 8:50 am Welcoming:30 ­ 5:30 "Criticality without frustration for quantum spin-1 chains" Sergey Bravyi 6:30 pm Dinner at Triumph Brewery 138 Nassau Street Princeton, NJ 08542 609-924-7855 Quantum Statistical Mechanics

155

A Criterion for Holism in Quantum Mechanics  

E-print Network

A Criterion for Holism in Quantum Mechanics # M.P Seevinck # # Utrecht University, The Netherlands, June 2003. # 1 #12; # Motivation # . The question whether or not quantum mechanics (QM) gives rise. Orthodox Quantum Mechanics . Criterion for Holism in the Quantum Formalism . Orthodox QM is Holistic

Seevinck, Michiel

156

A Criterion for Holism in Quantum Mechanics  

E-print Network

A Criterion for Holism in Quantum Mechanics M.P Seevinck Utrecht University, The Netherlands, June 2003. 1 #12; Motivation · The question whether or not quantum mechanics (QM) gives rise to some. Orthodox Quantum Mechanics · Criterion for Holism in the Quantum Formalism · Orthodox QM is Holistic

Seevinck, Michiel

157

ccsd00002942, ON SUPERSYMMETRIC QUANTUM MECHANICS  

E-print Network

ccsd­00002942, version 1 ­ 25 Sep 2004 ON SUPERSYMMETRIC QUANTUM MECHANICS M.R. KIBLER Institut de Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl supersymmetric Quantum Mechanics corresponds to k = 2. A connection between fractional supersymmetric Quantum

158

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

159

THE OBJECTIVE INDEFINITENESS INTERPRETATION OF QUANTUM MECHANICS: Partition logic, logical information theory, and quantum mechanics  

E-print Network

THE OBJECTIVE INDEFINITENESS INTERPRETATION OF QUANTUM MECHANICS: Partition logic, logical information theory, and quantum mechanics David Ellerman University of California at Riverside www ago that quantum mechanics was not compatible with Boolean logic, then the natural thing to do would

Wüthrich, Christian

160

The Perfect Distinguishability of Quantum Operations  

E-print Network

We provide a feasible necessary and sufficient condition for when an unknown quantum operation (quantum device) secretely selected from a set of known quantum operations can be identified perfectly within a finite number of queries, and thus complete the characterization of the perfect distinguishability of quantum operations. We further design an optimal protocol which can achieve the perfect discrimination between two quantum operations by a minimal number of queries. Interestingly, employing the techniques from the theory of $q$-numerical range we find that an optimal perfect discrimination between two isometries is always achievable without using auxiliary systems or entanglement.

Runyao Duan; Yuan Feng; Mingsheng Ying

2009-08-03

161

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

162

Doubly special quantum and statistical mechanics from quantum $?$-Poincaré algebra  

E-print Network

Recently Amelino--Camelia proposed a ``Doubly Special Relativity'' theory with two observer independent scales (of speed and mass) that could replace the standard Special Relativity at energies close to the Planck scale. Such a theory might be a starting point in construction of quantum theory of space-time. In this paper we investigate the quantum and statistical mechanical consequences of such a proposal. We construct the generalized Newton--Wigner operator and find relations between energy/momentum and frequency/wavevector for position eigenstates of this operator. These relations indicate the existence of a minimum length scale. Next we analyze the statistical mechanics of the corresponding systems. We find that depending on the value of a parameter defining the canonical commutational algebra one has to do either with system with maximal possible temperature or with the one, which in the high temperature limit becomes discrete.

J. Kowalski-Glikman

2001-11-12

163

Remarks on osmosis, quantum mechanics, and gravity  

E-print Network

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

Robert Carroll

2011-04-03

164

Remarks on osmosis, quantum mechanics, and gravity  

E-print Network

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

Carroll, Robert

2011-01-01

165

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

2007-01-26

166

Canonical Transformations in Quantum Mechanics  

E-print Network

Quantum canonical transformations are defined algebraically outside of a Hilbert space context. This generalizes the quantum canonical transformations of Weyl and Dirac to include non-unitary transformations. The importance of non-unitary transformations for constructing solutions of the Schr\\"odinger equation is discussed. Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can be realized quantum mechanically as a product of these transformations. Each transformation corresponds to a familiar tool used in solving differential equations, and the procedure of solving a differential equation is systematized by the use of the canonical transformations. Several examples are done to illustrate the use of the canonical transformations. [This is an extensively revised version of hep-th-9205080: the first third of the paper is new material; the notation has been simplified, and further discussion has been added to the remainder.

Arlen Anderson

1993-05-13

167

Quantum operation, quantum Fourier transform and semi-definite programming  

E-print Network

We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier transform, is found for this class of operations. A more general class of operations on qudits is also considered and its completely positive condition is reduced to the well-known semi-definite programming problem.

Runyao Duan; Zhengfeng Ji; Yuan Feng; Mingsheng Ying

2003-04-22

168

Atomic quantum transistor based on swapping operation  

E-print Network

We propose an atomic quantum transistor based on exchange by virtual photons between two atomic systems through the control gate-atom. The quantum transistor is realized in two QED cavities coupled in nano-optical scheme. We have found novel effect in quantum dynamics of coupled three-node atomic system which provides control-SWAP(\\theta) processes in quantum transistor operation. New possibilities of quantum entanglement in an example of bright and dark qubit states have been demonstrated for quantum transport in the atomic chain. Potentialities of the proposed nano-optical design for quantum computing and fundamental issues of multi-atomic physics are also discussed.

Sergey A. Moiseev; Sergey N. Andrianov; Eugene S. Moiseev

2011-08-31

169

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

170

CPT and Quantum Mechanics Tests with Kaons  

E-print Network

In this review we first discuss the theoretical motivations for possible CPT violation and deviations from ordinary quantum-mechanical behavior of field-theoretic systems in the context of an extended class of quantum-gravity models. Then we proceed to a description of precision tests of CPT symmetry using mainly neutral kaons. We emphasize the possibly unique role of neutral meson factories in providing specific tests of models where the quantum-mechanical CPT operator is not well-defined, leading to modifications of Einstein-Podolsky-Rosen particle correlators. Finally, we present tests of CPT, T, and CP using charged kaons, and in particular K_l4 decays, which are interesting due to the high statistics attainable in experiments.

Jose Bernabeu; John Ellis; Nick E. Mavromatos; Dimitri V. Nanopoulos; Joannis Papavassiliou

2006-07-28

171

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

172

Quantum mechanics of Yano tensors: Dirac equation in curved spacetime  

Microsoft Academic Search

In spacetimes admitting Yano tensors, the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was

Marco Cariglia

2004-01-01

173

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

174

A quantum genetic algorithm with quantum crossover and mutation operations  

NASA Astrophysics Data System (ADS)

In the context of evolutionary quantum computing in the literal meaning, a quantum crossover operation has not been introduced so far. Here, we introduce a novel quantum genetic algorithm that has a quantum crossover procedure performing crossovers among all chromosomes in parallel for each generation. A complexity analysis shows that a quadratic speedup is achieved over its classical counterpart in the dominant factor of the run time to handle each generation.

SaiToh, Akira; Rahimi, Robabeh; Nakahara, Mikio

2013-11-01

175

Quantum Secret Sharing Schemes and Reversibility of Quantum Operations  

E-print Network

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 \\textbf{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.

Tomohiro Ogawa; Akira Sasaki; Mitsugu Iwamoto; Hirosuke Yamamoto

2005-04-30

176

Generalization of Classical Statistical Mechanics to Quantum Mechanics and Stable Property of Condensed Matter  

E-print Network

Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new general continuous eigenvalue equation and a general discrete eigenvalue equation in quantum mechanics, and discover that a eigenvalue of quantum mechanics is just an extreme value of an operator in possibility distribution, the eigenvalue f is just classical observable quantity. A general classical statistical uncertain relation is further given, the general classical statistical uncertain relation is generally generalized to quantum uncertainty principle, the two lost conditions in classical uncertain relation and quantum uncertainty principle, respectively, are found. We generally expound the relations among uncertainty principle, singularity and condensed matter stability, discover that quantum uncertainty principle prevents from the appearance of singularity of the electromagnetic potential between nucleus and electrons, and give the failure conditions of quantum uncertainty principle. Finally, we discover that the classical limit of quantum mechanics is classical statistical mechanics, the classical statistical mechanics may further be degenerated to classical mechanics, and we discover that only saying that the classical limit of quantum mechanics is classical mechanics is mistake. As application examples, we deduce both Shrodinger equation and state superposition principle, deduce that there exist decoherent factor from a general mathematical representation of state superposition principle, and the consistent difficulty between statistical interpretation of quantum mechanics and determinant property of classical mechanics is overcome.

Y. C. Huang; F. C. Ma; N. Zhang

2005-06-09

177

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

178

Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology  

Microsoft Academic Search

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

Murray Gell-Mann; James B. Hartle

1993-01-01

179

Delay Time in Quaternionic Quantum Mechanics  

E-print Network

In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. The study shows in which energy region it is possible to amplify the difference between quaternionic and complex quantum mechanics.

Stefano De Leo; Gisele Ducati

2012-04-11

180

Star Products for Relativistic Quantum Mechanics  

E-print Network

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

P. Henselder

2007-05-24

181

Quantum Mechanics Joachim Burgdorfer and Stefan Rotter  

E-print Network

1 1 Quantum Mechanics Joachim Burgd¨orfer and Stefan Rotter 1.1 Introduction 3 1.2 Particle and Quantization 8 1.5 Angular Momentum in Quantum Mechanics 9 1.6 Formalism of Quantum Mechanics 12 1.7 Solution Quantization 33 1.9.3 Gutzwiller Trace Formula 34 1.10 Conceptual Aspects of Quantum Mechanics 35 1

Rotter, Stefan

182

Entanglement and Disentanglement in Relativistic Quantum Mechanics  

E-print Network

Entanglement and Disentanglement in Relativistic Quantum Mechanics Jeffrey A. Barrett August 16, 2014 Abstract A satisfactory formulation of relativistic quantum mechanics re- quires that one be able in relativistic quantum mechanics must ultimately depend on the details of one's strategy for addressing

Stanford, Kyle

183

Quantum Mechanics: From Realism to Intuitionism  

E-print Network

Quantum Mechanics: From Realism to Intuitionism A mathematical and philosophical investigation with the idea for this thesis I didn't know very much about the funda- ments of quantum mechanics. Discussions that the incomprehensibility of quantum mechanics is not easily stepped over. This became clearer to me when I followed

Bosma, Wieb

184

Quantum Mechanics Revisited Jean Claude Dutailly  

E-print Network

Quantum Mechanics Revisited Jean Claude Dutailly Paris (France) August 20, 2014 Abstract The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general a new theoretical foundation. ii) The quantum mechanics (QM) which is presented in all the books

Boyer, Edmond

185

From Quantum Mechanics to String Theory  

E-print Network

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Particle Interaction Summary quantum mechanics and special relativity together imply the existence of anti-particles forces are mediated

186

Quantum Mechanics for Mathematicians: Introduction and Overview  

E-print Network

Quantum Mechanics for Mathematicians: Introduction and Overview Peter Woit Department Richard Feynman goes "I think it is safe to say that no one understands quantum mechanics."[1 was contrasting quantum mechanics with the theory of general relativity, a supposedly equally hard to understand

Woit, Peter

187

Probability in modal interpretations of quantum mechanics  

E-print Network

Probability in modal interpretations of quantum mechanics Dennis Dieks Institute for the History interpretations have the ambition to construe quantum mechanics as an ob- jective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix

Seevinck, Michiel

188

Quantum Mechanics: Structures, Axioms and Paradoxes  

E-print Network

Quantum Mechanics: Structures, Axioms and Paradoxes Diederik Aerts Center Leo Apostel, Brussels present an analysis of quantum mechanics and its problems and para- doxes taking into account the results a genuine incomplete- ness of standard quantum mechanics, however not an incompleteness that means

Aerts, Diederik

189

A Criterion for Holism in Quantum Mechanics  

E-print Network

A Criterion for Holism in Quantum Mechanics M.P Seevinck E-mail: M.P.Seevinck@phys.uu.nl Utrecht University, The Netherlands, August 2003. 1 #12; Motivation · The question whether or not quantum mechanics is it that makes quantum mechanics a holistic theory (if so), and other physical theories not (if so). · I propose

Seevinck, Michiel

190

On a realistic interpretation of quantum mechanics  

E-print Network

On a realistic interpretation of quantum mechanics Arnold Neumaier Institut fur Mathematik respecting the indeter- ministic nature of quantum mechanics, allows to speak of de#12;nite values for all], there are at least two levels of inter- preting quantum mechanics: the statistical interpretation in the narrower

Neumaier, Arnold

191

Visualizing quantum mechanics in phase space  

E-print Network

We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner function formalism resembles the mathematical language of classical mechanics of non-interacting particles. Thus, it allows a more direct comparison between classical and quantum dynamical features.

Heiko Bauke; Noya Ruth Itzhak

2011-01-11

192

The Postulates of Quantum Mechanics (from Quantum Mechanics by Claude Cohen-Tannoudji, Bernard Diu, and  

E-print Network

The Postulates of Quantum Mechanics (from Quantum Mechanics by Claude Cohen-Tannoudji, Bernard Diu, and Franck Lalo¨e) Introduction The postulates of quantum mechanics are the theory. Their physical content to the following questions: (i) How is the state of a quantum mechanical system at a given time described

Nielsen, Steven O.

193

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

194

Game Theory in Categorical Quantum Mechanics  

E-print Network

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

Ali Nabi Duman

2014-05-17

195

Probabilistic Approach to Teaching the Principles of Quantum Mechanics  

ERIC Educational Resources Information Center

Approaches the representation of quantum mechanics through Hilbert space postulates. Demonstrates that if the representation is to be accurate, an evolution operator of the form of a Hamiltonian must be used. (CP)

Santos, Emilio

1976-01-01

196

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

197

Helping Students Learn Quantum Mechanics for Quantum Computing  

NSDL National Science Digital Library

Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research in quantum computing because there is a lack of emphasis in the current curriculum on quantum formalism and dynamics. We are investigating the difficulties students have with quantum mechanics and are developing and evaluating quantum interactive learning tutorials (QuILTs) to reduce the difficulties. Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. We discuss the implications of our research and development project on helping students learn quantum mechanics relevant for quantum computing.

Singh, Chandralekha

2007-11-25

198

A concise introduction to quantum probability, quantum mechanics, and quantum computation  

E-print Network

A concise introduction to quantum probability, quantum mechanics, and quantum computation Greg called "non-commutative probability". Recently quantum computation has entered as a new reason for both mathematicians and computer scientists to learn the precepts of quantum mechan- ics. Just as randomized

Thomases, Becca

199

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

200

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

201

Treating time travel quantum mechanically  

NASA Astrophysics Data System (ADS)

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

Allen, John-Mark A.

2014-10-01

202

Treating Time Travel Quantum Mechanically  

E-print Network

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

John-Mark A. Allen

2014-01-20

203

Quantum mechanics: Myths and facts  

E-print Network

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.

H. Nikolic

2006-09-21

204

Quantum mechanics: Myths and facts  

E-print Network

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.

Nikolic, H

2006-01-01

205

Quantum Mechanics: Myths and Facts  

NASA Astrophysics Data System (ADS)

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of “myths”, that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.

Nikoli?, Hrvoje

2007-11-01

206

On the Limits of Information Retrieval in Quantum Mechanics  

E-print Network

The widely considered assertion is that the unitarity of quantum mechanical evolution assures the preservation of information. It is even promoted in popular literature as an established fact. (Susskind, 2008) Yet, a simple chain of reasoning demonstrates that: 1) almost any evolutionary operator can be well approximated by a degenerate (finite-rank) operator and 2) one needs an eternity to retrieve information exactly from a nonstationary quantum state and to distinguish between arbitrary unitary operator and its finite-dimensional approximations.

Peter B. Lerner

2013-11-26

207

Z Theory and its Quantum-Relativistic Operators  

E-print Network

The view provided by Z theory, based on its quantum-relativistic operators, is an integrated picture of the micro and macro quantities relationships. The axiomatic formulation of the theory is presented in this paper. The theory starts with the existence of the wave function, the existence of three fundamental constants h, c and G as well as the physical quantity Rc (the radius of the space-time continuum) plus the definition of a general form for the quantum-relativistic functional operators. Using such starting point the relationships between relativity, quantum mechanics and cosmological quantities can be clarified.

Pietro Giorgio Zerbo

2006-02-08

208

A quantum mechanical model of "dark matter"  

E-print Network

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

V. V. Belokurov; E. T. Shavgulidze

2014-03-28

209

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

210

Errors and paradoxes in quantum mechanics  

E-print Network

Errors and paradoxes in quantum mechanics, entry in the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, ed. F. Weinert, K. Hentschel, D. Greenberger and B. Falkenburg (Springer), to appear

D. Rohrlich

2007-08-28

211

On a commutative ring structure in quantum mechanics  

E-print Network

In this article, I propose a concept of the $p$-on which is modelled on the multi-photon absorptions in quantum optics. It provides a commutative ring structure in quantum mechanics. Using it, I will give an operator representation of the Riemann $\\zeta$ function.

