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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

Tensor Operators in Noncommutative Quantum Mechanics

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

Amorim, Ricardo [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21945-970 Rio de Janeiro (Brazil)

2008-08-22

3

Tensor operators in noncommutative quantum mechanics.

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

Amorim, Ricardo

2008-08-22

4

Dirac Operator on Complex Manifolds and Supersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

We explore a simple N = 2 supersymmetric quantum mechanics (SQM) model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holomorphic derivative, such that the model realizes the twisted Dolbeault complex. The sum Q+\\bar Q can be interpreted as the Dirac operator: the standard Dirac operator if the manifold is Kähler and the Dirac operator involving certain particular extra torsions for a generic complex manifold. Focusing on the Kähler case, we give new simple physical proofs of the two mathematical facts: (i) the equivalence of the twisted Dirac and twisted Dolbeault complexes and (ii) the Atiyah-Singer theorem.

Ivanov, E. A.; Smilga, A. V.

2012-10-01

5

The modern tools of quantum mechanics. A tutorial on quantum states, measurements, and operations

NASA Astrophysics Data System (ADS)

We address the basic postulates of quantum mechanics and point out that they are formulated for a closed isolated system. Since we are mostly dealing with systems that interact or have interacted with the rest of the universe one may wonder whether a suitable modification is needed, or in order. This is indeed the case and this tutorial is devoted to review the modern tools of quantum mechanics, which are suitable to describe states, measurements, and operations of realistic, not isolated, systems. We underline the central role of the Born rule and and illustrate how the notion of density operator naturally emerges, together with the concept of purification of a mixed state. In reexamining the postulates of standard quantum measurement theory, we investigate how they may be formally generalized, going beyond the description in terms of selfadjoint operators and projective measurements, and how this leads to the introduction of generalized measurements, probability operator-valued measures (POVMs) and detection operators. We then state and prove the Naimark theorem, which elucidates the connections between generalized and standard measurements and illustrates how a generalized measurement may be physically implemented. The "impossibility" of a joint measurement of two non commuting observables is revisited and its canonical implementation as a generalized measurement is described in some details. The notion of generalized measurement is also used to point out the heuristic nature of the so-called Heisenberg principle. Finally, we address the basic properties, usually captured by the request of unitarity, that a map transforming quantum states into quantum states should satisfy to be physically admissible, and introduce the notion of complete positivity (CP). We then state and prove the Stinespring/Kraus-Choi-Sudarshan dilation theorem and elucidate the connections between the CP-maps description of quantum operations, together with their operator-sum representation, and the customary unitary description of quantum evolution. We also address transposition as an example of positive map which is not completely positive, and provide some examples of generalized measurements and quantum operations.

Paris, M. G. A.

2012-04-01

6

Feynman disentangling of noncommuting operators in quantum mechanics

Feynman’s disentangling theorem is applied to noncommuting operators in the problem of quantum parametric oscillator, which\\u000a is mathematically equivalent to the problem of SU(1, 1) pseudospin rotation. The number states of the oscillator correspond to unitary irreducible representations of the SU(1, 1) group. Feynman disentangling is combined with group-theoretic arguments to obtain simple analytical formulas for the\\u000a matrix elements and

V. S. Popov

2005-01-01

7

The structure of Poincaré covariant tensor operators in quantum mechanical models

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

Wayne N. Polyzou; W. H. Klink

1988-01-01

8

Supersymmetric Quantum Mechanics and Euclidean-Dirac Operator with Complexified Quaternions

NASA Astrophysics Data System (ADS)

We propose an alternative formulation of the supersymmetric quantum mechanics and Euclidean Dirac and Dirac-Yang-Mills (DYM) operators in terms of complexified quaternions. 4×4 matrix representations of the complexified quaternions are used to express the Euclidean-Dirac operator and Yang-Mills gauge field.

Tani?li, Murat; Kansu, Mustafa Emre; Demir, Süleyman

2013-03-01

9

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

NSDL National Science Digital Library

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

Michielsen, Kristel; De Raedt, Hans

2004-03-04

11

NASA Astrophysics Data System (ADS)

We show that the quantum-mechanical fundamental representations, say, the coordinate representation, the coherent state representation, the Fan-Klauder entangled state representation can be recast into s-ordering operator expansion, which is elegant in form and has many applications in deriving new operator identities. This demonstrates that Dirac's symbolic method can be merged into Newton-Leibniz integration theory in a broad way.

Fan, HongYi; Xu, YeJun; Yuan, HongChun

2011-12-01

12

The structure of Poincaré covariant tensor operators in quantum mechanical models

NASA Astrophysics Data System (ADS)

The structure of operators that transform covariantly in Poincaré invariant quantum mechanical models is analyzed. These operators are shown to have an interaction dependence that comes from the geometry of the Poincaré group. The operators can be expressed in terms of matrix elements in a complete set of eigenstates of the mass and spin operators associated with the dynamical representation of the Poincaré group. The matrix elements are factored into geometrical coefficients (Clebsch-Gordan coefficients for the Poincaré group) and invariant matrix elements. The geometrical coefficients are fixed by the transformation properties of the operator and the eigenvalue spectrum of the mass and spin. The invariant matrix elements, which distinguish between different operators with the same transformation properties, are given in terms of a set of invariant form factors.

Polyzou, Wayne N.; Klink, W. H.

1988-08-01

13

NASA Astrophysics Data System (ADS)

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

Bilodeau, Alex; Tremblay, Sébastien

2013-10-01

14

Supersymmetric quantum mechanics.

National Technical Information Service (NTIS)

We summarize recent developments of supersymmetric quantum mechanics. We start from the susy oscillator, mention the factorization schemes and discuss the order of levels of Schroedinger operators as an example. We mention soliton equation and the inverse...

H. Grosse

1989-01-01

15

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

NASA Astrophysics Data System (ADS)

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.

B?aszak, Maciej; Doma?ski, Ziemowit

2014-05-01

16

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

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

2013-01-01

17

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

18

Quantum Operation Time Reversal

The dynamics of an open quantum system can be described by a quantum operation: A linear, complete positive map of operators. Here, I exhibit a compact expression for the time reversal of a quantum operation, which is closely analogous to the time reversal of a classical Markov transition matrix. Since open quantum dynamics are stochastic, and not, in general, deterministic, the time reversal is not, in general, an inversion of the dynamics. Rather, the system relaxes toward equilibrium in both the forward and reverse time directions. The probability of a quantum trajectory and the conjugate, time reversed trajectory are related by the heat exchanged with the environment.

Crooks, Gavin E.

2008-03-25

19

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

Fan Hongyi [CCAST (World Laboratory), P.O. Box 8730, Beijing 100080 (China); Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026 (China); Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 (China); Lu Hailiang [Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 (China)]. E-mail: luhailiang@sjtu.edu.cn; Fan Yue [Intel Corporation 2200 Mission College Blvd., Santa Clara, CA 95052-8119 (United States)

2006-02-15

20

IMSL and Matrix Signatures of Quantum Mechanical Operators in the Rayleigh-Ritz-Galerkin Method

NASA Astrophysics Data System (ADS)

A central issue in many applications of quantum mechanics is the solution of a wave equation to find the energy eigenvalues and eigenfunctions. An alternative to the standard procedure of numerical solutions is the Rayleigh-Ritz-Galerkin method, where the wave function is expanded in terms of a complete set of basis functions. Then the eigenvalue problem reduces to that of diagonalizing a Hamiltonian matrix. An efficient basis for many three-dimensional bound state problems is a radial function that combines an exponential confining factor, an angular momentum barrier factor and a Laguerre polynomial. Then analytic expressions can be found for the linear and Coulomb potential energy matrix elements and the matrix elements of the square of the momentum operator. The range of applications is expanded considerably by using certain algorithms to compute representatives of additional operators from characteristic signatures of these basic matrices. Several examples will be presented. Applications to nonlocal relativistic wave equations, for which the standard numerical techniques of second-order differential equations do not apply, will also be considered.

Fulcher, L. P.

1997-05-01

21

Supersymmetry in quantum mechanics

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

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

2004-12-23

22

NASA Astrophysics Data System (ADS)

Part I. Second Quantization: 1. Elementary quantum mechanics; 2. Identical particles; 3. Second quantization; Part II. Examples: 4. Magnetism; 5. Superconductivity; 6. Superfluidity; Part III. Fields and Radiation: 7. Classical fields; 8. Quantization of fields; 9. Radiation and matter; 10. Coherent states; Part IV. Dissipative Quantum Mechanics: 11. Dissipative quantum mechanics; 12. Transitions and dissipation; Part V. Relativistic Quantum Mechanics: 13. Relativistic quantum mechanics; Index.

Nazarov, Yuli V.; Danon, Jeroen

2013-01-01

23

Newton–Leibniz integration rule only applies to commuting functions of continuum variables, while operators made of Dirac’s symbols (ket versus bra, e.g., |q??q| of continuous parameter q) in quantum mechanics are usually not commutative. Therefore, integrations over the operators of type |??| cannot be directly performed by Newton–Leibniz rule. We invented an innovative technique of integration within an ordered product (IWOP)

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

2006-01-01

24

Biorthogonal quantum mechanics

NASA Astrophysics Data System (ADS)

The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called ‘biorthogonal quantum mechanics’, is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems.

Brody, Dorje C.

2014-01-01

25

Schmidt number for quantum operations

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

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

2006-05-15

26

Making sense of quantum operators, eigenstates and quantum measurements

NASA Astrophysics Data System (ADS)

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

2012-02-01

27

Emergent mechanics, quantum and un-quantum

NASA Astrophysics Data System (ADS)

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

Ralston, John P.

2013-10-01

28

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

29

NASA Astrophysics Data System (ADS)

Gravity and quantum mechanics tend to stay out of each other's way, but this might change as we devise new experiments to test the applicability of quantum theory to macroscopic systems and larger length scales.

Amelino-Camelia, Giovanni

2014-04-01

30

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

31

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

32

Operational interpretations of quantum discord

Quantum discord quantifies non-classical correlations going beyond the standard classification of quantum states into entangled and unentangled ones. Although it has received considerable attention, it still lacks any precise interpretation in terms of some protocol in which quantum features are relevant. Here we give quantum discord its first information-theoretic operational meaning in terms of entanglement consumption in an extended quantum

Marco Piani; Daniel Cavalcanti; Leandro Aolita; Sergio Boixo; Kavan Modi; Andreas Winter

2011-01-01

33

Quantum Mechanical Operator Equivalents and Magnetic Anisotropy of the Heavy Rare Earth Metals.

National Technical Information Service (NTIS)

A tensor operator formalism that in a convenient way describes the interactions of magnetic systems is treated. Further, a creation operator and annihilation operator formalism describing the excited states of magnetic systems is introduced. On this backg...

O. Danielsen

1973-01-01

34

NASA Astrophysics Data System (ADS)

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

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

2012-10-01

35

NASA Astrophysics Data System (ADS)

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

Kapustin, Anton

2013-06-01

36

Speculation on Quantum Mechanics and the Operation of Life Giving Catalysts

The origin of life necessitated the formation of catalytic functionalities in order to realize a number of those capable of\\u000a supporting reactions that led to the proliferation of biologically accessible molecules and the formation of a proto-metabolic\\u000a network. Here, the discussion of the significance of quantum behavior on biological systems is extended from recent hypotheses\\u000a exploring brain function and DNA

Nathan Haydon; Shawn E. McGlynn; Olin Robus

2011-01-01

37

Operational interpretations of quantum discord

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

D. Cavalcanti; L. Aolita; S. Boixo; K. Modi; M. Piani; A. Winter

2011-01-01

38

Operational interpretations of quantum discord

Quantum discord quantifies non-classical correlations going beyond the\\u000astandard classification of quantum states into entangled and unentangled ones.\\u000aAlthough it has received considerable attention, it still lacks any precise\\u000ainterpretation in terms of some protocol in which quantum features are\\u000arelevant. Here we give quantum discord its first operational meaning in terms\\u000aof entanglement consumption in an extended quantum state

D. Cavalcanti; L. Aolita; S. Boixo; K. Modi; M. Piani; A. Winter

2010-01-01

39

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

40

PT-symmetric quantum mechanics

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

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

1999-01-01

41

Quantum mechanics for space applications

This paper is an introduction to the following articles in the scope of quantum mechanics for space study initiated by ESA and lead by ONERA. The context of quantum mechanics for space is summarised, and the fields under development are briefly introduced. Technological applications of quantum mechanics in space are explored and some tests of quantum mechanics are outlined. We

A. Bresson; Y. Bidel; P. Bouyer; B. Leone; E. Murphy; P. Silvestrin

2006-01-01

42

NSDL National Science Digital Library

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

Group, Kansas S.; Zollman, Dean A.

2003-10-10

43

Supersymmetric quantum mechanics with reflections

NASA Astrophysics Data System (ADS)

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 wavefunctions of extended Scarf I potentials with different parameters are presented.

Post, Sarah; Vinet, Luc; Zhedanov, Alexei

2011-10-01

44

Self-Referential Quantum Mechanics

NASA Astrophysics Data System (ADS)

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

Mitchell, Mark Kenneth

1993-01-01

45

NSDL National Science Digital Library

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

Thaller, Bernd

2009-05-14

46

Noncommutative quantum mechanics

NASA Astrophysics Data System (ADS)

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

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

2001-09-01

47

Time Asymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

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

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

2011-09-01

48

NASA Astrophysics Data System (ADS)

The axiomatic way of teaching quantum mechanics (QM) is analyzed in the light of its effectiveness in making students ready to understand and use QM. A more intuitive method of teaching QM is proposed. An outline of how a course implementing that method could be structured is presented.

Deumens, Erik

49

Supersymmetric Quantum Mechanics.

National Technical Information Service (NTIS)

We give a general construction for supersymmetric Hamiltonians in quantum mechanics. We find that N-extended supersymmetry imposes very strong constraints, and for N > 4 the Hamiltonian is integrable. We give a variety of examples, for one-particle and fo...

M. de Crombrugghe V. Rittenberg

1982-01-01

50

Geometrizing Relativistic Quantum Mechanics

NASA Astrophysics Data System (ADS)

We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation that recover both of them in the non-relativistic limit.

Falciano, F. T.; Novello, M.; Salim, J. M.

2010-12-01

51

Constructing quantum localization operators using conformal symmetry

NASA Astrophysics Data System (ADS)

We review the difficulties in merging quantum theory with relativity. In particular, we discuss the issue of localization in quantum mechanics. We introduce the conformal group, a supergroup of the Poincar'e group and give its generators and the corresponding algebra. We then illustrate how this allows us to create a space-time localization operator that is consistent with special relativity and quantum theory. We give an explicit expression of the localization operators in 1+1 dimensions and discuss the challenges of generalizing it to higher dimensions.

Earl, Lucas; van Huele, Jean-Francois

2008-10-01

52

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

Fan Hongyi [Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 (China); Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026 (China)], E-mail: fhym@sjtu.edu.cn

2008-06-15

53

Causality and Probability in Quantum Mechanics

NASA Astrophysics Data System (ADS)

This paper critically examines the view of quantum mechanics that emerged shortly after the introduction of quantum mechanics and that has been widespread ever since. Although N. Bohr, P. A. M. Dirac, and W. Heisenberg advanced this view earlier, it is best exemplified by J. von Neumann's argument in Mathematical Foundations of Quantum Mechanics (1932) that the transformation of ``a [quantum] state ... under the action of an energy operator ... is purely causal,'' while, ``on the other hand, the state ... which may measure a [given] quantity ... undergoes in a measurement a non-casual change.'' Accordingly, while the paper discusses all four of these arguments, it will especially focus on that of von Neumann. The paper also offers an alternative, noncausal, view of the quantum-mechanical situation and considers the differences between the ensemble and the Bayesian approaches to quantum mechanics from this perspective.

Plotnitsky, Arkady

2009-03-01

54

Operational quantum logic: An overview

The term quantum logic has different connotations for different people, having been considered as everything from a metaphysical attack on classical reasoning to an exercise in abstract algebra. Our aim here is to give a uniform presentation of what we call operational quantum logic, highlighting both its concrete physical origins and its purely mathematical structure. To orient readers new to

Bob Coecke; David Moore; Alexander Wilce

2000-01-01

55

Feynman's simple quantum mechanics

NASA Astrophysics Data System (ADS)

This sample class presents an alternative to the conventional introduction to quantum mechanics and describes its current use in a credit course. This alternative introduction rests on theory presented in professional and popular writings by Richard Feynman. Feynman showed that Nature gives a simple command to the electron: ``Explore all paths.'' All of nonrelativistic quantum mechanics, among other fundamental results, comes from this command. With a desktop computer the student points and clicks to tell a modeled electron which paths to follow. The computer then shows the results, which embody the elemental strangeness and paradoxical behaviors of the world of the very small. Feynman's approach requires few equations and provides a largely non-mathematical introduction to the wave function of conventional quantum mechanics. Draft software and materials already used for two semesters in an e-mail computer conference credit university course show that Feynman's approach works well with a variety of students. The sample class explores computer and written material and describes the next steps in its development.

Taylor, Edwin F.

1997-03-01

56

Logical foundation of quantum mechanics

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

57

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

Fan Hongyi [Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026 (China); Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 (China)], E-mail: fhym@sjtu.edu.cn

2008-02-15

58

Relating the Quantum Mechanics of Discrete Systems to Standard Canonical Quantum Mechanics

NASA Astrophysics Data System (ADS)

Standard canonical quantum mechanics makes much use of operators whose spectra cover the set of real numbers, such as the coordinates of space, or the values of the momenta. Discrete quantum mechanics uses only strictly discrete operators. We show how one can transform systems with pairs of integer-valued, commuting operators and , to systems with real-valued canonical coordinates and their associated momentum operators . The discrete system could be entirely deterministic while the corresponding ( p, q) system could still be typically quantum mechanical.

't Hooft, Gerard

2014-04-01

59

Quantum–classical correspondence via a deformed kinetic operator

We propose an approach to quantum–classical correspondence based on a deformation of the momentum and kinetic operators of quantum mechanics. Making use of the factorization method, we construct classical versions of the momentum and kinetic operators which, in addition to the standard quantum expressions, contain terms that are functionals of the N-particle density. We show that this implementation of quantum–classical

Ricardo A. Mosna; Ian P. Hamilton; Luigi Delle Site

2005-01-01

60

Crypto-Unitary Forms of Quantum Evolution Operators

NASA Astrophysics Data System (ADS)

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

Znojil, Miloslav

2013-06-01

61

NASA Astrophysics Data System (ADS)

A human being viewing a defocused television tube with sweep voltages turned off will see point scintillations at sufficiently low intensities. We show that quantum mechanics predicts these scintillations. Furthermore, by assuming a response of the human nervous system of a type not inconsistent with experiment, measurement theory is used to show that these scintillations will be distributed in proportion to the magnitude squared of the electron wave function incident upon the television tube screen. This nervous system response is to break up the wave incident upon a spot on the retina into a number of similar waves transmitted by different nerves to the brain. The number of these waves is proportional to the incident energy density. Since the theory itself predicts the proper probability distribution, it is unnecessary to introduce a postulate for it.

Broyles, A. A.

1984-06-01

62

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

63

Quantum mechanics without measurements

Many of the conceptual problems students have in understanding quantum\\u000amechanics arise from the way probabilities are introduced in standard\\u000a(textbook) quantum theory through the use of measurements. Introducing\\u000aconsistent microscopic probabilities in quantum theory requires setting up\\u000aappropriate sample spaces taking proper account of quantum incompatibility.\\u000aWhen this is done the Schrodinger equation can be used to calculate\\u000aprobabilities

Robert B. Griffiths

2006-01-01

64

Dissipative Forces and Quantum Mechanics

ERIC Educational Resources Information Center

Shows how to include the dissipative forces of classical mechanics in quantum mechanics by the use of non-Hermetian Hamiltonians. The Ehrenfest theorem for such Hamiltonians is derived, and simple examples which show the classical correspondences are given. (MLH)

Eck, John S.; Thompson, W. J.

1977-01-01

65

Modern Approach to Quantum Mechanics

NASA Astrophysics Data System (ADS)

Inspired by Richard Feynman and J.J. Sakurai, A Modern Approach to Quantum Mechanics lets professors expose their undergraduates to the excitement and insight of Feynman's approach to quantum mechanics while simultaneously giving them a textbook that is well-ordered, logical, and pedagogically sound. This book covers all the topics that are typically presented in a standard upper-level course in quantum mechanics, but its teaching approach is new: Rather than organizing his book according to the historical development of the field and jumping into a mathematical discussion of wave mechanics, Townsend begins his book with the quantum mechanics of spin. Thus, the first five chapters of the book succeed in laying out the fundamentals of quantum mechanics with little or no wave mechanics, so the physics is not obscured by mathematics. Starting with spin systems gives students something new and interesting while providing elegant but straightforward examples of the essential structure of quantum mechanics. When wave mechanics is introduced later, students perceive it correctly as only one aspect of quantum mechanics and not the core of the subject. Praised for its pedagogical brilliance, clear writing, and careful explanations, this book is destined to become a landmark text.

Townsend, John S.

66

Application of nonstandard analysis to quantum mechanics

Quantum mechanics is formulated using a nonstandard Hilbert space. The concept of an eigen vector of a linear operator, which applies to standard as well as nonstandard Hilbert spaces, is replaced by the more general concept of an ultra eigen vector, which applies to nonstandard Hilbert spaces alone. Ultra eigen vectors corresponding to all spectral points of internal self?adjoint operators

M. O. Farrukh

1975-01-01

67

Noncommutative Quantum Mechanics and Quantum Cosmology

NASA Astrophysics Data System (ADS)

We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity between momenta is shown to be relevant. We also discuss some qualitative features of the GQW such as the Berry phase. In the context of quantum cosmology we consider a Kantowski-Sachs cosmological model and obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and a suitable Seiberg-Witten (SW) map. The WDW equation is explicitly dependent on the noncommutative parameters, ? and ?. We obtain numerical solutions of the noncommutative WDW equation for different values of the noncommutative parameters. We conclude that the noncommutativity in the momenta sector leads to a damped wave function implying that this type of noncommmutativity can be relevant for a selection of possible initial states for the universe.

Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno

68

Quantum duality, unbounded operators, and inductive limits

In this paper, we investigate the inductive limits of quantum normed (or operator) spaces. This construction allows us to treat the space of all noncommutative continuous functions over a quantum domain as a quantum (or local operator) space of all matrix continuous linear operators equipped with S-quantum topology. In particular, we classify all quantizations of the polynormed topologies compatible with the given duality proposing a noncommutative Arens-Mackey theorem. Further, the inductive limits of operator spaces are used to introduce locally compact and locally trace class unbounded operators on a quantum domain and prove the dual realization theorem for an abstract quantum space.

Dosi, Anar [Middle East Technical University Northern Cyprus Campus, Guzelyurt, KKTC, Mersin 10 (Turkey)

2010-06-15

69

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

70

Quantum mechanics of Proca fields

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 (P), generalized time-reversal (T), and generalized charge or chirality (C) operators for this system and offer a physical interpretation for its PT-, C-, and CPT-symmetries.

Zamani, Farhad [Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan 45195-1159 (Iran, Islamic Republic of); Mostafazadeh, Ali [Department of Mathematics, Koc University, Rumelifeneri Yolu, Sariyer, Istanbul 34450 (Turkey)

2009-05-15

71

Quantum Mechanics: Ontology Without Individuals

NASA Astrophysics Data System (ADS)

The purpose of the present paper is to consider the traditional interpretive problems of quantum mechanics from the viewpoint of a modal ontology of properties. In particular, we will try to delineate a quantum ontology that (i) is modal, because describes the structure of the realm of possibility, and (ii) lacks the ontological category of individual. The final goal is to supply an adequate account of quantum non-individuality on the basis of this ontology.

da Costa, Newton; Lombardi, Olimpia

2014-03-01

72

Measurement Theory in Quantum Mechanics.

National Technical Information Service (NTIS)

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

G. Klein

1980-01-01

73

Adding control to arbitrary unknown quantum operations

Although quantum computers promise significant advantages, the complexity of quantum algorithms remains a major technological obstacle. We have developed and demonstrated an architecture-independent technique that simplifies adding control qubits to arbitrary quantum operations—a requirement in many quantum algorithms, simulations and metrology. The technique, which is independent of how the operation is done, does not require knowledge of what the operation is, and largely separates the problems of how to implement a quantum operation in the laboratory and how to add a control. Here, we demonstrate an entanglement-based version in a photonic system, realizing a range of different two-qubit gates with high fidelity.

Zhou, Xiao-Qi; Ralph, Timothy C.; Kalasuwan, Pruet; Zhang, Mian; Peruzzo, Alberto; Lanyon, Benjamin P.; O'Brien, Jeremy L.

2011-01-01

74

Noncommutative Poisson boundaries of unital quantum operations

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

75

NSDL National Science Digital Library

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

Galvez, Enrique; Holbrow, Charles

2005-04-16

76

Quantum Mechanics: Fundamentals

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

A Whitaker

2004-01-01

77

ERIC Educational Resources Information Center

Discusses the quantum theory of measurement and von Neumann's catastrophe of infinite regression." Examines three ways of escapint the von Neumann catastrophe, and suggests that the solution to the dilemma of inteterminism is a universe in which all possible outcomes of an experiment actually occur. Bibliography. (LC)

DeWitt, Bryce S.

1970-01-01

78

Quantum Mechanics Resource Packet

NSDL National Science Digital Library

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

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

2005-07-25

79

Towards polymer quantum mechanics for fermionic systems

NASA Astrophysics Data System (ADS)

Polymer quantum mechanics is based on models that mimic the loop quantization of gravity. It coincides with the results of the standard quantum mechanical treatment for such models when a certain length scale parameter is considered to be small. In this work we present some steps in the construction of the polymer representation of a Fermi oscillator, the fermonic counterpart of the harmonic oscillator. It is suggested that the non regular character of the bosonic polymer representation has as a counterpart the non superanalytic character of the fermonic polymer case. We propose a candidate Hamiltonian operator and investigate and contrast its energy spectrum with the standard one.

