Positive-Operator-Valued Time Observable in Quantum Mechanics
Riccardo Giannitrapani
1998-02-22
We examine the longstanding problem of introducing a time observable in Quantum Mechanics; using the formalism of positive-operator-valued measures we show how to define such an observable in a natural way and we discuss some consequences.
Phase operator problem and macroscopic extension of quantum mechanics
Ozawa, M.
1997-06-01
To find the Hermitian phase operator of a single-mode electromagnetic field in quantum mechanics, the Schr{umlt o}dinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis. The Hermitian phase operator is shown to exist on the extended Hilbert space. This operator is naturally considered as the controversial limit of the approximate phase operators on finite dimensional spaces proposed by Pegg and Barnett. The spectral measure of this operator is a Naimark extension of the optimal probability operator-valued measure for the phase parameter found by Helstrom. Eventually, the two promising approaches to the statistics of the phase in quantum mechanics are synthesized by means of the Hermitian phase operator in the macroscopic extension of the Schr{umlt o}dinger representation. {copyright} 1997 Academic Press, Inc.
Tensor Operators in Noncommutative Quantum Mechanics
Amorim, Ricardo [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21945-970 Rio de Janeiro (Brazil)
2008-08-22
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.
Nonunique C operator in PT Quantum Mechanics
Carl M. Bender; S. P. Klevansky
2009-05-28
The three simultaneous algebraic equations, $C^2=1$, $[C,PT]=0$, $[C,H]=0$, which determine the $C$ operator for a non-Hermitian $PT$-symmetric Hamiltonian $H$, are shown to have a nonunique solution. Specifically, the $C$ operator for the Hamiltonian $H={1/2}p^2+{1/2}\\mu^2q^2+i\\epsilon q^3$ is determined perturbatively to first order in $\\epsilon$ and it is demonstrated that the $C$ operator contains an infinite number of arbitrary parameters. For each different $C$ operator, the corresponding equivalent isospectral Dirac-Hermitian Hamiltonian $h$ is calculated.
An Arrow of Time Operator for Standard Quantum Mechanics
Y. Strauss; J. Silman; S. Machnes; L. P. Horwitz
2008-02-18
We introduce a self-adjoint operator that indicates the direction of time within the framework of standard quantum mechanics. That is, as a function of time its expectation value decreases monotonically for any initial state. This operator can be defined for any system governed by a Hamiltonian with a uniformly finitely degenerate, absolutely continuous and semibounded spectrum. We study some of the operator's properties and illustrate them for a large equivalence class of scattering problems. We also discuss some previous attempts to construct such an operator, and show that the no-go theorems developed in this context are not applicable to our construction.
Non Hermitian Operators with Real Spectrum in Quantum Mechanics
João da Providência; Natália Bebiano; João Pinheiro da Providência
2009-09-29
Examples are given of non-Hermitian Hamiltonian operators which have a real spectrum. Some of the investigated operators are expressed in terms of the generators of the Weil-Heisenberg algebra. It is argued that the existence of an involutive operator $\\hat J$ which renders the Hamiltonian $\\hat J$-Hermitian leads to the unambiguous definition of an associated positive definite norm allowing for the standard probabilistic interpretation of quantum mechanics. Non-Hermitian extensions of the Poeschl-Teller Hamiltonian are also considered. Hermitian counterparts obtained by similarity transformations are constructed.
Generalized raising and lowering operators for supersymmetric quantum mechanics
Mark W. Coffey
2015-01-27
Supersymmetric quantum mechanics has many applications, and typically uses a raising and lowering operator formalism. For one dimensional problems, we show how such raising and lowering operators may be generalized to include an arbitrary function. As a result, the usual Rodrigues' formula of the theory of orthogonal polynomials may be recovered in special cases, and it may otherwise be generalized to incorporate an arbitrary function. We provide example generalized operators for several important classical orthogonal polynomials, including Chebyshev, Gegenbauer, and other polynomials. In particular, as concerns Legendre polynomials and associated Legendre functions, we supplement and generalize results of Bazeia and Das.
The SCOP-formalism: an Operational Approach to Quantum Mechanics
D'Hooghe, Bart [Leo Apostel Center for Interdisciplinary Studies, Vrije Universiteit Brussel (VUB) (Belgium)
2010-05-04
We present the SCOP-formalism, an operational approach to quantum mechanics. If a State-COntext-Property-System (SCOP) satisfies a specific set of 'quantum axioms,] it fits in a quantum mechanical representation in Hilbert space. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter N. In the case N = 2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N->infinity the system is classical. For the intermediate cases it is impossible to define an orthocomplementation on the set of properties. Another interesting feature is that the probability of a state transition also depends on the context which induces it. This contrasts sharply with standard quantum mechanics for which Gleason's theorem states the uniqueness of the state transition probability and independent of measurement context. We show that if a SCOP satisfies a Gleason-like condition, namely that all state transition probabilities are independent of which measurement context induces the change of state, then the lattice of properties is orthocomplemented.
Taeseung Choi
2014-12-01
A relativistic spin operator is to be the difference between the total and orbital angular momentum. As the unique position operator for a localized state, the remarkable Newton-Wigner position operator, which has all desirable commutation relations as a position operator, can give a proper spin operator. Historically important three spin operators respectively proposed by Bogolubov et al., Pryce, and Foldy-Woutheysen are investigated to manifest a corresponding spin operator to the Newton-Wigner position operator. We clarify a unique spin operator in relativistic quantum mechanics described by the Dirac Hamiltonian.
A dynamical time operator in Dirac's relativistic quantum mechanics
NASA Astrophysics Data System (ADS)
Bauer, M.
2014-03-01
A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The ensuing time-energy uncertainty relation involves the uncertainty in the instant of time when the wave packet passes a particular spatial position and the energy uncertainty associated with the wave packet at the same time, as envisaged originally by Bohr. The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in electron channeling, in interference in time, in Zitterbewegung-like effects in spintronics, graphene and superconducting systems and in cosmology is noted.
The velocity operator in quantum mechanics in noncommutative space
Samuel Kovacik; Peter Presnajder
2013-09-18
We tested in the framework of quantum mechanics the consequences of a noncommutative (NC from now on) coordinates. We restricted ourselves to 3D rotationally invariant NC configuration spaces with dynamics specified by the Hamiltonian H = H(kin) + U, H(kin) is an analogue of kinetic energy and U = U(r) denotes an arbitrary rotationally invariant potential. We introduced the velocity operator by Heisenberg relation using the commutator of the coordinate and the Hamiltonian operators. We found that the NC velocity operator possesses various general, independent of potential, properties: 1) uncertainty relations indicate an existence of a natural kinetic energy cut-off, 2) vanishing commutator relations for velocity components, which is non-trivial in the NC case, 3) modified relation between the velocity operator and H(kin) that indicates the existence of maximal velocity and confirms the kinetic energy cut-off, 4) All these results sum up in canonical (general, not depending on a particular form of the central potential) commutation relations of the Euclidean group E(4), 5) NC Heisenberg equation for the velocity operator, relating acceleration to derivatives of the potential.
The velocity operator in quantum mechanics in noncommutative space
NASA Astrophysics Data System (ADS)
Ková?ik, Samuel; Prešnajder, Peter
2013-10-01
We tested the consequences of noncommutative (NC from now on) coordinates xk, k = 1, 2, 3 in the framework of quantum mechanics. We restricted ourselves to 3D rotationally invariant NC configuration spaces with dynamics specified by the Hamiltonian hat{H} = hat{H}_0 + hat{U}, where hat{H}_0 is an analogue of kinetic energy and hat{U} = hat{U}(hat{r}) denotes an arbitrary rotationally invariant potential. We introduced the velocity operator by hat{V}_k = - i [hat{X}_k, hat{H}] (hat{X}_k being the position operator), which is a NC generalization of the usual gradient operator (multiplied by -i). We found that the NC velocity operators possess various general, independent of potential, properties: (1) uncertainty relations [hat{V}_i,hat{X}_j] indicate an existence of a natural kinetic energy cut-off, (2) commutation relations [hat{V}_i,hat{V}_j] = 0, which is non-trivial in the NC case, (3) relation between hat{V}^2 and hat{H}_0 that indicates the existence of maximal velocity and confirms the kinetic energy cut-off, (4) all these results sum up in canonical (general, not depending on a particular form of the central potential) commutation relations of Euclidean group E(4) = SO(4)?T(4), (5) Heisenberg equation for the velocity operator, relating acceleration dot{hat{V}}_k = -i[hat{V}_k, hat{H}] to derivatives of the potential.