Shigeki Matsutani

2009-10-10

212

Quantum selfish gene (biological evolution in terms of quantum mechanics)  

E-print Network

I propose to treat the biological evolution of genoms by means of quantum mechanical tools. We start with the concept of meta- gene, which specifies the "selfish gene" of R.Dawkins. Meta- gene encodes the abstract living unity, which can live relatively independently of the others, and can contain a few real creatures. Each population of living creatures we treat as the wave function on meta- genes, which module squared is the total number of creatures with the given meta-gene, and the phase is the sum of "aspirations" to change the classical states of meta- genes. Each individual life thus becomes one of possible outcomes of the virtual quantum measurement of this function. The evolution of genomes is described by the unitary operator in the space of psi-functions or by Kossovsky-Lindblad equation in the case of open biosystems. This operator contains all the information about specific conditions under which individuals are, and how "aspirations" of their meta- genes may be implemented at the biochemical level. We show the example of quantum description of the population with two parts of meta-gene: "wolves" and "deer", which can be simultaneously in the same abstract living unity. "Selfish gene" reconciled with the notion of individuality of alive beings that gives possibility to consider evolutionary scenarios and their possible physical causes from the single position.

Yuri I. Ozhigov

2013-12-07

213

Exploration of similarities between classical wave mechanics and quantum mechanics  

Microsoft Academic Search

This dissertation explores classical analogs of one particle wave mechanics and multiparticle quantum entanglement by using classical wave optics. We develop classical measurement techniques to simulate one particle wave mechanics and quantum entanglement for up to four particles. Classical simulation of multi-particle entanglement is useful for quantum information processing (QIP) because much of the QIP does not require collapse and

Kim Fook Lee

2002-01-01

214

An approach to nonstandard quantum mechanics  

E-print Network

We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to non-relativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the M{\\o}ller wave operators and the S-Matrix.

Andreas Raab

2006-12-27

215

Transfer of Learning in Quantum Mechanics  

NSDL National Science Digital Library

We investigate the difficulties that undergraduate students in quantum mechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting individual interviews. Quantum mechanics is abstract and its paradigm is very different from the classical one. A good grasp of the principles of quantum mechanics requires creating and organizing a knowledge structure consistent with the quantum postulates. Previously learned concepts such as the principle of superposition and probability can be useful in quantum mechanics if students are given opportunity to build associations between new and prior knowledge. We also discuss the need for better alignment between quantum mechanics and modern physics courses taken previously because semi-classical models can impede internalization of the quantum paradigm in more advanced courses.

Singh, Chandralekha

2010-01-18

216

Quantum mechanical light harvesting mechanisms in photosynthesis  

NASA Astrophysics Data System (ADS)

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

Scholes, Gregory

2012-02-01

217

Storing unitary operators in quantum states  

E-print Network

We present a scheme to store unitary operators with self-inverse generators in quantum states and a general circuit to retrieve them with definite success probability. The continuous variable of the operator is stored in a single-qubit state and the information about the kind of the operator is stored in classical states with finite dimension. The probability of successful retrieval is always 1/2 irrespective of the kind of the operator, which is proved to be maximum. In case of failure, the result can be corrected with additional quantum states. The retrieving circuit is almost as simple as that which handles only the single-qubit rotations and CNOT as the basic operations. An interactive way to transfer quantum dynamics, that is, to distribute naturally copy-protected programs for quantum computers is also presented using this scheme.

Jaehyun Kim; Yongwook Cheong; Jae-Seung Lee; Soonchil Lee

2001-09-20

218

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

219

Depicting qudit quantum mechanics and mutually unbiased qudit theories  

E-print Network

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

André Ranchin

2014-04-04

220

Quantum mechanics without state vectors  

NASA Astrophysics Data System (ADS)

Because the state vectors of isolated systems can be changed in entangled states by processes in other isolated systems, keeping only the density matrix fixed, it is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying only on density matrices. The density matrix is defined here by the formula giving the mean values of physical quantities, which implies the same properties as the usual definition in terms of state vectors and their probabilities. This change in the description of physical states opens up a large variety of new ways that the density matrix may transform under various symmetries, different from the unitary transformations of ordinary quantum mechanics. Such new transformation properties have been explored before, but so far only for the symmetry of time translations into the future, treated as a semigroup. Here, new transformation properties are studied for general symmetry transformations forming groups, not just semigroups. Arguments that such symmetries should act on the density matrix as in ordinary quantum mechanics are presented, but all of these arguments are found to be inconclusive.

Weinberg, Steven

2014-10-01

221

Identical Particles in Quantum Mechanics  

E-print Network

If, in a system of identical particles, the one particle state is defined by the partial trace to one of the component spaces of the total Hilbert space, then all one particle states are identical. The particles are indistinguishable. This is often thought to be a typical quantum mechanical phenomenon. I will show however that an analogous procedure to define particle states exists in classical mechanics, which results in classical indistinguishable identical particles. From this analogy it follows that the indistinguishability of identical particles depends on how we define particle states. It is not an inevitable result of the symmetry postulate. Indeed, if particles are defined by partial traces, consistent use of the symmetry postulate leads to the conclusion that all identical particles in the universe are indistinguishable, so that particles can never be pointed at, not even in the classical limit. This does not correspond to the way the term particle is actually used in practice. I will argue that a particle should be defined in such a way that in the classical limit the quantum particle state becomes the state of a classical particle. This will lead us to a definition of particles which is in line with the way the term particle is actually used by physicists.

Andrea Lubberdink

2009-10-24

222

Quantum Mechanics and Closed Timelike Curves  

E-print Network

General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal region of space-time are investigated. If the correspondence principle is true, then all generalizations of quantum mechanics on acausal manifolds are not renormalizable. Therefore quantum mechanics can only be defined on global hyperbolic manifolds and all general relativity solutions exhibiting time travel are unphysical.

Florin Moldoveanu

2007-04-23

223

Bohmian particle trajectories contradict quantum mechanics  

E-print Network

The Bohmian interpretation of quantum mechanics adds particle trajectories to the wave function and ensures that the probability distribution of the particle positions agrees with quantum mechanics at any time. This is not sufficient to avoid contradictions with quantum mechanics. There are correlations between particle positions at different times which cannot be reproduced with real particle trajectories. A simple rearrangement of an experimental test of the Bell-CHSH inequality demonstrates this.

Michael Zirpel

2009-03-23

224

Optimal guidance law in quantum mechanics  

NASA Astrophysics Data System (ADS)

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

Yang, Ciann-Dong; Cheng, Lieh-Lieh

2013-11-01

225

The Arrow of Time in Rigged Hilbert Space Quantum Mechanics  

E-print Network

Arno Bohm and Ilya Prigogine's Brussels-Austin Group have been working on the quantum mechanical arrow of time and irreversibility in rigged Hilbert space quantum mechanics. A crucial notion in Bohm's approach is the so-called preparation/registration arrow. An analysis of this arrow and its role in Bohm's theory of scattering is given. Similarly, the Brussels-Austin Group uses an excitation/de-excitation arrow for ordering events, which is also analyzed. The relationship between the two approaches is initially discussed focusing on their semi-group operators and time arrows. Finally a possible realist interpretation of the rigged Hilbert space formulation of quantum mechanics is considered.

Robert C. Bishop

2005-06-22

226

Quantum Statistical Mechanics. III. Equilibrium Probability  

E-print Network

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

Phil Attard

2014-04-10

227

A Process Model of Quantum Mechanics  

E-print Network

A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise through a non-uniform interpolation process. Standard non-relativistic quantum mechanics emerges under the limit of infinite information (the causal space grows to infinity) and infinitesimal scale (the separation between points goes to zero). The model has the potential to address several paradoxes in quantum mechanics while remaining computationally powerful.

William Sulis

2014-04-13

228

Improved lattice actions for supersymmetric quantum mechanics  

E-print Network

We analyze the Euclidean version of supersymmetric quantum mechanics on the lattice by means of a numerical path integral. We consider two different lattice derivatives and improve the actions containing them with respect to supersymmetry by systematically adding interaction terms with non-zero extent. To quantize this improvement, we measure boson and fermion masses and Ward identities for the naive as well as the improved models. The masses are degenerate in all models, but the magnitude of the Ward identities decreases significantly for both derivative operators using the improved actions. This is a clear sign that the breaking of supersymmetry due to lattice artifacts is reduced.

Sebastian Schierenberg; Falk Bruckmann

2012-10-19

229

Quantum Mechanics Dung-Hai Lee  

E-print Network

Quantum Mechanics Dung-Hai Lee Summer 2000 #12;Contents 1 A brief reminder of linear Algebra 3 1.5 Bell's inequality . . . . . . . . . . . . . . . . . . . . . . . 20 3 Quantum dynamics 23 3 . . . . . . . . . . . . . . . . . . . 43 3.12 Classical approximation . . . . . . . . . . . . . . . . . . 45 3.13 Quantum statistical

Murayama, Hitoshi

230

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

231

Improving Students' Understanding of Quantum Mechanics  

NSDL National Science Digital Library

Richard Feynman once famously stated that nobody understands quantum mechanics. He was, of course, referring to the many strange, unintuitive foundational aspects of quantum theory such as its inherent indeterminism and state reduction during measurement according to the Copenhagen interpretation. But despite its underlying fundamental mysteries, the theory has remained a cornerstone of modern physics. Most physicists, as students, are introduced to quantum mechanics in a modern-physics course, take quantum mechanics as advanced undergraduates, and then take it again in their first year of graduate school. One might think that after all this instruction, students would have become certified quantum mechanics, able to solve the Schrödinger equation, manipulate Dirac bras and kets, calculate expectation values, and, most importantly, interpret their results in terms of real or thought experiments. That sort of functional understanding of quantum mechanics is quite distinct from the foundational issues alluded to by Feynman.

Singh, Chandralekha; Belloni, Mario; Christian, Wolfgang

2008-06-23

232

Path integral in energy representation in quantum mechanics  

E-print Network

In this paper we develop the alternative path-integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is Laplace transform of a evolution operator) in a form which has a sense of ``the sum over paths'' but it is much more better defined than the usual functional integral. We investigate this representation from various directions and compare such approach to quantum mechanics with the standard ones.

P. Putrov

2006-05-17

233

Advances in relativistic molecular quantum mechanics  

NASA Astrophysics Data System (ADS)

A quantum mechanical equation H?=E? is composed of three components, viz., Hamiltonian H, wave function ?, and property E(?), each of which is confronted with fundamental issues in the relativistic regime, e.g., (1) What is the most appropriate relativistic many-body Hamiltonian? How to solve the resulting equation? (2) How does the relativistic wave function behave at the coalescence of two electrons? How to do relativistic explicit correlation? (3) How to formulate relativistic properties properly?, to name just a few. It is shown here that the charge-conjugated contraction of Fermion operators, dictated by the charge conjugation symmetry, allows for a bottom-up construction of a relativistic Hamiltonian that is in line with the principles of quantum electrodynamics (QED). Various approximate but accurate forms of the Hamiltonian can be obtained based entirely on physical arguments. In particular, the exact two-component Hamiltonians can be formulated in a general way to cast electric and magnetic fields, as well as electron self-energy and vacuum polarization, into a unified framework. While such algebraic two-component Hamiltonians are incompatible with explicit correlation, four-component relativistic explicitly correlated approaches can indeed be made fully parallel to the nonrelativistic counterparts by virtue of the ‘extended no-pair projection’ and the coalescence conditions. These findings open up new avenues for future developments of relativistic molecular quantum mechanics. In particular, ‘molecular QED’ will soon become an active and exciting field.

Liu, Wenjian

2014-04-01

234

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

235

Kindergarten Quantum Mechanics lectures notes  

E-print Network

These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in quant-ph/0402130 and [4]) which subsumes my Logic of Entanglement quant-ph/0402014. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes quant-ph/0506132. In a last section we provide some pointers to the body of technical literature on the subject.

Coecke, B

2005-01-01

236

Kindergarten Quantum Mechanics: Lecture Notes  

SciTech Connect

These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns 'doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I which subsumes my Logic of Entanglement. For a survey on the 'what', the 'why' and the 'hows' I refer to a previous set of lecture notes. In a last section we provide some pointers to the body of technical literature on the subject.

Coecke, Bob [Oxford University Computing Laboratory, Wolfson Building, Parks rd, OX1 3QD Oxford (United Kingdom)

2006-01-04

237

Tests of CPT and Quantum Mechanics: experiment  

NASA Astrophysics Data System (ADS)

Neutral kaons provide one of the systems most sensitive to quantum mechanics and CPT violation. Models predicting quantum mechanics violation, also related to CPT violation, have been tested at the CPLEAR and KLOE experiments. In this report results of CPLEAR obtained by studying the time evolution of single and two entangled kaons are reviewed. New or improved limits on decoherence and CPT violation parameters have been obtained by KLOE studying the quantum interference in the channel ??KK?????. No deviations from the expectations of quantum mechanics and CPT symmetry have been observed.

Ambrosino, F.; Antonelli, A.; Antonelli, M.; Bacci, C.; Barva, M.; Beltrame, P.; Bencivenni, G.; Bertolucci, S.; Bini, C.; Bloise, C.; Bocchetta, S.; Bocci, V.; Bossi, F.; Bowring, D.; Branchini, P.; Bulychjov, S. A.; Caloi, R.; Campana, P.; Capon, G.; Capussela, T.; Carboni, G.; Ceradini, F.; Cervelli, F.; Chi, S.; Chiefari, G.; Ciambrone, P.; Conetti, S.; De Lucia, E.; De Santis, A.; De Simone, P.; De Zorzi, G.; Dell'Agnello, S.; Denig, A.; Di Domenico, A.; Di Donato, C.; Di Falco, S.; Di Micco, B.; Doria, A.; Dreucci, M.; Farilla, A.; Felici, G.; Ferrari, A.; Ferrer, M. L.; Finocchiaro, G.; Fiore, S.; Forti, C.; Franzini, P.; Gatti, C.; Gauzzi, P.; Giovannella, S.; Gorini, E.; Graziani, E.; Incagli, M.; Kluge, W.; Kulikov, V.; Lacava, F.; Lanfranchi, G.; Lee-Franzini, J.; Leone, D.; Martemianov, M.; Martini, M.; Massarotti, P.; Matsyuk, M.; Mei, W.; Meola, S.; Messi, R.; Miscetti, S.; Moulson, M.; Müller, S.; Murtas, F.; Napolitano, M.; Nguyen, F.; Palutan, M.; Pasqualucci, E.; Passalacqua, L.; Passeri, A.; Patera, V.; Perfetto, F.; Pontecorvo, L.; Primavera, M.; Santangelo, P.; Santovetti, E.; Saracino, G.; Schamberger, R. D.; Sciascia, B.; Sciubba, A.; Scuri, F.; Sfiligoi, I.; Sibidanov, A.; Spadaro, T.; Spiriti, E.; Tabidze, M.; Testa, M.; Tortora, L.; Valente, P.; Valeriani, B.; Venanzoni, G.; Veneziano, S.; Ventura, A.; Ventura, S.; Versaci, R.; Villella, I.; Xu, G.; KLOE Collaboration

2007-05-01

238

Operators versus functions: from quantum dynamical semigroups to tomographic semigroups  

NASA Astrophysics Data System (ADS)

Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the so-called generalized Wigner functions or (group-covariant) tomograms, obtained by means of group-theoretical methods. A typical problem arising in this context is to express the evolution of a quantum system in terms of tomograms. In the case of a (suitable) open quantum system, the dynamics can be described by means of a quantum dynamical semigroup 'in disguise', namely, by a semigroup of operators acting on tomograms rather than on density operators. We focus on a special class of quantum dynamical semigroups, the twirling semigroups, that have interesting applications, e.g., in quantum information science. The 'disguised counterparts' of the twirling semigroups, i.e., the corresponding semigroups acting on tomograms, form a class of semigroups of operators that we call tomographic semigroups. We show that the twirling semigroups and the tomographic semigroups can be encompassed in a unique theoretical framework, a class of semigroups of operators including also the probability semigroups of classical probability theory, so achieving a deeper insight into both the mathematical and the physical aspects of the problem.

Aniello, Paolo

2013-11-01

239

PERSPECTIVE Quantum Mechanics of Black Holes  

E-print Network

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

240

QUANTUM MECHANICS AND DUALISM JEFFREY A. BARRETT  

E-print Network

mechanics, a strong variety of mind-body dualism provides a natural criterion for when collapses occur record. We will also consider options for avoiding a commitment to at least mind-body dualism. 1. Quantum of quantum mechanics requires one to endorse a strong variety of mind-body dualism. In particular, he argued

Stanford, Kyle

241

Quaternionic Formulation of Supersymmetric Quantum Mechanics  

E-print Network

Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions. Supercharges, superpartner Hamiltonians and energy eigenvalues are discussed and it has been shown that the results are consistent with the results of quantum mechanics.