García-Chung, Angel A.; Morales-Técotl, Hugo A.; Reyes, Juan D.

2013-07-01

80

An Introduction to Quantum Mechanics

NSDL National Science Digital Library

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

Hanlin, Heath; Kitagawa, Midori; Lilas, Zil; Mcdonald, Neal; Singer, Sherwin J. (Sherwin Jeffrey), 1954-; Timasheva, Anna

2007-06-12

81

Kowalevski top in quantum mechanics

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

82

Optimal guidance law in quantum mechanics

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

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

2013-11-15

83

Comment on ``Arrival time in quantum mechanics'' and ``Time of arrival in quantum mechanics''

NASA Astrophysics Data System (ADS)

Contrary to claims contained in papers by Grot, Rovelli, and Tate [Phys. Rev. A 54, 4676 1996)] and Delgado and Muga [Phys. Rev. A 56, 3425 (1997)], the ``time operator,'' which I have constructed [Rep. Math. Phys. 6, 361 (1974)] in an axiomatic way, is a self-adjoint operator existing in a usual Hilbert space of (nonrelativistic or relativistic) quantum mechanics.

Kijowski, Jerzy

1999-01-01

84

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

85

Faster than Hermitian quantum mechanics.

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

86

We show that the technique of integration within normal ordering of operators [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480–494] applied to tackling Newton–Leibniz integration over ket–bra projection operators, can be generalized to the technique of integration within Weyl ordered product (IWWOP) of operators. The Weyl ordering symbol is introduced to find the Wigner operator’s Weyl ordering

Hong-Yi Fan

2008-01-01

87

Quantum Mechanics and Physical Reality

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

88

A quantum mechanical twin paradox

When a quantummechanical wavepacket undergoes a series of Galilean boosts, the Schrödinger theory predicts the occurrence of a geometrical phase effect that is an example of Berry's phase (Sagnac's phase). In the present paper the conceptual consequences of this phenomenon are considered, in particular for the status of Galilean invariance in nonrelativistic quantum mechanics, and for the relation between that

Dennis Dieks

1990-01-01

89

A quantum mechanical twin paradox

NASA Astrophysics Data System (ADS)

When a quantummechanical wavepacket undergoes a series of Galilean boosts, the Schrödinger theory predicts the occurrence of a geometrical phase effect that is an example of Berry's phase (Sagnac's phase). In the present paper the conceptual consequences of this phenomenon are considered, in particular for the status of Galilean invariance in nonrelativistic quantum mechanics, and for the relation between that theory and classical physics.

Dieks, Dennis

1990-08-01

90

Fun with Supersymmetric Quantum Mechanics.

National Technical Information Service (NTIS)

One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup alpha / for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpo...

B. Freedman F. Cooper

1984-01-01

91

NASA Astrophysics Data System (ADS)

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

Moshinsky, Marcos

1999-03-01

92

Quantum mechanics and the psyche

NASA Astrophysics Data System (ADS)

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

Galli Carminati, G.; Martin, F.

2008-07-01

93

Quantum Logical Operations on Encoded Qubits

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

Wojciech Hubert Zurek; Raymond Laflamme

1996-01-01

94

Quantum mechanics on noncommutative spacetime

We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a nonrelativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note, however, that noncommutative intrinsic dipole moments are not observable in present experiments searching for an electric dipole moment of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moments are thus incorrect.

Calmet, Xavier; Selvaggi, Michele [Service de Physique Theorique, CP225 Boulevard du Triomphe B-1050 Brussels (Belgium)

2006-08-01

95

Modern Undergraduate Quantum Mechanics Experiments

NSDL National Science Digital Library

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

Beck, Mark

2004-07-10

96

Complementarity in Categorical Quantum Mechanics

NASA Astrophysics Data System (ADS)

We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a `point-free' definition of copyability we link (i) commutative von Neumann subalgebras, (ii) classical structures, and (iii) Boolean subalgebras.

Heunen, Chris

2012-07-01

97

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

98

Faster than Hermitian Quantum Mechanics

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

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

2007-01-26

99

Helping Students Learn Quantum Mechanics for Quantum Computing

NASA Astrophysics Data System (ADS)

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

2007-01-01

100

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

NASA Astrophysics Data System (ADS)

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

Radtke, T.; Fritzsche, S.

2007-05-01

101

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

102

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

103

Curvature operator for loop quantum gravity

NASA Astrophysics Data System (ADS)

We introduce a new operator in loop quantum gravity—the 3D curvature operator—related to the three-dimensional scalar curvature. The construction is based on Regge calculus. We define this operator starting from the classical expression of the Regge curvature, we derive its properties and discuss some explicit checks of the semiclassical limit.

Alesci, E.; Assanioussi, M.; Lewandowski, J.

2014-06-01

104

Cohomological operators and covariant quantum superalgebras

We obtain an interesting realization of the de Rham cohomological operators of differential geometry in terms of the noncommutative q-superoscillators for the supersymmetric quantum group GLqp(1|1). In particular, we show that a unique quantum superalgebra, obeyed by the bilinears of fermionic and bosonic noncommutative q-(super)oscillators of GLqp(1|1), is exactly identical to that obeyed by the de Rham cohomological operators. A

R. P. Malik

2004-01-01

105

Epistemic restrictions in Hilbert space quantum mechanics

NASA Astrophysics Data System (ADS)

A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results in quantum information theory. This analysis provides a quantum mechanical understanding of some recent work that shows that certain kinds of quantum behavior are exhibited by a fully classical model if by hypothesis an observer's knowledge of its state is appropriately limited.

Griffiths, Robert B.

2013-10-01

106

Propagators in polymer quantum mechanics

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

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

2013-09-15

107

Twist deformations of the supersymmetric quantum mechanics

NASA Astrophysics Data System (ADS)

The mathcal{N} -extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even mathcal{N} one can identify the 1 D mathcal{N} -extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.

Castro, Paulo G.; Chakraborty, Biswajit; Kuznetsova, Zhanna; Toppan, Francesco

2011-06-01

108

Twist deformation of rotationally invariant quantum mechanics

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

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

2010-11-15

109

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

110

NASA Astrophysics Data System (ADS)

In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to the commutator of the True and False operators of matrix logic, still with a quantum superposed state related to a Moebius surface, and as the physical field at the basis of Spencer-Brown's primitive distinction in the protologic of the calculus of distinction. In this setting, paradox, self-reference, depth, time and space, higher-order non-dual logic, perception, spin and a time operator, the Klein bottle, hypernumbers due to Musès which include non-trivial square roots of ±1 and in particular non-trivial nilpotents, quantum field operators, the transformation of cognition to spin for two-state quantum systems, are found to be keenly interwoven in a world conception compatible with the philosophical approach taken for basis of this article. The Klein bottle is found not only to be the topological in-formation for self-reference and paradox whose logical counterpart in the calculus of indications are the paradoxical imaginary time waves, but also a classical-quantum transformer (Hadamard's gate in quantum computation) which is indispensable to be able to obtain a complete multivalued logical system, and still to generate the matrix extension of classical connective Boolean logic. We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation, generates the matrix logic which supersedes the classical logic of connectives and which has for particular subtheories fuzzy and quantum logics. Thus, from a primitive distinction in the vacuum plane and the axioms of the calculus of distinction, we can derive by incorporating paradox, the world conception succinctly described above.

Rapoport, Diego L.

2011-01-01

111

Sensible Quantum Mechanics:. are Probabilities Only in the Mind?

NASA Astrophysics Data System (ADS)

Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so that it contains nothing probabilistic except conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by expectation values of positive-operator-valued awareness operators. Ratios of the measures for these sets of perceptions can be interpreted as frequency-type probabilities for many actually existing sets. These probabilities generally cannot be given by the ordinary quantum “probabilities” for a single set of alternatives. Probabilism, or ascribing probabilities to unconscious aspects of the world, may be seen to be an aesthemamorphic myth.

Page, Don N.

112

Quantum Mechanical Approximations in Quantum Field Theory.

National Technical Information Service (NTIS)

Some cooperative, coherent effects in quantum field theory, such as spontaneous symmetry violation, bound states, and entrapment of various excitations, can be exposed only by approximation procedures which do not rely on analyticity or regularity in the ...

R. Jackiw

1975-01-01

113

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

114

New Formulation of Statistical Mechanics Using Thermal Pure Quantum States

NASA Astrophysics Data System (ADS)

We formulate statistical mechanics based on a pure quantum state, which we call a "thermal pure quantum (TPQ) state". A single TPQ state gives not only equilibrium values of mechanical variables, such as magnetization and correlation functions, but also those of genuine thermodynamic variables and thermodynamic functions, such as entropy and free energy. Among many possible TPQ states, we discuss the canonical TPQ state, the TPQ state whose temperature is specified. In the TPQ formulation of statistical mechanics, thermal fluctuations are completely included in quantum-mechanical fluctuations. As a consequence, TPQ states have much larger quantum entanglement than the equilibrium density operators of the ensemble formulation. We also show that the TPQ formulation is very useful in practical computations, by applying the formulation to a frustrated two-dimensional quantum spin system.

Sugiura, Sho; Shimizu, Akira

2014-03-01

115

Quantum mechanical Hamiltonian models of discrete processes

Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement.

Benioff, P.

1981-03-01

116

Improved lattice actions for supersymmetric quantum mechanics

NASA Astrophysics Data System (ADS)

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 nonzero 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.

Schierenberg, Sebastian; Bruckmann, Falk

2014-01-01

117

Can quantum mechanics help distributed computing?

We present a brief survey of results where quantum information processing is useful to solve distributed computation tasks. We describe problems that are impossible to solve using classical resources but that become feasible with the help of quantum mechanics. We also give examples where the use of quantum information significantly reduces the need for communication. The main focus of the

Anne Broadbent; Alain Tapp

2008-01-01

118

Are All Probabilities Fundamentally Quantum Mechanical?

The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated that all probabilities may be fundamentally quantum mechanical in the sense that they may all be derived from the corresponding amplitudes. The classical coin-toss and the quantum

Rajat Kumar Pradhan

2011-01-01

119

Moyal quantum mechanics: The semiclassical Heisenberg dynamics

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

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

1995-07-01

120

Characterizations of fixed points of quantum operations

Let {phi}{sub A} be a general quantum operation. An operator B is said to be a fixed point of {phi}{sub A}, if {phi}{sub A}(B)=B. In this note, we shall show conditions under which B, a fixed point {phi}{sub A}, implies that B is compatible with the operation element of {phi}{sub A}. In particular, we offer an extension of the generalized Lueders theorem.

Li Yuan [College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062 (China)

2011-05-15

121

Quantum mechanics: A new chapter?

NASA Astrophysics Data System (ADS)

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

Hofer, Werner A.

2012-12-01

122

Kindergarten Quantum Mechanics: Lecture Notes

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

123

Kindergarten Quantum Mechanics: Lecture Notes

NASA Astrophysics Data System (ADS)

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 [3, 4]) which subsumes my Logic of Entanglement [11]. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes [12, 13]. In a last section we provide some pointers to the body of technical literature on the subject.

Coecke, Bob

2006-01-01

124

Thermodynamic integration from classical to quantum mechanics.

We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable. PMID:22168684

Habershon, Scott; Manolopoulos, David E

2011-12-14

125

The Quantum Mechanical Many-Body Problem.

National Technical Information Service (NTIS)

A wide variety of quantum mechanical many-body problems were investigated. The two significant accomplishments of this research are as follows: The development of DCF (dynamical characteristic function) method for treating the statistical mechanics of qua...

A. E. Glassgold

1969-01-01

126

On a realistic interpretation of quantum mechanics

The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This opens the door for an interpretation that, while respecting the indeterministic nature of quantum mechanics, allows to speak of definite values for all

Arnold Neumaier

1999-01-01

127

Quantum Mechanics and physical calculations

NASA Astrophysics Data System (ADS)

We suggest to realize the computer simulation and calculation by the algebraic structure built on the basis of the logic inherent to processes in physical systems (called physical computing). We suggest a principle for the construction of quantum algorithms of neuroinformatics of quantum neural networks. The role of academician Sahakyan is emphasized in the development of quantum physics in Armenia.

Karayan, H. S.

2014-03-01

128

Optical simulation of the quantum Hadamard operator

NASA Astrophysics Data System (ADS)

A possible way to optically simulate quantum algorithms is by making use of the spatial distribution of light in a laser beam. In this approach, the quantum states are represented by the amplitudes of the electromagnetic field in the beam. Temporal evolution is simulated by using optical elements such as lenses and phase shifters. Different elements are required depending on the operation whose implementation is desired. In this paper, we present an optical module to simulate the Hadamard transformation operating on a single qubit. The system is composed by a set of lenses, a phase plate and a phase grating and it could be used as a part of more complex arrangements. As an example, we make use of our Hadamard optical module as a part of the quantum circuit that solves the Deutsch problem. We show the obtained experimental results and we discuss the limitations of the proposal.

Francisco, D.; Iemmi, C.; Paz, J. P.; Ledesma, S.

2006-12-01

129

Polymer quantum mechanics and its continuum limit

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

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

2007-08-15

130

Quantum mechanics of open systems

NASA Astrophysics Data System (ADS)

In quantum mechanics, there is a set of problems where the system of interest interacts with another system, usually called "environment". This interaction leads to the exchange of energy and information and makes the dynamics of the system of interest essentially non-unitary. Such problems often appeared in condensed matter physics and attracted much attention after recent advances in nanotechnology. As broadly posed as they are, these problems require a variety of different approaches. This thesis is an attempt to examine several of these approaches in applications to different condensed matter problems. The first problem concerns the so-called "Master equation" approach which is very popular in quantum optics. I show that analytic properties of environmental correlators lead to strong restrictions on the applicability of the approach to the strong-coupling regime of interest in condensed matter physics. In the second problem, I use path integrals to treat the localization of particles on attractive short-range potentials when the environment produces an effective viscous friction force. I find that friction changes drastically the localization properties and leads to much stronger localization in comparison to the non-dissipative case. This has implications for the motion of heavy particles in fermionic liquids and, as will be argued below, is also relevant to the problem of high-temperature superconductivity. Finally, the third problem deals with the interplay of geometric phases and energy dissipation which occurs in the motion of vortices in superconductors. It is shown that this interplay leads to interesting predictions for vortex tunneling in high-temperature superconductors which have been partially confirmed by experiments.

Melikidze, Akakii

131

Logical operator tradeoff for local quantum codes

NASA Astrophysics Data System (ADS)

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

Haah, Jeongwan; Preskill, John

2011-03-01

132

Loop quantum cosmology: II. Volume operators

Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs constraint imposed on the reduced connection variables is necessary, a complete solution of which is given for isotropic models; in this case the volume spectrum can be calculated explicitly.

Martin Bojowald

2000-01-01

133

Nonlinear quantum mechanics: Results and open questions

NASA Astrophysics Data System (ADS)

About 15 years ago, we (Heinz-Dietrich Doebner and I) proposed a special type of nonlinear modification of the usual Schrödinger time-evolution equation in quantum mechanics. Our equation was motivated by certain unitary representations of the group of diffeomorphisms of physical space, in the framework of either nonrelativistic local current algebra or quantum Borel kinematics. Subsequently, we developed this and related approaches to nonlinearity in quantum mechanics considerably further, to incorporate theories of measurement, groups of nonlinear gauge transformations, symmetry and invariance properties, unification of a large family of nonlinear perturbations, and possible physical contexts for quantum nonlinearity. Some of our results and highlights of some open questions are summarized.

Goldin, G. A.

2008-05-01

134

Emergence of classical theories from quantum mechanics

NASA Astrophysics Data System (ADS)

Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's "first kind of dynamics", and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.

Hájí?ek, P.

2012-05-01

135

Riemann hypothesis and quantum mechanics

NASA Astrophysics Data System (ADS)

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

Planat, Michel; Solé, Patrick; Omar, Sami

2011-04-01

136

Noncommutative quantum mechanics as a gauge theory

The classical counterpart of noncommutative quantum mechanics is a constrained system containing only second-class constraints. The embedding procedure formulated by Batalin, Fradkin and Tyutin (BFT) enables one to transform this system into an Abelian gauge theory exhibiting only first class constraints. The appropriateness of the BFT embedding, as implemented in this work, is verified by showing that there exists a one to one mapping linking the second-class model with the gauge invariant sector of the gauge theory. As is known, the functional quantization of a gauge theory calls for the elimination of its gauge freedom. Then, we have at our disposal an infinite set of alternative descriptions for noncommutative quantum mechanics, one for each gauge. We study the relevant features of this infinite set of correspondences. The functional quantization of the gauge theory is explicitly performed for two gauges and the results compared with that corresponding to the second-class system. Within the operator framework the gauge theory is quantized by using Dirac's method.

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

2009-06-15

137

The formal path integral and quantum mechanics

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

138

Quantum mechanics, CPT violation, and neutral kaons

NASA Astrophysics Data System (ADS)

The neutral kaon system offers a unique possibility to perform fundamental tests of the basic principles of quantum mechanics and of CPT symmetry. The most recent limits obtained by the KLOE experiment at the DA?NE e+e- collider on several kinds of possible decoherence and CPT violation mechanisms, which in some cases might be justified in a quantum gravity framework, are reviewed. No deviation from the expectations of quantum mechanics and CPT symmetry is observed, while the precision of the measurements, in some cases, reaches the interesting Planck scale region. Finally, prospects for this kind of experimental studies at KLOE-2 are presented.

Domenico, Antonio Di

2012-03-01

139

ADDENDUM: Chaos in Bohmian quantum mechanics

In our recently published paper 'Chaos in Bohmian quantum mechanics' we criticized a paper by Parmenter and Valentine (1995 Phys. Lett. A 201 1), because the authors made an incorrect calculation of the Lyapunov exponent in the case of Bohmian orbits in a quantum system of two uncoupled harmonic oscillators. After our paper was published, we became aware of an

C. Efthymiopoulos; G. Contopoulos

2006-01-01

140

Improving Student Understanding of Quantum Mechanics

NASA Astrophysics Data System (ADS)

We are investigating the difficulties that students have in learning upper-level quantum mechanics and designing quantum interactive learning tutorials (QuILTs). Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. The preliminary results from the QuILTs are promising. Coauthors: Mario Belloni and Wolfgang Christian, Davidson College.

Singh, Chandralekha

2006-04-01

141

Operational mechanism of conjugated polyelectrolytes.

Conjugated polyelectrolytes (CPEs) are versatile materials used in a range of organic optoelectronic applications. Because of their ionic/electronic nature, characterizing these materials is nontrivial, and their operational mechanism is not fully understood. In this work we use a methodology that combines constant-voltage-driven current-density transient measurements with fast current vs voltage scans to allow decoupling of ionic and electronic phenomena. This technique is applied to diodes prepared with cationic CPEs having different charge-compensating anions. Our results indicate that the operational mechanism of these devices is governed by electrochemical doping of the CPE. On the basis of the notion that the saturated depletion layer for the anions consists of the same ?-conjugated backbone material, we discern how the extent and speed of formation of the doped region depend on the anion structure. Apart from addressing fundamental transport questions, this work provides a tool for future characterization of different CPEs and other similar systems. PMID:24855971

Tordera, Daniel; Kuik, Martijn; Rengert, Zachary D; Bandiello, Enrico; Bolink, Henk J; Bazan, Guillermo C; Nguyen, Thuc-Quyen

2014-06-18

142

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

143

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

144

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

145

Quantum mechanical stabilization of Minkowski signature wormholes

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

Visser, M.

1989-05-19

146

SSQM (Supersymmetric Quantum Mechanics) and Nonlinear Equations.

National Technical Information Service (NTIS)

The method for obtaining the superpartner potential in the supersymmetric quantum mechanics (SSQM) is discussed in connection with the nonlinear equations and the reflectionless potentials. The correspondence between a new class of the soliton solutions t...

J. Hruby V. G. Makhan'kov

1987-01-01

147

Supersymmetric Quantum Mechanics and New Potentials.

National Technical Information Service (NTIS)

Using the supersymmetric quantum mechanics the following potential are generalized. The particle in the box, Poeschl-Teller and Rosen-Morse. The new potentials are evaluated and their eigenfunctions and spectra are indicated. (Atomindex citation 20:038198...

E. Drigo Filho

1988-01-01

148

Supersymmetric quantum mechanics for string-bits.

National Technical Information Service (NTIS)

The authors develop possible versions of supersymmetric single particle quantum mechanics, with application to superstring-bit models in view. The authors focus principally on space dimensions d = 1,2,4,8, the transverse dimensionalities of superstring in...

C. B. Thorn

1997-01-01

149

Functional integral in supersymmetric quantum mechanics.

National Technical Information Service (NTIS)

The solution of the square root of the Schroedinger equation for the supersymmetric quantum mechanics is expressed in the form of series. The formula may be considered as a functional integral of the chronological exponent of the super-pseudodifferential ...

D. V. Ktitarev

1990-01-01

150

Supersymmetric Quantum Mechanics of the Relativistic Particle.

National Technical Information Service (NTIS)

An alternative formulation for the superparticle in a scalar potential is presented. This method is based on a combination between the ground state wave function representation and supersymmetric quantum mechanics. For the free relativistic particle case,...

J. Gamboa J. Zanelli

1986-01-01

151

Fundamental Quantum Mechanics--A Graphic Presentation

ERIC Educational Resources Information Center

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

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

1977-01-01

152

Symmetry and symmetry breaking in quantum mechanics.

National Technical Information Service (NTIS)

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

P. Chomaz

1998-01-01

153

Using Optical Transforms To Teach Quantum Mechanics

Wave-particle duality, the superposition principle, the uncertainty principle, and single-particle interference are the most fundamental quantum mechanical concepts. The purpose of this paper is to demonstrate that these quantum mechanical principles are illuminated by a study of diffraction patterns created with laser light and a variety of two-dimensional masks. The principles of X-ray crystallography are generally taught using the Bragg

Frank Rioux; Brian J. Johnson

154

Noncommutative quantum mechanics from noncommutative quantum field theory.

We derive noncommutative multiparticle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Particles of opposite charges are found to have opposite noncommutativity. As a result, there is no noncommutative correction to the hydrogen atom spectrum at the tree level. We also comment on the obstacles to take noncommutative phenomenology seriously and propose a way to construct noncommutative SU(5) grand unified theory. PMID:11955188

Ho, Pei-Ming; Kao, Hsien-Chung

2002-04-15

155

Macroscopic quantum mechanics in a classical spacetime.

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

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

2013-04-26

156

Cohomological operators and covariant quantum superalgebras

We obtain an interesting realization of the de Rham cohomological operators\\u000aof differential geometry in terms of the noncommutative q-superoscillators for\\u000athe supersymmetric quantum group GL_{qp} (1|1). In particular, we show that a\\u000aunique superalgebra, obeyed by the bilinears of fermionic and bosonic\\u000anoncommutative q-(super)oscillators of GL_{qp} (1|1), is exactly identical to\\u000athat obeyed by the de Rham cohomological operators.

R. P. Malik; S. N. Bose; Sector-III Block-JD

2004-01-01

157

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

158

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

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

2007-09-15

159

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

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

160

Probabilistic quantum logic operations using polarizing beam splitters

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

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

2001-01-01

161

BOOK REVIEWS: Quantum Mechanics: Fundamentals

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

Kurt Gottfri; Tung-Mow Yan

2004-01-01

162

Lyapounov variable: Entropy and measurement in quantum mechanics

We discuss the question of the dynamical meaning of the second law of thermodynamics in the framework of quantum mechanics. Previous discussion of the problem in the framework of classical dynamics has shown that the second law can be given a dynamical meaning in terms of the existence of so-called Lyapounov variables—i.e., dynamical variables varying monotonically in time without becoming contradictory. It has been found that such variables can exist in an extended framework of classical dynamics, provided that the dynamical motion is suitably unstable. In this paper we begin to extend these results to quantum mechanics. It is found that no dynamical variable with the characteristic properties of nonequilibrium entropy can be defined in the standard formulation of quantum mechanics. However, if the Hamiltonian has certain well-defined spectral properties, such variables can be defined but only as a nonfactorizable superoperator. Necessary nonfactorizability of such entropy operators M has the consequence that they cannot preserve the class of pure states. Physically, this means that the distinguishability between pure states and corresponding mixtures must be lost in the case of a quantal system for which the algebra of observables can be extended to include a new dynamical variable representing nonequilibrium entropy. We discuss how this result leads to a solution of the quantum measurement problem. It is also found that the question of existence of entropy of superoperators M is closely linked to the problem of defining an operator of time in quantum mechanics.

Misra, B.; Prigogine, I.; Courbage, M.

1979-01-01

163

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

164

Relativistic quantum mechanics of supersymmetric particles

NASA Astrophysics Data System (ADS)

The quantum mechanics of an electron in an external field is developed by Hamiltonian path integral methods. The electron is described classically by an action which is invariant under gauge supersymmetry transformations as well as worldline reparametrizations. The simpler case of a spinless particle is first reviewed and it is pointed out that a strictly canonical approach does not exist. This follows formally from the gauge invariance properties of the action and physically it corresponds to the fact that particles can travel backwards as well as forward in coordinate time. However, appropriate application of path integral techniques yields directly the proper time representation of the Feynman propagator. Next we extend the formalism to systems described by anticommuting variables. This problem presents some difficulty when the dimension of the phase space is odd, because the holomorphic representation does not exist. It is shown, however, that the usual connection between the evolution operator and the path integral still holds provided one indludes in the action the boundary term that makes the classical variational principle well defined. The path integral for the relativistic spinning particle is then evaluated and it is shown to lead directly to a representation for the Feynman propagator in terms of two proper times, one commuting, the other anticommuting, which appear in a symmetric manner. This representation is used to derive scattering amplitudes in an external field. In this step the anticommuting proper time is integrated away and the analysis is carried in terms of one (commuting) proper time only, just as in the spinless case. Finally, some properties of the quantum mechanics of the ghost particles that appear in the path integral for constrained systems are developed in an appendix.