NASA Astrophysics Data System (ADS)
Ihly, Rachelle
This thesis explores the understanding of the chemistry and physics of colloidal quantum dots for practical solar energy photoconversion. Solar cell devices that make use of PbS quantum dots generally rely on constant and unchanged optical properties such that band gap energies remain tuned within the device. The design and development of unique experiments to ascertain mechanisms of optical band gap shifts occurring in PbS quantum dot thin-films exposed to air are discussed. The systematic study of the absorption properties of PbS quantum dot films exposed to air, heat, and UV illumination as a function of quantum dot size has been described. A method to improve the air-stability of films with atomic layer deposition of alumina is demonstrated. Encapsulation of quantum dot films using a protective layer of alumina results in quantum dot solids that maintain tuned absorption for 1000 hours. This thesis focuses on the use of atomic force microscopy and electrical variants thereof to study the physical and electrical characteristics of quantum dot arrays. These types of studies have broad implications in understanding charge transport mechanisms and solar cell device operation, with a particular emphasis on quantum dot transistors and solar cells. Imaging the channel potential of a PbSe quantum dot thin-film in a transistor showed a uniform distribution of charge coinciding with the transistor current voltage characteristics. In a second study, solar cell device operation of ZnO/PbS heterojunction solar cells was investigated by scanning active cross-sections with Kelvin probe microscopy as a function of applied bias, illumination and device architecture. This technique directly provides operating potential and electric field profiles to characterize drift and diffusion currents occurring in the device. SKPM established a field-free region occurring in the quantum dot layer, indicative of diffusion-limited transport. These results provide the path to optimization of future architectures that may employ drift-based transport in the quantum dot layer for enhanced charge extraction and power conversion efficiency.
Overcoming Misconceptions in Quantum Mechanics with the Time Evolution Operator
ERIC Educational Resources Information Center
Quijas, P. C. Garcia; Aguilar, L. M. Arevalo
2007-01-01
Recently, there have been many efforts to use the research techniques developed in the field of physics education research to improve the teaching and learning of quantum mechanics. In particular, part of this research is focusing on misconceptions held by students. For instance, a set of misconceptions is associated with the concept of stationary…
Quantum Mechanical Operators and Commutation C I. Bra-Ket Notation
Simons, Jack
Quantum Mechanical Operators and Commutation C I. Bra-Ket Notation It is conventional to represent notation, which is referred to as 'Dirac' or 'bra-ket' notation, can be summarized as follows: A as a 'bra'
Physical Properties as Modal Operators in the Topos Approach to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Freytes, H.; Domenech, G.; de Ronde, C.
2014-12-01
In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras. It allows us to introduce a classical type study of the mentioned properties.
Physical properties as modal operators in the topos approach to quantum mechanics
Hector Freytes; Graciela Domenech; Christian de Ronde
2014-12-21
In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras. It allows us to introduce a classical type study of the mentioned properties.
Vector Operators and Spherical Harmonics in Quantum Mechanics.
ERIC Educational Resources Information Center
Andrews, M.
1979-01-01
Shows that the basic properties of spherical harmonics follow in a simple and elegant way from the commutation relations for angular momentum operators and the commutation relations between these operators and arbitrary vector operators. (Author/HM)
Ladder Operators for Some Spherically Symmetric Potentials in Quantum Mechanics
ERIC Educational Resources Information Center
Newmarch, J. D.; Golding, R. M.
1978-01-01
The energy levels of the free field, Coulomb potential, and the three-dimensional harmonic oscillator are found using the Dirac operator formalism by the construction of suitable ladder operators. The degeneracy of each level is also discussed. (Author/GA)
NASA Astrophysics Data System (ADS)
Fan, Hong-yi; Lu, Hai-liang; Fan, Yue
2006-02-01
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) 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.
Positive-operator-valued measures in the Hamiltonian formulation of quantum mechanics
NASA Astrophysics Data System (ADS)
Arsenovi?, D.; Buri?, N.; Popovi?, D. B.; Radonji?, M.; Prvanovi?, S.
2015-06-01
In the Hilbert space formulation of quantum mechanics, ideal measurements of physical variables are discussed using the spectral theory of Hermitian operators and the corresponding projector-valued measures (PVMs). However, more general types of measurements require the treatment in terms of positive-operator-valued measures (POVMs). In the Hamiltonian formulation of quantum mechanics, canonical coordinates are related to PVM. In this paper the results of an analysis of various aspects of applications of POVMs in the Hamiltonian formulation are reported. Several properties of state parameters and quantum observables given by POVMs or represented in an overcomplete basis, including the general Hamiltonian treatment of the Neumark extension, are presented. An analysis of the phase operator, given by the corresponding POVMs, in the Hilbert space and the Hamiltonian frameworks is also given.
Generalized space and linear momentum operators in quantum mechanics
Bruno G. da Costa; Ernesto P. Borges
2013-05-27
We propose a modification of a recently introduced generalized translation operator, by including a $q$-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator $\\hat{p}_q$, and its canonically conjugate deformed position operator $\\hat{x}_q$. A canonical transformation leads the Hamiltonian of a position-dependent mass particle to another Hamiltonian of a particle with constant mass in a conservative force field of a deformed phase space. The equation of motion for the classical phase space may be expressed in terms of the generalized dual $q$-derivative. A position-dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed.
Generalized space and linear momentum operators in quantum mechanics
Costa, Bruno G. da, E-mail: bruno.costa@ifsertao-pe.edu.br [Instituto Federal de Educação, Ciência e Tecnologia do Sertão Pernambucano, Campus Petrolina, BR 407, km 08, 56314-520 Petrolina, Pernambuco (Brazil); Instituto de Física, Universidade Federal da Bahia, R. Barão de Jeremoabo s/n, 40170-115 Salvador, Bahia (Brazil); Borges, Ernesto P., E-mail: ernesto@ufba.br [Instituto de Física, Universidade Federal da Bahia, R. Barão de Jeremoabo s/n, 40170-115 Salvador, Bahia (Brazil)
2014-06-15
We propose a modification of a recently introduced generalized translation operator, by including a q-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator p{sup ^}{sub q}, and its canonically conjugate deformed position operator x{sup ^}{sub q}. A canonical transformation leads the Hamiltonian of a position-dependent mass particle to another Hamiltonian of a particle with constant mass in a conservative force field of a deformed phase space. The equation of motion for the classical phase space may be expressed in terms of the generalized dual q-derivative. A position-dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed.
Renormalizing the Kinetic Energy Operator in Elementary Quantum Mechanics
ERIC Educational Resources Information Center
Coutinho, F. A. B.; Amaku, M.
2009-01-01
In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form [psi](r) = u(r)/r, where u(0) [is not equal to] 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly…
Towards a general operational and realistic framework for quantum mechanics and relativity theory
Aerts, Diederik
Towards a general operational and realistic framework for quantum mechanics and relativity theory with the macroscopic material entities that have emerged from the microworld. This clarifies why general relativity relativity theory the set of events is taken a priori to be the time-space continuum. Hence in general
NASA Astrophysics Data System (ADS)
Fan, Hong-Yi; Lou, Sen-Yue
2015-07-01
Based on the operator Hermite polynomials method (OHPM), we study Stirling numbers in the context of quantum mechanics, i.e., we present operator realization of generating function formulas of Stirling numbers with some applications. As a by-product, we derive a summation formula involving both Stirling number and Hermite polynomials. Project supported by the National Natural Science Foundation of China (Grant No. 11175113).
Wigner operator's new transformation in phase space quantum mechanics and its applications
Hong-yi Fan
2009-03-10
Using operators' Weyl ordering expansion formula (Hong-yi Fan,\\emph{\\}J. Phys. A 25 (1992) 3443) we find new two-fold integration transformation about the Wigner operator $\\Delta(q',p')$ ($q$-number transform) in phase space quantum mechanics, \\[ \\iint_{-\\infty}^\\infty dp' dq'/\\pi \\Delta (q',p') e^{-2i(p-p') (q-q')} =\\delta (p-P) \\delta (q-Q), \\] and its inverse \\[\\iint_{-\\infty}^\\infty dq dp \\delta (p-P) \\delta (q-Q) e^{2i(p-p') (q-q')}=\\Delta (q',p'), \\] where $Q,$ $P$ are the coordinate and momentum operators, respectively. We apply it to studying mutual converting formulas among $Q-P$ ordering, $P-Q$ ordering and Weyl ordering of operators. In this way, the contents of phase space quantum mechanics can be enriched.