Seema Rawat; O. P. S. Negi

2007-03-18

242

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

243

From Quantum Mechanics to String Theory  

E-print Network

of location Over time, the spike will often spread out again into a wave similar to the one it startedFrom Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics lengths and times to change depending on reference frame Any physical observable (the result

244

From Quantum Mechanics to String Theory  

E-print Network

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification from the interaction energy Thursday, June 4, 2009 #12;String Theory: A different kind of unification

245

From Quantum Mechanics to String Theory  

E-print Network

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

246

From Quantum Mechanics to String Theory  

E-print Network

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

247

Quantum Mechanics: Bell and Quantum Entropy for the Classroom  

E-print Network

In this article we are willing to give some first steps to quantum mechanics and a motivation of quantum mechanics and its interpretation for undergraduate students not from physics. After a short historical review in the development we discuss philosophical, physical and mathematical interpretation. We define local realism, locality and hidden variable theory which ends up in the EPR paradox, a place where questions on completeness and reality comes into play. The fundamental result of the last century was maybe Bell's that states that local realism is false if quantum mechanics is true. From this fact we can obtain the so called Bell inequalities. After a didactic example of the fact what these inequalities means we describe the key concept of quantum entanglement motivated here by quantum information theory. Also classical entropy and von Neuman entropy is discussed.

Pluch, Philipp

2014-01-01

248

An entropic picture of emergent quantum mechanics  

E-print Network

Quantum mechanics emerges a la Verlinde from a foliation of space by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantised in units of Boltzmann's constant k. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on space. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant h from Boltzmann's constant k.

D. Acosta; P. Fernandez de Cordoba; J. M. Isidro; J. L. G. Santander

2011-07-10

249

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

250

Collimation processes in quantum mechanics interpreted in quantum real numbers  

Microsoft Academic Search

We reexamine the theory of quantum mechanics using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from entities in the standard Hilbert space formulation of the theory. Our motivation is to elucidate certain apparently paradoxical features of the standard theory by enlarging the class of real numbers that physical quantities can take as numerical values. The concept

John Vincent Corbett; Thomas Durt

2009-01-01

251

Quantum network of superconducting qubits through opto-mechanical interface  

E-print Network

We propose a scheme to realize quantum networking of superconducting qubits based on the opto-mechanical interface. The superconducting qubits interact with the microwave photons, which then couple to the optical photons through the opto-mechanical interface. The interface generates a quantum link between superconducting qubits and optical flying qubits with tunable pulse shapes and carrier frequencies, enabling transmission of quantum information to other superconducting or atomic qubits. We show that the scheme works under realistic experimental conditions and it also provides a way for fast initialization of the superconducting qubits under $1$ K instead of $20$ mK operation temperature.

Zhang-qi Yin; W. L. Yang; L. Sun; L. M. Duan

2014-07-18

252

Polymer Quantum Mechanics and its Continuum Limit  

E-print Network

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

Alejandro Corichi; Tatjana Vukasinac; Jose A. Zapata

2007-03-31

253

Polymer quantum mechanics and its continuum limit  

SciTech Connect

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

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

2007-08-15

254

Improving Students' Understanding of Quantum Mechanics  

NSDL National Science Digital Library

Learning physics is challenging at all levels. Studentsâ difficulties in the introductory level physics courses have been widely studied and many instructional strategies have been developed to help students learn introductory physics. However, research shows that there is a large diversity in studentsâ preparation and skills in the upper-level physics courses and it is necessary to provide scaffolding support to help students learn advanced physics. This thesis explores issues related to studentsâ common difficulties in learning upper-level undergraduate quantum mechanics and how these difficulties can be reduced by research-based learning tutorials and peer instruction tools. We investigated studentsâ difficulties in learning quantum mechanics by administering written tests and surveys to many classes and conducting individual interviews with a subset of students. Based on these investigations, we developed Quantum Interactive Learning Tutorials (QuILTs) and peer instruction tools to help students build a hierarchical knowledge structure of quantum mechanics through a guided approach. Preliminary assessments indicate that studentsâ understanding of quantum mechanics is improved after using the research-based learning tools in the junior-senior level quantum mechanics courses. We also designed a standardized conceptual survey that can help instructors better probe studentsâ understanding of quantum mechanics concepts in one spatial dimension. The validity and reliability of this quantum mechanics survey is discussed.

Zhu, Guangtian

2011-07-31

255

On Time in Quantum Mechanics  

E-print Network

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

Nicola Vona

2014-03-11

256

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

257

Operational quantum theory without predefined time  

E-print Network

The current operational formulation of quantum theory is based on the concept of operation with an input and an output system, which assumes a prior notion of time and is asymmetric under time reversal. But in certain contexts, such as those involving gravity, time is expected to be dynamical and not predefined. Here, we propose an operational formulation of quantum theory without any predefined notion of time. It is based on a generalization of the concept of operation motivated by an epistemic approach: an operation is a description of knowledge about the events in a given region, which can be updated conditionally on information obtained from that region. Each such region has a set of boundary systems which by definition provide the sole means of information exchange between the events in the region and the events in other regions. Separate operations can be connected in networks through their boundary systems with no directionality assumed for the connections, which generalizes the standard circuit pictur...

Oreshkov, Ognyan

2014-01-01

258

Is Quantum Mechanics Falsifiable? A computational perspective on the foundations of Quantum Mechanics  

E-print Network

Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity. We describe how QM can be tested in this regime by extending the usual scientific paradigm to include {\\it interactive experiments}.

Dorit Aharonov; Umesh Vazirani

2012-06-16

259

Quantum-mechanical analysis of single molecule quantum electronic devices  

Microsoft Academic Search

This paper documents the need to coherently apply quantum mechanics in order to analyze microscopic devices. We examine device physics and study characteristics of single-molecule processing devices. The device physics of the proposed single-molecule device is based on the controlled propagation of electrons. By applying quantum mechanics and advanced numeric schemes, we perform the device-level analysis researching electron propagation (motion),

Sergey Edward Lyshevski

2011-01-01

260

OPTI 570A-Quantum Mechanics Course Description  

E-print Network

OPTI 570A- Quantum Mechanics Course Description: This is a one-semester course designed to provide students with a solid understanding of quantum mechanics formalism, techniques, and important example physics, quantum optics, relativistic quantum mechanics and other advanced quantum mechanics topics

Arizona, University of

261

Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics-I  

E-print Network

The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics could prove to be valuable for larger objectives such as understanding of gravity.

Aalok Pandya

2008-09-08

262

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

263

Playing Games with Quantum Mechanics  

E-print Network

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

Simon J. D. Phoenix; Faisal Shah Khan

2012-02-21

264

Riemann hypothesis and Quantum Mechanics  

E-print Network

In their 1995 paper, Jean-Beno\\^{i}t Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function $\\zeta(\\beta)$, where $\\beta$ is an inverse temperature. We formulate Riemann hypothesis (RH) as a property of the low temperature Kubo-Martin-Schwinger (KMS) states of this theory. More precisely, the expectation value of the BC phase operator can be written as $$\\phi_{\\beta}(q)=N_{q-1}^{\\beta-1} \\psi_{\\beta-1}(N_q), $$ where $N_q=\\prod_{k=1}^qp_k$ is the primorial number of order $q$ and $ \\psi_b $ a generalized Dedekind $\\psi$ function depending on one real parameter $b$ as $$ \\psi_b (q)=q \\prod_{p \\in \\mathcal{P,}p \\vert q}\\frac{1-1/p^b}{1-1/p}.$$ Fix a large inverse temperature $\\beta >2.$ The Riemann hypothesis is then shown to be equivalent to the inequality $$ N_q |\\phi_\\beta (N_q)|\\zeta(\\beta-1) >e^\\gamma \\log \\log N_q, $$ for $q$ large enough. Under RH, extra formulas for high temperatures KMS states ($1.5< \\beta <2$) are derived.

Michel Planat; Patrick Solé; Sami Omar

2010-12-21

265

Quantum chaos and operator fidelity metric  

E-print Network

We show that the recently introduced operator fidelity metric provides a natural tool to investigate the cross-over to quantum chaotic behaviour. This metric is an information-theoretic measure of the global stability of a unitary evolution against perturbations. We use random matrix theory arguments to conjecture that the operator fidelity metric can be used as an "order parameter" to discriminates phases with regular behaviour from quantum chaotic ones. A numerical study of the onset of chaotic in the Dicke model is given in order to support the conjecture

Paolo Giorda; Paolo Zanardi

2009-03-06

266

Kinetic potentials in quantum mechanics  

NASA Astrophysics Data System (ADS)

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

Hall, Richard L.

1984-09-01

267

Imperfect cloning operations in algebraic quantum theory  

E-print Network

No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal $\\epsilon$-imperfect cloning operation which tolerates a finite loss $\\epsilon$ of fidelity in the cloned state, and show that an individual system's algebra of observables is Abelian if and only if there is a universal $\\epsilon$-imperfect cloning operation in the case where the loss of fidelity is less than 1/4. Therefore, in this case no universal $\\epsilon$-imperfect cloning operation is possible in algebraic quantum theory.

Yuichiro Kitajima

2014-09-30

268

The formal path integral and quantum mechanics  

SciTech Connect

Given an arbitrary Lagrangian function on R{sup d} and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.

Johnson-Freyd, Theo [Department of Mathematics, University of California - Berkeley, 970 Evans Hall, Berkeley, California 94720 (United States)

2010-11-15

269

Strange Bedfellows: Quantum Mechanics and Data Mining  

NASA Astrophysics Data System (ADS)

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

2010-02-01

270

Strange Bedfellows: Quantum Mechanics and Data Mining  

E-print Network

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

Weinstein, Marvin

2009-01-01

271

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

272

Strange Bedfellows: Quantum Mechanics and Data Mining  

E-print Network

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

Marvin Weinstein

2009-11-03

273

Quantum circuits cannot control unknown operations  

NASA Astrophysics Data System (ADS)

One of the essential building blocks of classical computer programs is the ‘if’ clause, which executes a subroutine depending on the value of a control variable. Similarly, several quantum algorithms rely on applying a unitary operation conditioned on the state of a control system. Here we show that this control cannot be performed by a quantum circuit if the unitary is completely unknown. The task remains impossible even if we allow the control to be done modulo a global phase. However, this no-go theorem does not prevent implementing quantum control of unknown unitaries in practice, as any physical implementation of an unknown unitary provides additional information that makes the control possible. We then argue that one should extend the quantum circuit formalism to capture this possibility in a straightforward way. This is done by allowing unknown unitaries to be applied to subspaces and not only to subsystems.

Araújo, Mateus; Feix, Adrien; Costa, Fabio; Brukner, ?aslav

2014-09-01

274

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

275

Canonical distribution and incompleteness of quantum mechanics  

E-print Network

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

V. A. Skrebnev

2012-01-04

276

Four-dimensional understanding of quantum mechanics  

E-print Network

In this paper I will try to convince that quantum mechanics does not have to lead to indeterminism, but is just a natural consequence of four-dimensional nature of our world - that for example particles shouldn't be imagined as 'moving points' in space, but as their trajectories in the spacetime like in optimizing action formulation of Lagrangian mechanics. There will be analyzed simplified model - Boltzmann distribution among trajectories occurs to give quantum mechanic like behavior - for example electron moving in proton's potential would make some concrete trajectory which average exactly to the probability distribution of the quantum mechanical ground state. We will use this model to build intuition about quantum mechanics and discuss its generalizations to get some effective approximation of physics. We will see that topological excitations of the simplest model obtained this way already creates known from physics particle structure, their decay modes and electromagnetic/gravitational interactions between them.

Jarek Duda

2009-10-14

277

Visual Quantum Mechanics: Online Interactive Programs  

NSDL National Science Digital Library

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

278

CPT and Quantum Mechanics Tests with Kaons: Theory  

E-print Network

In this talk I review theoretical motivations for possible CPT Violation and deviations from ordinary quantum mechanical behavior of field theoretic systems in some quantum gravity models, and I describe the relevant precision tests using neutral and charged Kaons. I emphasize the possibly unique role of neutral-meson factories in providing specific tests of models in which the CPT operator is not well-defined, leading to modifications of Einstein-Podolsky-Rosen (EPR) particle correlators.

Nick E. Mavromatos

2006-07-28

279

Space time symmetry in quantum mechanics  

E-print Network

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

Zinkoo Yun

2014-02-26

280

Local quantum mechanics with finite Planck mass  

E-print Network

In this paper the motion of quantum particles with initial mass m is investigated. The quantum mechanics equation is formulated and solved. It is shown that the wave function contains the component which is depended on the gravitation fine structure constant

M Kozlowski; J. Marciak -Kozlowska; M. pelc

2007-04-20

281

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

282

Stabilizer Formalism for Operator Quantum Error Correction  

E-print Network

Operator quantum error correction is a recently developed theory that provides a generalized framework for active error correction and passive error avoiding schemes. In this paper, we describe these codes in the stabilizer formalism of standard quantum error correction theory. This is achieved by adding a "gauge" group to the standard stabilizer definition of a code that defines an equivalence class between encoded states. Gauge transformations leave the encoded information unchanged; their effect is absorbed by virtual gauge qubits that do not carry useful information. We illustrate the construction by identifying a gauge symmetry in Shor's 9-qubit code that allows us to remove 4 of its 8 stabilizer generators, leading to a simpler decoding procedure and a wider class of logical operations without affecting its essential properties. This opens the path to possible improvements of the error threshold of fault-tolerant quantum computing.

David Poulin

2005-08-18

283

Gerbes, Quantum Mechanics and Gravity  

E-print Network

We prove that invariance of a quantum theory under the semiclassical vs. strong-quantum duality $S/\\hbar\\longleftrightarrow\\hbar/S$, where S is the classical action, is equivalent to noncommutativity (of the Heisenberg-algebra type) of the coordinates of the space on which S is defined. We place these facts in correspondence with gerbes and Neveu-Schwarz B-fields and discuss their implications for a quantum theory of gravity. Feynman's propagator turns out to be closely related to the trivialisation of a gerbe on configuration space.

J. M. Isidro

2005-10-10

284

CLNS 96/1399 Peculiarities of Quantum Mechanics  

E-print Network

CLNS 96/1399 Peculiarities of Quantum Mechanics: Origins and Meaning Yuri F. Orlov Floyd R. Newman, specifically quantum, features of quantum mechanics --- quan­ tum nonlocality, indeterminism, interference are quantum observables themselves and are represented in quantum mechanics by density matrices of pure states

285

On a New Form of Quantum Mechanics (II)  

E-print Network

The correspondence of a new form of quantum mechanics based on a quantum version of the action principle, which was proposed earlier [arXiv:0807.3508], with the ordinary quantum mechanics is established. New potentialities of the quantum action principle in the interpretation of quantum mechanics are considered.

N. Gorobey; A. Lukyanenko; I. Lukyanenko

2009-12-16

286

On the hypothesis that quantum mechanism manifests classical mechanics: Numerical approach to the correspondence in search of quantum chaos  

SciTech Connect

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

Lee, Sang-Bong

1993-09-01

287

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

288

Lecture Notes in Quantum Mechanics Doron Cohen  

E-print Network

, scattering resonances · The Aharonov-Bohm effect · Magnetic field (Landau levels, Hall effect) · Motion · Spherical geometry, phase shifts · Cross section, optical theorem, resonances Quantum mechanics in practice

Cohen, Doron

289

Student Difficulties in Learning Quantum Mechanics.  

ERIC Educational Resources Information Center

Reports on a preliminary project that uses a phenomenographic approach to explore the ways in which a small number of fundamental ideas are conceptualized by students who are judged to have mastered quantum mechanics material. (DDR)

Johnston, I. D.; Crawford, K.; Fletcher, P. R.

1998-01-01

290

Quantum mechanical streamlines. I - Square potential barrier  

NASA Technical Reports Server (NTRS)

Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.

Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.

1974-01-01

291

Student difficulties in learning quantum mechanics  

NSDL National Science Digital Library

Reports on a preliminary project that uses a phenomenographic approach to explore the ways in which a small number of fundamental ideas are conceptualized by students who are judged to have mastered quantum mechanics material.

Johnston, Ian D.; Crawford, K.; Fletcher, P. R.

2006-06-19

292

Beyond Quantum Mechanics and General Relativity  

E-print Network

In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.

Andrea Gregori

2010-02-24

293

Distinguishability of Quantum States by Separable Operations  

E-print Network

We study the distinguishability of multipartite quantum states by separable operations. We first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations. An analytical version of this condition is derived for the case of $(D-1)$ pure states, where $D$ is the total dimension of the state space under consideration. A number of interesting consequences of this result are then carefully investigated. Remarkably, we show there exists a large class of $2\\otimes 2$ separable operations not being realizable by local operations and classical communication. Before our work only a class of $3\\otimes 3$ nonlocal separable operations was known [Bennett et al, Phys. Rev. A \\textbf{59}, 1070 (1999)]. We also show that any basis of the orthogonal complement of a multipartite pure state is indistinguishable by separable operations if and only if this state cannot be a superposition of 1 or 2 orthogonal product states, i.e., has an orthogonal Schmidt number not less than 3, thus generalize the recent work about indistinguishable bipartite subspaces [Watrous, Phys. Rev. Lett. \\textbf{95}, 080505 (2005)]. Notably, we obtain an explicit construction of indistinguishable subspaces of dimension 7 (or 6) by considering a composite quantum system consisting of two qutrits (resp. three qubits), which is slightly better than the previously known indistinguishable bipartite subspace with dimension 8.