Henneaux, Marc; Teitelboim, Claudio

1982-10-01

165

Relativistic quantum mechanics of supersymmetric particles

The quantum mechanics of an electron in an external field is developed by Hamiltonian path integral methods. The electron is described classically by an action which is invariant under gauge sypersymmetry transformations as well as worldline reparametrizations. The simpler case of a spinless particle is first reviewed and it is pointed out that a strictly canonical approach does not exist. This follows formally from the gauge invariance properties of the action and physically it corresponds to the fact that particles can travel backwards as well as forward in coordinate time. However, appropriate application of path integral techniques yields directly the proper time representation of the Feynman propagator. Next we extend the formalism to systems described by anticommuting variables. This problem presents some difficulty when the dimension of the phase space is odd, because the holomorphic representation does not exist. It is shown, however, that the usual connection between the evolution operator and the path integral still holds provided one includes in the action the bounary term that makes the classical variational principle well defined. The path integral for the relativistic spinning particle is then evaluated and it is shown to lead directly to a representation for the Feynman propagator in terms of two proper times, one commuting, the other anticommuting, which appear in a symmetric manner. This representation is used to derive scattering amplitudes in an external field. In this step the anticommuting proper time is integrated away and the analysis is carried in terms of one (commuting) proper time only, just as in the spinless case. Finally, some properties of the quantum mechanics of the ghost particles that appear in the path integral for constrained systems are developed in an appendix.

Henneaux, M.; Teitelboim, C.

1982-10-01

166

New methods for quantum mechanical reaction dynamics

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

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

1996-12-01

167

Can quantum mechanics and supersymmetric quantum mechanics be the multidimensional Ermakov theories?

NASA Astrophysics Data System (ADS)

For both the Schrödinger equation in quantum mechanics and the Riccati-type equation satisfied by the superpotential in supersymmetric quantum mechanics, we explicitly show that there exists an Ermakov-type functional invariant with respect to the space variable. An energy-like interpretation is suggested for this invariant.

Kaushal, R. S.; Parashar, D.

1996-02-01

168

Emergent quantum mechanics of finances

NASA Astrophysics Data System (ADS)

This paper is an attempt at understanding the quantum-like dynamics of financial markets in terms of non-differentiable price–time continuum having fractal properties. The main steps of this development are the statistical scaling, the non-differentiability hypothesis, and the equations of motion entailed by this hypothesis. From perspective of the proposed theory the dynamics of S&P500 index are analyzed.

Nastasiuk, Vadim A.

2014-06-01

169

Weyl-Wigner formulation of noncommutative quantum mechanics

We address the phase-space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativities. By resorting to a covariant generalization of the Weyl-Wigner transform and to the Darboux map, we construct an isomorphism between the operator and the phase-space representations of the extended Heisenberg algebra. This map provides a systematic approach to derive the entire structure of noncommutative quantum mechanics in phase space. We construct the extended star product and Moyal bracket and propose a general definition of noncommutative states. We study the dynamical and eigenvalue equations of the theory and prove that the entire formalism is independent of the particular choice of the Darboux map. Our approach unifies and generalizes all the previous proposals for the phase-space formulation of noncommutative quantum mechanics. For concreteness we rederive these proposals by restricting our formalism to some two-dimensional spaces.

Bastos, Catarina; Bertolami, Orfeu [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal); Dias, Nuno Costa; Prata, Joao Nuno [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Av. Campo Grande, 376, 1749-024 Lisboa (Portugal)

2008-07-15

170

NASA Astrophysics Data System (ADS)

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

Aspelmeyer, Markus; Schwab, Keith

2008-09-01

171

NASA Astrophysics Data System (ADS)

A quantum probability measure ? is a function on a ?-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but where the values of ? are positive operators acting on a complex Hilbert space, and a quantum random variable is a measurable operator valued function. Although quantum probability measures and random variables are used extensively in quantum mechanics, some of the fundamental probabilistic features of these structures remain to be determined. In this paper, we take a step toward a better mathematical understanding of quantum random variables and quantum probability measures by introducing a quantum analogue for the expected value E?[?] of a quantum random variable ? relative to a quantum probability measure ?. In so doing we are led to theorems for a change of quantum measure and a change of quantum variables. We also introduce a quantum conditional expectation which results in quantum versions of some standard identities for Radon-Nikodým derivatives. This allows us to formulate and prove a quantum analogue of Bayes' rule.

Farenick, Douglas; Kozdron, Michael J.

2012-04-01

172

Statistical mechanics based on fractional classical and quantum mechanics

NASA Astrophysics Data System (ADS)

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

Korichi, Z.; Meftah, M. T.

2014-03-01

173

Superstrings and the Foundations of Quantum Mechanics

NASA Astrophysics Data System (ADS)

It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are usually categorically rejected, because of Bell's powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions.

't Hooft, Gerard

2014-03-01

174

Superstrings and the Foundations of Quantum Mechanics

NASA Astrophysics Data System (ADS)

It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are usually categorically rejected, because of Bell's powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions.

't Hooft, Gerard

2014-05-01

175

Space and time from quantum mechanics

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

176

Two basic Uncertainty Relations in Quantum Mechanics

NASA Astrophysics Data System (ADS)

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 Schrödinger 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

2011-04-01

177

Noncommutative unification of general relativity and quantum mechanics

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

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

2005-12-15

178

Relational motivation for conformal operator ordering in quantum cosmology

NASA Astrophysics Data System (ADS)

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), for which all that is required is for the kinetic and potential factors to rescale in compensation to each other. These actions themselves mathematically sharply implement philosophical principles relevant to whole-universe modelling, so that the motivation for conformal operator ordering in quantum cosmology is thereby substantially strengthened. Relationalist product-type actions also give emergent times which amount to recovering Newtonian, proper and cosmic time in various 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 emergent time permits relating how this simplifies equations of motion with how affine parametrization simplifies geodesics.

Anderson, Edward

2010-02-01

179

A broken symmetry ontology: Quantum mechanics as a broken symmetry

The author proposes a new broken symmetry ontology to be used to analyze the quantum domain. This ontology is motivated and grounded in a critical epistemological analysis, and an analysis of the basic role of symmetry in physics. Concurrently, he is led to consider nonheterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows him to find a generalized principle of symmetry and a generalized symmetry-conservation formalisms. In particular, he clarifies the role of Noether's theorem in field theory. He shows how a broken symmetry ontology already operates in a description of the weak interactions. Finally, by showing how a broken symmetry ontology operates in the quantum domain, he accounts for the interpretational problem and the essential incompleteness of quantum mechanics. He proposes that the broken symmetry underlying this ontological domain is broken dilation invariance.

Buschmann, J.E.

1988-01-01

180

On the Lattice Structure of Probability Spaces in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Let {C} be the set of all possible quantum states. We study the convex subsets of {C} with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models' approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics.

Holik, Federico; Massri, César; Plastino, A.; Zuberman, Leandro

2013-06-01

181

NASA Astrophysics Data System (ADS)

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

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

2011-11-01

182

Quantum mechanics clearly violates the weak equivalence principle (WEP). This implies that quantum mechanics also violates the strong equivalence principle (SEP), as shown in this paper. Therefore a theory of quantum gravity may not be possible unless it is not based upon the equivalence principle, or if quantum mechanics can change its mass dependence. Neither of these possibilities seem likely

Mario Rabinowitz

2006-01-01

183

Can quantum mechanics fool the cosmic censor?

NASA Astrophysics Data System (ADS)

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

Matsas, G. E. A.; Richartz, M.; Saa, A.; da Silva, A. R. R.; Vanzella, D. A. T.

2009-05-01

184

Relativistic quantum mechanics of supersymmetric particles

The quantum mechanics of an electron in an external field is developed by Hamiltonian path integral methods. The electron is described classically by an action which is invariant under gauge sypersymmetry transformations as well as worldline reparametrizations. The simpler case of a spinless particle is first reviewed and it is pointed out that a strictly canonical approach does not exist.

Marc Henneaux; Claudio Teitelboim

1982-01-01

185

Student Difficulties with Quantum Mechanics Formalism

NSDL National Science Digital Library

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

Singh, Chandralekha

2007-06-26

186

Finite Size Scaling in Quantum Mechanics

The finite size scaling ansatz is combined with the variational method to extract information about critical behavior of quantum Hamiltonians. This approach is based on taking the number of elements in a complete basis set as the size of the system. As in statistical mechanics, the finite size scaling can then be used directly in the Schrodinger equation. This approach

Pablo Serra; Juan Pablo Neirotti; Sabre Kais

1998-01-01

187

Quantum mechanical hamiltonian models of turing machines

Quantum mechanical Hamiltonian models, which represent an aribtrary but finite number of steps of any Turing machine computation, are constructed here on a finite lattice of spin-1\\/2 systems. Different regions of the lattice correspond to different components of the Turing machine (plus recording system). Successive states of any machine computation are represented in the model by spin configuration states. Both

Paul Benioff

1982-01-01

188

Spacetime Probabilities in Nonrelativistic Quantum Mechanics

NASA Astrophysics Data System (ADS)

We demonstrate the existence of spacetime probabilities in nonrelativistic quantum mechanics, that is, quantum mechanical probabilities for a set of alternatives which are associated, not with a surface of constant time, but with spacetime domains with nonzero spatial and temporal width in Newtonian spacetime. We use the criterion that quantum mechanical probabilities can be defined for a set of alternatives if and only if the interference between any two different alternatives vanishes. Although generalized quantum mechanics was formulated on the basis of this criterion, the actual existence of spacetime probabilities has not been known. In this paper we consider a rectangular spacetime domain Omega and introduce a set of spacetime alternatives \\{Yes, No\\}: ``Yes'' is to find a particle in Omega and ``No'' is the complement to ``Yes''. We show that, if the initial amplitude of the particle belongs to a specific class, then the criterion of vanishing interference is met by ``Yes'' and ``No'' and spacetime probabilities can be therefore defined for the set \\{Yes, No\\}. Owing to the property of the initial amplitude belonging to the class, the resultant probabilities are associated with a clear measurement theoretical meaning.

Yamada, N.; Takagi, S.

1992-01-01

189

Understanding Kinetic Energy paradox in Quantum Mechanics

A concept of Kinetic Energy in Quantum Mechanics is analyzed. Kinetic Energy is not zero in many cases where there are no motion and flux. This paradox can be understood, using expansion of the wave function in Fourier integral, that is on the basis of virtual plane waves.

Yuri Kornyushin

2008-01-01

190

Kinetic and electrostatic energies in quantum mechanics

A concept of kinetic energy in quantum mechanics is analyzed. Kinetic energy is a non-zero positive value in many cases of bound states, when a wave function is a real-valued one and there are no visible motion and flux. This can be understood, using expansion of the wave function into Fourier integral, that is, on the basis of virtual plane

Yuri Kornyushin

2008-01-01

191

Inverse scattering with supersymmetric quantum mechanics

The application of supersymmetric quantum mechanics to the inverse scattering problem is reviewed. The main difference with standard treatments of the inverse problem lies in the simple and natural extension to potentials with singularities at the origin and with a Coulomb behaviour at infinity. The most general form of potentials which are phase-equivalent to a given potential is discussed. The

Daniel Baye; Jean-Marc Sparenberg

2004-01-01

192

Solution for quantum mechanical problem in physics

NASA Astrophysics Data System (ADS)

The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. In this Paper the solution is obtained by Variational Homotopy perturbation method which is coupling of Variational iteration method and Homotopy Perturbation Method. The solution describes how the wave function of a physical system evolves over time.

Daga, Amruta; Pradhan, V. H.

2013-06-01

193

Consistent interpretations of quantum mechanics

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

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

1992-04-01

194

A probabilistic approach to quantum mechanics based on tomograms

It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation of quantum states. This can be regarded as a classical-like formulation of quantum mechanics which avoids the counterintuitive concepts of wave function

Michele Caponigro; Stefano Mancini; V. I. Man'ko

2006-01-01

195

Novel symmetries in N=2 supersymmetric quantum mechanical models

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

196

Kink mass quantum shifts from SUSY quantum mechanics

NASA Astrophysics Data System (ADS)

In this paper a new version of the DHN (Dashen-Hasslacher-Neveu) formula, which is used to compute the one-loop order kink mass correction in (1+1)-dimensional scalar field theory models, is constructed. The new expression is written in terms of the spectral data coming from the supersymmetric partner operator of the second-order small kink fluctuation operator and allows us to compute the kink mass quantum shift in new models for which this calculation was out of reach by means of the old formula.

Izquierdo, Alberto Alonso; Guilarte, Juan Mateos; Plyushchay, Mikhail S.

2013-04-01

197

Quantum mechanical coherence, resonance, and mind

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

Stapp, H.P.

1995-03-26

198

Barrier engineered superlattice and quantum dot detectors for HOT operation

In this paper, we demonstrate a high operating temperature (HOT) quantum dot-in-a-well (DWELL) infrared photodetector with enhanced normal incidence (s-polarization) radiation photocurrent. The s-to-p polarization ratio was increased to 50%, compared to the 20% in conventional quantum dot detectors. This improvement was achieved through engineering the dot geometry and the quantum confinement via post growth capping materials of the quantum

Jiayi Shao; Thomas E. Vandervelde; Ajit Barve; Woo-Yong Jang; Andreas Stintz; Sanjay Krishna

2011-01-01

199

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

200

Emerging interpretations of quantum mechanics and recent progress in quantum measurement

NASA Astrophysics Data System (ADS)

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

Clarke, M. L.

2014-01-01

201

F-theory Yukawa couplings and supersymmetric quantum mechanics

NASA Astrophysics Data System (ADS)

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

Oikonomou, V. K.

2012-03-01

202

Novel symmetries in N=2 supersymmetric quantum mechanical models

NASA Astrophysics Data System (ADS)

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

Malik, R. P.; Khare, Avinash

2013-07-01

203

Quantum mechanics on Laakso spaces

NASA Astrophysics Data System (ADS)

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

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

2012-04-01

204

1/n expansion in quantum mechanics

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

205

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

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

206

Multicolor tunneling quantum dot infrared photodetectors operating at room temperature

Quantum dot structures designed for multi-color infrared detection and high temperature (or room temperature) operation are demonstrated. A novel approach, tunneling quantum dot (T-QD), was successfully demonstrated with a detector that can be operated at room temperature due to the reduction of the dark current by blocking barriers incorporated into the structure. Photoexcited carriers are selectively collected from InGaAs quantum

G. Ariyawansa; A. G. U. Perera; X. H. Su; S. Chakrabarti; P. Bhattacharya

2007-01-01

207

Neutrino oscillations: Quantum mechanics vs. quantum field theory

A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.

Akhmedov, Evgeny Kh.; Kopp, Joachim

2010-01-01

208

Radio frequency operation of a quantum point contact charge detector

Quantum point contact (QPC) charge detectors are sensitive electrometers, and their ease of fabrication and integration into semiconductor-based qubit systems makes them an attractive candidate as a readout device for spin or charge based qubits in quantum dots. Nevertheless, QPC performance to date has been limited by relatively low operational speeds and 1\\/f noise. Here we report the operation of

Madhu Thalakulam; A. J. Rimberg; L. N. Pfeiffer; K. W. West

2007-01-01

209

GENERALIZED WHITE NOISE OPERATOR FIELDS AND QUANTUM WHITE NOISE DERIVATIVES

Regarding a Fock space operator as a function of quantum white noise = ( at;a t ; t2 T ), we introduce its quantum white noise derivatives (qwn- derivatives) as a kind of functional derivatives with respect to at and a t . We prove that every white noise operator is dierentiable and the qwn-derivatives form a gen- eralized white

Un Cig Ji; Nobuaki Obata

210

Fast method for quantum mechanical molecular dynamics

NASA Astrophysics Data System (ADS)

As the processing power available for scientific computing grows, first-principles Born-Oppenheimer molecular dynamics simulations are becoming increasingly popular for the study of a wide range of problems in materials science, chemistry, and biology. Nevertheless, the computational cost of Born-Oppenheimer molecular dynamics still remains prohibitively large for many potential applications. Here we show how to avoid a major computational bottleneck: the self-consistent-field optimization prior to force calculations. The optimization-free quantum mechanical molecular dynamics method gives trajectories that are almost indistinguishable from an “exact” microcanonical Born-Oppenheimer molecular dynamics simulation even when low-prefactor linear scaling sparse matrix algebra is used. Our findings show that the computational gap between classical and quantum mechanical molecular dynamics simulations can be significantly reduced.

Niklasson, Anders M. N.; Cawkwell, Marc J.

2012-11-01

211

Applications of computational quantum mechanics

NASA Astrophysics Data System (ADS)

This original research dissertation is composed of a new numerical technique based on Chebyshev polynomials that is applied on scattering problems, a phenomenological kinetics study for CO oxidation on RuO2 surface, and an experimental study on methanol coupling with doped metal oxide catalysts. Minimum Error Method (MEM), a least-squares minimization method, provides an efficient and accurate alternative to solve systems of ordinary differential equations. Existing methods usually utilize matrix methods which are computationally costful. MEM, which is based on the Chebyshev polynomials as a basis set, uses the recursion relationships and fast Chebyshev transforms which scale as O(N). For large basis set calculations this provides an enormous computational efficiency in the calculations. Chebyshev polynomials are also able to represent non-periodic problems very accurately. We applied MEM on elastic and inelastic scattering problems: it is more efficient and accurate than traditionally used Kohn variational principle, and it also provides the wave function in the interaction region. Phenomenological kinetics (PK) is widely used in industry to predict the optimum conditions for a chemical reaction. PK neglects the fluctuations, assumes no lateral interactions, and considers an ideal mix of reactants. The rate equations are tested by fitting the rate constants to the results of the experiments. Unfortunately, there are numerous examples where a fitted mechanism was later shown to be erroneous. We have undertaken a thorough comparison between the phenomenological equations and the results of kinetic Monte Carlo (KMC) simulations performed on the same system. The PK equations are qualitatively consistent with the KMC results but are quantitatively erroneous as a result of interplays between the adsorption and desorption events. The experimental study on methanol coupling with doped metal oxide catalysts demonstrates the doped metal oxides as a new class of catalysts with novel properties. Doping a metal oxide may alter its intrinsic properties drastically. A catalytically non-active material can be activated by doping. In this study, we showed that pure zirconia (ZrO2) has almost no activity in methanol coupling reaction, whereas when it is doped with aluminum, the doped catalyst produces dimethyl ether (DME), which is valuable as an alternative future energy source.

Temel, Burcin

212

Collocation method for fractional quantum mechanics

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

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

2010-12-15

213

Grounding quantum probability in psychological mechanism.

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

Love, Bradley C

2013-06-01

214

Diffeomorphism groups and nonlinear quantum mechanics

NASA Astrophysics Data System (ADS)

This talk is dedicated to my friend and collaborator, Prof. Dr. Heinz-Dietrich Doebner, on the occasion of his 80th birthday. I shall review some highlights of the approach we have taken in deriving and interpreting an interesting class of nonlinear time-evolution equations for quantum-mechanical wave functions, with few equations; more detail may be found in the references. Then I shall comment on the corresponding hydrodynamical description.

Goldin, Gerald A.

2012-02-01

215

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

216

Relativistic non-Hermitian quantum mechanics

NASA Astrophysics Data System (ADS)

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

Jones-Smith, Katherine; Mathur, Harsh

2014-06-01

217

Hunting for Snarks in Quantum Mechanics

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

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

2009-12-08

218

It is shown that the Boltzmann operator in time correlation functions for complex molecular systems can be evaluated in a numerically exact way employing the multilayer formulation of the multiconfiguration time-dependent Hartree theory in combination with Monte Carlo importance sampling techniques. The performance of the method is illustrated by selected applications to photoinduced intervalence electron transfer reactions in the condensed phase. Furthermore, the validity of approximate schemes to evaluate the Boltzmann is discussed.

Wang, Haobin; Thoss, Michael [Department of Chemistry and Biochemistry, MSC 3C, New Mexico State University, Las Cruces, New Mexico 88003 (United States); Department of Chemistry, Technical University of Munich, 85748 Garching (Germany)

2006-01-21

219

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

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

220

Classical-Operation-Based Deterministic Secure Quantum Communication

NASA Astrophysics Data System (ADS)

We generalize the unitary-operation-based deterministic secure quantum communication (UODSQC) model (protocol) to describe the conventional deterministic secure quantum communication (DSQC) protocols in which unitary operations are usually utilized for encoding or decoding message. However, it is found that unitary operation for message encoding or decoding is not required and can be replaced with classical operation in DSQC. So the classical-operation-based deterministic secure quantum communication (CODSQC) model (protocol) is put forward. Then the rigorous mathematical analysis to explain the reason why classical operations can replace unitary operations to encode or decode secret deterministic message is given. Although unitary operations are still possibly needed in the whole communication of CODSQC model (protocol), those used for message encoding or decoding are omitted and replaced with classical operations in CODSQC model (protocol). As a result, the CODSQC model (protocol) is simpler and even more robust than the UODSQC one.

Liu, Zhi-Hao; Chen, Han-Wu; Wang, Dong; Xue, Xi-Ling

2014-02-01

221

Classical-Operation-Based Deterministic Secure Quantum Communication

NASA Astrophysics Data System (ADS)

We generalize the unitary-operation-based deterministic secure quantum communication (UODSQC) model (protocol) to describe the conventional deterministic secure quantum communication (DSQC) protocols in which unitary operations are usually utilized for encoding or decoding message. However, it is found that unitary operation for message encoding or decoding is not required and can be replaced with classical operation in DSQC. So the classical-operation-based deterministic secure quantum communication (CODSQC) model (protocol) is put forward. Then the rigorous mathematical analysis to explain the reason why classical operations can replace unitary operations to encode or decode secret deterministic message is given. Although unitary operations are still possibly needed in the whole communication of CODSQC model (protocol), those used for message encoding or decoding are omitted and replaced with classical operations in CODSQC model (protocol). As a result, the CODSQC model (protocol) is simpler and even more robust than the UODSQC one.

Liu, Zhi-Hao; Chen, Han-Wu; Wang, Dong; Xue, Xi-Ling

2014-06-01

222

From Cbits to Qbits: Teaching computer scientists quantum mechanics

NASA Astrophysics Data System (ADS)

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. Although the article as a whole addresses teachers of physics well versed in quantum mechanics, the central pedagogical development is addressed directly to computer scientists and mathematicians, with only occasional asides to their teacher. Physicists uninterested in quantum pedagogy may be amused (or irritated) by some of the views of standard quantum mechanics that arise naturally from this unorthodox perspective.

Mermin, N. David

2003-01-01

223

The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

Kustermans, Johan; Vaes, Stefaan

2000-01-01

224

Quantum operations fixing a convex cone of density operators on {{ T}}(H)

NASA Astrophysics Data System (ADS)

The unital quantum operation acting on infinite dimensional quantum states fixing a convex cone of density operators is completely characterized. Based on this result, we classify the commutativity of two quantum operations and determine what kind of measurement statistics are preserved by a unital quantum operation. Our work extends the results of Lee et al (2013 J. Phys. A: Math. Theor. 46 205305) to the infinite dimensional case and also corrects part (a) of theorem 6 in Lee et al (2013 J. Phys. A: Math. Theor. 46 205305).

Bai, Zhaofang; Du, Shuanping

2014-05-01

225

Representations for a spins-first approach to quantum mechanics

NSDL National Science Digital Library

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 A.; Gire, Elizabeth; Mcintyre, David; Tate, Janet

2012-05-15

226

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

227

Surveying Students' Understanding of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Development of research-based multiple-choice tests about quantum mechanics is important for assessing students' 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 instructional strategies.

Singh, Chandralekha; Zhu, Guangtian

2011-03-01

228

Surveying Students' Understanding of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Development of research-based multiple-choice tests about quantum mechanics is important for assessing students' 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

2010-10-01

229

Quantum mechanics with coordinate dependent noncommutativity

NASA Astrophysics Data System (ADS)

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.

2013-11-01

230

Quantum mechanics with coordinate dependent noncommutativity

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

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

2013-11-15

231

Topological quantum mechanics in 2 + 1 dimensions

The authors show that the classical and quantum covariant dynamics of spinning particles in flat space in 2 + 1 dimensions are derived from a pure Wess-Zumino term written on the space of adjoint orbits of the ISO(2,1) group. Similarly, the dynamics of spinning particles in 2 + 1 de Sitter (anti-de Sitter) space are derived from a Wess-Zumino term on the space of adjoint orbits of SO(3,1)(SO(2,2)). It is shown that a quantum mechanical description of spin is possible in 2 + 1 dimensions without introducing explicit spin degrees of freedom, but at the expense of having a noncommutative space-time geometry.

Skagerstam, B.S. (Inst. of Theoretical Physics, Chalmers Univ. of Technology, S-412 96 Goteborg (SE)); Stern, A. (Dept. of Physics and Astronomy, Univ. of Alabama, Tuscaloosa, AL (US))

1990-04-20

232

Quantum Mechanics à la Langevin and Supersymmetry

NASA Astrophysics Data System (ADS)

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.

Nicolis, S.

233

Generation of quantum logic operations from physical Hamiltonians

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

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

2005-05-15

234

Many-body quantum mechanics as a symplectic dynamical system

An approach is formulated to the problem of obtaining approximate solutions to many-body quantum mechanics. The starting point is the representation of quantum mechanics as Hamiltonian mechanics on a symplectic manifold (phase space). It is shown that Dirac's variation of an action integral provides a natural mechanism for constraining the dynamics to symplectic submanifolds and gives rise to a hierarchy

D. J. Rowe; A. Ryman; G. Rosensteel

1980-01-01

235

The Yukawa potential in semirelativistic formulation via supersymmetry quantum mechanics

NASA Astrophysics Data System (ADS)

We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation (SSE) with the Yukawa potential via the supersymmetric quantum mechanics (SUSYQM) for arbitrary quantum numbers. Useful figures and tables are also included.

Hassanabadi, S.; Ghominejad, M.; Zarrinkamar, S.; Hassanabadi, H.