Odake, Satoru
2008-01-01
Various examples of exactly solvable `discrete' quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilation-creation operators, the dynamical symmetry algebras and coherent states. The eigenfunctions are the (q-)Askey-scheme of hypergeometric orthogonal polynomials satisfying difference equation versions of the Schr\\"odinger equation. Various reductions (restrictions) of the symmetry algebra of the Askey-Wilson system are explored in detail.
Rigorous bra-ket formalism and wave function operator for one particle quantum mechanics
NASA Astrophysics Data System (ADS)
Bergeron, H.
2006-02-01
Following previous works dedicated to the mathematical meaning of the "bra-ket" formalism [I. M. Gel'fand and G. E. Shilov, Generalized Functions (Academic, New York, 1964), Vol. I; J. P. Antoine, J. Math. Phys. 10, 53 (1969); Yu. M. Berezanskii, Expansions of Self-adjoint Operators (American Mathematical Society, Providence, RI 1968); E. Prugove?ki, J. Math. Phys. 14, 1410 (1973); J. P. Antoine and A. Grossmann, J. Funct. Anal. 23, 369 (1976); 23, 379 (1976)], we develop a new rigorous mathematical approach, based on an operator representation of bras and kets. This leads to a formalism very similar to second quantization. Well-defined operators associated with local observables can be exhibited, intimately related to previous works of E. Prugove?ki [Stochastic Quantum Mechanics and Quantum Space-Time (Reidel, Dordrecht, 1986)].
NASA Astrophysics Data System (ADS)
Mandl, F.
1992-07-01
The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Quantum Mechanics aims to teach those parts of the subject which every physicist should know. The object is to display the inherent structure of quantum mechanics, concentrating on general principles and on methods of wide applicability without taking them to their full generality. This book will equip students to follow quantum-mechanical arguments in books and scientific papers, and to cope with simple cases. To bring the subject to life, the theory is applied to the all-important field of atomic physics. No prior knowledge of quantum mechanics is assumed. However, it would help most readers to have met some elementary wave mechanics before. Primarily written for students, it should also be of interest to experimental research workers who require a good grasp of quantum mechanics without the full formalism needed by the professional theorist. Quantum Mechanics features: A flow diagram allowing topics to be studied in different orders or omitted altogether. Optional "starred" and highlighted sections containing more advanced and specialized material for the more ambitious reader. Sets of problems at the end of each chapter to help student understanding. Hints and solutions to the problems are given at the end of the book.
Transforming quantum operations: quantum supermaps
G. Chiribella; G. M. D'Ariano; P. Perinotti
2008-10-22
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.
Transforming quantum operations: Quantum supermaps
NASA Astrophysics Data System (ADS)
Chiribella, G.; D'Ariano, G. M.; Perinotti, P.
2008-08-01
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.
A. L. Stewart; G. Scolarici; L. Solombrino
1963-01-01
We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with respect to a uniquely defined positive scalar product in a infinite dimensional (right) quaternionic Hilbert space. According to such results we obtain two alternative descriptions of a quantum
Natural star-products on symplectic manifolds and related quantum mechanical operators
B?aszak, Maciej, E-mail: blaszakm@amu.edu.pl; Doma?ski, Ziemowit, E-mail: ziemowit@amu.edu.pl
2014-05-15
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. -- Highlights: •Invariant representations of natural star-products on symplectic manifolds are considered. •Star-products induced by flat and non-flat connections are investigated. •Operator representations in Hilbert space of considered star-algebras are constructed.
Bohmian mechanics contradicts quantum mechanics
Neumaier, Arnold
Bohmian mechanics contradicts quantum mechanics Arnold Neumaier Institut fur Mathematik, Universit and quantum mechanics predict values of opposite sign for certain time correlations. The discrepancy can no loophole for claiming that Bohmian mechanics reproduces all predictions of quantum mechanics exactly
Bender, Carl M; DeKieviet, Maarten; Klevansky, S. P.
2013-01-01
-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter–antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantum mechanics. PMID:23509390
Speculation on Quantum Mechanics and the Operation of Life Giving Catalysts
NASA Astrophysics Data System (ADS)
Haydon, Nathan; McGlynn, Shawn E.; Robus, Olin
2011-02-01
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.
Canonical conjugate momentum of discrete label operators in quantum mechanics I: formalism
NASA Astrophysics Data System (ADS)
Cannata, F.; Ferrari, L.
1991-12-01
We discuss the inadequacy of the standard definition of canonical conjugation for a quantum operator having a discrete spectrum. A different definition is proposed, based on the analogy between continuous and discrete translations (or rotations). This definition can be applied to special operators which we call label operators. The general form of the conjugate momentum of a label operator is found and the resulting canonical commutation rules are discussed. It is shown that the canonical commutator acts like a c number in its domain ? I , but the domain does not coincide with the whole Hilbert space. The properties of the subspace ? I are also discussed.
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
on. #12;Applied quantum mechanics 3 Problem 9.4 Modify the computer program used in Exercise 9Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 9 problems LAST NAME FIRST NAME #12) such that the chemical potential EF« , where EF is the Fermi energy, then fk may be approximated by a Maxwell-Boltzmann
Introduction: quantum resonances Classical and quantum mechanics
Ramond, Thierry
: quantum resonances Classical and quantum mechanics Microlocal analysis Resonances associated;..... . .... . .... . ..... . .... . .... . .... . ..... . .... . .... . .... . ..... . .... . .... . .... . ..... . .... . ..... . .... . .... . Introduction: quantum resonances Classical and quantum mechanics Microlocal analysis Resonances associated with homoclinic orbits Outline Introduction: quantum resonances Classical and quantum mechanics Microlocal
Supersymmetry in quantum mechanics
NASA Astrophysics Data System (ADS)
Khare, Avinash
2004-12-01
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.
Quantum Operation Time Reversal
Crooks, Gavin E.
2008-03-25
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.
NASA Astrophysics Data System (ADS)
Császár, Attila G.; Handy, Nicholas C.
Forms for the exact non-relativistic quantum mechanical vibrational (J = 0) kinetic energy operators for sequentially bonded (A-B-C-D-E) and (A,B)-C-D-E-type penta-atomic molecules, expressed in valence internal coordinates, are presented. As advocated earlier (Handy, N. C., 1987, Molec. Phys., 61, 207), computer algebra has been employed during the derivation. The suggested use of these operators in calculations for vibrational energy levels of interesting penta-atomic molecules (e.g., C3O2, and H2CCO) is outlined.
Quantum Mechanics + Open Systems
Steinhoff, Heinz-Jürgen
Quantum Mechanics + Open Systems = Thermodynamics ? Jochen Gemmer T¨ubingen, 09.02.2006 #12., World Scientific) #12;Fundamental Law or Emergent Description? Quantum Mechanics i t = (- 2 2m + V or Emergent Description? Quantum Mechanics i t = (- 2 2m + V ) "Heisenberg Cut" Classical Mechanics: m d2
NASA Astrophysics Data System (ADS)
Gardner, David E.
This thesis describes qualitative research conducted to understand the problems students have when learning quantum mechanics. It differs from previous studies on educational issues associated with quantum mechanics in that I have examined the difficulties from the students' perspective. Three questions guided this research: What are the experiences of students learning quantum mechanics? What conceptual difficulties do students have with quantum mechanics? and, How do students approach learning quantum mechanics? From these questions, two themes emerged. First, students do not consider the quantum mechanical concepts of wave-particle duality or the uncertainty principle to be important sources of difficulties for them. Second, many of the difficulties students encounter are not related to conceptual understanding of specific topics, but stem from a mindset that is incongruent with the nature and structure of quantum mechanics. The implications for teaching are that the nature and structure of quantum mechanics should be emphasized and be an explicit part of instruction.
Introduction to Quantum Mechanics
Eduardo J. S. Villaseñor
2008-04-23
The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.
Galois Field Quantum Mechanics
Lay Nam Chang; Zachary Lewis; Djordje Minic; Tatsu Takeuchi
2013-01-06
We construct a discrete quantum mechanics using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete quantum mechanics cannot be reproduced with any hidden variable theory.
Chapin, Kimberly R.
1997-01-01
The role of time in quantum mechanics has been and is still very controversial. The purpose of this paper was to explore the historical interpretation of time in quantum mechanics, to determine the current status of this problem-L and to investigate...