Runyao Duan; Yuan Feng; Yu Xin; Mingsheng Ying

2007-05-06

294

Nonequilibrium quantum statistical mechanics and thermodynamics  

E-print Network

The purpose of this work is to discuss recent progress in deriving the fundamental laws of thermodynamics (0th, 1st and 2nd-law) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and different reversible and irreversible thermodynamic processes are studied from the point of view of quantum statistical mechanics. Special emphasis is put on new adiabatic theorems for steady states close to and far from equilibrium, and on investigating cyclic thermodynamic processes using an extension of Floquet theory.

Walid K. Abou Salem

2006-01-23

295

Quantum mechanics in de Sitter space  

E-print Network

We consider some possible phenomenological implications of the extended uncertainty principle, which is believed to hold for quantum mechanics in de Sitter spacetime. The relative size of the corrections to the standard results is however of the order of the ratio between the length scale of the quantum mechanical system and the de Sitter radius, and therefore exceedingly small. Nevertheless, the existence of effects due to the large scale curvature of spacetime in atomic experiments has a theoretical relevance.

Subir Ghosh; Salvatore Mignemi

2009-11-30

296

2T Physics and Quantum Mechanics  

E-print Network

We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit described by the same Hamiltonian. One of these formulations is used as a basis for a complementation of the usual quantum mechanics when in the presence of gravity.

W. Chagas-Filho

2008-02-20

297

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

298

Interpretations of Quantum Mechanics: a critical survey  

E-print Network

This brief survey analyzes the epistemological implications about the role of observer in the interpretations of Quantum Mechanics. As we know, the goal of most interpretations of quantum mechanics is to avoid the apparent intrusion of the observer into the measurement process. In the same time, there are implicit and hidden assumptions about his role. In fact, most interpretations taking as ontic level one of these fundamental concepts as information, physical law and matter bring us to new problematical questions. We think, that no interpretation of the quantum theory can avoid this intrusion until we do not clarify the nature of observer.

Michele Caponigro

2008-11-24

299

Interpretations of Quantum Mechanics: a critical survey  

E-print Network

This brief survey analyzes the epistemological implications about the role of observer in the interpretations of Quantum Mechanics. As we know, the goal of most interpretations of quantum mechanics is to avoid the apparent intrusion of the observer into the measurement process. In the same time, there are implicit and hidden assumptions about his role. In fact, most interpretations taking as ontic level one of these fundamental concepts as information, physical law and matter bring us to new problematical questions. We think, that no interpretation of the quantum theory can avoid this intrusion until we do not clarify the nature of observer.

Caponigro, Michele

2008-01-01

300

Testing foundations of quantum mechanics with photons  

NASA Astrophysics Data System (ADS)

Quantum mechanics continues to predict effects at odds with a classical understanding of nature. Experiments with light at the single-photon level have historically been at the forefront of fundamental tests of quantum theory and the current developments in photonic technologies enable the exploration of new directions. Here we review recent photonic experiments to test two important themes in quantum mechanics: wave-particle duality, which is central to complementarity and delayed-choice experiments; and Bell nonlocality, where the latest theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different experiments.

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

2014-04-01

301

Control landscapes for open system quantum operations  

NASA Astrophysics Data System (ADS)

The reliable realization of control operations is a key component of quantum information applications. In practice, meeting this goal is very demanding for open quantum systems. This paper investigates the landscape defined as the fidelity J between the desired and achieved quantum operations with an open system. The goal is to maximize J as a functional of the control variables. We specify the complete set of critical points of the landscape function in the so-called kinematic picture. An associated Hessian analysis of the landscape reveals that, upon the satisfaction of a particular controllability criterion, the critical topology is dependent on the particular environment, but no false traps (i.e. suboptimal solutions) exist. Thus, a gradient-type search algorithm should not be hindered in searching for the ultimate optimal solution with such controllable systems. Moreover, the maximal fidelity is proven to coincide with Uhlmann’s fidelity between the environmental initial states associated with the achieved and desired quantum operations, which provides a generalization of Uhlmann’s theorem in terms of Kraus maps.

Wu, Re-Bing; Rabitz, Herschel

2012-12-01

302

Quantum Mechanics with Basic Field Theory  

NASA Astrophysics Data System (ADS)

Preface; 1. Basic formalism; 2. Fundamental commutator and time evolution of state vectors and operators; 3. Dynamical equations; 4. Free particles; 5. Particles with spin 1/2; 6. Gauge invariance, angular momentum and spin; 7. Stern-Gerlach experiments; 8. Some exactly solvable bound state problems; 9. Harmonic oscillator; 10. Coherent states; 11. Two-dimensional isotropic harmonic oscillator; 12. Landau levels and quantum Hall effect; 13. Two-level problems; 14. Spin 1/2 systems in the presence of magnetic field; 15. Oscillation and regeneration in neutrino and neutral K-mesons as two-level systems; 16. Time-independent perturbation for bound states; 17. Time-dependent perturbation; 18. Interaction of charged particles and radiation in perturbation theory; 19. Scattering in one dimension; 20. Scattering in three dimensions - a formal theory; 21. Partial wave amplitudes and phase shifts; 22. Analytic structure of the S-matrix; 23. Poles of the Green's function and composite systems; 24. Approximation methods for bound states and scattering; 25. Lagrangian method and Feynman path integrals; 26. Rotations and angular momentum; 27. Symmetry in quantum mechanics and symmetry groups; 28. Addition of angular momenta; 29. Irreducible tensors and Wigner-Eckart theorem; 30. Entangled states; 31. Special theory of relativity: Klein Gordon and Maxwell's equation; 32. Klein Gordon and Maxwell's equation; 33. Dirac equation; 34. Dirac equation in the presence of spherically symmetric potentials; 35. Dirac equation in a relativistically invariant form; 36. Interaction of Dirac particle with electromagnetic field; 37. Multiparticle systems and second quantization; 38. Interactions of electrons and phonons in condensed matter; 39. Superconductivity; 40. Bose Einstein condensation and superfluidity; 41. Lagrangian formulation of classical fields; 42. Spontaneous symmetry breaking; 43. Basic quantum electrodynamics and Feynman diagrams; 44. Radiative corrections; 45. Anomalous magnetic moment and Lamb shift; Appendix; References; Index.

Desai, Bipin R.

2009-12-01

303

A Modified Lax-Phillips Scattering Theory for Quantum Mechanics  

E-print Network

The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems) then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.

Yossi Strauss

2014-07-24

304

Hidden algebra method (quasi-exact-solvability in quantum mechanics)  

SciTech Connect

A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.

Turbiner, Alexander [Institute for Theoretical and Experimental Physics, Moscow 117259 (Russian Federation); Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado, Postal 70-543, 04510 Mexico, D. F. (Mexico)

1996-02-20

305

Taming the zoo of supersymmetric quantum mechanical models  

NASA Astrophysics Data System (ADS)

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

Smilga, A. V.

2013-05-01

306

Taming the zoo of supersymmetric quantum mechanical models  

E-print Network

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

A. V. Smilga

2013-01-30

307

Taming the zoo of supersymmetric quantum mechanical models  

E-print Network

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

Smilga, A V

2013-01-01

308

Deformation quantization: Quantum mechanics lives and works in phase space  

NASA Astrophysics Data System (ADS)

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

Zachos, Cosmas K.

2014-09-01

309

Treating Time Travel Quantum Mechanically  

E-print Network

The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilising the quantum circuit formalism has given rise to two theories: D-CTCs and P-CTCs. In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their non-linearity and time travel paradoxes. In particular, the "equivalent circuit model"---which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory---is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of new theories are identified. One such theory, the theory of T-CTCs, is fully developed. The theory of T-CTCs is shown to not have undesirable features--...

Allen, John-Mark A

2014-01-01

310

Operational quantum theory without predefined time  

E-print Network

The current operational formulation of quantum theory is based on the concept of operation with an input and an output system, which assumes a prior notion of time and is asymmetric under time reversal. But in certain contexts, such as those involving gravity, time is expected to be dynamical and not predefined. Here, we propose an operational formulation of quantum theory without any predefined notion of time. It is based on a generalization of the concept of operation motivated by an epistemic approach: an operation is a description of knowledge about the events in a given region, which can be updated conditionally on information obtained from that region. Each such region has a set of boundary systems, which by definition provide the sole means of information exchange between the events in the region and the events in other regions. Separate operations can be connected in networks through their boundary systems with no directionality assumed for the connections, which generalizes the standard circuit picture. The events associated with an operation are described by positive semidefinite operators on the Hilbert spaces of the boundary systems, while the connections between regions are described by entangled states that encode a nontrivial physical symmetry. A simple rule provides the joint probabilities for the events in a network of operations. We discuss how it may be possible to understand the emergence of a causal structure from properties of the operators on the boundaries of compact space-time regions. The framework allows for indefinite causal order, timelike loops, and other acausal structures. As part of this work, we obtain a generalization of Wigner's theorem, which is based on the preservation of probabilities of actual events and thus puts the concept of time reversal symmetry on operational grounds. It contains the possibility for a new class of symmetry transformations.

Ognyan Oreshkov; Nicolas J. Cerf

2014-06-15

311

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

312

A quantum information approach to statistical mechanics  

E-print Network

We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all classical spin models (including models in different dimensions, different types of many-body interactions, different symmetries, etc) can be mapped to the partition function of a single model. Second, we give efficient quantum algorithms to estimate the partition function of various classical spin models, such as the Ising or the Potts model. The proofs of these two results are based on a mapping from partition functions to quantum states and to quantum circuits, respectively. Finally, we show how classical spin models can be used to describe certain fluctuating lattices appearing in models of discrete quantum gravity.

Gemma De las Cuevas

2013-12-20

313

Quantum mechanics and the equivalence principle  

E-print Network

A quantum particle moving in a gravitational field may penetrate the classically forbidden region of the gravitational potential. This raises the question of whether the time of flight of a quantum particle in a gravitational field might deviate systematically from that of a classical particle due to tunnelling delay, representing a violation of the weak equivalence principle. I investigate this using a model quantum clock to measure the time of flight of a quantum particle in a uniform gravitational field, and show that a violation of the equivalence principle does not occur when the measurement is made far from the turning point of the classical trajectory. I conclude with some remarks about the strong equivalence principle in quantum mechanics.

P. C. W. Davies

2004-03-03

314

Notes on Quantum Entanglement of Local Operators  

E-print Network

This is an expanded version of the short report arXiv:1401.0539, where we stud- ied the (Renyi) entanglement entropies for the excited state defined by acting a given local operator on the ground state. We introduced the (Renyi) entanglement entropies of given local operators which measure the degrees of freedom of local operators and characterize them in conformal field theories from the viewpoint of quantum entanglement. In present paper, we explain how to compute them in free massless scalar field theories and we also investigate their time evolution. The results are interpreted in terms of relativistic propagation of an entangled pair. The main new results which we acquire in the present paper are as follows. Firstly, we provide an explanation which shows that the (Renyi) entanglement entropies of a specific operator are given by (Renyi) entanglement entropies of binomial distribution by the replica method. That operator is constructed of only scalar field. Secondly, we found the sum rule which (Renyi) entanglement entropies of those local operators obey. Those local operators are located separately. Moreover we argue that (Renyi) entanglement entropies of specific operators in conformal field theories are given by (Renyi) entanglement entropies of binomial distribution. These specific operators are constructed of single-species operator. We also argue that general operators obey the sum rule which we mentioned above.

Masahiro Nozaki

2014-05-22

315

Notes on quantum entanglement of local operators  

NASA Astrophysics Data System (ADS)

This is an expanded version of the short report arXiv:1401.0539, where we studied the time evolution of (Renyi) entanglement entropies for the excited state defined by acting a given local operator on the ground state. In the present paper, we introduce (Renyi) entanglement entropies of given local operators which are defined by late time values of excesses of (Renyi) entanglement entropies. They measure the degrees of freedom of local operators and characterize them in conformal field theories from the viewpoint of quantum entanglement. We explain how to compute them in free massless scalar field theories and we also investigate their time evolution. Our results can be interpreted in terms of the relativistic propagation of entangled pairs. The main new results which we acquire in the present paper are as follows. Firstly, we provide an explanation which shows that (Renyi) entanglement entropies of a specific operator are given by (Renyi) entanglement entropies whose reduced density matrices are given by the binomial distribution. That operator is constructed of only the scalar field. Secondly, we found the sum rule which (Renyi) entanglement entropies of those local operators obey. Those local operators are located separately. Moreover we argue that (Renyi) entanglement entropies of specific operators in conformal field theories are given by (Renyi) entanglement entropies whose reduced density matrices are given by the binomial distribution. These specific operators are constructed of single-species operators. We also argue that general operators obey the sum rule which we mentioned above.

Nozaki, Masahiro

2014-10-01

316

1 Introduction to quantum mechanics Quantum mechanics is the basic tool needed to describe, understand and devise  

E-print Network

1­1 1 Introduction to quantum mechanics Quantum mechanics is the basic tool needed to describe, understand and devise NMR experiments. Fortunately for NMR spectroscopists, the quantum mechanics of nuclear mathematical concepts frequently encountered in quantum mechanics and NMR. 0DWKHPDWLFDO FRQFHSWV 1.1.1 Complex

Foster, Mark P.

317

A length operator for canonical quantum gravity  

E-print Network

We construct an operator that measures the length of a curve in four-dimensional Lorentzian vacuum quantum gravity. We work in a representation in which a $SU(2)$ connection is diagonal and it is therefore surprising that the operator obtained after regularization is densely defined, does not suffer from factor ordering singularities and does not require any renormalization. We show that the length operator admits self-adjoint extensions and compute part of its spectrum which like its companions, the volume and area operators already constructed in the literature, is purely discrete and roughly is quantized in units of the Planck length. The length operator contains full and direct information about all the components of the metric tensor which faciliates the construction of a new type of weave states which approximate a given classical 3-geometry.

T. Thiemann

1996-06-29

318

Notes on Quantum Mechanics and Consciousness  

E-print Network

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

Elemer E Rosinger

2005-08-13

319

Quantum mechanics: last stop for reductionism  

E-print Network

The state space of a homogeneous body is derived under two different assumptions: infinitesimal reducibility and irreducibility. The first assumption leads to a real vector space, used in classical mechanics, while the second one leads to a complex vector space, used in quantum mechanics.

Gabriele Carcassi

2012-03-16

320

The Measure of Momentum in Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The de Broglie relation p = h/? is often used in the heuristic deduction of the Schrödinger equation. Yet, this relation does not appear among the postulates of quantum theory. Actually, in most textbooks the physical definition of the quantum concept of momentum is often neglected. In this paper we show that the definition of momentum as derived quantity, operationally founded on the typical measurement of the so called "flight time", not only fits very well with the physical principles of the quantum theory, but can also help to avoid common ambiguities in the enunciation of Heisenberg's uncertainty principle.

Logiurato, Fabrizio; Tarsitani, Carlo

2006-06-01

321

Objective and Subjective Probabilities in Quantum Mechanics  

E-print Network

The concept of probability was prominent in the original foundations of quantum mechanics, and continues to be so today. Indeed, the controversies regarding objective and subjective interpretations of probability have again become active. I argue that, although both objective and subjective probabilities have domains of relevance in QM, their roles are quite distinct. Even where both are legitimate, the objective and subjective probabilities differ, both conceptually and numerically. There are quantum probabilities that have no useful subjective interpretations, and there are subjective probabilities that cannot be realized as quantum probabilities.

Leslie Ballentine

2007-10-31

322

Quantum mechanical counterpart of nonlinear optics  

E-print Network

Raman-type laser excitation of a trapped atom allows one to realize the quantum mechanical counterpart of phenomena of nonlinear optics, such as Kerr-type nonlinearities, parametric amplification, and multi-mode mixing. Additionally, huge nonlinearities emerge from the interference of the atomic wave function with the laser waves. They lead to a partitioning of the phase space accompanied by a significantly different action of the time evolution in neighboring phase-space zones. For example, a nonlinearly modified coherent "displacement" of the motional quantum state may induce strong amplitude squeezing and quantum interferences.

S. Wallentowitz; W. Vogel

1997-05-15

323

On Time. 6b: Quantum Mechanical Time  

E-print Network

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

C. K. Raju

2008-08-09

324

A Primer on Resonances in Quantum Mechanics  

E-print Network

After a pedagogical introduction to the concept of resonance in classical and quantum mechanics, some interesting applications are discussed. The subject includes resonances occurring as one of the effects of radiative reaction, the resonances involved in the refraction of electromagnetic waves by a medium with a complex refractive index, and quantum decaying systems described in terms of resonant states of the energy. Some useful mathematical approaches like the Fourier transform, the complex scaling method and the Darboux transformation are also reviewed.