2013-06-01

236

Quantum discord, local operations, and Maxwell's demons

Quantum discord was proposed as a measure of the quantumness of correlations. There are at least three different discordlike quantities, two of which determine the difference between the efficiencies of a Szilard's engine under different sets of restrictions. The three discord measures vanish simultaneously. We introduce an easy way to test for zero discord, relate it to the Cerf-Adami conditional entropy and show that there is no simple relation between the discord and the local distinguishability.

Brodutch, Aharon; Terno, Daniel R. [Department of Physics and Astronomy, Faculty of Science, Macquarie University, New South Wales 2109 (Australia)

2010-06-15

237

Quantum discord, local operations, and Maxwell's demons

NASA Astrophysics Data System (ADS)

Quantum discord was proposed as a measure of the quantumness of correlations. There are at least three different discordlike quantities, two of which determine the difference between the efficiencies of a Szilard’s engine under different sets of restrictions. The three discord measures vanish simultaneously. We introduce an easy way to test for zero discord, relate it to the Cerf-Adami conditional entropy and show that there is no simple relation between the discord and the local distinguishability.

Brodutch, Aharon; Terno, Daniel R.

2010-06-01

238

Loop quantum cosmology: III. Wheeler-DeWitt operators

Within the framework of loop quantum cosmology anomaly-free quantizations of the Hamiltonian constraint for Bianchi class A, locally rotationally symmetric and isotropic models are given. Basic ideas of the construction in (non-symmetric) loop quantum gravity can be used, but there are also further inputs because the special structure of symmetric models has to be respected by operators. In particular, the

Martin Bojowald

2001-01-01

239

Effectiveness of Quantum Operations for Eavesdropping on Sealed Messages.

National Technical Information Service (NTIS)

A quantum protocol is described which enables a user to send sealed messages and that allows for the detection of active eavesdroppers. We examine a class of eavesdropping strategies, those that make use of quantum operations, and we determine the informa...

P. A. Lopata T. B. Bahder

2007-01-01

240

Quantum fluctuations of the light field used for continuous position detection produce stochastic back-action forces and ultimately limit the sensitivity. To overcome this limit, the back-action forces can be avoided by giving up complete knowledge of the motion, and these types of measurements are called "back-action evading" or "quantum nondemolition" detection. We present continuous two-tone back-action evading measurements with a superconducting electromechanical device, realizing three long-standing goals: detection of back-action forces due to the quantum noise of a microwave field, reduction of this quantum back-action noise by 8.5 ± 0.4 decibels (dB), and measurement imprecision of a single quadrature of motion 2.4 ± 0.7 dB below the mechanical zero-point fluctuations. Measurements of this type will find utility in ultrasensitive measurements of weak forces and nonclassical states of motion. PMID:24831528

Suh, J; Weinstein, A J; Lei, C U; Wollman, E E; Steinke, S K; Meystre, P; Clerk, A A; Schwab, K C

2014-06-13

241

From classical to quantum mechanics: ``How to translate physical ideas into mathematical language''

NASA Astrophysics Data System (ADS)

Following previous works by E. Prugove?ki [Physica A 91A, 202 (1978) and Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)] on common features of classical and quantum mechanics, we develop a unified mathematical framework for classical and quantum mechanics (based on L2-spaces over classical phase space), in order to investigate to what extent quantum mechanics can be obtained as a simple modification of classical mechanics (on both logical and analytical levels). To obtain this unified framework, we split quantum theory in two parts: (i) general quantum axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoints operators, and so on) and (ii) quantum mechanics proper that specifies the Hilbert space as L2(Rn); the Heisenberg rule [pi,qj]=-i??ij with p=-i??, the free Hamiltonian H=-?2?/2m and so on. We show that general quantum axiomatics (up to a supplementary ``axiom of classicity'') can be used as a nonstandard mathematical ground to formulate physical ideas and equations of ordinary classical statistical mechanics. So, the question of a ``true quantization'' with ``?'' must be seen as an independent physical problem not directly related with quantum formalism. At this stage, we show that this nonstandard formulation of classical mechanics exhibits a new kind of operation that has no classical counterpart: this operation is related to the ``quantization process,'' and we show why quantization physically depends on group theory (the Galilei group). This analytical procedure of quantization replaces the ``correspondence principle'' (or canonical quantization) and allows us to map classical mechanics into quantum mechanics, giving all operators of quantum dynamics and the Schrödinger equation. The great advantage of this point of view is that quantization is based on concrete physical arguments and not derived from some ``pure algebraic rule'' (we exhibit also some limit of the correspondence principle). Moreover spins for particles are naturally generated, including an approximation of their interaction with magnetic fields. We also recover by this approach the semi-classical formalism developed by E. Prugove?ki [Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)].

Bergeron, H.

2001-09-01

242

Testing Quantum Mechanics on New Ground

NASA Astrophysics Data System (ADS)

Preface; Acknowledgements; 1. Wave-particle duality; 2. Cavity quantum electrodynamics; 3. Quantum nondemolition measurements; 4. Topological phases; 5. Macroscopic quantum coherence; 6. The quantum Zeno paradox; 7. Testing collapse; 8. Macroscopic quantum jumps; 9. Nonlocality; 10. Tunneling times; References; Indexes.

Ghose, Partha

2006-11-01

243

Scattering in PT-symmetric quantum mechanics

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

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

2007-02-15

244

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

245

Quantum Superspace, q-EXTENDED Supersymmetry and Parasupersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

We describe q-deformation of the extended supersymmetry and construct q-extended supersymmetric Hamiltonian. For this purpose we formulate q-superspace formalism and construct q-supertransformation group. On this basis q-extended supersymmetric Lagrangian is built. The canonical quantization of this system is considered. The connection with multi-dimensional matrix representations of the parasupersymmetric quantum mechanics is discussed and q-extended supersymmetric harmonic oscillator is considered as a simplest example of the described constructions. We show that extended supersymmetric Hamiltonians obey not only extended SUSY but also the whole family of symmetries (q-extended supersymmetry) which is parametrized by continuous parameter q on the unit circle.

Ilinski, K. N.; Uzdin, V. M.

246

Generic quantum walk using a coin-embedded shift operator

NASA Astrophysics Data System (ADS)

The study of quantum walk processes has been widely divided into two standard variants, the discrete-time quantum walk (DTQW) and the continuous-time quantum walk (CTQW). The connection between the two variants has been established by considering the limiting value of the coin operation parameter in the DTQW, and the coin degree of freedom was shown to be unnecessary [F. W. Strauch, Phys. Rev. A 74, 030301(R) (2006)]. But the coin degree of freedom is an additional resource which can be exploited to control the dynamics of the QW process. In this paper we present a generic quantum walk model using a quantum coin-embedded unitary shift operation UC . The standard version of the DTQW and the CTQW can be conveniently retrieved from this generic model, retaining the features of the coin degree of freedom in both variants.

Chandrashekar, C. M.

2008-11-01

247

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

2013-08-01

248

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

249

Universal programmable quantum circuit schemes to emulate an operator

NASA Astrophysics Data System (ADS)

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.

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

2012-12-01

250

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

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

251

Mind, Matter and Quantum Mechanics (2nd edition)

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

252

Probability in the formalism of quantum mechanics on phase space

NASA Astrophysics Data System (ADS)

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

Schroeck, Franklin E., Jr.

2012-02-01

253

a Proper Nonlocal Formulation of Quantum Maximum Entropy Principle in Statistical Mechanics

NASA Astrophysics Data System (ADS)

By considering Wigner formalism, the quantum maximum entropy principle (QMEP) is here asserted as the fundamental principle of quantum statistical mechanics when it becomes necessary to treat systems in partially specified quantum states. From one hand, the main difficulty in QMEP is to define an appropriate quantum entropy that explicitly incorporates quantum statistics. From another hand, the availability of rigorous quantum hydrodynamic (QHD) models is a demanding issue for a variety of quantum systems. Relevant results of the present approach are: (i) The development of a generalized three-dimensional Wigner equation. (ii) The construction of extended quantum hydrodynamic models evaluated exactly to all orders of the reduced Planck constant ?. (iii) The definition of a generalized quantum entropy as global functional of the reduced density matrix. (iv) The formulation of a proper nonlocal QMEP obtained by determining an explicit functional form of the reduced density operator, which requires the consistent introduction of nonlocal quantum Lagrange multipliers. (v) The development of a quantum-closure procedure that includes nonlocal statistical effects in the corresponding quantum hydrodynamic system. (vi) The development of a closure condition for a set of relevant quantum regimes of Fermi and Bose gases both in thermodynamic equilibrium and nonequilibrium conditions.

Trovato, M.; Reggiani, L.

254

NASA Astrophysics Data System (ADS)

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.; Caban, P.; Ciborowski, J.; Enders, J.; Köhler, A.; Kozela, A.; Rembieli?ski, J.; Rozpedzik, D.; W?odarczyk, M.; Zejma, J.

2013-11-01

255

Multiplication of distributions and Dirac formalism of quantum mechanics

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

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

2010-02-15

256

Twisting all the way: From classical mechanics to quantum fields

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

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

2008-01-15

257

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

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

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

2008-02-15

258

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

Natalia Kanaan; Sergio Martí; Vicent Moliner; Amnon Kohen

2007-01-01

259

Coulomb problem in non-commutative quantum mechanics

NASA Astrophysics Data System (ADS)

The aim of this paper is to find out how it would be possible for space non-commutativity (NC) to alter the quantum mechanics (QM) solution of the Coulomb problem. The NC parameter ? is to be regarded as a measure of the non-commutativity - setting ? = 0 which means a return to the standard quantum mechanics. As the very first step a rotationally invariant NC space R?3, an analog of the Coulomb problem configuration space (R3 with the origin excluded) is introduced. R?3 is generated by NC coordinates realized as operators acting in an auxiliary (Fock) space . The properly weighted Hilbert-Schmidt operators in form ?, a NC analog of the Hilbert space of the wave functions. We will refer to them as ``wave functions'' also in the NC case. The definition of a NC analog of the hamiltonian as a hermitian operator in ? is one of the key parts of this paper. The resulting problem is exactly solvable. The full solution is provided, including formulas for the bound states for E < 0 and low-energy scattering for E > 0 (both containing NC corrections analytic in ?) and also formulas for high-energy scattering and unexpected bound states at ultra-high energy (both containing NC corrections singular in ?). All the NC contributions to the known QM solutions either vanish or disappear in the limit ? --> 0.

Gáliková, Veronika; Prešnajder, Peter

2013-05-01

260

Relationship between quantum-mechanical systems with and without monopoles

It is shown that the inclusion of the monopole field in the three- and five-dimensional spherically symmetric quantum-mechanical systems, with the addition of the special centrifugal term, leads to the lift of the range of the total and azimuth quantum numbers only. Meanwhile the functional dependence of the energy spectra on quantum numbers does not undergo any changes. We also

Levon Mardoyan; Armen Nersessian; Armen Yeranyan

2007-01-01

261

Induced representations of quantum kinematical algebras and quantum mechanics

NASA Astrophysics Data System (ADS)

Unitary representations of kinematical symmetry groups of quantum systems are fundamental in quantum theory. In this paper we propose their generalization to quantum kinematical groups. Using the method, proposed by us in a recent paper (Arratia O and del Olmo M A 2001 Preprint math.QA/0110275) to induce representations of quantum bicrossproduct algebras, we construct the representations of the family of standard quantum inhomogeneous algebras U?(iso?(2)). This family contains the quantum Euclidean, Galilei and Poincaré algebras, all of them in (1+1) dimensions. As byproducts we obtain the actions of these quantum algebras on regular co-spaces that are an algebraic generalization of the homogeneous spaces and q-Casimir equations which play the role of q-Schrödinger equations.

Arratia, Oscar; del Olmo, Mariano A.

2002-10-01

262

Elementary Quantum Mechanics in a Space-Time Lattice

NASA Astrophysics Data System (ADS)

Studies of quantum fields and gravity suggest the existence of a minimal length, such as Planck length. It is natural to ask how the existence of a minimal length may modify the results in elementary quantum mechanics (QM) problems familiar to us. In this paper we address a simple problem from elementary non-relativistic quantum mechanics, called "particle in a box", where the usual continuum (1+1)-space-time is supplanted by a space-time lattice. Our lattice consists of a grid of ? 0× ? 0 rectangles, where ? 0, the lattice parameter, is a fundamental length (say Planck length) and, we take ? 0 to be equal to ? 0/ c. The corresponding Schroedinger equation becomes a difference equation, the solution of which yields the q-eigenfunctions and q-eigenvalues of the energy operator as a function of ? 0. The q-eigenfunctions form an orthonormal set and both q-eigenfunctions and q-eigenvalues reduce to continuum solutions as ? 0?0. The corrections to eigenvalues because of the assumed lattice is shown to be O(?02). We then compute the uncertainties in position and momentum, ? x, ? p for the box problem and study the consequent modification of Heisenberg uncertainty relation due to the assumption of space-time lattice, in contrast to modifications suggested by other investigations.

Bhatia, Manjit; Swamy, P. Narayana

2011-06-01

263

a Quantum Mechanical Semiconductor Device Simulator.

NASA Astrophysics Data System (ADS)

Semiconductor device simulators have generally been based on either classical or semi-classical approaches. In these approaches, the Poisson's equation is solved with either the current continuity equation or the Boltzmann transport equation. Methods based on quantum mechanics have been generally very computer intensive, and thus until recently not much favored. However, with the availability of faster and more powerful computers this picture is changing. As the physical dimensions of the semiconductor devices are reduced, the assumptions made in the classical and the semi-classical approaches become invalid and the simulation results become inaccurate. For such cases, quantum mechanical concepts must be introduced to provide accurate simulation results. This dissertation presents the proof of concept of a semiconductor device simulator based on the quantum mechanical principals. The simulation technique is based on the self consistent solution of the Poisson's and time independent Schrodinger wave equation for a 1-D finite differenced grid. The applicability of the technique to a 2-D finite differenced grid is also presented. The simulation is performed by first solving for the Fermi energy distribution inside the simulation domain. The initial estimates about the carrier concentrations are developed from the Fermi energy distribution. Based on the carrier concentrations, the potential distribution inside the device is updated using the Poisson's equation. The updated potential distribution is then used in the time independent Schrodinger's equation and the carrier wave vectors are thus determined. The carrier wave vectors, along with appropriate density of state function and distribution function are used to update the carrier concentrations. For the 1-D case, the density of state function is based on a single dimension of a three dimensional volume with the assumption that the density of states is the same for all the three dimensions. The distribution function used is the Fermi-Dirac distribution function. The new carrier concentrations thus computed are then substituted back into the Poisson's equation, and self consistency is obtained when minimum error criteria have been met. The device simulator has the capability of simulating heterojunctions semiconductor devices fabricated from elemental semiconductors such as Si and Ge, as well as binary and tertiary compound semiconductors.

Bhutta, Imran Ahmed

264

Tampering detection system using quantum-mechanical systems

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

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

2011-12-13

265

Quantum mechanics and the direction of time

In recent papers the authors have discussed the dynamical properties of large Poincare systems (LPS), that is, nonintegrable systems with a continuous spectrum (both classical and quantum). An interesting example of LPS is given by the Friedrichs model of field theory. As is well known, perturbation methods analytic in the coupling constant diverge because of resonant denominators. They show that this Poincare catastrophe can be eliminated by a natural time ordering of the dynamical states. They obtain then a dynamical theory which incorporates a privileged direction of time (and therefore the second law of thermodynamics). However, it is only in very simple situations that his time ordering can be performed in an extended Hilbert space. In general, they need to go to the Liouville space (superspace) and introduce a time ordering of dynamical states according to the number of particles involved in correlations. This leads then to a generalization of quantum mechanics in which the usual Heisenberg's eigenvalue problem is replaced by a complex eigenvalue problem in the Liouville space.

Hasegawa, H.; Petrosky, T. (Univ. of Texas, Austin (United States)); Prigogine, I. (Univ. of Texas, Austin (United States) International Solvay Inst. for Physics and Chemistry, Brussels (Belgium)); Tasaki, S. (International Solvay Inst. for Physics and Chemistry, Brussels (Belgium))

1991-03-01

266

Hilbert space for quantum mechanics on superspace

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

267

Hilbert space for quantum mechanics on superspace

NASA Astrophysics Data System (ADS)

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

Coulembier, K.; de Bie, H.

2011-06-01

268

Quantum mechanics without an equation of motion

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

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

2011-06-15

269

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

270

Nonlinear supersymmetric quantum mechanics: concepts and realizations

NASA Astrophysics Data System (ADS)

The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum mechanics (QM) is reviewed. Its building from the chains (ladders) of linear SUSY systems is outlined and different one-dimensional and two-dimensional realizations are described. It is elaborated how the nonlinear SUSY approach provides two new methods of SUSY separation of variables for various two-dimensional models. In the framework of these methods, a partial and/or complete solution of some two-dimensional models becomes possible. The full classification of ladder-reducible and irreducible chains of SUSY algebras in one-dimensional QM is given. The emergence of hidden symmetries and spectrum generating algebras is elucidated in the context of the nonlinear SUSY in one-dimensional stationary and non-stationary, as well as in two-dimensional QM.

Andrianov, A. A.; Ioffe, M. V.

2012-12-01

271

Quantum mechanical evolution towards thermal equilibrium.

The circumstances under which a system reaches thermal equilibrium, and how to derive this from basic dynamical laws, has been a major question from the very beginning of thermodynamics and statistical mechanics. Despite considerable progress, it remains an open problem. Motivated by this issue, we address the more general question of equilibration. We prove, with virtually full generality, that reaching equilibrium is a universal property of quantum systems: almost any subsystem in interaction with a large enough bath will reach an equilibrium state and remain close to it for almost all times. We also prove several general results about other aspects of thermalization besides equilibration, for example, that the equilibrium state does not depend on the detailed microstate of the bath. PMID:19658469

Linden, Noah; Popescu, Sandu; Short, Anthony J; Winter, Andreas

2009-06-01

272

The measurement problem in quantum mechanics: A phenomenological investigation

NASA Astrophysics Data System (ADS)

This dissertation is a phenomenological investigation of the measurement problem in quantum mechanics. The primary subject matter for description and analysis is scientific instruments and their use in experiments which elicit the measurement problem. A methodological critique is mounted against the ontological commitments taken for granted in the canonical interpretations of quantum theory and the scientific activity of measurement as the necessary interface between theoretical interest and perceptual results. I argue that an aesthetic dimension of reality functions as aproto-scientific establishment of sense-making that constantly operates to set integratively all other cognitively neat determinations, including scientifically rendered objects that are intrinsically non-visualizable. The way in which data "key in" to the original and originative register of the sensible in observation is clarified by examining prostheses, measuring apparatuses and instruments that are sense-conveying and -integrative with the human sensorium. Experiments, technology and instrumentation are examined in order to understand how knowing and that which is known is bonded by praxis-aisthesis. Quantum measurement is a praxic-dynamie activity and homologically structured and structur ing functional engagement in terms of instantiation, quantifiability, and spatiotemporal differentiation. The distinctions between a beauty-aesthetic and praxis-aisthesis are delineated. It is argued that a beauty-aesthetic is a construal of the economic dimension of scientific objects and work, and is not the primary manner in which the aesthetic dimension is disclosed. The economic dimension of abstractions reduces to an austere aesthetic of calculative economy. Nature itself, however, is not stingy; it is intrinsically capacious, extravagant, full of surprise, nuance, ambiguity and allusiveness. The capaciousness of Nature and the way in which we are integratively set within Nature in a materiality-phenomenality correlation discloses Nature's constituent potential, a condition more primitive than causal interplay. Finally, the relation between a physical mechanism or process and its functional mathematical representation is clarified. No physical mechanism or process accounts for the empirical effects of measurement outcomes in some quantum mechanical experiments. Within the milieu of ordinary perceptual experience, complete with its horizonal structure of spatiality and temporality, something uncaused is encountered which resists full determination in terms of mathematical representation. Keywords: Quantum Mechanics, Measurement Problem, Phenomenology, Prosthesis, Aesthetic

Hunter, Joel Brooks

273

Wigner Distribution for Angle Coordinates in Quantum Mechanics.

ERIC Educational Resources Information Center

Shows how to extend Wigner distribution functions, and Weyl correspondence between quantum and classical variables, from the usual kind of canonically conjugate position and momentum operators to the case of an angle and angular momentum operator pair. (Author/GA)

Mukunda, N.

1979-01-01

274

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

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

Chu, Chong-Sun; Zumino, B.

1995-01-24

275

Demonstration of Nondeterministic Quantum Logic Operations Using Linear Optical Elements

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

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

2002-01-01

276

Operator Method for Nonperturbative Description of Quantum Systems

NASA Astrophysics Data System (ADS)

A nonperturbative method for describing quantum systems -- the operator method (OM) and the conception of a uniformly suitable estimation (USE) are considered for a series of real physical systems. It is shown that the OM zeroth-order approximation permits one to find the analytical approximation for eigenfunctions and eigenvalues with high accuracy within the entire range of the Hamiltonian parameters and any quantum numbers. The OM subsequent approximations converge rapidly to the exact solutions of the Schrödinger equation. The generalization of OM for quantum statistics is also developed.

Feranchuk, Ilya; Ivanov, Alexey

2004-11-01

277

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

NASA Astrophysics Data System (ADS)

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

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

2012-11-01

278

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

279

Rigorous solution to a quantum statistical mechanical laser model

A quantum mechanical laser model with relaxation and pumping mechanisms is solved rigorously. A basic equation for the density matrix is derived by the damping theory and is transformed into a corresponding c-number equation for a (quasi-) probability density. This is done with the aid of the quantum phase space method. The probability density is expanded in terms of orthogonal

Fumiaki Shibata; Chikako Uchiyama

1995-01-01

280

Inner-Shell Physics after Fifty Years of Quantum Mechanics.

National Technical Information Service (NTIS)

A historical view is given of how the development of quantum mechanics has been affected by the information relating to inner shells, gathered by physicists since the early days of atomic physics, and of the impact of quantum mechanics on the physics of i...

E. Merzbacher

1976-01-01

281

On the End of a Quantum Mechanical Romance

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

Gregory R. Mulhauser

1995-01-01

282

The Quantum and Fluid Mechanics of Global Warming

Quantum physics and fluid mechanics are the foundation of any understanding of the Earth's climate. In this talk I invoke three well-known aspects of quantum mechanics to explore what will happen as the concentrations of greenhouse gases such as carbon dioxide continue to increase. Fluid dynamical models of the Earth's atmosphere, demonstrated here in live simulations, yield further insight into

Brad Marston

2008-01-01

283

Effect of violation of quantum mechanics on neutrino oscillation

NASA Astrophysics Data System (ADS)

The effect of quantum mechanics violation due to quantum gravity on neutrino oscillation is investigated. It is found that the mechanism introduced by Ellis, Hagelin, Nanopoulos, and Srednicki through the modification of the Liouville equation can affect neutrino oscillation behavior and may be taken as a new solution of the solar neutrino problem.

Liu, Yong; Hu, Liangzhong; Ge, Mo-Lin

1997-11-01

284

Linear Logic for Generalized Quantum Mechanics

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

Vaughan Pratt

1993-01-01

285

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

NASA Astrophysics Data System (ADS)

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

Aguirre, Anthony; Tegmark, Max

2011-11-01

286

Lectures on Black Hole Quantum Mechanics

NASA Astrophysics Data System (ADS)

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

Wilczek, Frank

287

Quantum Operator Design for Lattice Baryon Spectroscopy

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

Adam Lichtl

2007-09-06

288

Multiple-event probability in general-relativistic quantum mechanics. II. A discrete model

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 [Phys. Rev. D 75, 084033 (2007)]. We consider a version of the model with unitary time evolution and a version without unitary time evolution.

Mondragon, Mauricio; Perez, Alejandro; Rovelli, Carlo [Centre de Physique Theorique de Luminy, Universite de la Mediterranee, F-13288 Marseille (France)

2007-09-15

289

Noncommutative quantum mechanics: Uniqueness of the functional description

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

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

2008-12-15

290

Logical-operator tradeoff for local quantum codes

NASA Astrophysics Data System (ADS)

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

Haah, Jeongwan; Preskill, John

2012-09-01

291

Mechanics of quantum and Sharvin conductors

NASA Astrophysics Data System (ADS)

Previously, the authors reported direct evidence of channel saturation and conductance quantization in atomic-sized gold constrictions through mechanical perturbation studies, and also showed that peaks in conductance histograms are insufficient in evaluating their mechanical stability [Armstrong , Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.82.195416 82, 195416 (2010)]. In the present study, gold constrictions spanning the range from quantum to semiclassical (Sharvin) conductance regimes are mechanically probed with picolevel resolution in applied force and deformation, along with simultaneous measurements of conductance. While reconfiguration from one constriction size to another is known to occur by apparently random discrete atomic displacements, results reveal a remarkable simplicity—the magnitude of discrete atomic displacements is limited to a small set of values that correspond to elementary slip distances in gold rather than Au-Au interatomic distance. Combined with measurements of the spring constant of constrictions, results reveal two fundamental crossovers in deformation modes with increasing contact diameter—first, from homogeneous shear to defect-mediated deformation at a diameter that is in close agreement with previous predictions [Sørensen , Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.57.3283 57, 3283 (1998)]; and second, the discovery of another crossover marking surface- to volume-dominated deformation. A remarkable modulus enhancement is observed when the size of the constrictions approaches the Fermi wavelength of the electrons, and in the limit of a single-atom constriction it is at least two times that for bulk gold. Results provide atomistic insight into the stability of these constrictions and an evolutionary trace of deformation modes, beginning with a single-atom contact.

Armstrong, Jason N.; Hua, Susan Z.; Chopra, Harsh Deep

2011-06-01

292

Entanglement witness operator for quantum teleportation.