Geometrization of Quantum Mechanics
J. F. Carinena; J. Clemente-Gallardo; G. Marmo
2007-03-23
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.
Noncommutative quantum mechanics
J. Gamboa; M. Loewe; J. C. Rojas
2001-01-01
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 theta, 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
Tadashi Okazaki
2014-11-03
We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the BLG-model and the ABJM-model compactified on a torus are N = 16 and N = 12 superconformal gauged quantum mechanics. After integrating out the auxiliary gauge fields we find OSp(16|2) and SU(1,1|6) quantum mechanics from the reduced systems. The curved Riemann surface is taken as a holomorphic curve in a Calabi-Yau space to preserve supersymmetry and we present a prescription of the topological twisting. We find the N = 8 superconformal gauged quantum mechanics that may describe the motion of two wrapped M2-branes in a K3 surface.
Covariant quantum mechanics and quantum symmetries
JanyÂ?ka, Josef
Covariant quantum mechanics and quantum symmetries Josef JanyÅ¸ska 1 , Marco Modugno 2 , Dirk Saller: quantum mechanics, classical mechanics, general relativity, infinitesimal symmetries. 2000 MSC: 81P99, 81Q Introduction 2 2 Covariant quantum mechanics 5 2.1 Classical background
Quantum mechanical effects from deformation theory
Much, A. [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)] [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)
2014-02-15
We consider deformations of quantum mechanical operators by using the novel construction tool of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a role. Furthermore, a quantum plane can be defined by using the deformation techniques. This in turn gives an experimentally verifiable effect.
Quantum mechanics from classical statistics
Wetterich, C.
2010-04-15
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.
Yamasaki, Terumasa; Mainz, D.T.; Goddard, W.A. III
2000-03-23
The workers apply correlation analysis of chemical bonds (CACB) to simple organic reaction paths. CACB, an operator-based formalism for analyzing the electronic structure for molecule, clarifies how bond exchange processes relate to changes in covalent bond orders and bond interaction coefficients. For single bond-exchange processes, the bonds correlation typically is negative for interchanging bonds. For two bond-exchange processes, this coefficient can be either negative or slightly positive near zero, reflecting the nature of the bond exchange process. The simplest formalism can, sometimes, lead to unphysical values for the atomic valence and the bonds correlation coefficient. The origin of this behavior was analyzed and attributed to the non-Hermitian property of the operator. The authors show how to avoid this problem by symmetrizing the operator through use of orthogonal atomic orbitals.
Operational interpretations of quantum discord
Cavalcanti, D.; Modi, K.; Aolita, L.; Boixo, S.; Piani, M.; Winter, A.
2011-03-15
Quantum discord quantifies nonclassical correlations beyond the standard classification of quantum states into entangled and unentangled. Although it has received considerable attention, it still lacks any precise interpretation in terms of some protocol in which quantum features are relevant. Here we give quantum discord its first information-theoretic operational meaning in terms of entanglement consumption in an extended quantum-state-merging protocol. We further relate the asymmetry of quantum discord with the performance imbalance in quantum state merging and dense coding.
Quantum Chaos and Statistical Mechanics
Mark Srednicki
1994-06-14
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
Principles of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Landé, Alfred
2013-10-01
Preface; Introduction: 1. Observation and interpretation; 2. Difficulties of the classical theories; 3. The purpose of quantum theory; Part I. Elementary Theory of Observation (Principle of Complementarity): 4. Refraction in inhomogeneous media (force fields); 5. Scattering of charged rays; 6. Refraction and reflection at a plane; 7. Absolute values of momentum and wave length; 8. Double ray of matter diffracting light waves; 9. Double ray of matter diffracting photons; 10. Microscopic observation of ? (x) and ? (p); 11. Complementarity; 12. Mathematical relation between ? (x) and ? (p) for free particles; 13. General relation between ? (q) and ? (p); 14. Crystals; 15. Transition density and transition probability; 16. Resultant values of physical functions; matrix elements; 17. Pulsating density; 18. General relation between ? (t) and ? (?); 19. Transition density; matrix elements; Part II. The Principle of Uncertainty: 20. Optical observation of density in matter packets; 21. Distribution of momenta in matter packets; 22. Mathematical relation between ? and ?; 23. Causality; 24. Uncertainty; 25. Uncertainty due to optical observation; 26. Dissipation of matter packets; rays in Wilson Chamber; 27. Density maximum in time; 28. Uncertainty of energy and time; 29. Compton effect; 30. Bothe-Geiger and Compton-Simon experiments; 31. Doppler effect; Raman effect; 32. Elementary bundles of rays; 33. Jeans' number of degrees of freedom; 34. Uncertainty of electromagnetic field components; Part III. The Principle of Interference and Schrödinger's equation: 35. Physical functions; 36. Interference of probabilities for p and q; 37. General interference of probabilities; 38. Differential equations for ?p (q) and Xq (p); 39. Differential equation for ?? (q); 40. The general probability amplitude ??' (Q); 41. Point transformations; 42. General theorem of interference; 43. Conjugate variables; 44. Schrödinger's equation for conservative systems; 45. Schrödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantum mechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantum mechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.
Rioux, Frank
. A particle with wavelength 8 has wave function (un-normalized) exp 2 x x i = However, according to de wave function coordinate space. * exp ipx p x x p - = = h Using the method outlined aboveMomentum Operator in Coordinate Space Wave-particle duality is at the heart of quantum mechanics
Kapustin, Anton [California Institute of Technology, Pasadena, California 91125 (United States)] [California Institute of Technology, Pasadena, California 91125 (United States)
2013-06-15
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.
Relativity and Quantum Mechanics
Braendas, Erkki J. [Department of Quantum Chemistry, Uppsala University, Box 518 S-751 20 Uppsala (Sweden)
2007-12-26
The old dilemma of quantum mechanics versus the theory of relativity is reconsidered via a first principles relativistically invariant theory. By analytic extension of quantum mechanics into the complex plane one may (i) include dynamical features such as time- and length-scales and (ii) examine the possibility and flexibility of so-called general Jordan block formations. The present viewpoint asks for a new perspective on the age-old problem of quantum mechanics versus the theory of relativity. To bring these ideas together, we will establish the relation with the Klein-Gordon-Dirac relativistic theory and confirm some dynamical features of both the special and the general relativity theory.
Quantum Mechanics Without Observers
W. H. Sulis
2013-03-03
The measurement problem and the role of observers have plagued quantum mechanics since its conception. Attempts to resolve these have introduced anthropomorphic or non-realist notions into physics. A shift of perspective based upon process theory and utilizing methods from combinatorial games, interpolation theory and complex systems theory results in a novel realist version of quantum mechanics incorporating quasi-local, nondeterministic hidden variables that are compatible with the no-hidden variable theorems and relativistic invariance, and reproduce the standard results of quantum mechanics to a high degree of accuracy without invoking observers.
Quantum Mechanics Without Wavefunctions
Jeremy Schiff; Bill Poirier
2012-01-11
We present a self-contained formulation of spin-free nonrelativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications - theoretical, computational, and interpretational - are discussed.
NASA Astrophysics Data System (ADS)
Fan, Hong-yi
2008-06-01
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.
Comment on "An Arrow of Time Operator for Standard Quantum Mechanics" - a sign of the time!
Michael J. W. Hall
2008-02-20
It is shown that the `arrow of time' operator, M_F, recently suggested by Strauss et al., in arXiv:0802.2448v1 [quant-ph], is simply related to the sign of the canonical `time' observable, T (apparently first introduced by Holevo). In particular, the monotonic decrease of corresponds to the fact that increases monotonically with time. This relationship also provides a physical interpretation of the property M_F < 1. Some further properties and possible generalisations are pointed out, including to almost-periodic systems.
Heat Transfer Operators Associated with Quantum Operations
Ç. Aksak; S. Turgut
2011-04-14
Any quantum operation applied on a physical system is performed as a unitary transformation on a larger extended system. If the extension used is a heat bath in thermal equilibrium, the concomitant change in the state of the bath necessarily implies a heat exchange with it. The dependence of the average heat transferred to the bath on the initial state of the system can then be found from the expectation value of a hermitian operator, which is named as the heat transfer operator (HTO). The purpose of this article is the investigation of the relation between the HTOs and the associated quantum operations. Since, any given quantum operation on a system can be realized by different baths and unitaries, many different HTOs are possible for each quantum operation. On the other hand, there are also strong restrictions on the HTOs which arise from the unitarity of the transformations. The most important of these is the Landauer erasure principle. This article is concerned with the question of finding a complete set of restrictions on the HTOs that are associated with a given quantum operation. An answer to this question has been found only for a subset of quantum operations. For erasure operations, these characterizations are equivalent to the generalized Landauer erasure principle. For the case of generic quantum operations however, it appears that the HTOs obey further restrictions which cannot be obtained from the entropic restrictions of the generalized Landauer erasure principle.