O. Rosas-Ortiz; N. Fernandez-Garcia; Sara Cruz y Cruz

2009-02-24

325

A Primer on Resonances in Quantum Mechanics  

E-print Network

After a pedagogical introduction to the concept of resonance in classical and quantum mechanics, some interesting applications are discussed. The subject includes resonances occurring as one of the effects of radiative reaction, the resonances involved in the refraction of electromagnetic waves by a medium with a complex refractive index, and quantum decaying systems described in terms of resonant states of the energy. Some useful mathematical approaches like the Fourier transform, the complex scaling method and the Darboux transformation are also reviewed.

Rosas-Ortiz, O; Cruz, Sara Cruz y; 10.1063/1.3040259

2009-01-01

326

Testing the limits of quantum mechanical superpositions  

NASA Astrophysics Data System (ADS)

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

Arndt, Markus; Hornberger, Klaus

2014-04-01

327

Testing the limits of quantum mechanical superpositions  

E-print Network

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

Markus Arndt; Klaus Hornberger

2014-10-01

328

The Mechanism of Quantum Computation  

Microsoft Academic Search

I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine\\u000a whose coordinates are submitted to a nonfunctional relation representing all the problem constraints; moving an input part,\\u000a reversibly and nondeterministically produces a solution through a many body interaction. The machine can be considered the\\u000a many body generalization of another perfect machine, the

Giuseppe Castagnoli

2008-01-01

329

Conditional probabilities and density operators in quantum modeling  

E-print Network

Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and operator-valued measures), thereby allowing applications of these entities to the modeling of a wider variety of physical situations. Conditional probabilities associated with projection-valued measures are expressed by introducing conditional density operators, identical in some but not all cases to the usual reduced density operators. By lifting density operators to the extended Hilbert space featured in Neumark's theorem, I show an obstacle to extending conditional density operators to arbitrary positive operator-valued measures (POVMs); however, tensor products of POVMs are compatible with conditional density operators. By way of application, conditional density operators together with the free choice of probe particles allow the so-called postulate of state reductions to be replaced by a theorem. A second application demonstrates an equivalence between one form of quantum key distribution and another, allowing a formulation of individual eavesdropping attacks against transmitted-state BB84 to work also for entangled-state BB84.

John M. Myers

2005-06-08

330

CLNS 96/1443 Peculiarities of Quantum Mechanics  

E-print Network

CLNS 96/1443 REVISED Peculiarities of Quantum Mechanics: Origins and Meaning 1 Yuri F. Orlov Floyd The most peculiar, specifically quantum, features of quantum mechanics --- quan­ tum nonlocality of pure states. Structurally, quantum mechanics is a result of applying non­Abelian symmetries to truth

331

Green's Functions and Their Applications to Quantum Mechanics  

E-print Network

Green's Functions and Their Applications to Quantum Mechanics Jeff Schueler June 2, 2011 Contents 1 Green's Functions in Quantum Mechanics and Many-body Theory 8 3.1 Time Independent Green's Fuctions, specifically in how they apply to quantum mechan- ics. I plan to introduce some of the fundamentals of quantum

Morrow, James A.

332

Quantum mechanics as "space-time statistical mechanics"?  

E-print Network

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

Anders Månsson

2005-01-24

333

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

334

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

335

First-Person Plural Quantum Mechanics  

E-print Network

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

Mohrhoff, Ulrich

2014-01-01

336

First-Person Plural Quantum Mechanics  

E-print Network

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

Ulrich Mohrhoff

2014-10-22

337

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

338

Quantum operator design for lattice baryon spectroscopy  

NASA Astrophysics Data System (ADS)

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. Group-theoretical projections onto the irreducible representations of the symmetry group of a cubic spatial lattice are used to endow the operators with lattice spin and parity quantum numbers, facilitating the identification of the JP quantum numbers of the corresponding continuum states. The number of resulting operators is very larger consequently a key aspect of this work is the development of a selection method for finding a sufficient subset of operators for accurately extracting the lowest seven or eight energy levels in each symmetry channel. A procedure in which the diagonal elements of the correlation matrix of the operators are first evaluated to remove noisy operators, followed by the selection of sixteen operators whose renormalized correlation matrix at a fixed small time separation has a low condition number for both the even- and odd-parity channels, is found to work well. These techniques are applied in the construction of nucleon operators. Correlation matrix elements between these operators are estimated using 200 configurations on a 123 x 48 anisotropic lattice in the quenched approximation with unphysically heavy u, d quark masses (the pion mass is approximately 700 MeV). After a change of basis operators using a variational method is applied, the energies of up to eight states are extracted in each symmetry channel. Although comparison with experiment is not justified, the pattern of levels obtained qualitatively agrees with the observed spectrum. A comparison with quark model predictions is also made; the quark model predicts more low-lying even-parity states than this study yields, but both the quark model and this study predict more odd-parity states near 2 GeV than currently observed in experiments.

Lichtl, Adam

339

Point form relativistic quantum mechanics and relativistic SU(6)  

NASA Technical Reports Server (NTRS)

The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.

Klink, W. H.

1993-01-01

340

From Cbits to Qbits: Teaching computer scientists quantum mechanics  

NSDL National Science Digital Library

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

Mermin, N. D.

2004-04-29

341

A proof of von Neumann's postulate in Quantum Mechanics  

SciTech Connect

A Clifford algebraic analysis is explained. It gives proof of von Neumann's postulate on quantum measurement. It is of basic significance to explain the problem of quantum wave function reduction in quantum mechanics.

Conte, Elio [Department of Pharmacology and Human Physiology, TIRES-Center for Innovative Technologies for Signal Detection and Processing, Department of Physics, University of Bari (Italy) and School of Advanced International Studies for Applied Theoretical and Non Linear Methodologies of Physics, Bari (Italy)

2010-05-04

342

Quantum mechanics of time travel through post-selected teleportation  

E-print Network

This paper discusses the quantum mechanics of closed-timelike curves (CTCs) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based ...

Maccone, Lorenzo

343

Deformation Quantization: From Quantum Mechanics to Quantum Field Theory  

E-print Network

The aim of this paper is to give a basic overview of Deformation Quantization (DQ) to physicists. A summary is given here of some of the key developments over the past thirty years in the context of physics, from quantum mechanics to quantum field theory. Also, we discuss some of the conceptual advantages of DQ and how DQ may be related to algebraic quantum field theory. Additionally, our previous results are summarized which includes the construction of the Fedosov star-product on dS/AdS. One of the goals of these results was to verify that DQ gave the same results as previous analyses of these spaces. Another was to verify that the formal series used in the conventional treatment converged by obtaining exact and nonperturbative results for these spaces.

P. Tillman

2006-10-31

344

Partitions and Objective Indefiniteness in Quantum Mechanics  

E-print Network

Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual to one another and which are developed in two mathematical logics, the usual Boolean logic of subsets and the more recent logic of partitions. Our sense-making strategy is "follow the math" by showing how the logic and mathematics of set partitions can be transported in a natural way to Hilbert spaces where it yields the mathematical machinery of QM--which shows that the mathematical framework of QM is a type of logical system over the complex numbers. And then we show how the machinery of QM can be transported the other way down to the set-like vector spaces over Z_2 showing how the classical logical finite probability calculus (in a "non-commutative" version) is a type of "quantum mechanics" over Z_2, i.e., over sets. In this way, we try to make sense out of objective indefiniteness and thus to interpret quantum mechanics.

David Ellerman

2014-01-10

345

Macroscopic Quantum Mechanics in a Classical Spacetime  

E-print Network

We apply the many-particle Schr\\"{o}dinger-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 found 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 they do not allow quantum uncertainty to be transferred from one object to another through gravity.

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

2012-10-01

346

A new introductory quantum mechanics curriculum  

NASA Astrophysics Data System (ADS)

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

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

2014-01-01

347

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

E-print Network

We show that when non-commutative quantum mechanics is formulated on the Hilbert space of Hilbert-Schmidt operators (referred to as quantum Hilbert space) 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 and general algorithm to compute this function. Using this we compute the distance between pure and mixed states on quantum Hilbert space and demonstrate a tantalizing link between statistics and geometry.

F. G. Scholtz; B. Chakraborty

2012-06-22

348

Foundations of quantum physics: a general realistic and operational approach  

E-print Network

Foundations of quantum physics: a general realistic and operational approach Diederik Aerts FUND of quantum physics: a general realistic and operational approach", International Journal of Theoretical examples in detail in the light of this formalism: a classical deterministic entity and a quantum entity

Aerts, Diederik

349

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

350

Open Source Physics: Quantum Mechanical Measurement  

NSDL National Science Digital Library

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

Belloni, Mario; Christian, Wolfgang

2008-06-02

351

Quantum Mechanics and Discrete Time from "Timeless" Classical Dynamics  

E-print Network

We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless'' reparametrization invariant model of a relativistic particle with two compactified extradimensions. In this example, discrete physical time is constructed based on quasi-local observables. - Generally, employing the path-integral formulation of classical mechanics developed by Gozzi et al., we show that these deterministic classical systems can be naturally described as unitary quantum mechanical models. The emergent quantum Hamiltonian is derived from the underlying classical one. It is closely related to the Liouville operator. We demonstrate in several examples the necessity of regularization, in order to arrive at quantum models with bounded spectrum and stable groundstate.

H. -T. Elze

2003-07-03

352

Quantum statistical mechanics, L-series, Anabelian Geometry  

E-print Network

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

Marcolli, Matilde

353

Subjective and Objective Probabilities in Quantum Mechanics  

E-print Network

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.

Mark Srednicki

2005-01-03

354

WEAK MEASUREMENT IN QUANTUM MECHANICS ABRAHAM NEBEN  

E-print Network

WEAK MEASUREMENT IN QUANTUM MECHANICS ABRAHAM NEBEN PHYS 342 Final Project March 10, 2011 Contents of Postselection 4 4. Impossible Spin Measurements 5 5. Hardy's Paradox 5 6. Controversy over Weak Measurement 8 7 of a Measurement of a Component of the Spin of a Spin-1/2 Particle Can Turn Out to be 100." [1] The topic

Rosner, Jonathan L.

355

Is Quantum Mechanics needed to explain consciousness ?  

E-print Network

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

Knud Thomsen

2007-11-13

356

Comparison of Classical and Quantum Mechanical Uncertainties.  

ERIC Educational Resources Information Center

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

Peslak, John, Jr.

1979-01-01

357

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

358

Spin Glass: A Bridge between quantum computation and statistical mechanics  

E-print Network

We show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Second, we show another interesting technique to employ quantum nature, quantum annealing. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.

Masayuki Ohzeki

2012-04-13

359

Perturbative expansions in quantum mechanics  

E-print Network

We prove a D=1 analytic versal deformation theorem for WKB expansions. We define the spectrum of an operator in local analytic terms. We use the Morse lemma to show that the perturbation series arising in a perturbed harmonic oscillator become analytic after a formal Borel transform.

Mauricio D. Garay

2005-02-08

360

Network implementation of covariant two-qubit quantum operations  

E-print Network

A six-qubit quantum network consisting of conditional unitary gates is presented which is capable of implementing a large class of covariant two-qubit quantum operations. Optimal covariant NOT operations for one and two-qubit systems are special cases contained in this class. The design of this quantum network exploits basic algebraic properties which also shed new light onto these covariant quantum processes.

J. Novotny; G. Alber; I. Jex

2007-01-09

361

Classical limit of relativistic quantum mechanical equations in the Foldy-Wouthuysen representation  

NASA Astrophysics Data System (ADS)

It is shown that, under the Wentzel-Kramers-Brillouin approximation conditions, using the Foldy-Wouthuysen (FW) representation allows the problem of finding a classical limit of relativistic quantum mechanical equations to be reduced to the replacement of operators in the Hamiltonian and quantum mechanical equations of motion by the respective classical quantities.

Silenko, A. Ya.

2013-03-01

362

Novel symmetries in N=2 supersymmetric quantum mechanical models  

SciTech Connect

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. -- Highlights: •Discrete symmetries of two completely different kinds of N=2 supersymmetric quantum mechanical models have been discussed. •The discrete symmetries provide physical realizations of Hodge duality. •The continuous symmetries provide the physical realizations of de Rham cohomological operators. •Our work sheds a new light on the meaning of the above abstract operators.

Malik, R.P., E-mail: malik@bhu.ac.in [Physics Department, BHU-Varanasi-221 005 (India); DST-CIMS, Faculty of Science, BHU-Varanasi-221 005 (India); Khare, Avinash, E-mail: khare@iiserpune.ac.in [Indian Institute of Science for Education and Research, Pune-411 021 (India)] [Indian Institute of Science for Education and Research, Pune-411 021 (India)

2013-07-15

363

Quantum mechanical coherence, resonance, and mind  

SciTech Connect

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

Stapp, H.P.

1995-03-26

364

Indistinguishable Particles in Quantum Mechanics: An Introduction  

E-print Network

In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This is, for electrons, the Pauli Exclusion Principle, or in general, the Symmetrization Postulate. Then, we introduce fermions and bosons and the distributions respectively describing their statistical behaviour in indistinguishable situations. Following that, we discuss the spin-statistics connection, as well as alternative statistics and experimental evidence for all these results, including the use of bunching and antibunching of particles emerging from a beam splitter as a signature for some bosonic or fermionic states.

Y. Omar

2005-11-01

365

The emergent Copenhagen interpretation of quantum mechanics  

NASA Astrophysics Data System (ADS)

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

Hollowood, Timothy J.

2014-05-01

366

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.

367

Quantum Hypothesis Testing Non-Equilibrium Statistical Mechanics  

E-print Network

Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics V. Jaksi´c1 , Y. Ogata2 , C with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large

Boyer, Edmond

368

Quantum harmonic oscillator with position-dependent mass in the displacement operator formalism  

NASA Astrophysics Data System (ADS)

The position-dependent effective mass quantum harmonic oscillator problem is considered within the displacement operator framework. Using the analytic and the algebraic approaches, exact expressions for quantum mechanical quantities of the system have been obtained. In the limit of no deformation, results of the constant mass oscillator are recovered.

Tchoffo, M.; Vubangsi, M.; Fai, L. C.

2014-10-01

369

The ZX-calculus is complete for stabilizer quantum mechanics  

NASA Astrophysics Data System (ADS)

The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics (QM), meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer QM, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations.

Backens, Miriam

2014-09-01

370

Relational Motivation for Conformal Operator Ordering in Quantum Cosmology  

E-print Network

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. It is particularly naturally and simply manifest in relationalist product-type actions (such as the Jacobi action for mechanics or Baierlein-Sharp-Wheeler type actions for general relativity), for which all that is required for the kinetic and potential factors to rescale in compensation to each other. These actions themselves mathematically sharply implementing philosophical principles relevant to whole-universe modelling, the motivation for conformal operator-ordering in quantum cosmology is substantially strengthened. Relationalist product-type actions also give emergent times which amount to recovering Newtonian, proper and cosmic time in the various relevant contexts. The conformal scaling of these actions directly tells us how emergent time scales; if one follows suit with the Newtonian time or the lapse in the more commonly used difference-type Euler--Lagrange or Arnowitt--Deser--Misner type actions, one sees how these too obey a more complicated conformal invariance. Moreover, our discovery of the conformal scaling of the time involved permits relating how it simplifies equations of motion with how affine parametrization simplifies geodesics.

Edward Anderson

2009-05-20

371

Quantum Entanglement and Decoherence: Beyond Particle Models. A Farewell to Quantum Mechanics's Weirdness  

E-print Network

Combining abstract to laboratory projected quantum states a general analysis of headline quantum phenomena is presented. Standard representation mode is replaced; instead quantum states sustained by elementary material constituents occupy its place. Renouncing to assign leading roles to language originated in classical physics when describing genuine quantum processes, together with sustainment concept most, if not all weirdness associated to Quantum Mechanics vanishes.

O. Tapia

2014-04-02

372

1/n expansion in quantum mechanics  

SciTech Connect

The classical approximation (/ell/ = n - 1 /yields/ /infinity/) for the energy /var epsilon/(/sup 0/) and the semiclassical expansion in problems of quantum mechanics are discussed. A recursive method is proposed for calculating the quantum corrections of arbitrary order to /var epsilon/ (/sup 0/), this being valid for both bound and quasistationary states. The generalization of the method to states with an arbitrary number of nodes and the possibility of a more general choice of the parameter of the semiclassical expansion are considered. The method is illustrated by the example of the Yukawa and funnel potentials and for the Stark effect in the hydrogen atom. These examples demonstrate the rapid convergence of the 1/n expansion even for small quantum numbers.

Vainberg, V.M.; Mur, V.D.; Popov, V.S.; Sergeev, A.V.; Shcheblykin, A.V.