The ability of entangled states to act as a resource for teleportation is linked to a property of the fully entangled fraction. We show that the set of states with their fully entangled fraction bounded by a threshold value required for performing teleportation is both convex and compact. This feature enables the existence of Hermitian witness operators, the measurement of which could distinguish unknown states useful for performing teleportation. We present an example of such a witness operator illustrating it for different classes of states. PMID:22243295

Ganguly, Nirman; Adhikari, Satyabrata; Majumdar, A S; Chatterjee, Jyotishman

2011-12-30

293

Interagency mechanical operations group numerical systems group

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

NONE

1997-09-01

294

Wigner and Weyl functions for p-adic quantum mechanics

NASA Astrophysics Data System (ADS)

A quantum system with positions in Zp and momenta in Qp/Zp is studied. The displacement operators and also the displaced parity operators in the Zp × Qp/Zp phase space of this system, are studied. The Weyl functions (which are intimately related to the displacement operators) and the Wigner functions (which are intimately related to the displaced parity operators) are discussed.

Vourdas, A.

2010-02-01

295

On physical and mathematical causality in quantum mechanics

NASA Astrophysics Data System (ADS)

This paper critically examines the view of quantum phenomena that has persisted since the introduction of quantum mechanics and that still remains prevalent in the foundational literature on quantum theory. According to this view, the independent behavior of quantum systems is causal, while the experimentally manifest lack of causality in observable quantum phenomena and, as a result, the probabilistic nature of our predictions concerning these phenomena are due to the disruption of this causal behavior by interfering with it through the measuring process. It appears that this view originates with P. A. M. Dirac and his work on the transformation theory (introduced by him and P. Jordan), which brought together W. Heisenberg's and E. Schrödinger's versions of quantum mechanics within a single scheme. Other founding figures of quantum theory, specifically N. Bohr, W. Heisenberg, and J. von Neumann, also advanced this view and helped to establish its prominence. The paper discusses these arguments and contends them to be insufficient to support the view that the independent behavior quantum systems is physically causal. It suggests that one can meaningfully speak of mathematical causality in quantum theory, and advocates an alternative, physically noncausal, interpretation of quantum mechanics.

Plotnitsky, Arkady

2010-01-01

296

Quantum mechanics/molecular mechanics restrained electrostatic potential fitting.

We present a quantum mechanics/molecular mechanics (QM/MM) method to evaluate the partial charges of amino acid residues for use in MM potentials based on their protein environment. For each residue of interest, the nearby residues are included in the QM system while the rest of the protein is treated at the MM level of theory. After a short structural optimization, the partial charges of the central residue are fit to the electrostatic potential using the restrained electrostatic potential (RESP) method. The resulting charges and electrostatic potential account for the individual environment of the residue, although they lack the transferable nature of library partial charges. To evaluate the quality of the QM/MM RESP charges, thermodynamic integration is used to measure the pKa shift of the aspartic acid residues in three different proteins, turkey egg lysozyme, beta-cryptogein, and Thioredoxin. Compared to the AMBER ff99SB library values, the QM/MM RESP charges show better agreement between the calculated and experimental pK(a) values for almost all of the residues considered. PMID:24176005

Burger, Steven K; Schofield, Jeremy; Ayers, Paul W

2013-12-01

297

Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation

NASA Astrophysics Data System (ADS)

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

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

2013-08-01

298

Quantum mechanical model for Maya Blue

NASA Astrophysics Data System (ADS)

This work is about Maya Blue (MB), a pigment developed by Mesoamerican civilizations between the 5th and 16th centuries from an aluminosilicate mineral (palygorskite) and an organic dye (indigo). Two different supramolecular quantum-mechanical models afford explanations for the unusual stability of MB based on the oxidation of the indigo molecule during the heating process and its interaction with palygorskite. A model considering indigo derivatives attached to several aluminates shows the principal features of the experimental visible spectrum of MB within the TD-DFT methodology. Another model of an indigo oxidized species confined within an inorganic supramolecular cavity system, that involves about 170 atoms, was calculated after a large configuration interaction of single excited determinants within the NDOL approximation (Montero-Cabrera et al., J Chem Phys, 2007, 127, 145102). It allows a correct reproduction and interpretation of the corresponding spectrum. This second methodology provides the most satisfactory results, being able to manage very big molecular systems at a QM level. Structural explanation for the unusual stability of MB is also provided.

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

299

Quantum Mechanical Studies of DNA and LNA

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

Shim, Irene; Lindow, Morten; ?rum, Henrik

2014-01-01

300

Q-spaces and the Foundations of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We build a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic) theory, coping also with the physical theory’s underlying logic and mathematics.

Domenech, Graciela; Holik, Federico; Krause, Décio

2008-11-01

301

Controlled remote implementation of partially unknown quantum operation

NASA Astrophysics Data System (ADS)

A protocol for controlled remote implementation of a partially unknown operation on an arbitrary quantum state is proposed. In this protocol, a task can be performed using a GHZ state shared among three distant parties: Alice, Bob and the controller Charlie. This protocol is also generalized to the multi-party control system based on sharing an N-qubit GHZ state.

Fan, Qiubo; Liu, Dongdong

2008-11-01

302

NASA Astrophysics Data System (ADS)

The purpose of this study was to construct a valid and reliable multiple-choice achievement test to assess students' understanding of core concepts of introductory quantum mechanics. Development of the Quantum Mechanics Visualization Instrument (QMVI) occurred across four successive semesters in 1999--2001. During this time 213 undergraduate and graduate students attending the Pennsylvania State University (PSU) at University Park and Arizona State University (ASU) participated in this development and validation study. Participating students were enrolled in four distinct groups of courses: Modern Physics, Undergraduate Quantum Mechanics, Graduate Quantum Mechanics, and Chemistry Quantum Mechanics. Expert panels of professors of physics experienced in teaching quantum mechanics courses and graduate students in physics and science education established the core content and assisted in the validating of successive versions of the 24-question QMVI. Instrument development was guided by procedures outlined in the Standards for Educational and Psychological Testing (AERA-APA-NCME, 1999). Data gathered in this study provided information used in the development of successive versions of the QMVI. Data gathered in the final phase of administration of the QMVI also provided evidence that the intended score interpretation of the QMVI achievement test is valid and reliable. A moderate positive correlation coefficient of 0.49 was observed between the students' QMVI scores and their confidence levels. Analyses of variance indicated that students' scores in Graduate Quantum Mechanics and Undergraduate Quantum Mechanics courses were significantly higher than the mean scores of students in Modern Physics and Chemistry Quantum Mechanics courses (p < 0.05). That finding is consistent with the additional understanding and experience that should be anticipated in graduate students and junior-senior level students over sophomore physics majors and majors in another field. The moderate positive correlation coefficient of 0.42 observed between students' QMVI scores and their final course grades was also consistent with expectations in a valid instrument. In addition, the Cronbach-alpha reliability coefficient of the QMVI was found to be 0.82. Limited findings were drawn on students' understanding of introductory quantum mechanics concepts. Data suggested that the construct of quantum mechanics understanding is most likely multidimensional and the Main Topic defined as "Quantum Mechanics Postulates" may be an especially important factor for students in acquiring a successful understanding of quantum mechanics.

Cataloglu, Erdat

303

Testing Quantum Mechanics in High-Energy Physics

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

Beatrix C. Hiesmayr

304

What Is a Quantum-Mechanical ``Weak Value'' the Value of?

NASA Astrophysics Data System (ADS)

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

Svensson, Bengt E. Y.

2013-10-01

305

Quantum mechanics model on a Kähler conifold

We propose an exactly solvable model of the quantum oscillator on the class of Kähler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum number, when the space has nonconstant curvature. We reduce the model to a three-dimensional system interacting with the Dirac monopole. Owing to noncommutativity of the reduction

Stefano Bellucci; Armen Nersessian; Armen Yeranyan

2004-01-01

306

Radio frequency operation of a quantum point contact charge detector

NASA Astrophysics Data System (ADS)

Quantum point contact (QPC) charge detectors are sensitive electrometers, and their ease of fabrication and integration into semiconductor-based qubit systems makes them an attractive candidate as a readout device for spin or charge based qubits in quantum dots. Nevertheless, QPC performance to date has been limited by relatively low operational speeds and 1/f noise. Here we report the operation of a QPC charge sensor realized in an GaAs/AlGaAs two dimensional electron gas at radio- frequencies (RF-QPC), in a mode analogous to rf operation of the single electron transistor [1]. For a typical QPC detector coupled to a quantum dot (QD), a charge oscillation of one electron in the QD corresponds to a change in the QPC conductance of 1-3 percent. We simulate these operating conditions by applying a small ac voltage to the QPC gate to cause a similar change in the zero bias QPC conductance. When operated this way the signal to noise ratio of the RF-QPC is about 30dB, which corresponds to a charge sensitivity of about 7x10-4e/?Hz referred to the dot charge. The operational characteristics of the RF-QPC at 4.2K also will be discussed. [1] R. J. Schoelkopf et al., Science 280, 1238 1242 (1998).

Thalakulam, Madhu; Rimberg, A. J.; Pfeiffer, L. N.; West, K. W.

2007-03-01

307

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

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

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

2000-06-01

308

Quantum molecular dynamics: Propagating wavepackets and density operators using the

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

Hans-Dieter Meyer; Graham A. Worthy

309

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

Chou, Chia-Chun; Kouri, Donald J

2013-04-25

310

OSP Quantum Mechanics: Single Measurments of Spin States Worksheet

NSDL National Science Digital Library

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

Belloni, Mario; Christian, Wolfgang

2010-01-11

311

Possibility of a Geometric Constraint in the Schrödinger Quantum Mechanics

NASA Astrophysics Data System (ADS)

Within the framework of some straightforward mathematical terms it is argued that there exists a space-invariant in the Schrödinger quantum mechanics (SQM). As an alternative to the geometric features of localized nature dictated by the prescribed boundary conditions in a potential problem in SQM, this spatial invariant is expected to account for some global geometric features of the quantum system.

Kaushal, R. S.

312

Optical coupling mechanisms in quantum well infrared photodetectors

Light coupling systems such as gratings are required because Quantum Well Infrared Photodetectors do not respond to normal incident light due to the quantum mechanical selection rules associated with intersubband transitions. The resolution of the photolithography and accuracy of the etching become key issues in producing smaller grating feature sizes especially in shorter wavelengths. An enhancement factor of three due

Sumith Bandara; Sarath Gunapala; John Liu; Winn Hong; Jin Park

313

Proposed experiment to assess operation of quantum cellular automaton cells

NASA Astrophysics Data System (ADS)

We propose an experiment for the detection of quantum cellular automaton (QCA) operation in a cell made up of four silicon quantum dots. We show that correlated switching between the two pairs of dots forming the cell can be clearly detected from the locking of the Coulomb blockade current peaks through each pair. We have performed numerical simulations on the basis of capacitance values obtained from experimental results on cells fabricated with silicon-on-insulator technology. This approach is shown to allow detection of QCA switching without the need for additional charge detectors, although fabrication parameters are rather critical.

Macucci, M.; Gattobigio, M.; Iannaccone, G.

2001-12-01

314

Demonstration of nondeterministic quantum logic operations using linear optical elements.

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

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

2002-06-24

315

NASA Astrophysics Data System (ADS)

We report pulse modulation caused by the exciton quantum beat in a GaAs/AlAs multiple quantum well. The modulation was evaluated by measuring the cross-correlation signal, which is the second harmonic light generated by the probe pulse reflected from the sample and the gate pulse. The intensity of the correlation-signal decreases owing to the generation of the exciton quantum beat, and recovers with dephasing of the quantum beat oscillation. Moreover, we found that the decrease caused by the quantum beat is larger than that by changing the refractive index due to the exciton generation. These results indicate that quantum beats can be a potential mechanism to enable low-power operation of ultrafast optical switches.

Kojima, Osamu; Hayashii, Ken; Kita, Takashi; Akahane, Kouichi

2014-03-01

316

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

E. Celeghini; M. A. del Olmo

1969-01-01

317

Double Occupancy Errors in Quantum Computing Operations: Corrections to Adiabaticity

NASA Astrophysics Data System (ADS)

We study the corrections to adiabatic dynamics of two coupled quantum dot spin-qubits, each dot singly occupied with an electron, in the context of a quantum computing operation. Tunneling causes double occupancy at the conclusion of an operation and constitutes a processing error. We model the gate operation with an effective two- level system, where non-adiabatic transitions correspond to double occupancy. The model is integrable and possesses three independent parameters. We confirm the accuracy of Dykhne's formula, a nonperturbative estimate of transitions, and discuss physically intuitive conditions for its validity. Our semiclassical results are in excellent agreement with numerical simulations of the exact time evolution. A similar approach applies to two-level systems in different contexts.

Requist, Ryan; Schliemann, John; Abanov, Alexander; Loss, Daniel

2005-03-01

318

Double occupancy errors in quantum computing operations: Corrections to adiabaticity

NASA Astrophysics Data System (ADS)

We study the corrections to adiabatic dynamics of two coupled quantum dot spin qubits, each dot singly occupied with an electron, in the context of a quantum computing operation. Tunneling causes double occupancy at the conclusion of an operation and constitutes a processing error. We model the gate operation with an effective two-level system, where nonadiabatic transitions correspond to double occupancy. The model is integrable and possesses three independent parameters. We confirm the accuracy of Dykhne’s formula, a nonperturbative estimate of transitions, and discuss physically intuitive conditions for its validity. Our semiclassical results are in excellent agreement with numerical simulations of the exact time evolution. A similar approach applies to two-level systems in different contexts.

Requist, Ryan; Schliemann, John; Abanov, Alexander G.; Loss, Daniel

2005-03-01

319

Spectral geometry of power-law potentials in quantum mechanics

NASA Astrophysics Data System (ADS)

It is supposed that a single particle moves in openR3 in an attractive central power-law potential V(q)(r)=sgn(q)rq, q>-2, and obeys nonrelativistic quantum mechanics. This paper is concerned with the question: How do the discrete eigenvalues Enl(q) of the Hamiltonian H=-?+V(q) depend on the power parameter q\\? Pure power-law potentials have the elementary property that, for poperators of the form H'=-?+, A(q)?openR. This geometrical approach greatly simplifies the description of the spectra and also facilitates the construction of some general eigenvalue bounds and approximation formulas.

Hall, Richard L.

1989-06-01

320

Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

NASA Astrophysics Data System (ADS)

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

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

2013-10-01

321

A Simplified Quantum Mechanical Model of Diatomic Molecules

ERIC Educational Resources Information Center

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

Nielsen, Lars Drud

1978-01-01

322

Born series and unitarity in noncommutative quantum mechanics

This paper is dedicated to present model independent results for noncommutative quantum mechanics. We determine sufficient conditions for the convergence of the Born series and, in the sequel, unitarity is proved in full generality.

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

2008-01-15

323

Quantum Mechanical Balance Equation Approach to Semiconductor Device Simulation.

National Technical Information Service (NTIS)

This research project was focused on the development of a quantum mechanical balance equation based device simulator that can model advanced, compound, submicron devices, under all transport conditions (AC, DC, and transient response). This report documen...

L. L. Cui

1997-01-01

324

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

NASA Astrophysics Data System (ADS)

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

Goff, Allan

2006-11-01

325

Level Comparison Theorems and Supersymmetric Quantum Mechanics.

National Technical Information Service (NTIS)

The sign of the Laplacian of the spherical symmetric potential determines the order of energy levels with the same principal Coulomb quantum number. This recently derived theorem has been generalized, extended and applied to various situations in particle...

B. Baumgartner H. Grosse A. Martin

1986-01-01

326

Relativistic models of nonlinear quantum mechanics

I present and discuss a class of nonlinear quantum-theory models, based on simple relativistic field theories, in which the parameters depend on the state of the system via expectation values of local functions of the fields.

T. W. B. Kibble

1978-01-01

327

Quantum circuits for measuring Levin-Wen operators

NASA Astrophysics Data System (ADS)

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

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

2012-10-01

328

Quantum Mechanics in Biology: Photoexcitations in DNA

\\u000a We consider here the theoretical and quantum chemical description of the photoexcitated states in DNA duplexes. We discuss\\u000a the motivation and limitations of an exciton model and use this as the starting point for more detailed excited state quantum\\u000a chemical evaluations. In particular, we focus upon the role of interbase proton transfer between Watson\\/Crick pairs in localizing\\u000a an excitation and

Eric R. Bittner; Arkadiusz Czader

2009-01-01

329

Mechanism Of The Quantum Speed-up

NASA Astrophysics Data System (ADS)

Bob chooses a function and gives to Alice the black box that computes it. Alice, without knowing Bob's choice, should find a character of the function (e. g. its period) by computing its value for different arguments. There is naturally correlation between Bob's choice and the solution found by Alice. We show that, in quantum algorithms, this correlation becomes quantum. This highlights an overlooked measurement problem: sharing between two completely or partly redundant measurements the determination of completely or partly correlated measurement outcomes. All is like Alice, by reading the solution at the end of the algorithm, contributed to the initial choice of Bob, with half of it in quantum superposition for all the possible ways of taking this half. This contribution, back evolved to before running the algorithm, where Bob's choice is located, becomes Alice knowing in advance half of the choice. The quantum algorithm is the quantum superposition of all the possible ways of taking half of Bob's choice and, given the advanced knowledge of it, classically computing the missing half. The quantum speed-up comes from comparing two classical algorithms, with and without advanced knowledge of half of Bob's choice.

Castagnoli, Giuseppe

2011-11-01

330

Combined quantum and molecular mechanics (QM/MM).

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

Friesner, Richard A

2004-12-01

331

Testing quantum mechanics in the neutral kaon system

The neutral kaon system is a sensitive probe of quantum mechanics. We revive a parametrization of non-quantum-mechanical effects that is motivated by considerations of the nature of space-time foam, and show how it can be constrained by new measurements of KL-->2pi and KL,S semileptonic decays at LEAR or a phi factory. Permanent address: Center for Theoretical Physics, Department of Physics,

Jonathan Richard Ellis; Nikolaos E Mavromatos; Dimitri V Nanopoulos

1992-01-01

332

Probability in the Many-Worlds Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

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

Vaidman, Lev

333

The Use of Quantum Mechanics in the Treatment of Waveguides

NASA Astrophysics Data System (ADS)

In this paper we give a quantum description of guided waves. A Klein-Gordon type equation is derived for wave propagation in an ideal uniform waveguide, and the appropriate quantum-mechanical interpretation is given. Making use of such methods, we give an analysis of guided waves, of inhomogeneously filled waveguides, of waveguide discontinuities, and generally of passive microwave circuits. A spinorial formalism is employed to derive the equivalent Dirac-type equation. The general applicability of the quantum-mechanical concepts to waveguides is also discussed.

Marinescu, N.

334

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

We consider the problem of testing whether a given matrix in the Hilbert space formulation of quantum mechanics or a function considered in the phase space formulation of quantum theory represents a quantum state. We propose several practical criteria for recognising states in these two versions of quantum physics. After minor modifications, they can be applied to check positivity of any operators acting in a Hilbert space or positivity of any functions from an algebra with a ?-product of Weyl type. -- Highlights: ? Methods of testing whether a given matrix represents a quantum state. ? The Stratonovich–Weyl correspondence on an arbitrary symplectic manifold. ? Criteria for checking whether a function on a symplectic space is a Wigner function.

Tosiek, J., E-mail: tosiek@p.lodz.pl; Brzykcy, P., E-mail: 800289@edu.p.lodz.pl

2013-05-15

335

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

This article presents the realization of many self-reversible quantum logic gates using two-qubit quadrupolar spin 3/2 systems. Such operations are theoretically described using propagation matrices for the RF pulses that include the effect of the quadrupolar evolution during the pulses. Experimental demonstrations are performed using a generalized form of the recently developed method for quantum state tomography in spin 3/2 systems. By doing so, the possibility of controlling relative phases of superimposed pseudo-pure states is demonstrated. In addition, many aspects of the effect of the quadrupolar evolution, occurring during the RF pulses, on the quantum operations performance are discussed. Most of the procedures presented can be easily adapted to describe selective pulses of higher spin systems (>3/2) and for spin 1/2 under J couplings. PMID:15921938

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

2005-08-01

336

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

NASA Astrophysics Data System (ADS)

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

Mahler, G.

2004-07-01

337

Quantum mechanical states as attractors for Nelson processes

NASA Astrophysics Data System (ADS)

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

Petroni, Nicola Cufaro; Guerra, Francesco

1995-02-01

338

The Quantum Field Theory of the Ensemble Operator

Quantum field theory (QFT) provides a systematic investigative tool for ensembles of molecules. The grand-canonical ensemble operator (GCEO) for an ideal gas is presented in terms of the Fock creation and annihilation operators. The ideal GCEO can be shown to obey a simple equation which facilitates calculation of quantum-statistical properties of bosonic and fermionic molecules. Examples are linked-cluster QFT derivations of the grand-canonical partition function and the Poisson distribution for non-interacting molecules. The Boltzmann limit is achieved by omitting exchange diagrams. Summations of Feynman diagrams for long- and short-range interactions to infinite order lead to a useful model of the pair-correlation function and a new avenue for the study of dynamics near the critical point for gas-liquid phase transitions.

Porter, Richard N. [Department of Chemistry, State University of New York, Stony Brook, New York, 11794-3400 (United States)

2009-03-09

339

Quantum entanglement of local operators in conformal field theories.

We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles. PMID:24702348

Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi

2014-03-21

340

Multiple-event probability in general-relativistic quantum mechanics

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

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

2007-04-15

341

High-Fidelity Quantum Logic Operations Using Linear Optical Elements

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

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

2002-01-01

342

'Mysticism' in quantum mechanics: the forgotten controversy

NASA Astrophysics Data System (ADS)

This paper argues that a European controversy over a 'mystical' hypothesis, one assigning the mind a role to play at the material level of reality, shaped much of the debate over the interpretation of the quantum equations. It traces back the controversy to the past two decades, beginning in the late 1920s—birth of quantum theory—and concluding with Erwin Schrödinger's lectures published as 'Mind and Matter'. Becoming aware of the issues at stake can help us understand the historical, philosophical and cultural background from which today's physics emerged.

Marin, Juan Miguel

2009-07-01

343

Derivation of quantum mechanics from the Boltzmann equation for the Planck aether

The Planck aether hypothesis assumes that space is densely filled with an equal number of locally interacting positive and negative Planck masses obeying an exactly nonrelativistic law of motion. The Planck masses can be described by a quantum mechanical two-component nonrelativistic operator field equation having the form of a two-component nonlinear Schrödinger equation, with a spectrum of quasiparticles obeying Lorentz

F. Winterberg

1995-01-01

344

Universal upper bound for the Holevo information induced by a quantum operation

NASA Astrophysics Data System (ADS)

Let HA?HB be a bipartite system and ? a quantum state on HA?HB, ?A=TrB(?), ?B=TrA(?). Then each quantum operation ?B on the quantum system HB can induce a quantum ensemble {(p?,?)} on quantum system HA. In this Letter, we show that the Holevo quantity ?{(p?,?)} of the quantum ensemble {(p?,?)} can be upper bounded by both subsystem entropies. By using the result, we answer partly a conjecture of Fannes, de Melo, Roga and ?yczkowski.

Zhang, Lin; Wu, Junde; Fei, Shao-Ming

2012-11-01

345

Evading Quantum Mechanics: Engineering a Classical Subsystem within a Quantum Environment

NASA Astrophysics Data System (ADS)

Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement backaction 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 backaction 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, backaction 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 broadband squeezed light for use in interferometric gravitational-wave detection, experiments using entangled atomic-spin ensembles, and implementations of the quantum Toffoli gate.

Tsang, Mankei; Caves, Carlton M.

2012-07-01

346

Quantum mechanics with spontaneous localization and the quantum theory of measurement

Summary Quantum mechanics with spontaneous localization (QMSL) is a recently proposed stochastic modification of theN-body Schrödinger equation consistent both with microphysics and macrophysics. QMSL is applied here to the measurement problem.\\u000a It is shown that the replacement of standard quantum mechanics by QMSL has the only effect of producing an actual reduction\\u000a of the wave function.

F. Benatti; G. C. Ghirardi; A. Rimini; T. Weber

1987-01-01

347

The Transactional Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction: quantum peculiarities; 2. The map vs the territory; 3. The original TI: fundamentals; 4. The new possibilist TI: fundamentals; 5. Challenges, replies, and applications; 6. PTI and relativity; 7. The metaphysics of possibility; 8. PTI and 'spacetime'; 9. Epilogue: more than meets the eye; Appendixes; References; Index.

Kastner, Ruth E.

2012-10-01

348

THE QUANTUM MECHANICAL FOUNDATIONS OF PHILOSOPHY

Many of the most familiar features of our everyday environment, and some of our basic notions about it, stem from Relativistic Quantum Field Theory (RQFT). We argue in particular that the origin of common names, verbs, adjectives such as full and empty, the concepts of identity, similar- ity, Plato's Universals, natural numbers, and existence versus non-existence can be traced to

Cihan Saclõoglu

349

A semiclassical correction for quantum mechanical energy levels

We propose a semiclassical method for correcting molecular energy levels obtained from a quantum mechanical variational calculation. A variational calculation gives the energy level (i.e., eigenvalue) as the expectation value of the molecular Hamiltonian <{phi}|H|{phi}>, where |{phi}> is the trial wave function. The true (i.e., exact) eigenvalue E can thus be expressed as this variational result plus a correction, i.e., E=<{phi}|H|{phi}>+{Delta}E, the correction being due to the lack of exactness of the trial wave function. A formally exact expression for {Delta}E is usually given (via Loewdin partitioning methodology) in terms of the Greens function of the Hamiltonian projected onto the orthogonal complement of |{phi}>. Formal treatment of this expression (using Brillouin-Wigner perturbation theory to infinite order) leads to an expression for {Delta}E that involves matrix elements of the Greens function for the unprojected, i.e., full molecular Hamiltonian, which can then be approximated semiclassically. (Specifically, the Greens function is expressed as the Fourier transform of the quantum mechanical time evolution operator, e{sup -}iHt/({h_bar}/2{pi}), which in turn is approximated by using an initial value representation of semiclassical theory.) Calculations for several test problems (a one dimensional quartic potential, and vibrational energy levels of H{sub 2}O and H{sub 2}CO) clearly support our proposition that the error in the total eigenvalue E arises solely due to the semiclassical error in approximating {Delta}E, which is usually a small fraction of the total energy E itself.