Physicalism versus quantum mechanics
Stapp, Henry P; Theoretical Physics Group; Physics Division
2009-01-01
efficacious brain activity that possesses its causal power.power to causally effect the course of events in his or her quantum mechanically described brain, andbrain activity that causes its effects: “If anything is to exercize causal power
Supersymmetry in quantum mechanics
Avinash Khare
1997-01-01
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical\\u000a problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable. In\\u000a this lecture I review the theoretical formulation of supersymmetric quantum mechanics and discuss many of its applications.\\u000a I show that the well-known exactly solvable
Quantum Mechanics From the Cradle?
ERIC Educational Resources Information Center
Martin, John L.
1974-01-01
States that the major problem in learning quantum mechanics is often the student's ignorance of classical mechanics and that one conceptual hurdle in quantum mechanics is its statistical nature, in contrast to the determinism of classical mechanics. (MLH)
Supersymmetric Quantum Mechanics with Reflections
S. Post; L. Vinet; A. Zhedanov
2011-08-09
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q-> -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wave functions of extended Scarf I potentials with different parameters are presented.
Quantum mechanical Carnot engine
C. M. Bender; D. C. Brody; B. K. Meister
2000-07-03
A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum-mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical processes.
Heinosaari, Teiko; Jivulescu, Maria A.; Reeb, David; Wolf, Michael M.
2012-10-15
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.
QUANTUM MECHANICS II Physics 342
Rosner, Jonathan L.
QUANTUM MECHANICS II Physics 342 KPTC 103 9:00 10:20 a.m. 1 Tues., Thurs. Winter Quarter 2011 quantum mechanics at the graduate level. The text for Quantum Mechanics II will be J. J. Sakurai and Jim Napolitano, Modern Quantum Mechanics, Second Edition (Addison-Wesley, San Francisco, 2011). For supplemental
Algebraic Quantum Mechanics and Pregeometry
NASA Astrophysics Data System (ADS)
Bohm, D. J.; Davies, P. G.; Hiley, B. J.
2006-01-01
We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points", we suggest an approach that may make it possible to dispense with an a priori given space-time manifold. In this approach the algebra itself would carry the symmetries of translation, rotation, etc. Our suggestion is illustrated in a preliminary way by using a particular generalized Clifford algebra proposed originally by Weyl, which approaches the ordinary Heisenberg algebra a suitable limit. We thus obtain a certain insight into how quantum mechanics may be regarded as a purely algebraic theory, provided that we further introduce a new set of "neighbourhood operators", which remove an important kind of arbitrariness that has thus far been present in the attempt to treat quantum mechanics solely in terms of a Heisenberg algebra.
Principles of a 2nd Quantum Mechanics
Mioara Mugur-Schächter
2014-10-23
A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this representation as a reference-and-imbedding-structure, the foundations of an intelligible reconstruction of the Hilbert-Dirac formulation of Quantum Mechanics is developed. Inside this reconstruction the measurement problem as well as the other major problems raised by the quantum mechanical formalism, dissolve.
Effectively calculable quantum mechanics
Arkady Bolotin
2015-08-16
According to mathematical constructivism, a mathematical object can exist only if there is a way to compute (or "construct") it; so, what is non-computable is non-constructive. In the example of the quantum model, whose Fock states are associated with Fibonacci numbers, this paper shows that the mathematical formalism of quantum mechanics is non-constructive since it permits an undecidable (or effectively impossible) subset of Hilbert space. On the other hand, as it is argued in the paper, if one believes that testability of predictions is the most fundamental property of any physical theory, one need to accept that quantum mechanics must be an effectively calculable (and thus mathematically constructive) theory. With that, a way to reformulate quantum mechanics constructively, while keeping its mathematical foundation unchanged, leads to hypercomputation. In contrast, the proposed in the paper superselection rule, which acts by effectively forbidding a coherent superposition of quantum states corresponding to potential and actual infinity, can introduce computable constructivism in a quantum mechanical theory with no need for hypercomputation.
Self-Referential Quantum Mechanics
NASA Astrophysics Data System (ADS)
Mitchell, Mark Kenneth
1993-01-01
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.
Physical realizations of quantum operations
Buscemi, Francesco; D'Ariano, G. Mauro; Sacchi, Massimiliano F.
2003-10-01
Quantum operations (QO's) describe any state change allowed in quantum mechanics, such as the evolution of an open system or the state change due to a measurement. We address the problem of which unitary transformations and which observables can be used to achieve a QO with generally different input and output Hilbert spaces. We classify all unitary extensions of a QO and give explicit realizations in terms of free-evolution direct-sum dilations and interacting tensor-product dilations. In terms of Hilbert space dimensionality the free-evolution dilations minimize the physical resources needed to realize the QO, and for this case we provide bounds for the dimension of the ancilla space versus the rank of the QO. The interacting dilations on the other hand, correspond to the customary ancilla-system interaction realization, and for these we derive a majorization relation which selects the allowed unitary interactions between system and ancilla.
NSDL National Science Digital Library
Thaller, Bernd
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.
W. Chagas-Filho
2009-05-11
We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position or in the momentum representation. As a way to support this complementation, starting from the action that describes conformal gravity in the world-line formalism, we show that there are duality transformations that relate the dynamics in the presence of position dependent vector and tensor fields to the dynamics in the presence of momentum dependent vector and tensor fields.
Noncommutative quantum mechanics
NASA Astrophysics Data System (ADS)
Gamboa, J.; Loewe, M.; Rojas, J. C.
2001-09-01
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.
Argyris Nicolaidis
2012-11-09
We suggest that the inner syntax of Quantum Mechanics is relational logic, a form of logic developed by C. S. Peirce during the years 1870 - 1880. The Peircean logic has the structure of category theory, with relation serving as an arrow (or morphism). At the core of the relational logical system is the law of composition of relations. This law leads to the fundamental quantum rule of probability as the square of an amplitude. Our study of a simple discrete model, extended to the continuum, indicates that a finite number of degrees of freedom can live in phase space. This "granularity" of phase space is determined by Planck's constant h. We indicate also the broader philosophical ramifications of a relational quantum mechanics.
Quantum Mechanics in Phase Space
Ali Mohammad Nassimi
2008-06-11
The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.
QUICK QUANTUM MECHANICS ---Introduction ---
Jackson, Andrew D.
to their students. Thus, it was natural that the historical evolution of quantum mechanics relied on some aspects sin 2 ` â?? OE 2 ] \\Gamma V (r) : (2) The time evolution of the system is given once we determine, replace it by q(t) + ffif (t) where ffif (t) is completely arbitrary except for the facts
Galois Field Quantum Mechanics
NASA Astrophysics Data System (ADS)
Chang, Lay Nam; Lewis, Zachary; Minic, Djordje; Takeuchi, Tatsu
2013-04-01
We construct a discrete quantum mechanics (QM) using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete QM cannot be reproduced with any hidden variable theory.
Supersymmetry and quantum mechanics
Fred Cooper; Avinash Khare; Uday Sukhatme
1995-01-01
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of
Quantum Mechanics and Gravitation
A. Westphal
2003-04-08
In summer 1999 an experiment at ILL, Grenoble was conducted. So-called ultra-cold neutrons (UCN) were trapped in the vertical direction between the Fermi-potential of a smooth mirror below and the gravitational potential of the earth above [Ne00, Ru00]. If quantum mechanics turns out to be a sufficiently correct description of the phenomena in the regime of classical, weak gravitation, one should observe the forming of quantized bound states in the vertical direction above a mirror. Already in a simplified view, the data of the experiment provides strong evidence for the existence of such gravitationally bound quantized states. A successful quantum-mechanical description would then provide a convincing argument, that the socalled first quantization can be used for gravitation as an interaction potential, as this is widely expected. Furthermore, looking at the characteristic length scales of about 10 mikron of such bound states formed by UCN, one sees, that a complete quantum mechanical description of this experiment additionally would enable one to check for possible modifications of Newtonian gravitation on distance scales being one order of magnitude below currently available tests [Ad00]. The work presented here deals mainly with the development of a quantum mechanical description of the experiment.