1988-09-01

373

Quantum Mechanics Joachim Burgd orfer and Stefan Rotter  

E-print Network

1 1 Quantum Mechanics Joachim BurgdË? orfer and Stefan Rotter 1.1 Introduction 3 1.2 Particle and Quantization 8 1.5 Angular Momentum in Quantum Mechanics 9 1.6 Formalism of Quantum Mechanics 12 1.7 Solution Quantization 33 1.9.3 Gutzwiller Trace Formula 34 1.10 Conceptual Aspects of Quantum Mechanics 35 1

Rotter, Stefan

374

Hidden algebra method (quasi-exact-solvability in quantum mechanics)  

SciTech Connect

A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland {ital N}-body problems ass ociated with an existence of the hidden algebra {ital sl}{sub {ital N}} is discussed extensively. {copyright} {ital 1996 American Institute of Physics.}

Turbiner, A. [Institute for Theoretical and Experimental Physics, Moscow 117259 (Russia)]|[Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado, Postal 70-543, 04510 Mexico, D. F. (Mexico)

1996-02-01

375

Quantum Signature Scheme Using a Single Qubit Rotation Operator  

NASA Astrophysics Data System (ADS)

We present a quantum signature scheme using a single qubit rotation operator. In this protocol, the trusted center confirms the quantum signature and thus conforms with other quantum signature schemes. Utilizing the unitary properties of a single qubit rotation operator and Pauli operators, our protocol provides signature security and enhances the efficiency of communication. In addition, our protocol - using only a single qubit measurement - facilitates the ease of implementation and enhances convenience for users. The security of the protocol is analyzed.

Kang, Min-Sung; Hong, Chang-Ho; Heo, Jino; Lim, Jong-In; Yang, Hyung-Jin

2014-08-01

376

The Objective Inde...niteness Interpretation of Quantum Mechanics  

E-print Network

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

Wüthrich, Christian

377

Quantum statistical mechanics, L-series, Anabelian Geometry  

E-print Network

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

Marcolli, Matilde

378

Quantum statistical mechanics, L-series, Anabelian Geometry  

E-print Network

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

Marcolli, Matilde

379

Harvard University Physics 143b: Quantum Mechanics II  

E-print Network

Harvard University Physics 143b: Quantum Mechanics II Instructor : Subir Sachdev, Lyman 343@fas.harvard.edu This is the second half of an introductory course on quantum mechanics. The course will complete the text book: the photon 5. Relativistic quantum mechanics: the Dirac equation 6. Einstein-Podolsky-Rosen "paradox", Bell

380

Harvard University Physics 143b: Quantum Mechanics II  

E-print Network

Harvard University Physics 143b: Quantum Mechanics II Instructor : Subir Sachdev, Lyman 343@physics.harvard.edu This is the second half of an introductory course on quantum mechanics. The course will complete the text book: the photon 5. Relativistic quantum mechanics: the Dirac equation 6. Scattering theory. 7. Einstein

381

Faculty Disagreement about the Teaching of Quantum Mechanics  

E-print Network

Faculty Disagreement about the Teaching of Quantum Mechanics Michael Dubson1 , Steve Goldhaber1 (matter wave vs. information wave vs. something else). Keywords: upper-division quantum mechanics, curriculum reform, faculty survey, quantum mechanics textbooks PACS: 01.40.-d, 01.40.Fk, 01.40.gb, 01.40.G

Colorado at Boulder, University of

382

Physica D 145 (2000) 330348 Lyapunov exponent in quantum mechanics.  

E-print Network

Physica D 145 (2000) 330­348 Lyapunov exponent in quantum mechanics. A phase-space approach V extension of the notion of Lyapunov exponent to quantum mechanics, the method that is developed is also trajectories in phase-space, it is not obvious what the corresponding quantities in quantum mechanics should be

Vilela Mendes, Rui

383

The syllabus of the Course 624 Quantum Mechanics 2  

E-print Network

The syllabus of the Course 624 Quantum Mechanics 2 Spring 2009. Instructor V.L. Pokrovsky. 1. Many-body quantum mechanics. Second quantization. Spin and statistics. Bose- Einstein condensation. 6's phase. Landau-Zener theory. Principal textbook: E. Merzbacher, Quantum Mechanics, 3-d edition, Wiley

384

Quantum Mechanics as a Science -Religion Bridge By Stanley Klein  

E-print Network

Quantum Mechanics as a Science - Religion Bridge By Stanley Klein (May 1, 2002) Stanley Klein and for fitting contact lenses. Klein's interest in quantum mechanics and brain research has led him to explore of more than 20 years, DUALITY, summarizes his theme that the duality of quantum mechanics provides

Klein, Stanley

385

Quantum Mechanics Summary/Review Spring 2009 Compton Lecture Series  

E-print Network

time, the spike will generally spread out again, and the information about position will be lost one component at a time. · Planck's constant determines the scale at which quantum mechanical effectsQuantum Mechanics Summary/Review Spring 2009 Compton Lecture Series: From Quantum Mechanics

386

A Chaotic, Deterministic Model for Quantum Mechanics  

E-print Network

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

Carl Frederick

2014-06-20

387

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

388

On Quantum Mechanics in Friedmann-Robertson-Walker Universe  

E-print Network

It is shown that only in the space-times admitting a 1+3-foliation by flat Cauchy hypesurfaces (i.e., in the Bianchi I type space-times the isotropic version of which the spatially flat Friedmann-Robertson-Walker space-times are) the canonical quantization of geodesic motion and quantum-mechanics obtained as an asymptotics of the quantum theory of scalar field lead to the same canonical commutation relations (CCR). Otherwise, the field-theoretical approach leads to a deformation of CCR (particularly, operators of coordinates do not commute), and the Principle of Correspondence is broken in a sense. Thus, the spatially flat cosmology is distinguished intrinsically in the quantum theory.

E. A. Tagirov

2000-11-03

389

Clocks And Dynamics In Quantum Mechanics  

E-print Network

We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of quantum uncertainty lies with the absence of infinities or infinitesimals in observational data and that our concept of time derives from observing changing data (events). We argue that the fundamentally important content of the Superposition Principle is not the "probability amplitude" of posterior state observation but future state availability conditional only on prior information. Since event detection also implies posterior conditions (e.g. a specific type of detectable event occurred) as well as prior conditions, the probabilities of detected outcomes are also conditional on properties of the posterior properties of the observation. Such posterior conditions cannot affect the prior state availabilities and this implies violation of counter-factual definiteness. A componen...

York, Michael

2014-01-01

390

Beyond relativity and quantum mechanics: space physics  

NASA Astrophysics Data System (ADS)

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

Lindner, Henry H.

2011-09-01

391

The preparation of states in quantum mechanics  

E-print Network

The important problem of how to prepare a quantum mechanical system, $S$, in a specific initial state of interest - e.g., for the purposes of some experiment - is addressed. Three distinct methods of state preparation are described. One of these methods has the attractive feature that it enables one to prepare $S$ in a preassigned initial state with certainty; i.e., the probability of success in preparing $S$ in a given state is unity. This method relies on coupling $S$ to an open quantum-mechanical environment, $E$, in such a way that the dynamics of $S \\vee E$ pulls the state of $S$ towards an "attractor", which is the desired initial state of $S$. This method is analyzed in detail.

Juerg Froehlich; Baptiste Schubnel

2014-09-28

392

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

393

Physical Interpretations of Nilpotent Quantum Mechanics  

E-print Network

Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit construction of vacuum. Physical interpretation of the nilpotent formalism is discussed with respect to boson and baryon structures, the mass-gap problem, zitterbewgung, Berry phase, renormalization, and related issues.

Peter Rowlands

2010-04-09

394

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

395

Chiral quantum mechanics (CQM) for antihydrogen systems  

E-print Network

A first deception of QM on antiH already appears in one-center integrals for two-center systems (G. Van Hooydonk, physics/0511115). In reality, full QM is a theory for chiral systems but the QM establishment was wrong footed with a permutation of reference frames. With chiral quantum mechanics (CQM), the theoretical ban on natural antiH must be lifted as soon as possible.

G. Van Hooydonk

2005-12-03

396

Quantum Mechanics and Motion: A Modern Perspective  

E-print Network

This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum, yields a world-line. If a force acts on the particle, its probability distribution is accordingly modified. This must also be true for macroscopic objects, although now the description is far more complicated by the structure of matter and associated surface physics.

Gerald E. Marsh

2009-12-27

397

Sixty years of quantum wave mechanics  

NASA Astrophysics Data System (ADS)

We present an inaugural lecture, originally given by the author on 2 June 1987 at the Queen's University of Belfast, but in an edited version, on the topic "Sixty years of quantum wave mechanics". A short historical survey is given as an introduction to some of the author's own personal research in the theory of atomic collisions, notably heavy-particle collisions and semiclassical methods.

Crothers, D. S. F.

1989-11-01

398

Euclidean Quantum Mechanics and Universal Nonlinear Filtering  

Microsoft Academic Search

An important problem in applied science is the continuous nonlinear filtering\\u000aproblem, i.e., the estimation of a Langevin state that is observed indirectly.\\u000aIn this paper, it is shown that Euclidean quantum mechanics is closely related\\u000ato the continuous nonlinear filtering problem. The key is the configuration\\u000aspace Feynman path integral representation of the fundamental solution of a\\u000aFokker-Planck type

Bhashyam Balaji

2009-01-01

399

Relativistic Non-Hermitian Quantum Mechanics  

E-print Network

We develop relativistic wave equations in the framework of the new non-hermitian ${\\cal PT}$ quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of ${\\cal PT}$-symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that in particular the mass matrix be Hermitian also allows for models that have no counterpart in conventional quantum mechanics. For example it is well-known that a quartet of Weyl spinors coupled by a Hermitian mass matrix reduces to two independent Dirac fermions; here we show that the same quartet of Weyl spinors, when coupled by a non-Hermitian but $\\cal{PT}$ symmetric mass matrix, describes a single relativistic particle that can have massless dispersion relation even though the mass matrix is non-zero.The ${\\cal PT}$-generalized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a non-interacting theory it violates ${\\cal P}$ and ${\\cal T}$ individually. The relativistic wave equations are reformulated as canonical fermionic field theories to facilitate the study of interactions, and are shown to maintain many of the canonical structures from Hermitian field theory, but with new and interesting new possibilities permitted by the non-hermiticity parameter $m_2$.

Katherine Jones-Smith; Harsh Mathur

2009-08-28

400

Quantum mechanics and low energy nucleon dynamics  

E-print Network

We discuss the problem of consistency of quantum mechanics as applied to low energy nucleon dynamics with the symmetries of QCD. It is shown that the dynamics consistent with these symmetries is not governed by the Schrodinger equation. We present a new way to formulate the effective theory of nuclear forces as an inevitable consequence of the basic principles of quantum mechanics and the symmetries of strong interactions. We show that being formulated in this way the effective theory of nuclear forces can be put on the same firm theoretical grounds as the quantum mechanics of atomic phenomena. In this case the effective theory allows one to describe with a given accuracy not only two-nucleon scattering, but also the evolution of nucleon systems, and places the constraints on the off-shell behavior of the two-nucleon interaction. In this way we predict the off-shell behavior of the S wave two-nucleon T-matrix at very low energies when the pionless theory is applicable. Further extensions and applications of this approach are discussed.

Renat Kh. Gainutdinov; Aigul A. Mutygullina

2003-04-03

401

Hunting for Snarks in Quantum Mechanics  

SciTech Connect

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

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

2009-12-08

402

Hunting for Snarks in Quantum Mechanics  

NASA Astrophysics Data System (ADS)

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

Hestenes, David

2009-12-01

403

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

E-print Network

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

Casey Blood

2010-09-23

404

FIG. 1: Size-dependent color emission of quantum dots. This is a purely quantum mechanical FIG. 2: Size-dependent color emission of quantum dots. This is a purely quantum mechanical  

E-print Network

FIG. 1: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect. FIG. 2: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect. 1 #12;FIG. 3: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect

Nielsen, Steven O.

405

Pseudo-random unitary operators for quantum information processing.  

PubMed

In close analogy to the fundamental role of random numbers in classical information theory, random operators are a basic component of quantum information theory. Unfortunately, the implementation of random unitary operators on a quantum processor is exponentially hard. Here we introduce a method for generating pseudo-random unitary operators that can reproduce those statistical properties of random unitary operators most relevant to quantum information tasks. This method requires exponentially fewer resources, and hence enables the practical application of random unitary operators in quantum communication and information processing protocols. Using a nuclear magnetic resonance quantum processor, we were able to realize pseudorandom unitary operators that reproduce the expected random distribution of matrix elements. PMID:14684815

Emerson, Joseph; Weinstein, Yaakov S; Saraceno, Marcos; Lloyd, Seth; Cory, David G

2003-12-19

406

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

E-print Network

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

H. Nikolic

2006-10-12

407

Probabilistic Quantum Logic Operations Using Polarizing Beam Splitters  

E-print Network

It has previously been shown that probabilistic quantum logic operations can 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 can be combined to implement a controlled-NOT (CNOT) gate. All of these gates can be constructed using polarizing beam splitters that completely transmit one state of polarization and totally reflect the orthogonal state of polarization, which allows a simple explanation of each operation. We also describe a polarizing beam splitter implementation of a CNOT gate that is closely analogous to the quantum teleportation technique previously suggested by Gottesman and Chuang [Nature 402, p.390 (1999)]. Finally, our approach has the interesting feature that it makes practical use of a quantum-eraser technique.

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

2001-07-18

408

Combining semiclassical time evolution and quantum Boltzmann operator to evaluate reactive flux correlation function for thermal rate  

E-print Network

ARTICLES Combining semiclassical time evolution and quantum Boltzmann operator to evaluate reactive representation IVR provides a way for including quantum effects into classical molecular dynamics simulations to describe any quantum mechanical aspects of the dynamics. There has thus been a recent revival of interest

Miller, William H.

409

Microscopic models of quantum jump super-operators  

E-print Network

We discuss the quantum jump operation in an open system, and show that jump super-operators related to a system under measurement can be derived from the interaction of that system with a quantum measurement apparatus. We give two examples for the interaction of a monochromatic electromagnetic field in a cavity (the system) with 2-level atoms and with a harmonic oscillator (representing two different kinds of detectors). We show that derived quantum jump super-operators have `nonlinear' form which depends on assumptions made about the interaction between the system and the detector. A continuous transition to the standard Srinivas--Davies form of the quantum jump super-operatoris shown.

A. V. Dodonov; S. S. Mizrahi; V. V. Dodonov

2005-06-15

410

Attosecond delays in photoionization: time and quantum mechanics  

NASA Astrophysics Data System (ADS)

This article addresses topics regarding time measurements performed on quantum systems. The motivation is linked to the advent of ‘attophysics’ which makes feasible to follow the motion of electrons in atoms and molecules, with time resolution at the attosecond (1 as = 10?18 s) level, i.e. at the natural scale for electronic processes in these systems. In this context, attosecond ‘time-delays’ have been recently measured in experiments on photoionization and the question arises if such advances could cast a new light on the still active discussion on the status of the time variable in quantum mechanics. One issue still debatable is how to decide whether one can define a quantum time operator with eigenvalues associated to measurable ‘time-delays’, or time is a parameter, as it is implicit in the Newtonian classical mechanics. One objective of this paper is to investigate if the recent attophysics-based measurements could shed light on this parameter–operator conundrum. To this end, we present here the main features of the theory background, followed by an analysis of the experimental schemes that have been used to evidence attosecond ‘time-delays’ in photoionization. Our conclusion is that these results reinforce the view that time is a parameter which cannot be defined without reference to classical mechanics.

Maquet, Alfred; Caillat, Jérémie; Taïeb, Richard

2014-10-01

411

A quantum key distribution system operating at gigahertz clock rates  

Microsoft Academic Search

A fiber-optic based quantum key distribution system, operating at a wavelength of 850 nm, has been developed capable of operating up to a clock frequency of 1 GHz, creating significantly increased key exchange rates

K. J. Gordon; V. Fernandez; G. S. Buller; P. D. Townsend; S. D. Cova; S. Tisa

2004-01-01

412

Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime  

E-print Network

In spacetimes admitting Yano tensors the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank two, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors.

Marco Cariglia

2003-05-17

413

Quantum mechanics of Yano tensors: Dirac equation in curved spacetime  

NASA Astrophysics Data System (ADS)

In spacetimes admitting Yano tensors, the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank 2, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors.

Cariglia, Marco

2004-02-01

414

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

415

Finite quantum mechanical model for the stock market  

E-print Network

The price of a given stock is exactly known only at the time of sale when the stock is between the traders. If we know the price (owner) then we have no information on the owner (price). A more general description including cases when we have partial information on both price and ownership is obtained by using the quantum mechanics methods. The relation price-ownership is similar to the relation position-momentum. Our approach is based on the mathematical formalism used in the case of quantum systems with finite-dimensional Hilbert space. The linear operator corresponding to the ownership is obtained from the linear operator corresponding to the price by using the finite Fourier transform. In our idealized model, the Schrodinger type equation describing the time evolution of the stock price is solved numerically.