Kaledin, Alexey L. [Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322 (United States); McCurdy, C. William [Department of Applied Science and Department of Chemistry, University of California, Davis, California 95616, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Miller, William H. [Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, California (United States) and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)

2010-08-07

350

Quantum mechanics on profinite groups and partial order

NASA Astrophysics Data System (ADS)

Inverse limits and profinite groups are used in a quantum mechanical context. Two cases are considered: a quantum system with positions in the profinite group { {Z}}_p and momenta in the group { {Q}}_p/{ {Z}}_p, and a quantum system with positions in the profinite group {\\widehat{ {Z}}} and momenta in the group { {Q}}/{ {Z}}. The corresponding Schwatz-Bruhat spaces of wavefunctions and the Heisenberg-Weyl groups are discussed. The sets of subsystems of these systems are studied from the point of view of partial order theory. It is shown that they are directed-complete partial orders. It is also shown that they are topological spaces with T0-topologies, and this is used to define continuity of various physical quantities. The physical meaning of profinite groups, non-Archimedean metrics, partial orders and T0-topologies, in a quantum mechanical context, is discussed.

Vourdas, A.

2013-02-01

351

Comment on 'Nonlocality, Counterfactuals and Quantum Mechanics'

A recent proof [H. P. Stapp, Am. J. Phys. 65, 300 (1997)], formulated in the symbolic language of modal logic, claims to show that contemporary quantum theory, viewed as a set of rules that allow us to calculate statistical predictions among certain kinds of observations, cannot be imbedded in any rational framework that conforms to the principles that (1) the experimenters' choices of which experiments they will perform can be considered to be free choices, (2) outcomes of measurements are unique, and (3) the free choices just mentioned have no backward-in-time effects of any kind. This claim is similar to Bell's theorem, but much stronger, because no reality assumption alien to quantum philosophy is used. The paper being commented on [W. Unruh, Phys. Rev. A 59, 126 (1999)] argues that some such reality assumption has been ''smuggled'' in. That argument is examined here and shown, I believe, to be defective.

Stapp, H.P.

1999-04-14

352

Some thoughts about consciousness: from a quantum mechanics perspective.

The article explores some of the basic findings of quantum physics and information theory and their possible usefulness in offering new vistas for understanding psychoanalysis and the patient-analyst interchange. Technical terms are explained and placed in context, and examples of applying quantum models to clinical experience are offered. Given the complexity of the findings of quantum mechanics and information theory, the article aims only to introduce some of the major concepts from these disciplines. Within this framework the article also briefly addresses the question of mind as well as the problematic of reducing the experience of consciousness to neurological brain functioning. PMID:23865992

Gargiulo, Gerald J

2013-08-01

353

ysteries, Puzzles, and Paradoxes in Quantum Mechanics. Proceedings

These proceedings represent papers presented at the Mysteries, Puzzles, and Paradoxes in Quantum Mechanics Workshop held in Italy, in August 1998. The Workshop was devoted to recent experimental and theoretical advances such as new interference, effects, the quantum eraser, non{minus}disturbing and Schroedinger{minus}cat{minus}like states, experiments, EPR correlations, teleportation, superluminal effects, quantum information and computing, locality and causality, decoherence and measurement theory. Tachyonic information transfer was also discussed. There were 45 papers presented at the conference,out of which 2 have been abstracted for the Energy,Science and Technology database.(AIP)

Rodolfo, B. [Department of Physics, University of Milan, (Italy)

1999-02-01

354

Maximum-power quantum-mechanical Carnot engine

In their work [J. Phys. AJPHAC50305-447010.1088\\/0305-4470\\/33\\/24\\/302 33, 4427 (2000)], Bender, Brody, and Meister have shown by employing a two-state model of a particle confined in the one-dimensional infinite potential well that it is possible to construct a quantum-mechanical analog of the Carnot engine through changes of both the width of the well and the quantum state in a specific manner.

Sumiyoshi Abe

2011-01-01

355

On the relation between classical and quantum statistical mechanics

Classical and quantum statistical mechanics are compared in the high temperature limit ?=1\\/kT?0. While this limit is rather trivial for spin systems, we obtain some rigorous results which suggest (and sometimes prove) different asymptotics for continuous systems, depending on the behaviour of the two-body potential for small distances: the difference between suitable classical and quantum variables vanishes as ?2 for

W. Wreszinski; G. Scharf

1987-01-01

356

Quantum Mechanics Emerges from Information Theory Applied to Causal Horizons

NASA Astrophysics Data System (ADS)

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

Lee, Jae-Weon

2011-04-01

357

Quantum mechanics from an equivalence principle

The authors show that requiring diffeomorphic equivalence for one-dimensional stationary states implies that the reduced action S{sub 0} satisfies the quantum Hamilton-Jacobi equation with the Planck constant playing the role of a covariantizing parameter. The construction shows the existence of a fundamental initial condition which is strictly related to the Moebius symmetry of the Legendre transform and to its involutive character. The universal nature of the initial condition implies the Schroedinger equation in any dimension.

Faraggi, A.E. [Univ. of Florida, Gainesville, FL (United States). Inst. for Fundamental Theory; Matone, M. [Univ. of Padova (Italy)

1997-05-15

358

Exploring the radiative limits of dark current operation in InGaAs quantum well solar cells

NASA Astrophysics Data System (ADS)

While radiative recombination is a well-known intrinsic loss mechanism in photovoltaic devices, nonradiative recombination mechanisms typically dominate compound semiconductor diode currents and limit the performance of even state-of-the-art devices. However, recent advances in device structure design have allowed quantum well structures to begin reaching the radiative limits of dark current operation. In this work, a novel extended heterojunction structure is employed in InGaAs quantum well devices to reduce non-radiative recombination and expose the limiting n=1 radiative component of the diode current. Short circuit current versus open circuit voltage curves derived from illuminated currentvoltage measurements indicate that the underlying dark diode currents of the InGaAs quantum well devices vary with well thickness and emission energy. Analysis of the extracted n=1 saturation current densities indicate that these high-voltage InGaAs quantum well devices are operating in a regime of suppressed radiative recombination.

Welser, Roger E.

2012-02-01

359

NASA Astrophysics Data System (ADS)

The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given as a second-order difference equation which, by a complex phase change, we turn into a discrete Schrödinger-like equation. The introduction of discrete potential-like functions reveals the surprising crucial role here of hidden symmetries, first discovered by Regge for the quantum mechanical 6j symbols; insight is provided into the underlying geometric features. The spectrum and wavefunctions of the volume operator are discussed from the viewpoint of the Hamiltonian evolution of an elementary ‘quantum of space’, and a transparent asymptotic picture of the semiclassical and classical regimes emerges. The definition of coordinates adapted to the Regge symmetry is exploited for the construction of a novel set of discrete orthogonal polynomials, characterizing the oscillatory components of torsion-like modes.

Aquilanti, Vincenzo; Marinelli, Dimitri; Marzuoli, Annalisa

2013-05-01

360

NASA Astrophysics Data System (ADS)

Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the application of nontrivial logical gate operations to the encoded qubits. Here, we present examples of such operations by implementing, in addition to the identity operation, the NOT and the Hadamard gate to a logical qubit encoded in a five qubit system that allows correction of arbitrary single-qubit errors. We perform quantum process tomography of the encoded gate operations, demonstrate the successful correction of all possible single-qubit errors, and measure the fidelity of the encoded logical gate operations.

Zhang, Jingfu; Laflamme, Raymond; Suter, Dieter

2012-09-01

361

Drug-Target Binding Investigated by Quantum Mechanical/Molecular Mechanical (QM/MM) Methods

NASA Astrophysics Data System (ADS)

Many important drugs, also used in the clinics, exert their function by binding covalently to their targets. Understanding their action requires quantum mechanical simulations. Here, after briefly reviewing few basic concepts of thermodynamics and kinetics of drug-target binding, we summarize principles and applications of Car-Parrinello quantum mechanics/molecular mechanics (QM/MM) simulations. From this discussion, this approach emerges as a computational methodology particularly well suited to investigate covalent binding in systems of pharmacological relevance.

Rothlisberger, U.; Carloni, P.

362

The operation principle of the well in quantum dot stack infrared photodetector

NASA Astrophysics Data System (ADS)

The well in the quantum dot stack infrared photodetector (WD-QDIP) is proposed which can be operated at high temperature ˜230 K. The operation principle of this device is investigated, including the carrier transport and the enhancement in the photocurrent. The WD-QDIPs with different well numbers are fabricated to study the mechanisms. It is realized that the carrier transport from the emitter to the collector in traditional quantum dot infrared photodetectors consists of two channels deduced from current-voltage characteristics and dark current activation energy at different temperatures. At temperatures below 77 K, the current transports through the InAs quantum dot channel, whereas at temperatures higher than 77 K, the current is dominated by the GaAs leakage channel. In addition, the non-equilibrium situation at low temperatures is also observed owing to the presence of photovoltaic phenomenon. The carrier distribution inside the QDs is simulated to investigate the reasons for the increase of photocurrent. Based on the simulation and the photocurrent response, the hot carrier (electron) scattering effect by the insertion of a quantum well layer is inferred as the most probable reason that lead to the enhancement of the response and regarded as the key factor to achieve high- temperature operation.

Lee, Jheng-Han; Wu, Zong-Ming; Liao, Yu-Min; Wu, Yuh-Renn; Lin, Shih-Yen; Lee, Si-Chen

2013-12-01

363

Investigations of fundamental phenomena in quantum mechanics with neutrons

NASA Astrophysics Data System (ADS)

Neutron interferometer and polarimeter are used for the experimental investigations of quantum mechanical phenomena. Interferometry exhibits clear evidence of quantum-contextuality and polarimetry demonstrates conflicts of a contextual model of quantum mechanics á la Leggett. In these experiments, entanglements are achieved between degrees of freedom in a single-particle: spin, path and energy degrees of freedom are manipulated coherently and entangled. Both experiments manifest the fact that quantum contextuality is valid for phenomena with matter waves with high precision. In addition, another experiment is described which deals with error-disturbance uncertainty relation: we have experimentally tested error-disturbance uncertainty relations, one is derived by Heisenberg and the other by Ozawa. Experimental results confirm the fact that the Heisenberg's uncertainty relation is often violated and that the new relation by Ozawa is always larger than the limit. At last, as an example of a counterfactual phenomenon of quantum mechanics, observation of so-called quantum Cheshire Cat is carried out by using neutron interferometer. Experimental results suggest that pre- and post-selected neutrons travel through one of the arms of the interferometer while their magnetic moment is located in the other arm.

Hasegawa, Yuji

2014-04-01

364

PREFACE: Progress in supersymmetric quantum mechanics

NASA Astrophysics Data System (ADS)

The theory of integrable systems is grounded in the very beginning of theoretical physics: Kepler's system is an integrable system. This field of dynamical systems, where one looks for exact solutions of the equations of motion, has attracted most of the great figures in mathematical physics: Euler, Lagrange, Jacobi, etc. Liouville was the first to formulate the precise mathematical conditions ensuring solvability `by quadrature' of the dynamical equations, and his theorem still lies at the heart of the recent developments. The modern era started about thirty years ago with the systematic formulation of soliton solutions to nonlinear wave equations. Since then, impressive developments arose both for the classical and the quantum theory. Subtle mathematical techniques were devised for the resolution of these theories, relying on algebra (group theory), analysis and algebraic geometry (Riemann theory of surfaces). We therefore clearly see that the theory of integrable systems lies ab initio at a crossing of physics and mathematics, and that the developments of these last thirty years have strengthened this dual character, which makes it into an archetypal domain of mathematical physics. As regards the classical theory, beyond the direct connections to the various domains of classical soliton physics (hydrodynamics, condensed matter physics, laser optics, particle physics, plasma, biology or information coding), one has witnessed in these recent years more unexpected (and for some of them not yet well understood) connections to a priori farther fields of theoretical physics: string theory (through matrix models), topological field theories (two dimensional Yang--Mills, three dimensional Chern--Simons--Witten), or supersymmetric field theories (for instance the correspondence discovered by Seiberg and Witten between classical integrable models and quantum potentials). Quantum integrable theories provide examples of exactly (non perturbatively) solvable physical models. They thus allow one to obtain descriptions of non trivial phenomena such as second order phase transition in condensed systems (spin lattices) and exact solution of relativistic quantum field theories (Sine--Gordon...). On the other hand, they supply an excellent example of fruitful interface between physics and mathematics: the theory of quantum groups (and the germane theory of special functions) is a perfect illustration of this rôle and perspectives of such new developments appear very promising. The purpose of the first RAQIS meeting was to bring together researchers from the various fields of mathematics and physics connected to the theory of quantum integrable systems. This conference was held in the framework of the European TMR network EUCLID `Integrable models and applications: from strings to condensed matter', contract number HPRN-CT-2002-00325. The RAQIS03 meeting took place at the Laboratoire d'Annecy-le-vieux de Physique Théorique (LAPTH, France) from 25 March to 28 March, 2003. The organising committee consisted of Daniel Arnaudon, Jean Avan, Luc Frappat, Éric Ragoucy and Paul Sorba. Financial support was provided by Université de Savoie and CNRS-DRI (Centre National de la Recherche Scientifique, Direction des Relations Internationales). In particular various scientific contacts with several Japanese participants were initiated thanks to the CNRS PICS contract number 911. This special issue of Journal of Physics A: Mathematical and General is dedicated to the subject of the RAQIS03 meeting in Annecy-le-vieux. Most of the contributors to this issue took part in the meeting, but this volume does not aim to be a proceedings in the usual sense of the word: contributions do not necessarily coincide with the reports presented at the meeting, nor are the contributors restricted exclusively to those people that were present. The intention of the special issue is to benefit from the occasion offered by the RAQIS03 meeting to highlight the important new areas in quantum integrability, by collecting together in one single volume a selection of article

Aref'eva, I.; Fernández, D. J.; Hussin, V.; Negro, J.; Nieto, L. M.; Samsonov, B. F.

2004-10-01

365

On the complexity of classical and quantum algorithms for numerical problems in quantum mechanics

NASA Astrophysics Data System (ADS)

Our understanding of complex quantum mechanical processes is limited by our inability to solve the equations that govern them except for simple cases. Numerical simulation of quantum systems appears to be our best option to understand, design and improve quantum systems. It turns out, however, that computational problems in quantum mechanics are notoriously difficult to treat numerically. The computational time that is required often scales exponentially with the size of the problem. One of the most radical approaches for treating quantum problems was proposed by Feytiman in 1982 [46]: he suggested that quantum mechanics itself showed a promising way to simulate quantum physics. This idea, the so called quantum computer, showed its potential convincingly in one important regime with the development of Shor's integer factorization algorithm which improves exponentially on the best known classical algorithm. In this thesis we explore six different computational problems from quantum mechanics, study their computational complexity and try to find ways to remedy them. In the first problem we investigate the reasons behind the improved performance of Shor's and similar algorithms. We show that the key quantum part in Shor's algorithm, the quantum phase estimation algorithm, achieves its good performance through the use of power queries and we give lower bounds for all phase estimation algorithms that use power queries that match the known upper bounds. Our research indicates that problems that allow the use of power queries will achieve similar exponential improvements over classical algorithms. We then apply our lower bound technique for power queries to the Sturm-Liouville eigenvalue problem and show matching lower bounds to the upper bounds of Papageorgiou and Wozniakowski [85]. It seems to be very difficult, though, to find nontrivial instances of the Sturm-Lionville problem for which power queries can be simulated efficiently. A quantum computer differs from a classical computer that uses randomness, because it allows "negative probabilities" that can cancel each other (destructive interference). Ideally we would like to transfer classical randomized algorithms to the quantum computer and get speed improvements. One of the simplest classical randomized algorithm is the random walk and we study the behavior of the continuous-time quantum random walk. We analyze this random walk in one dimension and give analytical formulas for its behavior that demonstrate its interference properties. Is interference or cancellation really the most important advantage that a quantum computer has over a classical computer? To answer that question we study the class StociMA of "stochastic quantum" algorithms that only use classical gates, but are given a quantum "witness", i.e. an arbitrary quantum state that can guide the algorithm in computing the correct answer, but should not be able to "fool" it. We show that there exists a complete problem for this class, which we call the stoquastic local Hamiltonian problem. In this problem we try to compute the lowest eigenvalue of a Hamiltonian with interactions that span only a fixed number of particles and all contribute negatively. With the help of this problem we prove that MA ? StocIMA ? SBP ? QMA. This shows that interference is one of the most important parts of quantum computation. The simulation of the evolution of a general quantum system in time requires a computational time that is exponential in the dimension of the system. But maybe the problem that we ask for is too general and we can simulate special systems in polynomial time. In particular it would be interesting to study quantum systems of "limited energy", i.e. for which the state at starting time consists mainly out of components with small energy. We model this in the theory of weighted reproducing kernel Hilbert spaces with two different sets of weights: product weights and finite-order weights. We will show that the information cost of computing the evolution for start

Bessen, Arvid J.

366

The Quantum-Like Brain Operating on Subcognitive and Cognitive Time Scales

We propose a {\\\\it quantum-like} (QL) model of the functioning of the brain. It should be sharply distinguished from the reductionist {\\\\it quantum} model. By the latter cognition is created by {\\\\it physical quantum processes} in the brain. The crucial point of our modelling is that discovery of the mathematical formalism of quantum mechanics (QM) was in fact discovery of

Andrei Yu. Khrennikov

2007-01-01

367

A deformation quantization theory for noncommutative quantum mechanics

We show that the deformation quantization of noncommutative quantum mechanics previously considered by Dias and Prata ['Weyl-Wigner formulation of noncommutative quantum mechanics', J. Math. Phys. 49, 072101 (2008)] and Bastos, Dias, and Prata ['Wigner measures in non-commutative quantum mechanics', e-print arXiv:math-ph/0907.4438v1; Commun. Math. Phys. (to appear)] can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef ['A new approach to the *-genvalue equation', Lett. Math. Phys. 85, 173-183 (2008)].

Costa Dias, Nuno; Prata, Joao Nuno [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Av. Campo Grande, 376, 1749-024 Lisboa (Portugal) and Grupo de Fisica Matematica, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa (Portugal); Gosson, Maurice de [NuHAG Fakultaet fuer Mathematik, Universitaet Wien, Wien 1090 (Austria); Luef, Franz [NuHAG Fakultaet fuer Mathematik, Universitaet Wien, Wien 1090 (Austria); Department of Mathematics, UC Berkeley, 847 Evans Hall, Berkeley, California 94720-3840 (United States)

2010-07-15

368

Quantum-mechanical transport equation for atomic systems.

NASA Technical Reports Server (NTRS)

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

Berman, P. R.

1972-01-01

369

Nambu quantum mechanics on discrete 3-tori

NASA Astrophysics Data System (ADS)

We propose a quantization of linear, volume preserving, maps on the discrete and finite 3-torus \\mathbb{T}_N^3 represented by elements of the group SL(3,\\mathbb{Z}_N) . These flows can be considered as special motions of the Nambu dynamics (linear Nambu flows) in the three-dimensional toroidal phase space and are characterized by invariant vectors a of \\mathbb{T}_N^3 . We quantize all such flows, which are necessarily restricted on a planar two-dimensional phase space, embedded in the 3-torus, transverse to the vector a. The corresponding maps belong to the little group of \\bm{a} \\in SL(3,\\mathbb{Z}_N) , which is an SL(2,\\mathbb{Z}_N) subgroup. The associated linear Nambu maps are generated by a pair of linear and quadratic Hamiltonians (Clebsch-Monge potentials of the flow) and the corresponding quantum maps realize the metaplectic representation of SL(3,\\mathbb{Z}_N) on the discrete group of three-dimensional magnetic translations, i.e. the non-commutative 3-torus with a deformation parameter the Nth root of unity. Other potential applications of our construction are related to the quantization of deterministic chaos in turbulent maps as well as to quantum tomography of three-dimensional objects.

Axenides, M.; Floratos, E. G.; Nicolis, S.

2009-07-01

370

Quantum mechanisms of density wave transport.

We report on new developments in the quantum picture of correlated electron transport in charge and spin density waves. The model treats the condensate as a quantum fluid in which charge soliton domain wall pairs nucleate above a Coulomb blockade threshold field. We employ a time-correlated soliton tunneling model, analogous to the theory of time-correlated single electron tunneling, to interpret the voltage oscillations and nonlinear current-voltage characteristics above threshold. An inverse scaling relationship between threshold field and dielectric response, originally proposed by Grüner, emerges naturally from the model. Flat dielectric and other ac responses below threshold in NbSe(3) and TaS(3), as well as small density wave phase displacements, indicate that the measured threshold is often much smaller than the classical depinning field. In some materials, the existence of two distinct threshold fields suggests that both soliton nucleation and classical depinning may occur. In our model, the ratio of electrostatic charging to pinning energy helps determine whether soliton nucleation or classical depinning dominates. PMID:22711979

Miller, John H; Wijesinghe, Asanga I

2012-06-01

371

Study on a Possible Darwinian Origin of Quantum Mechanics

NASA Astrophysics Data System (ADS)

A sketchy subquantum theory deeply influenced by Wheeler's ideas (Am. J. Phys. 51:398-404, 1983) and by the de Broglie-Bohm interpretation (Goldstein in Stanford Encyclopedia of Philosophy, 2006) of quantum mechanics is further analyzed. In this theory a fundamental system is defined as a dual entity formed by bare matter and a methodological probabilistic classical Turing machine. The evolution of the system would be determined by three Darwinian informational regulating principles. Some progress in the derivation of the postulates of quantum mechanics from these regulating principles is reported. The entanglement in a bipartite system is preliminarily considered.

Baladrón, C.

2011-03-01

372

Terahertz quantum-cascade laser operating up to 137 K.

We report operation of a terahertz quantum-cascade laser at 3.8 THz ({lambda} {approx} 79 {micro}m) up to a heat-sink temperature of 137 K. A resonant phonon depopulation design was used with a low-loss metal-metal waveguide, which provided a confinement factor of nearly unity. A threshold current density of 625 A/cm{sup 2} was obtained in pulsed mode at 5 K. Devices fabricated using a conventional semi-insulating surface-plasmon waveguide lased up to 92 K with a threshold current density of 670 A/cm{sup 2} at 5 K.

Callebaut, Hans (Massachusetts Institute of Technology, Cambridge, MA); Kumar, Sushil (Massachusetts Institute of Technology, Cambridge, MA); Williams, Benjamin S. (Massachusetts Institute of Technology, Cambridge, MA); Hu, Qing (Massachusetts Institute of Technology, Cambridge, MA); Reno, John Louis

2003-08-01

373

Conceptual and mathematical barriers to students learning quantum mechanics

NASA Astrophysics Data System (ADS)

Quantum mechanics has revolutionized the way we view the physical world. This theory has required a dramatic revision in the structure of the laws of mechanics governing the behavior of the particles and led to the discovery of macroscopic quantum effects ranging from lasers and superconductivity to neutron stars and radiation from black holes. Though its validity is well confirmed by the experimental evidence available, quantum mechanics remains somewhat of a mystery. The purpose of this study is to identify students' conceptual and mathematical difficulties in learning the core concepts of introductory quantum mechanics, with the eventual goal of developing instructional material to help students with these difficulties. We have investigated student understanding of several core topics in the introductory courses, including quantum measurement, probability, Uncertainty Principle, wave functions, energy eigenstates, recognizing symmetry in physical systems, and mathematical formalism. Student specific difficulties with these topics are discussed throughout this dissertation. In addition, we have studied student difficulties in learning, applying, and making sense out of complex mathematical processes in the physics classroom. We found students' achievement in quantum courses is not independent of their math backgrounds (correlation coefficient 0.547 for P631 and 0.347 for P263). In addition, there is a large jump in the level of mathematics at which one needs to succeed in physics courses after the sophomore level in The Ohio State University's physics curriculum. Many students do not have a functional understanding of probability and its related terminologies. For example, many students confuse the "expectation value" with "probability density" in measurement and some students confuse "probability density" with "probability amplitude" or describe the probability amplitude as a "place" or "area." Our data also suggested that students tend to use classical models when interpreting quantum systems; for example, some students associate a higher energy to a larger amplitude in a wave function. Others, have difficulty differentiating wave functions from energy eigenstates. Furthermore, some students do not use the relationship between the wave function and the wavenumber as a primary resource in for qualitative analysis of wave functions in regions of different potential. Many students have difficulty recognizing mathematical symbols for a given graph and lack the ability to associate the correct functions with their respective graphs. I addition, students do not distinguish an oscillatory function such as e-ix from an exponential decay function such as e-x. The results reported suggest recommendations for further study of student understanding of quantum mechanics and for the development of materials to aid understanding. These recommendations have potentially important implications for the teaching of introductory quantum mechanics and for the development of teaching aids, texts, and technology resources.

Sadaghiani, Homeyra R.

374

On Quantum Statistical Mechanics of a Schwarzschild Black Hole

NASA Astrophysics Data System (ADS)

Quantum theory of geometry, developed recently in the framework of non-perturbative quantum gravity, is used in an attempt to explain thermodynamics of Schwarzschild black holes on the basis of a microscopical (quantum) description of the system. We work with the formulation of thermodynamics in which the black hole is enclosed by a spherical surface B and a macroscopic state of the system is specified by two parameters: the area of the boundary surface and a quasilocal energy contained within it. To derive thermodynamical properties of the system from its microscopics we use the standard statistical mechanical method of Gibbs. Under a certain number of assumptions on the quantum behavior of the system, we find that its microscopic (quantum) states are described by states of quantum Chern-Simons theory defined by sets of points on B with spins attached. The level of the Chern-Simons theory turns out to be proportional to the horizon area of the black hole measured in Planck units. The statistical mechanical analysis turns out to be especially simple in the case when the entire interior of B is occupied by a black hole. We find in this case that the entropy contained within B, that is, the black hole entropy, is proportional to the horizon surface area.

Krasnov, Kirill V.