Quantum mechanical irreversibility
NASA Astrophysics Data System (ADS)
Bohm, A.; Maxson, S.; Loewe, Mark; Gadella, M.
1997-02-01
Microphysical irreversibility is distinguished from the extrinsic irreversibility of open systems. The rigged Hilbert space (RHS) formulation of quantum mechanics is justified based on the foundations of quantum mechanics. Unlike the Hilbert space formulation of quantum mechanics, the rigged Hilbert space formulation of quantum mechanics allows for the description of decay and other irreversible processes because it allows for a preferred direction of time for time evolution generated by a semi-bounded, essentially self-adjoint Hamiltonian. This quantum mechanical arrow of time is obtained and applied to a resonance scattering experiment. Within the cintext of a resonance scattering experiment, it is shown how the dichotomy of state and observable leads to a pair of RHSs, one for states and one for observables. Using resonance scattering, it is shown how the Gamow vectors describing decaying states with complex energy eigenvalues ( ER - i?/2) emerge from the first-order resonance poles of the S-matrix. Then, these considerations are extended to S-matrix poles order N and it shown that this leads to Gamow vectors of higher order k = 0, 1, …, N - 1 which are also Jordan vectors of degree k + 1 = 1, 2,…, N. The matrix elements of the self-adjoint Hamiltonian between these vectors from a Jordan block of degree N. The two semigroups of time evolution generated by the Hamiltonian are obtained for Gamow vectors of any order. It is shown how the irreversible time evolution of Gamow vectors enables the derivation of an exact Golden Rule for the calculation of decay probabilities, from which the standard (approximate) Golden Rule is obtained as the Born approximation in the limit ?R ? ER.
Physicalism versus quantum mechanics
Henry P. Stapp
2008-03-11
In the context of theories of the connection between mind and brain, physicalism is the demand that all is basically purely physical. But the concept of "physical" embodied in this demand is characterized essentially by the properties of the physical that hold in classical physical theories. Certain of these properties contradict the character of the physical in quantum mechanics, which provides a better, more comprehensive, and more fundamental account of phenomena. It is argued that the difficulties that have plaged physicalists for half a century, and that continue to do so, dissolve when the classical idea of the physical is replaced by its quantum successor. The argument is concretized in a way that makes it accessible to non-physicists by exploiting the recent evidence connecting our conscious experiences to macroscopic measurable synchronous oscillations occurring in well-separated parts of the brain. A specific new model of the mind-brain connection that is fundamentally quantum mechanical but that ties conscious experiences to these macroscopic synchronous oscillations is used to illustrate the essential disparities between the classical and quantum notions of the physical, and in particular to demonstrate the failure in the quantum world of the principle of the causal closure of the physical, a failure that goes beyond what is entailed by the randomness in the outcomes of observations, and that accommodates the efficacy in the brain of conscious intent.
On Randomness in Quantum Mechanics
Alberto C. de la Torre
2007-07-19
The quantum mechanical probability densities are compared with the probability densities treated by the theory of random variables. The relevance of their difference for the interpretation of quantum mechanics is commented.
NASA Astrophysics Data System (ADS)
Ellerman, David
2014-03-01
In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantum mechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.
TRANSIENT QUANTUM MECHANICAL PROCESSES
L. COLLINS; J. KRESS; R. WALKER
1999-07-01
Our principal objective has centered on the development of sophisticated computational techniques to solve the time-dependent Schroedinger equation that governs the evolution of quantum mechanical systems. We have perfected two complementary methods, discrete variable representation and real space product formula, that show great promise in solving these complicated temporal problems. We have applied these methods to the interaction of laser light with molecules with the intent of not only investigating the basic mechanisms but also devising schemes for actually controlling the outcome of microscopic processes. Lasers now exist that produce pulses of such short duration as to probe a molecular process many times within its characteristic period--allowing the actual observation of an evolving quantum mechanical system. We have studied the potassium dimer as an example and found agreement with experimental changes in the intermediate state populations as a function of laser frequency--a simple control prescription. We have also employed elaborate quantum chemistry programs to improve the accuracy of basic input such as bound-bound and bound-free coupling moments. These techniques have far-ranging applicability; for example, to trapped quantum systems at very low temperatures such as Bose-Einstein condensates.
Glenn Eric Johnson
2014-12-21
The quantum field theories (QFT) constructed in [1,2] include phenomenology of interest. The constructions approximate: scattering by $1/r$ and Yukawa potentials in non-relativistic approximations; and the first contributing order of the Feynman series for Compton scattering. To have a semi-norm, photon states are constrained to transverse polarizations and for Compton scattering, the constructed cross section deviates at large momentum exchanges from the cross section prediction of the Feynman rules. Discussion includes the incompatibility of canonical quantization with the constructed interacting fields, and the role of interpretations of quantum mechanics in realizing QFT.
Quantum remote control: Teleportation of unitary operations
S. F. Huelga; J. A. Vaccaro; A. Chefles; M. B. Plenio
2000-07-04
We consider the implementation of an arbitrary unitary operation U upon a distant quantum system. This teleportation of U can be viewed as a quantum remote control. We investigate protocols which achieve this using local operations, classical communication and shared entanglement (LOCCSE). Lower bounds on the necessary entanglement and classical communication are determined using causality and the linearity of quantum mechanics. We examine in particular detail the resources required if the remote control is to be implemented as a classical black box. Under these circumstances, we prove that the required resources are, necessarily, those needed for implementation by bidirectional state teleportation.
Aalok Pandya
2009-01-19
The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of probability in Quantum Mechanics and its interpretations. We give yet another interpretation to the notion of Faraday lines and loops as the locus of probability flow. Also, the possibilities of visualization of spectra of area operators by means of classical geometric forms and conventional Quantum Mechanics are explored.
Andrzejewski, K
2015-01-01
The quantum mechanics of one degree of freedom exhibiting the exact conformal SL(2,R) symmetry is presented. The starting point is the classification of the unitary irreducible representations of the SL(2,R) group (or, to some extent, its universal covering). The coordinate representation is defined as the basis diagonalizing the special conformal generator K. It is indicated how the resulting theory emerges from the canonical/geometric quantization of the Hamiltonian dynamics on the relevant coadjoint orbits.
K. Andrzejewski
2015-06-18
The quantum mechanics of one degree of freedom exhibiting the exact conformal SL(2,R) symmetry is presented. The starting point is the classification of the unitary irreducible representations of the SL(2,R) group (or, to some extent, its universal covering). The coordinate representation is defined as the basis diagonalizing the special conformal generator K. It is indicated how the resulting theory emerges from the canonical/geometric quantization of the Hamiltonian dynamics on the relevant coadjoint orbits.
Feynman's simple quantum mechanics
NASA Astrophysics Data System (ADS)
Taylor, Edwin F.
1997-03-01
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.
Quantum Mechanics and Multiply Connected Spaces
B. G. Sidharth
2006-05-16
t is well known that the difference between Quantum Mechanics and Classical Theory appears most crucially in the non Classical spin half of the former theory and the Wilson-Sommerfelt quantization rule. We argue that this is symptomatic of the fact that Quantum Theory is actually a theory in multiply connected space while Classical Theory operates in simply connected space.
Quantum Mechanics and the Generalized Uncertainty Principle
Jang Young Bang; Micheal S. Berger
2006-11-30
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.
The Mechanism of Quantum Computation
NASA Astrophysics Data System (ADS)
Castagnoli, Giuseppe
2008-08-01
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine whose coordinates are submitted to a nonfunctional relation representing all the problem constraints; moving an input part, reversibly and nondeterministically produces a solution through a many body interaction. The machine can be considered the many body generalization of another perfect machine, the bouncing ball model of reversible computation. The mathematical description of the machine’s motion, as it is, is applicable to quantum problem solving, an extension of the quantum algorithms that comprises the physical representation of the interdependence between the problem and the solution. The configuration space of the classical machine is replaced by the phase space of the quantum machine. The relation between the coordinates of the machine parts now applies to the populations of the reduced density operators of the parts of the computer register throughout state vector reduction. Thus, reduction produces the solution of the problem under a nonfunctional relation representing the problem-solution interdependence. At the light of this finding, the quantum speed up turns out to be “precognition” of the solution, namely the reduction of the initial ignorance of the solution due to backdating, to before running the algorithm, a part of the state vector reduction on the solution (a time-symmetric part in the case of unstructured problems); as such, it is bounded by state vector reduction through an entropic inequality. The computation mechanism under discussion might also explain the wholeness appearing in the introspective analysis of perception.