Liviu-Adrian Cotfas

2012-08-30

416

Quantum mechanics with coordinate dependent noncommutativity  

SciTech Connect

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

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

2013-11-15

417

Surveying Studentsâ Understanding of Quantum Mechanics  

NSDL National Science Digital Library

Development of research-based multiple-choice tests about quantum mechanics is important for assessing studentsâ difficulties and for evaluating curricula and pedagogies that strive to reduce the difficulties. We explore the difficulties that the undergraduate and graduate students have with non-relativistic quantum mechanics of one particle in one spatial dimension. We developed a research-based conceptual multiple-choice survey that targets these issues to obtain information about the common difficulties and administered it to more than a hundred students from seven different institutions. The issues targeted in the survey include the set of possible wavefunctions, bound and scattering states, quantum measurement, expectation values, the role of the Hamiltonian, time-dependence of wavefunction and time-dependence of expectation value. We find that the advanced undergraduate and graduate students have many common difficulties with these concepts and that research-based tutorials and peer-instruction tools can significantly reduce these difficulties. The survey can be administered to assess the effectiveness of various intructional strategies.

Singh, Chandralekha; Zhu, Guangtian

2010-12-31

418

Path integration in relativistic quantum mechanics  

E-print Network

The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple relativistic action proportional to its proper time. This propagator is nonvanishing outside the light cone, implying that spacelike trajectories must be included in the path integral. The propagator matches the WKB approximation to the corresponding configuration-space path integral far from the light cone; outside the light cone that approximation consists of the contribution from a single spacelike geodesic. This propagator also has the unusual property that its short-time limit does not coincide with the WKB approximation, making the construction of a concrete skeletonized version of the path integral more complicated than in nonrelativistic theory.

Ian H. Redmount; Wai-Mo Suen

1992-10-28

419

Quantum Mechanics of a Rotating Billiard  

E-print Network

Integrability of a square billiard is spontaneously broken as it rotates about one of its corners. The system becomes quasi-integrable where the invariant tori are broken with respect to a certain parameter, $\\lambda = 2E/\\omega^{2}$ where E is the energy of the particle inside the billiard and $\\omega$ is the angular frequency of rotation of billiard. We study the system classically and quantum mechanically in view of obtaining a correspondence in the two descriptions. Classical phase space in Poincar\\'{e} surface of section shows transition from regular to chaotic motion as the parameter $\\lambda$ is decreased. In the Quantum counterpart, the spectral statistics shows a transition from Poisson to Wigner distribution as the system turns chaotic with decrease in $\\lambda$. The wavefunction statistics however show breakdown of time-reversal symmetry as $\\lambda$ decreases.

Nandan Jha; Sudhir R. Jain

2014-06-12

420

Quantum Mechanics à la Langevin and Supersymmetry  

E-print Network

We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under ${\\mathcal N}=1$ SUSY, but can be obtained from a, manifestly, supersymmetric expression, upon fixing a local fermionic symmetry, called $\\kappa-$symmetry. The kinetic term for the fermions is a total derivative and can contribute only on the boundaries. We define combinations that scale appropriately, as the lattice spacing is taken to zero and the lattice size to infinity and provide evidence, by numerical simulations, that the correlation functions of the auxiliary field do satisfy Wick's theorem. We show, in particular, that simulations can be carried out using a purely bosonic action. The physical import is that the classical trajectory, $\\phi(\\tau)$, becomes a (chiral) superfield, $(\\phi(\\tau),\\psi_{\\alpha}(\\tau),F(\\tau))$, when quantum fluctuations are taken into account.

S. Nicolis

2013-11-14

421

Mechanics and Planning of Manipulator Pushing Operations  

Microsoft Academic Search

Pushing is an essential component of many manipulator operations. This paper presents a theoretical exploration of the mechanics of pushing and demonstrates application of the theory to analysis and synthesis of robotic manipulator oper ations.

Matthew T. Mason

1986-01-01

422

5.74 Introductory Quantum Mechanics II, Spring 2005  

E-print Network

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

Tokmakoff, Andrei

423

5.74 Introductory Quantum Mechanics II, Spring 2007  

E-print Network

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

Tokmakoff, Andrei

424

5.74 Introductory Quantum Mechanics II, Spring 2003  

E-print Network

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

Tokmakoff, Andrei

425

An Investigation on the Basic Conceptual Foundations of Quantum Mechanics by Using the Clifford Algebra  

E-print Network

We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the and Clifford algebras. This last algebra gives proof of the von Neumann basic postulates on the quantum measurement explaining thus in an algebraic manner the wave function collapse postulated in standard quantum theory. In this manner we reach the objective to expose a self-consistent version of quantum mechanics. We give proof of the quantum like Heisenberg uncertainty relations, the phenomenon of quantum Mach Zender interference as well as quantum collapse in some cases of physical interest We also discuss the problem of time evolution of quantum systems as well as the changes in space location. We also give demonstration of the Kocken-Specher theorem, and also we give an algebraic formulation and explanation of the EPR . By using the same approach we also derive Bell inequalities. Our formulation is strongly based on the use of idempotents that are contained in Clifford algebra. Their counterpart in quantum mechanics is represented by the projection operators that are interpreted as logical statements, following the basic von Neumann results. Using the Clifford algebra we are able to invert such result. According to the results previously obtained by Orlov in 1994, we are able to give proof that quantum mechanics derives from logic. We show that indeterminism and quantum interference have their origin in the logic.

Elio Conte

2011-06-14

426

Quantum mechanism helps agents combat "bad" social choice rules  

E-print Network

Quantum strategies have been successfully applied to game theory for years. However, as a reverse problem of game theory, the theory of mechanism design is ignored by physicists. In this paper, the theory of mechanism design is generalized to a quantum domain. The main result is that by virtue of a quantum mechanism, agents who satisfy a certain condition can combat "bad" social choice rules instead of being restricted by the traditional mechanism design theory.

Haoyang Wu

2010-02-23

427

Clocks And Dynamics In Quantum Mechanics  

E-print Network

We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of quantum uncertainty lies with the absence of infinities or infinitesimals in observational data and that our concept of time derives from observing changing data (events). We argue that the fundamentally important content of the Superposition Principle is not the "probability amplitude" of posterior state observation but future state availability conditional only on prior information. Since event detection also implies posterior conditions (e.g. a specific type of detectable event occurred) as well as prior conditions, the probabilities of detected outcomes are also conditional on properties of the posterior properties of the observation. Such posterior conditions cannot affect the prior state availabilities and this implies violation of counter-factual definiteness. A component of a quantum system may be chosen to represent a clock and changes in other components can then be expected to be correlated with clocks with which they are entangled. Instead of traditional time-dependent equations of motion we provide a specific mechanism whereby evolution of data is instead quasi-causally related to the relative \\availability\\ of states and equations of motion are expressed in terms of quantized clock variables. We also suggest that time-reversal symmetry-breaking in weak interactions is an artifice of a conventional choice of co-ordinate time-function. Analysis of a "free" particle suggests that conventional co-ordinate space-time emerges from how we measure the separation of objects and events.

Michael York

2014-05-05

428

Vertex operators and 2-representations of quantum affine algebras  

E-print Network

We construct 2-representations of quantum affine algebras from 2-representations of quantum Heisenberg algebras. The main tool in this construction are categorical vertex operators, which are certain complexes in a Heisenberg 2-representation that recover vertex operators after passing to the Grothendieck group. As an application we categorify the Frenkel-Kac-Segal homogeneous realization of the basic representation of (simply laced) quantum affine algebras. This gives rise to categorical actions of quantum affine (and toroidal) algebras on derived categories of coherent sheaves on Hilbert schemes of points of ALE spaces.

Cautis, Sabin

2011-01-01

429

Protected quantum computing: interleaving gate operations with dynamical decoupling sequences.  

PubMed

Implementing precise operations on quantum systems is one of the biggest challenges for building quantum devices in a noisy environment. Dynamical decoupling attenuates the destructive effect of the environmental noise, but so far, it has been used primarily in the context of quantum memories. Here, we experimentally demonstrate a general scheme for combining dynamical decoupling with quantum logical gate operations using the example of an electron-spin qubit of a single nitrogen-vacancy center in diamond. We achieve process fidelities >98% for gate times that are 2 orders of magnitude longer than the unprotected dephasing time T2. PMID:24580577

Zhang, Jingfu; Souza, Alexandre M; Brandao, Frederico Dias; Suter, Dieter

2014-02-01

430

Operator equality on entropy production in quantum Markovian master equations  

E-print Network

An operator equality on the entropy production for general quantum Markovian master equations is derived without resorting quantum stochastic trajectory and priori quantum definition of entropy production. We find that, the equality can be still interpreted as a consequence of time-reversal asymmetry of the nonequilibrium processes of the systems. In contrast with the classical case, however, the first order expansion of the equality does not directly related to the mean entropy production, which arises from noncommute property of operators in quantum physics.

Fei Liu

2012-10-22

431

Renormalization group invariance of quantum mechanics  

NASA Astrophysics Data System (ADS)

We propose a framework to renormalize the nonrelativistic quantum mechanics with arbitrary singular interactions. The scattering equation is written to have one or more subtraction in the kernel at a given energy scale. The scattering amplitude is the solution of a nth order derivative equation in respect to the renormalization scale, which is the nonrelativistic counterpart of the Callan-Symanzik formalism. Scaled running potentials for the subtracted equations keep the physics invariant for a sliding subtraction point. An example of a singular potential, that requires more than one subtraction to renormalize the theory is shown.

Frederico, T.; Delfino, A.; Tomio, L.

2000-05-01

432

Hidden geometric character of relativistic quantum mechanics  

SciTech Connect

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

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

2007-01-15

433

Vector Models in PT Quantum Mechanics  

E-print Network

We present two examples of non-Hermitian Hamiltonians which consist of an unperturbed part plus a perturbation that behaves like a vector, in the framework of PT quantum mechanics. The first example is a generalization of the recent work by Bender and Kalveks, wherein the E2 algebra was examined; here we consider the E3 algebra representing a particle on a sphere, and identify the critical value of coupling constant which marks the transition from real to imaginary eigenvalues. Next we analyze a model with SO(3) symmetry, and in the process extend the application of the Wigner-Eckart theorem to a non-Hermitian setting.

Katherine Jones-Smith; Rudolph Kalveks

2013-04-21

434

Euclidean Quantum Mechanics and Universal Nonlinear Filtering  

E-print Network

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

Bhashyam Balaji

2008-09-25

435

Wigner Measures in Noncommutative Quantum Mechanics  

E-print Network

We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner measure, for a Gaussian to be a noncommutative Wigner measure, and derive certain properties of the marginal distributions which are not shared by ordinary Wigner measures. Moreover, we derive the Robertson-Schr\\"odinger uncertainty principle. Finally, we show explicitly how the set of noncommutative Wigner measures relates to the sets of Liouville and (commutative) Wigner measures.

C. Bastos; N. C. Dias; J. N. Prata

2009-07-25

436

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

437

The metaphysics of quantum mechanics: Modal interpretations  

NASA Astrophysics Data System (ADS)

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

Gluck, Stuart Murray

2004-11-01

438

Bhomian Mechanics vs. Standard Quantum Mechanics: a Difference in Experimental Predictions  

E-print Network

Standard Quantum Mechanics (QM) predicts an anti-intuitive fenomenon here referred to as "quantum autoscattering", which is excluded by Bhomian Mechanics. The scheme of a gedanken experiment testing the QM prediction is briefly discussed.

Artur Szczepanski

2010-02-08

439

Accessing quantum secrets via local operations and classical communication  

NASA Astrophysics Data System (ADS)

Quantum secret-sharing and quantum error-correction schemes rely on multipartite decoding protocols, yet the nonlocal operations involved are challenging and sometimes infeasible. Here we construct a quantum secret-sharing protocol with a reduced number of quantum communication channels between the players. We introduce a scheme based on embedding a classical linear code into a quantum error-correcting code and then mapping the latter to a quantum secret-sharing protocol. In contrast to the Calderbank-Shor-Steane construction, we do not impose any restriction on the classical code; our protocol works with any arbitrary linear code. Our work paves the way towards the more general problem of simplifying the decoding of quantum error-correcting codes.

Gheorghiu, Vlad; Sanders, Barry C.

2013-08-01

440

Smallest Relational Mechanics Model of Quantum Cosmology  

E-print Network

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

Edward Anderson

2009-08-13

441

Quantum Mechanical Study of Nanoscale MOSFET  

NASA Technical Reports Server (NTRS)

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

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

2001-01-01

442

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

443

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

444

A note on the Landauer principle in quantum statistical mechanics  

E-print Network

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

Boyer, Edmond

445

LETTER TO THE EDITOR: Quantum black holes from null expansion operators  

NASA Astrophysics Data System (ADS)

Using a recently developed quantization of spherically symmetric gravity coupled to a scalar field, we give a construction of null expansion operators that allow a definition of general, fully dynamical quantum black holes. These operators capture the intuitive idea that classical black holes are defined by the presence of trapped surfaces, that is, surfaces from which light cannot escape outward. They thus provide a mechanism for classifying quantum states of the system into those that describe quantum black holes and those that do not. We find that quantum horizons fluctuate, confirming long-held heuristic expectations. We also give explicit examples of quantum black hole states. The work sets a framework for addressing the puzzles of black hole physics in a fully quantized dynamical setting.

Husain, Viqar; Winkler, Oliver

2005-11-01

446

Surveying Instructors' Attitudes and Approaches to Teaching Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Understanding instructors' attitudes and approaches to teaching quantum mechanics can be helpful in developing research-based learning tools. Here we discuss the findings from a survey in which 13 instructors reflected on issues related to quantum mechanics teaching. Topics included opinions about the goals of a quantum mechanics course, general challenges in teaching the subject, students' preparation for the course, comparison between their own learning of quantum mechanics vs. how they teach it and the extent to which contemporary topics are incorporated into the syllabus.

Siddiqui, Shabnam; Singh, Chandralekha

2010-10-01

447

Surveying Instructorsâ Attitudes and Approaches to Teaching Quantum Mechanics  

NSDL National Science Digital Library

Understanding instructorsâ attitudes and approaches to teaching quantum mechanics can be helpful in developing research-based learning tools. Here we discuss the findings from a survey in which 13 instructors reflected on issues related to quantum mechanics teaching. Topics included opinions about the goals of a quantum mechanics course, general challenges in teaching the subject, studentsâ preparation for the course, comparison between their own learning of quantum mechanics vs. how they teach it and the extent to which contemporary topics are incorporated into the syllabus.

Siddiqui, Shabnam; Singh, Chandralekha

2010-12-31

448

THE ROLE OF QUANTUM MECHANICS IN NEUTRINO FACTORIES.  

SciTech Connect

A compilation is made of the various ways in which quantum phenomena enter into the design and operation of a neutrino factory. They include production of pions, decay of pions into muons, ionization energy loss of muons in material, scattering and energy straggling of muons in material, polarization of muons, and the decay of muons into neutrinos, and the radiation effect of neutrinos. For each process formulas are presented which cover the basic mechanism. A discussion is presented of the areas of uncertainty and of the experiments, underway and proposed, which will reduce the uncertainty to an acceptable level.

GALLARDO,J.C.; SESSLER,A.M.; WURTELE,J.

2000-12-06

449

Study of quantum spin correlations of relativistic electron pairs - Testing nonlocality of relativistic quantum mechanics  

SciTech Connect

The Polish-German project QUEST aims at studying relativistic quantum spin correlations of the Einstein-Rosen-Podolsky-Bohm type, through measurement of the correlation function and the corresponding probabilities for relativistic electron pairs. The results will be compared to theoretical predictions obtained by us within the framework of relativistic quantum mechanics, based on assumptions regarding the form of the relativistic spin operator. Agreement or divergence will be interpreted in the context of non-uniqueness of the relativistic spin operator in quantum mechanics as well as dependence of the correlation function on the choice of observables representing the spin. Pairs of correlated electrons will originate from the Mo/ller scattering of polarized 15 MeV electrons provided by the superconducting Darmstadt electron linear accelerator S-DALINAC, TU Darmstadt, incident on a Be target. Spin projections will be determined using the Mott polarimetry technique. Measurements (starting 2013) are planned for longitudinal and transverse beam polarizations and different orientations of the beam polarization vector w.r.t. the Mo/ller scattering plane. This is the first project to study relativistic spin correlations for particles with mass.

Bodek, K.; Rozp?dzik, D.; Zejma, J. [Jagiellonian University, Faculty of Physics, Astronomy and Applied Informatics, Reymonta 4, 30059 Kraków (Poland); Caban, P.; Rembieli?ski, J.; W?odarczyk, M. [University of ?ód?, Faculty of Physics and Applied Informatics, Pomorska 149/153, 90236 ?ód? (Poland); Ciborowski, J. [University of Warsaw, Faculty of Physics, Hoza 69, 00681 Warsaw (Poland); Enders, J.; Köhler, A. [Technische Universität Darmstadt, Institut für Kernphysik, Schlossgartenstraße 9, 64289 Darmstadt (Germany); Kozela, A. [Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31342 Kraków (Poland)

2013-11-07

450

Quantum-mechanical description of Lense-Thirring effect for relativistic scalar particles  

E-print Network

Exact expression for the Foldy-Wouthuysen Hamiltonian of scalar particles is used for a quantum-mechanical description of the relativistic Lense-Thirring effect. The exact evolution of the angular momentum operator in the Kerr field approximated by a spatially isotropic metric is found. The quantum-mechanical description of the full Lense-Thirring effect based on the Laplace-Runge-Lenz vector is given in the nonrelativistic and weak-field approximation. Relativistic quantum-mechanical equations for the velocity and acceleration operators are obtained. The equation for the acceleration defines the Coriolis-like and centrifugal-like accelerations and presents the quantum-mechanical description of the frame-dragging effect.