1998-01-01

375

Quantum mechanics from Newton's second law and the canonical commutation relation [X, P] = i

NASA Astrophysics Data System (ADS)

Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian or Lagrangian formulations of mechanics. Here, we first derive the existing Heisenberg equations of motion from Newton's laws and the uncertainty principle using only the equations F=\\frac{dP}{dt}, P=m\\frac{dV}{dt}, and [X, P] = i. Then, a new expression for the propagator is derived that makes a connection between time evolution in quantum mechanics and the motion of a classical particle under Newton's laws. The propagator is solved for three cases where an exact solution is possible: (1) the free particle; (2) the harmonic oscillator; and (3) a constant force, or linear potential in the standard interpretation. We then show that for a general for a general force F(X), by Taylor expanding X(t) in time, we can use this methodology to reproduce the Feynman path integral formula for the propagator. Such a picture may be useful for students as they make the transition from classical to quantum mechanics and help solidify the equivalence of the Hamiltonian, Lagrangian, and Newtonian pictures of physics in their minds.

Palenik, Mark C.

2014-07-01

376

Quantum mechanical point of view to perturbative problems in classical mechanics.

National Technical Information Service (NTIS)

This paper shows that perturbative methods currently exploited in quantum mechanics can be used to treat a classical Liouville problem describing the evolution of an ensemble of non-collisional particles. The method we discuss is based on the introduction...

G. Dattoli A. Torre

1993-01-01

377

Conceptual and Mathematical Barriers to Students Learning Quantum Mechanics

NSDL National Science Digital Library

The purpose of this study is to identify students' conceptual and mathematical difficulties in learning the core concepts of introductory quantum mechanics, with the eventual goal of developing instructional material to help students with these difficulties. We have investigated student understanding of several core topics in the introductory courses, including quantum measurement, probability, Uncertainty Principle, wave functions, energy eigenstates, recognizing symmetry in physical systems, and mathematical formalism. Student specific difficulties with these topics are discussed throughout this dissertation. In addition, we have studied student difficulties in learning, applying, and making sense out of complex mathematical processes in the physics classroom. We found students' achievement in quantum courses is not independent of their math backgrounds. In addition, there is a large jump in the level of mathematics at which one needs to succeed in physics courses after the sophomore level in The Ohio State University's physics curriculum. The results reported suggest recommendations for further study of student understanding of quantum mechanics and for the development of materials to aid understanding. These recommendations have potentially important implications for the teaching of introductory quantum mechanics and for the development of teaching aids, texts, and technology resources.

Sadaghiani, Homeyra R.

2014-06-08

378

Quantum mechanical force field for water with explicit electronic polarization.

A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 10(6) self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across biological ion channels through membranes. PMID:23927266

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

2013-08-01

379

Quantum mechanical force field for water with explicit electronic polarization

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

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

2013-08-07

380

The quantum mechanics of perfect fluids

NASA Astrophysics Data System (ADS)

We consider the canonical quantization of an ordinary fluid. The resulting long-distance effective field theory is derivatively coupled, and therefore strongly coupled in the UV. The system however exhibits a number of peculiarities, associated with the vortex degrees of freedom. On the one hand, these have formally a vanishing strong-coupling energy scale, thus suggesting that the effective theory's regime of validity is vanishingly narrow. On the other hand, we prove an analog of Coleman's theorem, whereby the semiclassical vacuum has no quantum counterpart, thus suggesting that the vortex premature strong-coupling phenomenon stems from a bad identification of the ground state and of the perturbative degrees of freedom. Finally, vortices break the usual connection between short distances and high energies, thus potentially impairing the unitarity of the effective theory.

Endlich, Solomon; Nicolis, Alberto; Rattazzi, Riccardo; Wang, Junpu

2011-04-01

381

Probability distribution of arrival times in quantum mechanics

NASA Astrophysics Data System (ADS)

In a previous paper [V. Delgado and J. G. Muga, Phys. Rev. A 56, 3425 (1997)] we introduced a self-adjoint operator T⁁(X) whose eigenstates can be used to define consistently a probability distribution of the time of arrival at a given spatial point. In the present work we show that the probability distribution previously proposed can be well understood on classical grounds in the sense that it is given by the expectation value of a certain positive-definite operator J⁁(+)(X), which is nothing but a straightforward quantum version of the modulus of the classical current. For quantum states highly localized in momentum space about a certain momentum p0?0, the expectation value of J⁁(+)(X) becomes indistinguishable from the quantum probability current. This fact may provide a justification for the common practice of using the latter quantity as a probability distribution of arrival times.

Delgado, V.

1998-02-01

382

Statistical mechanical expression of entropy production for an open quantum system

NASA Astrophysics Data System (ADS)

A quantum statistical expression for the entropy of a nonequilibrium system is defined so as to be consistent with Gibbs' relation, and is shown to corresponds to dynamical variable by introducing analogous to the Heisenberg picture in quantum mechanics. The general relation between system-reservoir interactions and an entropy change operator in an open quantum system, relying just on the framework of statistical mechanics and the definition of von Neumann entropy. By using this formula, we can obtain the correct entropy production in the linear response framework. The present derivation of entropy production is directly based on the first principle of microscopic time-evolution, while the previous standard argument is due to the thermodynamic energy balance.

Majima, Hiroki; Suzuki, Akira

2013-02-01

383

Enhanced multipartite quantum correlation by non-Gaussian operations

NASA Astrophysics Data System (ADS)

We study how conditional photon operations can affect multipartite quantum correlations, specifically nonlocality and entanglement, of the continuous-variable Greenberger-Horne-Zeilinger (GHZ) states. We find that the violation of the Mermin-Klyshko inequality revealing the multipartite nonlocality can be made stronger with photon subtraction applied on each mode of the original GHZ states, particularly in a weak squeezing regime. Photon addition applied on local modes also turns out to enhance the degree of multipartite nonlocality in a broad range of parameters. We further investigate the effects of the photon operations on the degree of multipartite entanglement by looking into the Gaussian tangle, the fidelity of teleportation network, and the quadrature correlations. We find that photon subtraction applied on two modes enhances those entanglement characteristics in a practical squeezing regime while there is no improvement made by photon addition.

Kim, Ho-Joon; Kim, Jaewan; Nha, Hyunchul

2013-09-01

384

PREFACE: EmQM13: Emergent Quantum Mechanics 2013

NASA Astrophysics Data System (ADS)

These proceedings comprise the invited lectures of the second international symposium on Emergent Quantum Mechanics (EmQM13), which was held at the premises of the Austrian Academy of Sciences in Vienna, Austria, 3–6 October 2013. The symposium was held at the ''Theatersaal'' of the Academy of Sciences, and was devoted to the open exploration of emergent quantum mechanics, a possible ''deeper level theory'' that interconnects three fields of knowledge: emergence, the quantum, and information. Could there appear a revised image of physical reality from recognizing new links between emergence, the quantum, and information? Could a novel synthesis pave the way towards a 21st century, ''superclassical'' physics? The symposium provided a forum for discussing (i) important obstacles which need to be overcome as well as (ii) promising developments and research opportunities on the way towards emergent quantum mechanics. Contributions were invited that presented current advances in both standard as well as unconventional approaches to quantum mechanics. The EmQM13 symposium was co–organized by Gerhard Grössing (Austrian Institute for Nonlinear Studies (AINS), Vienna), and by Jan Walleczek (Fetzer Franklin Fund, USA, and Phenoscience Laboratories, Berlin). After a very successful first conference on the same topic in 2011, the new partnership between AINS and the Fetzer Franklin Fund in producing the EmQM13 symposium was able to further expand interest in the promise of emergent quantum mechanics. The symposium consisted of two parts, an opening evening addressing the general public, and the scientific program of the conference proper. The opening evening took place at the Great Ceremonial Hall (Grosser Festsaal) of the Austrian Academy of Sciences, and it presented talks and a panel discussion on ''The Future of Quantum Mechanics'' with three distinguished speakers: Stephen Adler (Princeton), Gerard 't Hooft (Utrecht) and Masanao Ozawa (Nagoya). The articles contained in these proceedings represent the talks of the invited speakers as written immediately after the symposium. The volume starts with a contribution by organizers Jan Walleczek and Gerhard Grössing, essentially explaining why emergent quantum mechanics, and other deterministic approaches to quantum theory, must be considered viable approaches in quantum foundations today. This is followed by the exposition of Stephen Adler's talk who introduced to a general audience key questions at the current frontiers of quantum mechanics during the opening evening (with the contents of his conference talk appearing elsewhere). The conference proceedings then continues with the presentations as given in their chronological order i.e. starting with the opening talk of the scientific program by Gerard 't Hooft. While the page number was restricted for all invited speakers, the paper by Jeff Tollaksen was given more space, as his invited collaborator Yakir Aharonov was unable to deliver a separate talk, in order to represent both contributions in one paper. Note that the talks of all speakers, including the talks of those who could not be represented in this volume (M. Arndt, B. Braverman, C. Brukner, S. Colin, Y. Couder, B. Poirier, A. Steinberg, G. Weihs and H. Wiseman) are freely available on the conference website as video presentations (http://www.emqm13.org). The organizers wish to express their gratitude to Siegfried Fussy and Herbert Schwabl from AINS for the organizational support. The organizers also wish to thank Bruce Fetzer, President and CEO, John E. Fetzer Memorial Trust, and the Members of the Board of Trustees, for their strong support and for funding this symposium. We also wish to thank the Austrian Academy of Sciences for allowing the symposium to be held on their premises, and Anton Zeilinger, President of the Austrian Academy of Sciences, for his welcome address. The expertise of the Members of the Scientific Advisory Board of the EmQM13 symposium, Ana Maria Cetto (Mexico), Lajos Diósi (Budapest), Maurice de Gosson (Vienna), Edward Nelson (Princeton), The

2014-04-01

385

Surveying students' understanding of quantum mechanics in one spatial dimension

NSDL National Science Digital Library

We explore the difficulties that advanced undergraduate and graduate students have with non-relativistic quantum mechanics of a single particle in one spatial dimension. To investigate these difficulties we developed a conceptual survey and administered it to more than 200 students at 10 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, and the time-dependence of the wavefunction and expectation values. We find that 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 findings also suggest that graduate quantum mechanics courses may not be effective at helping students to develop a better conceptual understanding of these topics, partly because such courses mainly focus on quantitative assessments.

Zhu, Guangtian; Singh, Chandralekha

2012-04-30

386

Scattering and reflection positivity in relativistic Euclidean quantum mechanics

NASA Astrophysics Data System (ADS)

In this paper I exhibit a class of reflection-positive Euclidean invariant four-point functions that can be used to formulate a Poincaré invariant quantum theory. I demonstrate the existence of scattering wave operators, which can be calculated without analytic continuation in this representation.

Polyzou, W. N.

2014-04-01

387

Poincaré resonances and the limits of quantum mechanics

In previous papers we have shown that the elimination of the resonance divergences in large Poincaré systems leads to complex irreducible spectral representations of the Liouville-von Neumann operator. This leads to an extended formulation of quantum theory on the level of density matrices. We consider in this paper potential scattering. Our theory applies to persistent scattering (beyond the S-matrix approach).

T. Petrosky; I. Prigogine

1993-01-01

388

Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

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

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

2013-10-15

389

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

NASA Astrophysics Data System (ADS)

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

Gong, Jiangbin; Wang, Qing-hai

2013-12-01

390

Parallelism in computational chemistry: Applications in quantum and statistical mechanics

NASA Astrophysics Data System (ADS)

Often very fundamental biochemical and biophysical problems defy simulations because of limitation in today's computers. We present and discuss a distributed system composed of two IBM-4341 and one IBM-4381, as front-end processors, and ten FPS-164 attached array processors. This parallel system-called LCAP-has presently a peak performance of about 120 MFlops; extensions to higher performance are discussed. Presently, the system applications use a modified version of VM/SP as the operating system: description of the modifications is given. Three applications programs have migrated from sequential to parallel; a molecular quantum mechanical, a Metropolis-Monte Carlo and a Molecular Dynamics program. Descriptions of the parallel codes are briefly outlined. As examples and tests of these applications we report on a study for proton tunneling in DNA base-pairs, very relevant to spontaneous mutations in genetics. As a second example, we present a Monte Carlo study of liquid water at room temperature where not only two- and three-body interactions are considered but-for the first time-also four-body interactions are included. Finally we briefly summarize a molecular dynamics study where two- and three-body interactions have been considered. These examples, and very positive performance comparison with today's supercomputers allow us to conclude that parallel computers and programming of the type we have considered, represent a pragmatic answer to many computer intensive problems.

Clementi, E.; Corongiu, G.; Detrich, J. H.; Kahnmohammadbaigi, H.; Chin, S.; Domingo, L.; Laaksonen, A.; Nguyen, N. L.

1985-08-01

391

Open Source Physics Curricular Material for Quantum Mechanics

NSDL National Science Digital Library

The Open Source Physics Curricular Material paper describes the interactive curricular material created as part of the Open Source Physics project for the teaching and learning of quantum mechanics. Here we focus on the measurement and time evolution of two-state superpositions in the context of bound states and spin.

Belloni, Mario; Christian, Wolfgang; Brown, Douglas

2008-05-30

392

Holographic duals to poisson sigma models and noncommutative quantum mechanics

NASA Astrophysics Data System (ADS)

Poisson sigma models are a very rich class of two-dimensional theories that includes, in particular, all two-dimensional dilaton gravities. By using the Hamiltonian reduction method, we show that a Poisson sigma model (with a sufficiently well-behaving Poisson tensor) on a finite cylinder is equivalent to a noncommutative quantum mechanics for the boundary data.

Vassilevich, D. V.

2013-05-01

393

New Approach to N-Body Relativistic Quantum Mechanics

In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac's equations. The classical approximation of this approach provides the exact Newtonian dynamics for many-body, and the nonrelativistic approximation gives the complete Schrödinger equation for many-body.

Ying-Qiu Gu

2007-01-01

394

The two-body quantum mechanical problem on spheres

The quantum mechanical two-body problem with a central interaction on the sphere Sn is considered. Using recent results in representation theory, an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.

Alexey V. Shchepetilov

2006-01-01

395

Completeness of the Coulomb Wave Functions in Quantum Mechanics

ERIC Educational Resources Information Center

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

Mukunda, N.

1978-01-01

396

Nonlinear nonlocal Schrödinger equation in the context of quantum mechanics

NASA Astrophysics Data System (ADS)

The nonlinear nonlocal equation describing the evolution of a fluctuating scalar field is studied. This nonlinear system naturally produces stable static configurations as a result of its relaxation to the dissipative attractors. It is found that the structures (and their spectra) observed in the frame of the model coincide with the eigenfunctions (and eigenvalues, respectively) of the linear quantum mechanical Schrödinger equation.

Filippov, A. E.

1996-02-01

397

Elementary Quantum Mechanics in a High-Energy Process

ERIC Educational Resources Information Center

Compares two approaches to strong absorption in elementary quantum mechanics; the black sphere and a model based on the continuum theory of nuclear reactions. Examines the application to proton-antiproton interactions at low momenta and concludes that the second model is the appropriate and simplest to use. (Author/GA)

Denville, A.; And Others

1978-01-01

398

a q-DEFORMATION of the Parasupersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

A q-deformation of the parasupersymmetric quantum mechanics of one boson and one parafermion of an arbitrary order p is constructed. The deformed commutators in the algebra generate braid-type relations which lift the degeneracy originally present in the undeformed case. The connection between the deformed algebra and a class of self-similar potentials is discussed.

Chakrabarti, R.; Jagannathan, R.

399

Quantum Mechanics of the Einstein-Hopf Model.

ERIC Educational Resources Information Center

The Einstein-Hopf model for the thermodynamic equilibrium between the electromagnetic field and dipole oscillators is considered within the framework of quantum mechanics. Both the wave and particle aspects of the Einstein fluctuation formula are interpreted in terms of the fundamental absorption and emission processes. (Author/SK)

Milonni, P. W.

1981-01-01

400

Quantum mechanics and faster-than-light communication: Methodological considerations

Summary A detailed quantum-mechanical analysis of a recent proposal of faster-than-light communication through wave packet reduction\\u000a is performed. The discussion allows us to focus some methodological problems about critical investigations on physical theories.

G. C. Ghirardi; T. Weber

1983-01-01

401

Quantum-mechanical theory of optomechanical Brillouin cooling

We analyze how to exploit Brillouin scattering of light from sound for the purpose of cooling optomechanical devices and present a quantum-mechanical theory for Brillouin cooling. Our analysis shows that significant cooling ratios can be obtained with standard experimental parameters. A further improvement of cooling efficiency is possible by increasing the dissipation of the optical anti-Stokes resonance.

Tomes, Matthew; Bahl, Gaurav; Carmon, Tal [Department of Electrical Engineering, University of Michigan, Ann Arbor, Michigan 48109 (United States); Marquardt, Florian [Institut fuer Theoretische Physik, Universitaet Erlangen-Nuernberg, Staudtstrasse 7, D-91058 Erlangen (Germany); Max Planck Institute for the Science of Light, Guenther-Scharowsky-Strasse 1/Bau 24, D-91058 Erlangen (Germany)

2011-12-15

402

Cell motility and thermodynamic fluctuations tailoring quantum mechanics for biology

Cell motility underlying muscle contraction is an instance of thermodynamics tailoring quantum mechanics for biology. Thermodynamics is intrinsically multi-agential in admitting energy consumers in the form of energy-deficient thermodynamic fluctuations. The onset of sliding movement of an actin filament on myosin molecules in the presence of ATP molecules to be hydrolyzed demonstrates that thermodynamic fluctuations transform their nature so as

Koichiro Matsuno

2001-01-01

403

Relativistic-Particle Quantum Mechanics (Applications and Approximations) II.

National Technical Information Service (NTIS)

In this lecture I hope to show that relativistic-particle quantum mechanics with direct interactions is a useful tool for building models applicable to hadron systems at intermediate energies. To do this I will first describe a class of models designed to...

F. Coester

1981-01-01

404

Physics on the boundary between classical and quantum mechanics

NASA Astrophysics Data System (ADS)

Nature's laws in the domain where relativistic effects, gravitational effects and quantum effects are all comparatively strong are far from understood. This domain is called the Planck scale. Conceivably, a theory can be constructed where the quantum nature of phenomena at such scales can be attributed to something fundamentally simpler. However, arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there can't be physical laws that require "conspiracy". It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In the lecture we will show several such counterexamples. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. This theory is often portrayed as to underly the quantum field theory of the subatomic particles, including the "Standard Model". So now the question is asked: how can this model feature "conspiracy", and how bad is that? Is there conspiracy in the vacuum fluctuations?

't Hooft, Gerard

2014-04-01

405

Quantum-mechanical coherence in cell microtubules: a realistic possibility?

We discuss the possibility of quantum-mechanical coherence in Cell MicroTubules (MT), based on recent developments in quantum physics. We focus on potential mechanisms for 'energy-loss-free' transport along the microtubules, which could be considered as realizations of Frohlich's ideas on the role of solitons for superconductivity and/or biological matter. In particular, by representing the MT arrangements as cavities, we review a novel scenario, suggested in collaboration with D.V. Nanopoulos, concerning the formation of macroscopic (or mesoscopic) quantum-coherent states, as a result of the (quantum-electromagnetic) interactions of the MT dimers with the surrounding molecules of the ordered water in the interior of the MT cylinders. We suggest specific experiments to test the above-conjectured quantum nature of the microtubular arrangements inside the cell. These experiments are similar in nature to those in atomic physics, used in the detection of the Rabi-Vacuum coupling between coherent cavity modes and atoms. Our conjecture is that a similar Rabi-Vacuum-splitting phenomenon occurs in the absorption (or emission) spectra of the MT dimers, which would constitute a manifestation of the dimer coupling with the coherent modes in the ordered-water environment (dipole quanta), which emerge due to the phenomenon of 'super-radiance'. PMID:10379540

Mavromatos, N E

1999-05-01

406

Quantum mechanics of null polygonal Wilson loops

NASA Astrophysics Data System (ADS)

Scattering amplitudes in maximally supersymmetric gauge theory are dual to super-Wilson loops on null polygonal contours. The operator product expansion for the latter revealed that their dynamics is governed by the evolution of multiparticle GKP excitations. They were shown to emerge from the spectral problem of an underlying open spin chain. In this work we solve this model with the help of the Baxter Q-operator and Sklyanin's Separation of Variables methods. We provide an explicit construction for eigenfunctions and eigenvalues of GKP excitations. We demonstrate how the former define the so-called multiparticle hexagon transitions in super-Wilson loops and prove their factorized form at leading order of 't Hooft coupling for particle number-preserving transitions that were suggested earlier in a generic case.

Belitsky, A. V.; Derkachov, S. E.; Manashov, A. N.

2014-05-01

407

Mechanisms of local and global molecular quantum gates and their implementation prospects.

We explore how the globality of quantum logic operations is ensured in the context of optimal control theory when qubits are encoded in vibrational eigenstates of different normal modes and specially shaped laser fields act as quantum logic operations. In a two-qubit model system, transition mechanisms for optimized laser fields generating single qubit flips, local NOT and global NOT and controlled-NOT (CNOT) gates are investigated and compared. We evaluate the participation of vibrational eigenstates beyond the qubit basis in the global gate mechanisms and how different features of CNOT and NOT gates relate to the characteristics of the vibrational manifold. When a non-qubit normal mode interacting via anharmonic resonances is introduced, neither the global gate mechanisms nor the optimized laser fields show a significant increase in complexity. Similar features of the global quantum gates in both model systems indicate a generality of the deduced principles. Finally, a primary concept for a realization of global quantum gates in an actual experiment referring to state-of-the-art techniques is presented. The possible reconstruction of optimized laser fields with sequences of simple Gaussian subpulses is demonstrated and some critical parameters are deduced. PMID:15945623

Troppmann, Ulrike; de Vivie-Riedle, Regina

2005-04-15

408

The molecular mechanism of hairpin ribozyme catalysis is studied with molecular dynamics simulations using a combined quantum mechanical and molecular mechanical (QM/MM) potential with a recently developed semiempirical AM1/d-PhoT model for phosphoryl transfer reactions. Simulations are used to derive one- and two-dimensional potentials of mean force to examine specific reaction paths and assess the feasibility of proposed general acid and base mechanisms. Density-functional calculations of truncated active site models provide complementary insight to the simulation results. Key factors utilized by the hairpin ribozyme to enhance the rate of transphosphorylation are presented, and the roles of A38 and G8 as general acid and base catalysts are discussed. The computational results are consistent with available experimental data, provide support for a general acid/base mechanism played by functional groups on the nucleobases, and offer important insight into the ability of RNA to act as a catalyst without explicit participation by divalent metal ions.

Nam, Kwangho; Gao, Jiali; York, Darrin M.

2009-01-01

409

An extended phase-space SUSY quantum mechanics

NASA Astrophysics Data System (ADS)

In the present paper, we will concern ourselves with the extended phase-space quantum mechanics of particles which have both bosonic and fermionic degrees of freedom, i.e., the quantum field theory in (0 + 1) dimensions in q-(position) and p-(momentum) spaces, exhibiting supersymmetry. We present (N = 2) realization of extended supersymmetry algebra and discuss the vacuum energy and topology of super-potentials. Shape invariance of exactly solvable extended SUSY potentials allows us to obtain analytic expressions for the entire energy spectrum of an extended Hamiltonian with, for example, Scarf potential without ever referring to an underlying differential equation.

Ter-Kazarian, G.

2009-02-01

410

Adiabatic approximation in PT-symmetric quantum mechanics

NASA Astrophysics Data System (ADS)

In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics, which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.

Guo, ZhiHua; Cao, HuaiXin; Lu, Ling

2014-05-01

411

Duality and the Equivalence Principle of Quantum Mechanics

Following a suggestion by Vafa, we present a quantum-mechanical model for\\u000aS-duality symmetries observed in the quantum theories of fields, strings and\\u000abranes. Our formalism may be understood as the topological limit of Berezin's\\u000ametric quantisation of the upper half-plane H, in that the metric dependence\\u000ahas been removed. Being metric-free, our prescription makes no use of global\\u000aquantum numbers.

Jose M. ISIDRO; G. Galilei

2000-01-01

412

NASA Astrophysics Data System (ADS)

The inflationary paradigm provides a mechanism to generate the primordial perturbations needed to explain the observed large-scale structures in the Universe. Inflation traces back all the inhomogeneities to quantum fluctuations although the structures look classical today. The squeezing of primordial quantum fluctuations along with the mechanism of decoherence accounts for many aspects of this quantum-to-classical transition, although it remains a matter of debate as to whether this is sufficient to explain the issue of the realization of a single outcome (i.e. the issue of macro-objectification) from a quantum ensemble given that the Universe is a closed system. A similar question of the emergence of classical behavior of macroscopic objects exists also for laboratory systems and apart from decoherence there have been attempts to resolve this issue through continuous spontaneous localization (CSL), which is a stochastic nonlinear modification of the nonrelativistic Schrödinger equation. Recently, Martin et al. have investigated whether a CSL-like mechanism with a constant strength parameter—when the Mukhanov-Sasaki variable is taken as the “collapse operator”—can explain how the primordial quantum perturbations generated during inflation become classical. Within the scope of their assumptions they essentially come to a negative conclusion. In the present work, we generalize their analysis by allowing the CSL strength parameter to depend on physical scales so as to capture the CSL amplification mechanism. We show that such a generalization provides a mechanism for the macro-objectification (i.e. classicalization) of the inflationary quantum perturbations, while also preserving the scale invariance of the power spectrum and the phase coherence of superhorizon perturbation modes in a particular class of these models.

Das, Suratna; Lochan, Kinjalk; Sahu, Satyabrata; Singh, T. P.

2013-10-01

413

Quantum mechanics and faster-than-light communication Methodological considerations

NASA Astrophysics Data System (ADS)

A critical analysis is made of proposals for faster-than-light communications schemes based on quantum mechanics concepts. The point of view taken is that no reduction in one physical system can have an instantaneous effect on another, isolated system. It is shown that the philosophical contradictions exposed by the Einstein-Podolsky Rosen can be directly transferred to an interpretation of physical events. Attention is directed toward the possibility of a photon, propagating in one direction with either circular or plane polarization, entering a nonselective laser tube. The photon originally emerged from a quantum decay process which yielded two photons traveling in opposite directions. The photon in the laser gain tube precipitates a beam which is polarized as the initiating photon. A first observer can then determine the polarization observed by a second observer (with the laser) before the signal arrives. It is concluded that the FLASH argument of Herbert (1982) therefore assumes a violation of quantum mechanical laws in order to use quantum mechanics to prove that faster-than-light communication is possible.