Quantum transfer operators and quantum scattering
Stéphane Nonnenmacher
2010-01-22
These notes describe a new method to investigate the spectral properties if quantum scattering Hamiltonians, developed in collaboration with J. Sj\\"ostrand and M.Zworski. This method consists in constructing a family of "quantized transfer operators" $\\{M(z,h)\\}$ associated with a classical Poincar\\'e section near some fixed classical energy E. These operators are finite dimensional, and have the structure of "open quantum maps". In the semiclassical limit, the family $\\{M(z,h)\\}$ encode the quantum dynamics near the energy E. In particular, the quantum resonances of the form $E+z$, for $z=O(h)$, are obtained as the roots of $\\det(1-M(z,h))=0$.
Three Pictures of Quantum Mechanics
Olszewski Jr., Edward A.
Relation #12;Quantum Statistics Â· The probability of an observation is found by computing matrix elementsThree Pictures of Quantum Mechanics Thomas R. Shafer April 17, 2009 #12;Outline of the Talk Â· Brief review of (or introduction to) quantum mechanics. Â· 3 different viewpoints on calculation. Â· SchrÃ¶dinger
Logical operators of quantum codes
NASA Astrophysics Data System (ADS)
Wilde, Mark M.
2009-06-01
I show how applying a symplectic Gram-Schmidt orthogonalization to the normalizer of a quantum code gives a different way of determining the code’s logical operators. This approach may be more natural in the setting where we produce a quantum code from classical codes because the generator matrices of the classical codes form the normalizer of the resulting quantum code. This technique is particularly useful in determining the logical operators of an entanglement-assisted code produced from two classical binary codes or from one classical quaternary code. Finally, this approach gives additional formulas for computing the amount of entanglement that an entanglement-assisted code requires.
Hierarchies of incoherent quantum operations
Streltsov, Alexander; Bera, Manabendra Nath; Lewenstein, Maciej
2015-01-01
The search for a simple description of fundamental physical processes is an important part of quantum theory. One example for such an abstraction can be found in the distance lab paradigm: if two separated parties are connected via a classical channel, it is notoriously difficult to characterize all possible operations these parties can perform. This class of operations is widely known as local operations and classical communication (LOCC). Surprisingly, the situation becomes comparably simple if the more general class of separable operations is considered, a finding which has been extensively used in quantum information theory for many years. Here, we propose a related approach for the resource theory of quantum coherence, where two distant parties can only perform measurements which do not create coherence and can communicate their outcomes via a classical channel. We call this class local incoherent operations and classical communication (LICC). While the characterization of this class is also difficult in...
Gravitomagnetism in quantum mechanics
Adler, Ronald J.; Chen Pisin
2010-07-15
We give a systematic treatment of the quantum mechanics of a spin zero particle in a combined electromagnetic field and a weak gravitational field that is produced by a slow moving matter source. The analysis is based on the Klein-Gordon equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The Klein-Gordon equation is recast into Schroedinger equation form, which we then analyze in the nonrelativistic limit. We include a discussion of some rather general observable physical effects implied by the Schroedinger equation form, concentrating on gravitomagnetism. Of particular interest is the interaction of the orbital angular momentum of the particle with the gravitomagnetic field.
Gravitomagnetism in Quantum Mechanics
Ronald J. Adler; Pisin Chen
2010-05-19
We give a systematic treatment of the quantum mechanics of a spin zero particle in a combined electromagnetic field and a weak gravitational field, which is produced by a slow moving matter source. The analysis is based on the Klein-Gordon equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The Klein-Gordon equation is recast into Schroedinger equation form (SEF), which we then analyze in the non-relativistic limit. We include a discussion of some rather general observable physical effects implied by the SEF, concentrating on gravitomagnetism. Of particular interest is the interaction of the orbital angular momentum of the particle with the gravitomagnetic field.
Supersymmetric Quantum Mechanics
David, J.; Fernandez, C.
2010-10-11
Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulae concerning SUSY QM of first second order for one-dimensional arbitrary systems, we will illustrate the method through the trigonometric Poeschl-Teller potentials. Some intrinsically related subjects, as the algebraic structure inherited by the new Hamiltonians and the corresponding coherent states will be analyzed. The technique will be as well implemented for periodic potentials, for which the corresponding spectrum is composed of allowed bands separated by energy gaps.
Gaussian effective potential: Quantum mechanics
NASA Astrophysics Data System (ADS)
Stevenson, P. M.
1984-10-01
We advertise the virtues of the Gaussian effective potential (GEP) as a guide to the behavior of quantum field theories. Much superior to the usual one-loop effective potential, the GEP is a natural extension of intuitive notions familiar from quantum mechanics. A variety of quantum-mechanical examples are studied here, with an eye to field-theoretic analogies. Quantum restoration of symmetry, dynamical mass generation, and "quantum-mechanical resuscitation" are among the phenomena discussed. We suggest how the GEP could become the basis of a systematic approximation procedure. A companion paper will deal with scalar field theory.
Advanced Concepts in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Esposito, Giampiero; Marmo, Giuseppe; Miele, Gennaro; Sudarshan, George
2014-11-01
Preface; 1. Introduction: the need for a quantum theory; 2. Experimental foundations of quantum theory; 3. Waves and particles; 4. Schrödinger picture, Heisenberg picture and probabilistic aspects; 5. Integrating the equations of motion; 6. Elementary applications: 1-dimensional problems; 7. Elementary applications: multidimensional problems; 8. Coherent states and related formalism; 9. Introduction to spin; 10. Symmetries in quantum mechanics; 11. Approximation methods; 12. Modern pictures of quantum mechanics; 13. Formulations of quantum mechanics and their physical implications; 14. Exam problems; Glossary of geometric concepts; References; Index.
Diffusion-Schrödinger Quantum Mechanics
NASA Astrophysics Data System (ADS)
Lasukov, V. V.; Lasukova, T. V.; Lasukova, O. V.; Novoselov, V. V.
2014-08-01
A quantum solution of a nonlinear differential equation of diffusion type with a potential term has been found. Diffusion-Schrödinger quantum mechanics can find wide application in quantum biology, biological electronics, synthetic biology, nanomedicine, the quantum theory of consciousness, cosmology, and other fields of science and technology. One consequence of the macroscopic nature of diffusion-Schrödinger quantum mechanics is the possibility of generation of hard photons. The dust plasma in the Universe can generate cosmic rays with ultra-relativistic energies in a galactic magnetic field via a diffusion mechanism.
Operational distance and fidelity for quantum channels
Belavkin, Viacheslav P.; D'Ariano, Giacomo Mauro; Raginsky, Maxim [Department of Mathematics, University of Nottingham, NG7 2RD Nottingham (United Kingdom); QUIT Group, INFM Unita di Pavia, Universita di Pavia, Dipartimento di Fisica 'A. Volta', via Bassi 6, I-27100 Pavia (Italy); Center for Photonic Communication and Computing, Department of Electrical and Computer Engineering, Northwestern University, Evanston, Illinois 60208-3118 (United States); Center for Photonic Communication and Computing, Department of Electrical and Computer Engineering, Northwestern University, Evanston, Illinois 60208-3118 (United States)
2005-06-01
We define and study a fidelity criterion for quantum channels, which we term the minimax fidelity, through a noncommutative generalization of maximal Hellinger distance between two positive kernels in classical probability theory. Like other known fidelities for quantum channels, the minimax fidelity is well defined for channels between finite-dimensional algebras, but it also applies to a certain class of channels between infinite-dimensional algebras (explicitly, those channels that possess an operator-valued Radon-Nikodym density with respect to the trace in the sense of Belavkin-Staszewski) and induces a metric on the set of quantum channels that is topologically equivalent to the CB-norm distance between channels, precisely in the same way as the Bures metric on the density operators associated with statistical states of quantum-mechanical systems, derived from the well-known fidelity ('generalized transition probability') of Uhlmann, is topologically equivalent to the trace-norm distance.