Alexander J. Silenko

2014-08-10

451

Fundamental phenomena of quantum mechanics explored with neutron interferometers  

E-print Network

Ongoing fascination with quantum mechanics keeps driving the development of the wide field of quantum-optics, including its neutron-optics branch. Application of neutron-optical methods and, especially, neutron interferometry and polarimetry has a long-standing tradition for experimental investigations of fundamental quantum phenomena. We give an overview of related experimental efforts made in recent years.

J. Klepp; S. Sponar; Y. Hasegawa

2014-07-09

452

On The Relation of Weyl Geometry and Bohmian Quantum Mechanics  

E-print Network

It is shown that the recently geometric formulation of quantum mechanics implies the use of Weyl geometry. It is discussed that the natural framework for both gravity and quantum is Weyl geometry. At the end a Weyl invariant theory is built, and it is shown that both gravity and quantum are present at the level of equations of motion.

Fatimah Shojai; Ali Shojai

2003-06-22

453

Symmetric angular momentum coupling, the quantum volume operator and the 7-spin network: a computational perspective  

E-print Network

A unified vision of the symmetric coupling of angular momenta and of the quantum mechanical volume operator is illustrated. The focus is on the quantum mechanical angular momentum theory of Wigner's 6j symbols and on the volume operator of the symmetric coupling in spin network approaches: here, crucial to our presentation are an appreciation of the role of the Racah sum rule and the simplification arising from the use of Regge symmetry. The projective geometry approach permits the introduction of a symmetric representation of a network of seven spins or angular momenta. Results of extensive computational investigations are summarized, presented and briefly discussed.

Marinelli, Dimitri; Aquilanti, Vincenzo; Anderson, Roger W; Bitencourt, Ana Carla P; Ragni, Mirco

2014-01-01

454

Symmetric angular momentum coupling, the quantum volume operator and the 7-spin network: a computational perspective  

E-print Network

A unified vision of the symmetric coupling of angular momenta and of the quantum mechanical volume operator is illustrated. The focus is on the quantum mechanical angular momentum theory of Wigner's 6j symbols and on the volume operator of the symmetric coupling in spin network approaches: here, crucial to our presentation are an appreciation of the role of the Racah sum rule and the simplification arising from the use of Regge symmetry. The projective geometry approach permits the introduction of a symmetric representation of a network of seven spins or angular momenta. Results of extensive computational investigations are summarized, presented and briefly discussed.

Dimitri Marinelli; Annalisa Marzuoli; Vincenzo Aquilanti; Roger W. Anderson; Ana Carla P. Bitencourt; Mirco Ragni

2014-10-04

455

Tampering detection system using quantum-mechanical systems  

DOEpatents

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

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

2011-12-13

456

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

457

On geometric aspects of topological quantum mechanics  

NASA Astrophysics Data System (ADS)

We construct a Chern-Simons gauge theory for dg Lie and L-infinity algebras on any one-dimensional manifold and quantize this theory using the Batalin-Vilkovisky formalism and Costello's renormalization techniques. Koszul duality and derived geometry allow us to encode topological quantum mechanics, a nonlinear sigma model of maps from a 1-manifold into a cotangent bundle T* X, as such a Chern-Simons theory. Our main result is that the partition function of this theory is naturally identified with the A genus of X. From the perspective of derived geometry, our quantization constructs a volume form on the derived loop space which can be identified with the A class.

Grady, Ryan E.

458

Quantum mechanical calculations to chemical accuracy  

NASA Technical Reports Server (NTRS)

The accuracy of current molecular-structure calculations is illustrated with examples of quantum mechanical solutions for chemical problems. Two approaches are considered: (1) the coupled-cluster singles and doubles (CCSD) with a perturbational estimate of the contribution of connected triple excitations, or CCDS(T); and (2) the multireference configuration-interaction (MRCI) approach to the correlation problem. The MRCI approach gains greater applicability by means of size-extensive modifications such as the averaged-coupled pair functional approach. The examples of solutions to chemical problems include those for C-H bond energies, the vibrational frequencies of O3, identifying the ground state of Al2 and Si2, and the Lewis-Rayleigh afterglow and the Hermann IR system of N2. Accurate molecular-wave functions can be derived from a combination of basis-set saturation studies and full configuration-interaction calculations.

Bauschlicher, Charles W., Jr.; Langhoff, Stephen R.

1991-01-01

459

Supersymmetric quantum mechanics and Painlevé equations  

NASA Astrophysics Data System (ADS)

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

Bermudez, David; Fernández C., David J.

2014-01-01

460

A causal net approach to relativistic quantum mechanics  

NASA Astrophysics Data System (ADS)

In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on Reichenbach-like conjunctive forks in proper time we can exactly derive the 1+1 dimension Dirac equation for a relativistic fermion and correctly model quantum mechanical statistics. Symmetries of the net provide various quantum mechanical effects such as quantum uncertainty and wavefunction, phase, spin, negative energy states and the effect of a potential. The causal net can be embedded in 3+1 dimensions and is consistent with the conventional Dirac equation. In the low velocity limit the causal net approximates to the Schrodinger equation and Pauli equation for an electromagnetic field. Extending to different momentum states the net is compatible with the Feynman path integral approach to quantum mechanics that allows calculation of well known quantum phenomena such as diffraction.

Bateson, R. D.

2012-05-01

461

A Causal Net Approach to Relativistic Quantum Mechanics  

E-print Network

In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on Reichenbach-like conjunctive forks in proper time we can exactly derive the 1+1 dimension Dirac equation for a relativistic fermion and correctly model quantum mechanical statistics. Symmetries of the net provide various quantum mechanical effects such as quantum uncertainty and wavefunction, phase, spin, negative energy states and the effect of a potential. The causal net can be embedded in 3+1 dimensions and is consistent with the conventional Dirac equation. In the low velocity limit the causal net approximates to the Schrodinger equation and Pauli equation for an electromagnetic field. Extending to different momentum states the net is compatible with the Feynman path integral approach to quantum mechanics that allows calculation of well known quantum phenomena such as diffraction.

R. D. Bateson

2010-07-14

462

Quantum mechanics, matter waves, and moving clocks  

E-print Network

This paper is divided into three parts. In the first (section 1), we demonstrate that all of quantum mechanics can be derived from the fundamental property that the propagation of a matter wave packet is described by the same gravitational and kinematic time dilation that applies to a clock. We will do so in several steps, first deriving the Schroedinger equation for a nonrelativistic particle without spin in a weak gravitational potential, and eventually the Dirac equation in curved space-time describing the propagation of a relativistic particle with spin in strong gravity. In the second part (sections 2-4), we present interesting consequences of the above quantum mechanics: that it is possible to use wave packets as a reference for a clock, to test general relativity, and to realize a mass standard based on a proposed redefinition of the international system of units, wherein the Planck constant would be assigned a fixed value. The clock achieved an absolute accuracy of 4 parts per billion (ppb). The experiment yields the fine structure constant $\\alpha = 7.297\\,352\\,589(15) \\times 10^{-3}$ with 2.0 ppb accuracy. We present improvements that have reduced the leading systematic error about 8-fold and improved the statistical uncertainty to 0.33 ppb in 6 hours of integration time, referred to $\\alpha$. In the third part (sections 5-7), we present possible future experiments with atom interferometry: A gravitational Aharonov-Bohm experiment and its application as a measurement of Newton's gravitational constant, antimatter interferometry, interferometry with charged particles, and interferometry in space. We will give a review of previously published material when appropriate, but will focus on new aspects that haven't been published before.

Holger Mueller

2013-12-23

463

Two-particle wave function as an integral operator and the random field approach to quantum correlations  

NASA Astrophysics Data System (ADS)

We propose a new interpretation of the wave function ? (x, y) of a two-particle quantum system, interpreting it not as an element of the functional space L 2 of square-integrable functions, i.e., as a vector, but as the kernel of an integral (Hilbert-Schmidt) operator. The first part of the paper is devoted to expressing quantum averages including the correlations in two-particle systems using the wave-function operator. This is a new mathematical representation in the framework of conventional quantum mechanics. But the new interpretation of the wave function not only generates a new mathematical formalism for quantum mechanics but also allows going beyond quantum mechanics, i.e., representing quantum correlations (including those in entangled systems) as correlations of (Gaussian) random fields.

Khrennikov, A. Yu.

2010-09-01

464

Creating, maintaining, and breaking of quantum entanglement in quantum operations  

NASA Astrophysics Data System (ADS)

We study the evolution of entanglement in quantum gates in terms of Choi-Jamiolkowski relative states negativity. SQiSW (generated by XY-interaction), CNOT and CZ gates are considered in ideal case and under amplitude and phase relaxation. In addition, we consider an important task of analyzing entanglement of "pure" noise, which is obtained by deducting an ideal gate from a noisy one.

Bogdanov, Yu. I.; Chernyavskiy, A. Yu.; Holevo, A. S.; Lukichev, V. F.; Orlikovsky, Alexander A.; Bantysh, B. I.

2013-01-01

465

Biological applications of hybrid quantum mechanics/molecular mechanics calculation.  

PubMed

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

Kang, Jiyoung; Hagiwara, Yohsuke; Tateno, Masaru

2012-01-01

466

Sheaf Logic, Quantum Set Theory and the Interpretation of Quantum Mechanics  

E-print Network

Based on the Sheaf Logic approach to set theoretic forcing, a hierarchy of Quantum Variable Sets is constructed which generalizes and simplifies the analogous construction developed by Takeuti on boolean valued models of set theory. Over this model two alternative proofs of Takeuti's correspondence, between self adjoint operators and the real numbers of the model, are given. This approach results to be more constructive showing a direct relation with the Gelfand representation theorem, revealing also the importance of these results with respect to the interpretation of Quantum Mechanics in close connection with the Deutsch-Everett multiversal interpretation. Finally, it is shown how in this context the notion of genericity and the corresponding generic model theorem can help to explain the emergence of classicality also in connection with the Deutsch- Everett perspective.

J. Benavides

2011-11-11

467

Quantum Sufficiency in the Operator Algebra Framework  

NASA Astrophysics Data System (ADS)

The paper is devoted to the investigation of the notion of sufficiency in quantum statistics. Three kinds of this notion are considered: plain sufficiency (called simply: sufficiency), Petz's sufficiency, and Umegaki's sufficiency. The problem of the existence and structure of the minimal sufficient subalgebra is analyzed in some detail, conditions yielding equivalence of the three modes of sufficiency are considered, and quantum Basu's theorem is obtained. Moreover, it is shown that an interesting "factorization theorem" of Jen?ová and Petz needs some corrections to hold true.

?uczak, Andrzej

2014-10-01

468

Physlets and Open Source Physics for Quantum Mechanics: Visualizing Quantum-mechanical Revivals  

NSDL National Science Digital Library

In this paper we describe our five-year effort to create interactive curricular material for upper-level quantum mechanics courses. This material uses both Physlets and newly created Open Source Physics applets and applications to make the teaching of quantum mechanics visual and interactive. These exercises and tools address both quantitative and conceptual difficulties experienced by many students. Because the materials are Web based, they are extremely flexible and are appropriate for use with various pedagogies, such as the Just-in-Time Teaching technique. We briefly outline the features of Physlets and Open Source Physics programs and then describe our suite of Java programs that solve and visualize the problem of a wave packet in an infinite square well. The materials described in this paper can be found on the Open Source Physics Web site and on the MERLOT and ComPADRE digital libraries.

Belloni, Mario; Christian, Wolfgang

2011-02-01

469

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

470

The relation between quantum mechanics and higher brain functions: Lessons from quantum computation and  

E-print Network

of QM (the best we can make in non-relativistic atomic physics and quantum computation (Mermin 20031 The relation between quantum mechanics and higher brain functions: Lessons from quantum computation and neurobiology Christof Koch1,2 and Klaus Hepp1 April 2. 2007 1 Institute for Neuroinformatics

Koch, Christof

471

Algorithmic Information Theoretic Issues in Quantum Mechanics  

E-print Network

.1 The unpublished ideas of Sidney Coleman and Andrew Lesniewski210 6.2 Karl Svozil's invention of Quantum 248 6.6 Peter Gacs' quantum algorithmic entropy . . . . . . . . . . . . . 248 6.7 The algorithmic

472

Quantum mechanical reaction probabilities with a power series Green's function  

E-print Network

Quantum mechanical reaction probabilities with a power series Green's function Scott M. Auerbach for use in the calculation of quantum mechanical reaction probabilities. This is an iterative technique Green's function to the calculation of the cumulative reaction probability for the benchmark collinear H

Miller, William H.

473

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

474

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

475

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

476

Environment-Induced Decoherence in Noncommutative Quantum Mechanics  

E-print Network

We address the question of the appearence of ordinary quantum mechanics in the context of noncommutative quantum mechanics. We obtain the noncommutative extension of the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators. We consider the particular case of an Ohmic regime.

Joao Nuno Prata; Nuno Costa Dias

2006-12-02

477

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

478

Interactive Quantum Mechanics Exercises for Just-in-Time Teaching  

NSDL National Science Digital Library

This is a collection of online curricular material for a one-semester quantum mechanics course. It consists of interactive Java applets, Physlets, for interactive out-of-class exercises. These applets stress the visualization of quantum mechanical concepts for better student understanding. There are also illustrations suitable for both in-class and out-of-class use.

Belloni, Mario; Cain, Laurence; Christian, Wolfgang

2004-04-04

479

Quaternionic quantum mechanics allows non-local boxes  

E-print Network

We consider non-local properties of quanternionic quantum mechanics, in which the complex numbers are replaced by the quaternions as the underlying algebra. Specifically, we show that it is possible to construct a non-local box. This allows one to rule out quaternionic quantum mechanics using assumptions about communication complexity or information causality.

Matthew McKague

2009-11-09

480

Quantum Mechanical Determination of Rotational Energy Transfer Cross Sections  

Microsoft Academic Search

Studies of the quantum mechanical determination of rotationally inelastic molecular collision rates are reported. A unified derivation of the coupled equations of scattering is given for four different quantum mechanical approximations. A new method for integrating the resulting coupled equations is studied and tested on a realistic potential surface. This method differs from conventional methods by not requiring the construction

William Shepherd Borer

1991-01-01

481

Course Information Course: Quantum Mechanics III (Physics 918)  

E-print Network

1: Lecture notes from the instructor Text for Part 2: J.J. Sakurai, Advanced Quantum Mechanics of the quantum-mechanical perturbation theory and classical electrodynamics. For updating/ refreshing your (instructor's lecture notes), but not allowed to use any other notes. QUIZZES (in-class): 9/14, 10/3, 11/2, 11

Farritor, Shane

482

The bridge between classical and quantum mechanics from Fisher information  

E-print Network

Fisher information measures a disorder system, which is specified by a corresponding probability, the likelihood. In this article, we provide a bridge to connect classical and quantum mechanics by using Fisher information. Following the principle of minimum Fisher information, we describe the mechanism of quantum world from the Hamilton-Jacobi equation.

Tzu-Chao Hung

2014-07-31

483

Comparison of Quantum Mechanics and Molecular Mechanics Dimerization Energy Landscapes for Pairs of Ring-Containing Amino Acids in Proteins  

E-print Network

Comparison of Quantum Mechanics and Molecular Mechanics Dimerization Energy Landscapes for Pairs interactions. We also find a reasonable degree of correlation between the molecular mechanics energy landscapes, quantum mechanical calculations on small molecule models, and molecular mechanics potential decomposition

Morozov, Alexandre V.

484

Multiple-event probability in general-relativistic quantum mechanics: a discrete model  

E-print Network

We introduce a simple quantum mechanical model in which time and space are discrete and periodic. These features avoid the complications related to continuous-spectrum operators and infinite-norm states. The model provides a tool for discussing the probabilistic interpretation of generally-covariant quantum systems, without the confusion generated by spurious infinities. We use the model to illustrate the formalism of general-relativistic quantum mechanics, and to test the definition of multiple-event probability introduced in a companion paper. We consider a version of the model with unitary time-evolution and a version without unitary time-evolution

Mauricio Mondragon; Alejandro Perez; Carlo Rovelli

2007-04-30

485

Cloning in nonlinear Hamiltonian quantum and hybrid mechanics  

NASA Astrophysics Data System (ADS)

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

Arsenovi?, D.; Buri?, N.; Popovi?, D. B.; Radonji?, M.; Prvanovi?, S.

2014-10-01

486