Ghirardi, G. C.; Weber, T.

1983-11-01

414

A perspective on quantum mechanics calculations in ADMET predictions.

Understanding the molecular basis of drug action has been an important objective for pharmaceutical scientists. With the increasing speed of computers and the implementation of quantum chemistry methodologies, pharmacodynamic and pharmacokinetic problems have become more computationally tractable. Historically the former has been the focus of drug design, but within the last two decades efforts to understand the latter have increased. It takes about fifteen years and over $1 billion dollars for a drug to go from laboratory hit, through lead optimization, to final approval by the U.S. Food and Drug Administration. While the costs have increased substantially, the overall clinical success rate for a compound to emerge from clinical trials is approximately 10%. Most of the attrition rate can be traced to ADMET (absorption, distribution, metabolism, excretion, and toxicity) problems, which is a powerful impetus to study these issues at an earlier stage in drug discovery. Quantum mechanics offers pharmaceutical scientists the opportunity to investigate pharmacokinetic problems at the molecular level prior to laboratory preparation and testing. This review will provide a perspective on the use of quantum mechanics or a combination of quantum mechanics coupled with other classical methods in the pharmacokinetic phase of drug discovery. A brief overview of the essential features of theory will be discussed, and a few carefully selected examples will be given to highlight the computational methods. PMID:23675934

Bowen, J Phillip; Güner, Osman F

2013-01-01

415

General-covariant quantum mechanics in Riemannian space-time III. The Dirac particle

NASA Astrophysics Data System (ADS)

A general covariant analog of standard nonrelativistic quantum mechanics with relativistic corrections is constructed for the Dirac particle in a normal geodesic frame in general Riemannian space-time. Not only the Pauli equation with a Hermitian Hamiltonian and the pre-Hilbert structure of the space of its solutions, but also matrix elements of the Hermitian operators of momentum, (curvilinear) spatial coordinates, and spin of the particle, are deduced, as a general-covariant asymptotic approximation in c-2 (c is the velocity of light), to their naturally determined general-relativistic pre-images. It is shown that the Pauli equation Hamiltonian, generated by the Dirac equation, is unitary-equivalent to the energy operator generated by the metric energymomentum tensor of the spinor field. Commutation and other properties of the observables associated with variation in the geometrical background of quantum mechanics are briefly discussed.

Tagirov, E. A.

1996-01-01

416

General-covariant Quantum Mechanics of Dirac particle in curved space-times

NASA Astrophysics Data System (ADS)

A general covariant analog of the standard non-relativistic Quantum Mechanics with relativistic corrections in normal geodesic frames in the general Riemannian space-time is constructed for the Dirac particle. Not only the Pauli equation with hermitian Hamiltonian and the pre-Hilbert structure of space of its solutions but also the matrix elements of hermitian operators of momentum, (curvilinear) spatial coordinates and spin of the particle are deduced as general-covariant asymptotic approximation in c(sup -2), c being the velocity of light, to their naturally determined general-relativistic pre images. It is shown that the Hamiltonian in the Pauli equation originated by the Dirac equation is unitary equivalent to the operator of energy, originated by the metric energy-momentum tensor of the spinor field. Commutation and other properties of the observables connected with the considered change of geometrical background of Quantum Mechanics are briefly discussed.

Tagirov, E. A.

1994-08-01

417

Quantum Mechanical Virial Theorem in Systems with Translational and Rotational Symmetry

NASA Astrophysics Data System (ADS)

Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If the conditions of translational and rotational symmetry together with the additional conditions of the theorem are satisfied, the matrix elements of the commutator [ G, H] are equal to zero on the subspace of the Hilbert space. Normalized simultaneous eigenvectors of the particular set of commuting operators which contains H, J 2, J z and additional operators form an orthonormal basis in this subspace. It is expected that the theorem is relevant for a large number of quantum mechanical N-particle systems with translational and rotational symmetry.

Kui?, Domagoj

2013-04-01

418

Quantum gauge models without (classical) Higgs mechanism

NASA Astrophysics Data System (ADS)

We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein-Glaser) renormalization. The BRST formulation of gauge invariance in this framework, starting from canonical quantization of massive (as well as massless) vector bosons as fundamental entities, and proceeding perturbatively, allows one to rederive the reductive group symmetry of interactions, the need for scalar fields in gauge theory, and the covariant derivative. Thus the presence of higgs particles is understood without recourse to a Higgs(-Englert-Brout-Guralnik-Hagen-Kibble) mechanism. Along the way, we dispel doubts about the compatibility of causal gauge invariance with grand unified theories.

Dütsch, Michael; Gracia-Bondía, José M.; Scheck, Florian; Várilly, Joseph C.

2010-10-01

419

NASA Astrophysics Data System (ADS)

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

Angraini, Lily Maysari; Suparmi; Variani, Viska Inda

2010-12-01

420

NASA Astrophysics Data System (ADS)

In addition to the usual supersymmetric (SUSY) continuous symmetry transformations for the general [InlineEquation not available: see fulltext.] SUSY quantum mechanical model, we show the existence of a set of novel discrete symmetry transformations for the Lagrangian of the above SUSY quantum mechanical model. Out of all these discrete symmetry transformations, a unique discrete transformation corresponds to the Hodge duality operation of differential geometry and the above SUSY continuous symmetry transformations (and their anticommutator) provide the physical realizations of the de Rham cohomological operators of differential geometry. Thus, we provide a concrete proof of our earlier conjecture that any arbitrary [InlineEquation not available: see fulltext.] SUSY quantum mechanical model is an example of a Hodge theory where the cohomological operators find their physical realizations in the language of symmetry transformations of this theory. Possible physical implications of our present study are pointed out, too.

Kumar, R.; Malik, R. P.

2013-08-01

421

Entropy production and equilibration in Yang-Mills quantum mechanics

NASA Astrophysics Data System (ADS)

The Husimi distribution provides for a coarse-grained representation of the phase-space distribution of a quantum system, which may be used to track the growth of entropy of the system. We present a general and systematic method of solving the Husimi equation of motion for an isolated quantum system, and we construct a coarse-grained Hamiltonian whose expectation value is exactly conserved. As an application, we numerically solve the Husimi equation of motion for two-dimensional Yang-Mills quantum mechanics (the x-y model) and calculate the time evolution of the coarse-grained entropy of a highly excited state. We show that the coarse-grained entropy saturates to a value that coincides with the microcanonical entropy corresponding to the energy of the system.

Tsai, Hung-Ming; Müller, Berndt

2012-01-01

422

Entropy production and equilibration in Yang-Mills quantum mechanics.

The Husimi distribution provides for a coarse-grained representation of the phase-space distribution of a quantum system, which may be used to track the growth of entropy of the system. We present a general and systematic method of solving the Husimi equation of motion for an isolated quantum system, and we construct a coarse-grained Hamiltonian whose expectation value is exactly conserved. As an application, we numerically solve the Husimi equation of motion for two-dimensional Yang-Mills quantum mechanics (the x-y model) and calculate the time evolution of the coarse-grained entropy of a highly excited state. We show that the coarse-grained entropy saturates to a value that coincides with the microcanonical entropy corresponding to the energy of the system. PMID:22400515

Tsai, Hung-Ming; Müller, Berndt

2012-01-01

423

NASA Astrophysics Data System (ADS)

The ongoing quantization of the four fundamental forces of nature represents one of the most fruitful grounds for cross-pollination between physics and mathematics. While remaining vastly open, substantial progress has been made in the last decades: the expression of all basic physical theories in terms of geometry, specifically as gauge theories. This is accomplished by the recognition of the strong, weak, and electromagnetic fields as Yang-Mills (gauge) fields, and by the re-writing of general relativity in terms of gauge connection variables. The method of canonical quantization offers several advantages in treating gauge theories: the gauge fields themselves are the basic variables, while gauge constraints promote to quantum operators whose commutation relations reflect the classical Poisson brackets. In this thesis I construct a zero-energy ground state for canonically quantized Yang-Mills theory, for a particular ("nonlinear normal") factor ordering of the Hamiltonian operator. The inspiration for this project is to find an alternative to the Chern-Simons and Kodama states. These are closely related ground state solutions for (respectively) quantum Yang-Mills theory and quantum gravity with a positive cosmological constant. Objections to the Chem-Simons and Kodama states come from, among other arguments, their apparent lack of well-defined decay "at infinity." The ground state I have constructed, as the exponentiation of a strictly non-positive functional, manifestly enjoys good decay properties. In addition, I have constructed a similar ground state for scalar ?4 theory. The construction of these ground states represents a generalization to quantum field theories of work done by my thesis advisor V. Moncrief, in collaboration with M. Ryan, for quantum mechanical situations. Gauge, rotation, and translation invariance are directly verifiable for the nonlinear normal ordered Yang-Mills ground state; invariance under boosts remains as a question for future work. The analogous state for the abelian case (free Maxwell theory) enjoys full Poincare invariance.

Maitra, Rachel Lash

424

Head-operating mechanism improves delayed coker safety, efficiency

Improved operator safety and process operations have been accomplished by the installation of an automatic mechanism for unheading coke drums at Champlin Refining and Chemicals Petroleum Co.'s Corpus Christi, Tex., refinery. The mechanism hydraulically opens and closes a hinged coke-drum bottom head. Automatic bottom head opening improved safety by allowing the operators to be away from the full coke drum

A. J. Nagy; L. P. Antalffy

1989-01-01

425

Differentiation in Hilbert Space and the Structure of Quantum Mechanics

An appropriate kind of curved Hilbert space is developed in such a manner that it admits operators of \\u000a \\u000a - and \\u000a \\u000a -differentiation, which are the analogues of the familiar covariant and D-differentiation available in a manifold. These tools are then employed to shed light on the space-time structure of Quantum\\u000a Mechanics, from the points of view of the Feynman ‘path integral’

D. J. Hurley; M. A. Vandyck

2009-01-01

426

Nonrelativistic quantum mechanics with consideration of influence of fundamental environment

NASA Astrophysics Data System (ADS)

Spontaneous transitions between bound states of an atomic system, the "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected with the influence of the quantum vacuum fluctuations ( fundamental environment (FE)), which are impossible to consider in the framework of standard quantum-mechanical approaches. The joint system quantum system (QS) and FE is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger type and is defined on the extended space ?3?? n , where ?3 and ? n are the Euclidean and functional spaces, respectively. The method of stochastic density matrix is developed and the von Neumann equation for reduced density matrix of QS with FE is generalized. The entropy of QS entangled with FE is defined and investigated. It is proved that the interaction of QS with the environment leads to emerging structures of various topologies which present new quantum-field properties of QS. It is shown that when the physical system (irrelatively to its being micro ormacro) breaks up into two fragments by means of FE, there arises between these fragments a nonpotential interaction which does not disappear at large distances.

Gevorkyan, A. S.

2013-08-01

427

The Brain as Quantum-like Machine Operating on Subcognitive and Cognitive Time Scales

We propose a quantum-like (QL) model of the functioning of the brain. It should be sharply distinguished from the reductionist quan- tum model. By the latter cognition is created by physical quantum processes in the brain. The crucial point of our modelling is that dis- covery of the mathematical formalism of quantum mechanics (QM) was in fact discovery of a

Andrei Yu. Khrennikov

428

Emergence of a New Quantum Mechanics by Multivalued Logic

NASA Astrophysics Data System (ADS)

Quantum Mechanics associated with new logic like Multivalued Logic and Fuzzy Logic has progressed in different ways and their applications can be found in many fields of sciences and technologies. All the concepts attached to this theory are far from the classical view. Classical mechanics can be viewed as crisp limit of a Fuzzy quantum mechanics. This leads to the following interpretation: It is the consequence of an assumption that a quantum particle "reside" in different place or in every path of the continuum of paths which collapse into a single "unique" trajectory of an observed classical motion The reality is "Fuzzy" and nonlocal not only in space but also in time. In this sense, idealised pointlike particles of classical mechanics corresponding to the ultimate sharpness of the fuzziness density emerge in a process of interaction between different parts of fuzzy wholeness. This process is viewed as a continuous process of defuzzification. It transforms a fuzzy reality into a crisp one. It is clear that the emerging crisp reality as a final step of measurements carries less of information that the underlying fuzzy reality. This means that there is an irreversible loss of information usually called "collapse of the wave function". It is not so much a "collapse" as a realization of one of the many possibilities existing within a fuzzy reality. Any measurements rearrange the fuzzy reality leading to different detection outcomes.

de Gerlicz, Claude Gaudeau; Antoine, Mathias; Bobola, Philippe; Flawisky, Nicolas; Hebras, Xavier; Mundedi, Musa

2013-09-01

429

Third emission mechanism in solid-state nanocavity quantum electrodynamics.

Photonic crystal (PC) nanocavities have been receiving a great deal of attention recently because of their ability to strongly confine photons in a tiny space with a high quality factor. According to cavity quantum electrodynamics (cavity QED), such confined photons can achieve efficient interactions with excitons in semiconductors, leading to the Purcell effect in the weak coupling regime and vacuum Rabi splitting (VRS) in the strong coupling regime. These features are promising for applications such as quantum information processing, highly efficient single photon sources and ultra-low threshold lasers. In this context, the coupled system of a semiconductor quantum dot (QD) and a PC nanocavity has been intensively investigated in recent years.Although experimental reports have demonstrated such fundamental features, two anomalous phenomena have also been observed. First, photon emission from the cavity occurs even when it is significantly detuned from the QD. Second, spectral triplets are formed by additional bare-cavity lines between the VRS lines. These features cannot be explained by standard cavity QED theories and have prompted controversy regarding their physical mechanisms. In this review we describe the recent experimental and theoretical progress made in the investigation of these phenomena. Similar mechanisms will also occur in many other coupled quantum systems, and thus the findings are applicable to a wide range of fields. PMID:22885777

Yamaguchi, Makoto; Asano, Takashi; Noda, Susumu

2012-09-01

430

Measurement and quasi-states in quantum mechanics

Part of the task of quantum logic is to account for the collapse of the state vector during measurement. A difficulty in this is that it is not obvious how to describe measurement quantum mechanically as the interaction of two or more systems; interacting quantum-mechanical systems do not possess states, so their states cannot collapse. This dissertation shows that component systems of a composite system possess families of state-like vectors. These are the quasi-projections of the state vector of the composite system, each associated with a family of commutable observables. Often these quasi-projections cluster so closely around a quasi-state that they are practically indistinguishable from it. A description of measurement based on quasi-projections reveals the apparent collapse of the state vector during measurement to be illusory. The continuous evolution of the state of the composite system give rise to abrupt changes in the quasi-projections which make it appear that the state has changed. The quasi-projections cease to cluster near one quasi-state, are momentarily scattered, and then cluster again near another quasi-state. The concept of quasi-projection is also used to generalize the quantum logic of Birkhoff and von Neumann in such a fashion that a proposition can always be assigned a truth value.

Harper, C.D.

1987-01-01

431

Delirium Quantum Or, where I will take quantum mechanics if it will let me

NASA Astrophysics Data System (ADS)

Once again, I take advantage of the wonderfully liberal and tolerant mood Andrei Khrennikov sets at his yearly conferences by submitting a nonstandard paper for the proceedings. This pseudo-paper consists of excerpts drawn from two of my samizdats [Quantum States: What the Hell Are They? and Darwinism All the Way Down (and Probabilism All the Way Back Up)] that I think best summarize what I am aiming for on the broadest scale with my quantum foundations program. Section 1 tries to draw a picture of a physical world whose essence is ``Darwinism all the way down.'' Section 2 outlines how quantum theory should be viewed in light of that, i.e., as being an expression of probabilism (in Bruno de Finetti or Richard Jeffrey's sense) all the way back up. Section 3 describes how the idea of ``identical'' quantum measurement outcomes, though sounding atomistic in character, nonetheless meshes well with a William Jamesian style ``radical pluralism.'' Sections 4 and 5 further detail how quantum theory should not be viewed so much as a ``theory of the world,'' but rather as a theory of decision-making for agents immersed within a quantum world-that is, a world in continual creation. Finally, Sections 6 and 7 attempt to sketch once again the very positive sense in which quantum theory is incomplete, but still just as complete is it can be. In total, I hope these heady speculations convey some of the excitement and potential I see for the malleable world quantum mechanics hints of.

Fuchs, Christopher A.

2007-02-01

432

Automatic computation of quantum-mechanical bound states and wavefunctions

NASA Astrophysics Data System (ADS)

We discuss the automatic solution of the multichannel Schrödinger equation. The proposed approach is based on the use of a CP method for which the step size is not restricted by the oscillations in the solution. Moreover, this CP method turns out to form a natural scheme for the integration of the Riccati differential equation which arises when introducing the (inverse) logarithmic derivative. A new Prüfer type mechanism which derives all the required information from the propagation of the inverse of the log-derivative, is introduced. It improves and refines the eigenvalue shooting process and implies that the user may specify the required eigenvalue by its index. Program summaryProgram title: MATCAS Catalogue identifier: AEON_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEON_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/license/license.html No. of lines in distributed program, including test data, etc.: 3822 No. of bytes in distributed program, including test data, etc.: 119814 Distribution format: tar.gz Programming language: Matlab. Computer: Personal computer architectures. Operating system: Windows, Linux, Mac (all systems on which Matlab can be installed). RAM: Depends on the problem size. Classification: 4.3. Nature of problem: Computation of eigenvalues and eigenfunctions of multichannel Schrödinger equations appearing in quantum mechanics. Solution method: A CP-based propagation scheme is used to advance the R-matrix in a shooting process. The shooting algorithm is supplemented by a Prüfer type mechanism which allows the eigenvalues to be computed according to index: the user specifies an integer k?0, and the code computes an approximation to the kth eigenvalue. Eigenfunctions are also available through an auxiliary routine, called after the eigenvalue has been determined. Restrictions: The program can only deal with non-singular problems. Additional comments: Along with the program's source code, we provide several sample configuration files. Running time: The running time depends on the size n of the problem and the number of eigenvalues/eigenfunctions computed. For a small problem the runtime should not exceed a few seconds.

Ledoux, V.; Van Daele, M.

2013-04-01

433

A quantum mechanical polarizable force field for biomolecular interactions

We introduce a quantum mechanical polarizable force field (QMPFF) fitted solely to QM data at the MP2/aTZ(-hp) level. Atomic charge density is modeled by point-charge nuclei and floating exponentially shaped electron clouds. The functional form of interaction energy parallels quantum mechanics by including electrostatic, exchange, induction, and dispersion terms. Separate fitting of each term to the counterpart calculated from high-quality QM data ensures high transferability of QMPFF parameters to different molecular environments, as well as accurate fit to a broad range of experimental data in both gas and liquid phases. QMPFF, which is much more efficient than ab initio QM, is optimized for the accurate simulation of biomolecular systems and the design of drugs.

Donchev, A. G.; Ozrin, V. D.; Subbotin, M. V.; Tarasov, O. V.; Tarasov, V. I.

2005-01-01

434

A quantum mechanical polarizable force field for biomolecular interactions.

We introduce a quantum mechanical polarizable force field (QMPFF) fitted solely to QM data at the MP2/aTZ(-hp) level. Atomic charge density is modeled by point-charge nuclei and floating exponentially shaped electron clouds. The functional form of interaction energy parallels quantum mechanics by including electrostatic, exchange, induction, and dispersion terms. Separate fitting of each term to the counterpart calculated from high-quality QM data ensures high transferability of QMPFF parameters to different molecular environments, as well as accurate fit to a broad range of experimental data in both gas and liquid phases. QMPFF, which is much more efficient than ab initio QM, is optimized for the accurate simulation of biomolecular systems and the design of drugs. PMID:15911753

Donchev, A G; Ozrin, V D; Subbotin, M V; Tarasov, O V; Tarasov, V I

2005-05-31

435

The equivalence principle of quantum mechanics: Uniqueness theorem

Recently the authors showed that the postulated diffeomorphic equivalence of states implies quantum mechanics. This approach takes the canonical variables to be dependent by the relation p = {partial_derivative}{sub q}S{sub 0} and exploits a basic GL(2,C)-symmetry which underlies the canonical formalism. In particular, they looked for the special transformations leading to the free system with vanishing energy. Furthermore, they saw that while on the one hand the equivalence principle cannot be consistently implemented in classical mechanics, on the other it naturally led to the quantum analogue of the Hamilton-Jacobi equation, thus implying the Schroedinger equation. In this letter they show that actually the principle uniquely leads to this solution. The authors also express the canonical and Schroedinger equations by means of the brackets recently introduced in the framework of N = 2 SYM. These brackets are the analogue of the Poisson brackets with the canonical variables taken as dependent.

Faraggi, A.E. [Univ. of Florida, Gainesville, FL (United States). Inst. for Fundamental Theory; Matone, M. [Univ. of Padova (Italy)

1997-10-28

436

Developing and evaluating animations for teaching quantum mechanics concepts

NASA Astrophysics Data System (ADS)

In this paper, we describe animations and animated visualizations for introductory and intermediate-level quantum mechanics instruction developed at the University of St Andrews. The animations aim to help students build mental representations of quantum mechanics concepts. They focus on known areas of student difficulty and misconceptions by including animated step-by-step explanations of key points. The animations are freely available, with additional resources available to instructors. We have investigated their educational effectiveness both in terms of student attitude and performance. Questionnaires showed that students are on the whole very positive about the animations and make substantial use of them. A diagnostic survey administered to level 2 and 3 students showed that level 2 students significantly outperformed level 3 students on topics which they had investigated using the animations.

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

2010-11-01

437

Quantum mechanical properties of graphene nano-flakes and quantum dots.

In recent years considerable attention has been given to methods for modifying and controlling the electronic and quantum mechanical properties of graphene quantum dots. However, as these types of properties are indirect consequences of the wavefunction of the material, a more efficient way of determining properties may be to engineer the wavefunction directly. One way of doing this may be via deliberate structural modifications, such as producing graphene nanostructures with specific sizes and shapes. In this paper we use quantum mechanical simulations to determine whether the wavefunction, quantified via the distribution of the highest occupied molecular orbital, has a direct and reliable relationship to the physical structure, and whether structural modifications can be useful for wavefunction engineering. We find that the wavefunction of small molecular graphene structures can be different from those of larger nanoscale counterparts, and the distribution of the highest occupied molecular orbital is strongly affected by the geometric shape (but only weakly by edge and corner terminations). This indicates that both size and shape may be more useful parameters in determining quantum mechanical and electronic properties, which should then be reasonably robust against variations in the chemical passivation or functionalisation around the circumference. PMID:22903345

Shi, Hongqing; Barnard, Amanda S; Snook, Ian K

2012-11-01

438

Optical pulse dynamics for quantum-dot logic operations in a photonic-crystal waveguide

We numerically demonstrate all-optical logic operations with quantum dots (QDs) embedded in a bimodal photonic-crystal waveguide using Maxwell-Bloch equations in a slowly varying envelope approximation (SVEA). The two-level QD excitation level is controlled by one or more femtojoule optical driving pulses passing through the waveguide. Specific logic operations depend on the relative pulse strengths and their detunings from an inhomogeneouslly broadened (about 1% for QD transitions centered at 1.5 {mu}m) QD transition. This excitation controlled two-level medium then determines passage of subsequent probe optical pulses. Envelope equations for electromagnetic waves in the linear dispersion and cutoff waveguide modes are derived to simplify solution of the coupled Maxwell-Bloch equations in the waveguide. These determine the quantum mechanical evolution of the QD excitation and its polarization, driven by classical electromagnetic (EM) pulses near a sharp discontinuity in the EM density of states of the bimodal waveguide. Different configurations of the driving pulses lead to distinctive relations between driving pulse strength and probe pulse passage, representing all-optical logic and, or, and not operations. Simulation results demonstrate that such operations can be done on picosecond time scales and within a waveguide length of about 10 {mu}m in a photonic-band-gap (PBG) optical microchip.

Ma, Xun; John, Sajeev [Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7 Canada (Canada)

2011-11-15

439

Optical pulse dynamics for quantum-dot logic operations in a photonic-crystal waveguide

NASA Astrophysics Data System (ADS)

We numerically demonstrate all-optical logic operations with quantum dots (QDs) embedded in a bimodal photonic-crystal waveguide using Maxwell-Bloch equations in a slowly varying envelope approximation (SVEA). The two-level QD excitation level is controlled by one or more femtojoule optical driving pulses passing through the waveguide. Specific logic operations depend on the relative pulse strengths and their detunings from an inhomogeneouslly broadened (about 1% for QD transitions centered at 1.5?m) QD transition. This excitation controlled two-level medium then determines passage of subsequent probe optical pulses. Envelope equations for electromagnetic waves in the linear dispersion and cutoff waveguide modes are derived to simplify solution of the coupled Maxwell-Bloch equations in the waveguide. These determine the quantum mechanical evolution of the QD excitation and its polarization, driven by classical electromagnetic (EM) pulses near a sharp discontinuity in the EM density of states of the bimodal waveguide. Different configurations of the driving pulses lead to distinctive relations between driving pulse strength and probe pulse passage, representing all-optical logic and, or, and not operations. Simulation results demonstrate that such operations can be done on picosecond time scales and within a waveguide length of about 10?m in a photonic-band-gap (PBG) optical microchip.

Ma, Xun; John, Sajeev

2011-11-01

440

Relationship between quantum mechanics with and without monopoles

We show that the inclusion of the monopole field in the three- and\\u000afive-dimensional spherically symmetric quantum mechanical systems, supplied by\\u000athe addition of the special centrifugal term, does not yield any change in the\\u000aradial wavefunction and in the functional dependence of the energy spectra on\\u000aquantum numbers. The only change in the spectrum is the lift of the

Levon Mardoyan; Armen Nersessian; Armen Yeranyan

2006-01-01