Quantum Mechanics in Terms of Symmetric Measurements
NASA Astrophysics Data System (ADS)
Fuchs, Christopher
2006-03-01
In the neo-Bayesian view of quantum mechanics that Appleby, Caves, Pitowsky, Schack, the author, and others are developing, quantum states are taken to be compendia of partial beliefs about potential measurement outcomes, rather than objective properties of quantum systems. Different observers may validly have different quantum states for a single system, and the ultimate origin of each individual state assignment is taken to be unanalyzable within physical theory---its origin, instead, comes from prior probability assignments at stages of physical investigation or laboratory practice previous to quantum theory. The objective content of quantum mechanics thus resides somewhere else than in the quantum state, and various ideas for where that ``somewhere else'' is are presently under debate. What is overwhelmingly agreed upon in this effort is only the opening statement. Still, quantum states are not Bayesian probability assignments themselves, and different representations of the theory (in terms of state vectors or Wigner functions or C*-algebras, etc.) can take one further from or closer to a Bayesian point of view. It is thus worthwhile thinking about which representation might be the most propitious for the point of view and might quell some of the remaining debate. In this talk, I will present several results regarding a representation of quantum mechanics in terms of symmetric bases of positive-semidefinite operators. I also argue why this is probably the most natural representation for a Bayesian-style quantum mechanics.
The parity operator in quantum optical metrology
Christopher C. Gerry; Jihane Mimih
2010-07-04
Photon number states are assigned a parity of if their photon number is even and a parity of if odd. The parity operator, which is minus one to the power of the photon number operator, is a Hermitian operator and thus a quantum mechanical observable though it has no classical analog, the concept being meaningless in the context of classical light waves. In this paper we review work on the application of the parity operator to the problem of quantum metrology for the detection of small phase shifts with quantum optical interferometry using highly entangled field states such as the so-called N00N states, and states obtained by injecting twin Fock states into a beam splitter. With such states and with the performance of parity measurements on one of the output beams of the interferometer, one can breach the standard quantum limit, or shot-noise limit, of sensitivity down to the Heisenberg limit, the greatest degree of phase sensitivity allowed by quantum mechanics for linear phase shifts. Heisenberg limit sensitivities are expected to eventually play an important role in attempts to detect gravitational waves in interferometric detection systems such as LIGO and VIRGO.
Gamification of Quantum Mechanics Teaching
Ole Eggers Bjælde; Mads Kock Pedersen; Jacob Sherson
2015-06-26
In this small scale study we demonstrate how a gamified teaching setup can be used effectively to support student learning in a quantum mechanics course. The quantum mechanics games were research games, which were played during lectures and the learning was measured with a pretest/posttest method with promising results. The study works as a pilot study to guide the planning of quantum mechanics courses in the future at Aarhus University in Denmark.
Gamification of Quantum Mechanics Teaching
Bjælde, Ole Eggers; Sherson, Jacob
2015-01-01
In this small scale study we demonstrate how a gamified teaching setup can be used effectively to support student learning in a quantum mechanics course. The quantum mechanics games were research games, which were played during lectures and the learning was measured with a pretest/posttest method with promising results. The study works as a pilot study to guide the planning of quantum mechanics courses in the future at Aarhus University in Denmark.
Graph reconstruction and quantum statistical mechanics
NASA Astrophysics Data System (ADS)
Cornelissen, Gunther; Marcolli, Matilde
2013-10-01
We study how far it is possible to reconstruct a graph from various Banach algebras associated to its universal covering, and extensions thereof to quantum statistical mechanical systems. It turns out that most the boundary operator algebras reconstruct only topological information, but the statistical mechanical point of view allows for complete reconstruction of multigraphs with minimal degree three.
Is quantum field theory a generalization of quantum mechanics?
A. V. Stoyanovsky
2009-09-10
We construct a mathematical model analogous to quantum field theory, but without the notion of vacuum and without measurable physical quantities. This model is a direct mathematical generalization of scattering theory in quantum mechanics to path integrals with multidimensional trajectories (whose mathematical interpretation has been given in a previous paper). In this model the normal ordering of operators in the Fock space is replaced by the Weyl-Moyal algebra. This model shows to be useful in proof of various results in quantum field theory: one first proves these results in the mathematical model and then "translates" them into the usual language of quantum field theory by more or less "ugly" procedures.
Renormalisation in Quantum Mechanics, Quantum Instantons and Quantum Chaos
H. Jirari; H. Kröger; X. Q. Luo; K. J. M. Moriarty
2001-02-05
We suggest how to construct non-perturbatively a renormalized action in quantum mechanics. We discuss similarties and differences with the standard effective action. We propose that the new quantum action is suitable to define and compute quantum instantons and quantum chaos.
Consistency of PT-symmetric quantum mechanics
Brody, Dorje C
2015-01-01
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully consistent with standard quantum mechanics. This follows from the surprising fact that the much-discussed metric operator on Hilbert space is not physically observable. In particular, for closed quantum systems in finite dimensions there is no statistical test that one can perform on the outcomes of measurements to determine whether the Hamiltonian is Hermitian in the conventional sense, or PT-symmetric---the two theories are indistinguishable. Nontrivial physical effects arising as a consequence of PT symmetry are expected to be observed, nevertheless, for open quantum systems with balanced gain and loss.
From Quantum Mechanics to Thermodynamics?
Steinhoff, Heinz-Jürgen
From Quantum Mechanics to Thermodynamics? Dresden, 22.11.2004 Jochen Gemmer Universit¨at Osnabr to thermodynamical behavior · Quantum approach to thermodynamical behavior · The route to equilibrium · Summary of thermodynamical behavior entirely on the basis of Hamilton models and Schr¨odinger-type quantum dynamics. · define
Bohmian Mechanics and Quantum Information
Goldstein, Sheldon
that quantum theory is about informa- tion, and that quantum theory is best understood as arising from prin theory can be understood from a Bohmian perspective. I would like to explore the hypothesis that the ideaBohmian Mechanics and Quantum Information Sheldon Goldstein Departments of Mathematics, Physics
Quantum chaos in elementary quantum mechanics
Yu. Dabaghian
2004-07-30
We introduce an analytical solution to the one of the most familiar problems from the elementary quantum mechanics textbooks. The following discussion provides simple illustrations to a number of general concepts of quantum chaology, along with some recent developments in the field and a historical perspective on the subject.
Klein's programme and quantum mechanics
NASA Astrophysics Data System (ADS)
Clemente-Gallardo, Jesús; Marmo, Giuseppe
2015-04-01
We review the geometrical formulation of quantum mechanics to identify, according to Klein's programme, the corresponding group of transformations. For closed systems, it is the unitary group. For open quantum systems, the semigroup of Kraus maps contains, as a maximal subgroup, the general linear group. The same group emerges as the exponentiation of the C*-algebra associated with the quantum system, when thought of as a Lie algebra. Thus, open quantum systems seem to identify the general linear group as associated with quantum mechanics and moreover suggest to extend the Klein programme also to groupoids. The usual unitary group emerges as a maximal compact subgroup of the general linear group.
Quantum mechanics of leptogenesis
NASA Astrophysics Data System (ADS)
Mendizabal, S.
2011-04-01
Thermal leptogenesis is an attractive mechanism that explains in a simple way the matter-antimatter asymmetry of the universe. It is usually studied via the Boltzmann equations, which describes the time evolution of particle densities or distribution functions in a thermal bath. The Boltzmann equations are classical equations and suffer from basic conceptual problems and they lack to include many quantum phenomena. We show how to address leptogenesis systematically in a purely quantum way, by describing non-equilibrium excitations of a Majorana particle in the Kadanoff-Baym equations with significant emphasis on the initial and boundary conditions of the solutions. We apply our results to thermal leptogenesis, computing analytically the asymmetry generated, comparing it with the semiclassical Boltzmann approach. The non-locality of the Kadanoff-Baym equations shows how off-shell effects can have a huge impact on the generated asymmetry. The insertion of standard model decay widths to the particles excitations of the bath is also discussed. We explain how with a trivial insertion of these widths we regain locality on the processes.
Kindergarten Quantum Mechanics
Bob Coecke
2005-10-04
These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in quant-ph/0402130 and [4]) which subsumes my Logic of Entanglement quant-ph/0402014. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes quant-ph/0506132. In a last section we provide some pointers to the body of technical literature on the subject.
Diagrammatic quantum mechanics
NASA Astrophysics Data System (ADS)
Kauffman, Louis H.; Lomonaco, Samuel J.
2015-05-01
This paper explores how diagrams of quantum processes can be used for modeling and for quantum epistemology. The paper is a continuation of the discussion where we began this formulation. Here we give examples of quantum networks that represent unitary transformations by dint of coherence conditions that constitute a new form of non-locality. Local quantum devices interconnected in space can form a global quantum system when appropriate coherence conditions are maintained.
Modern Approach to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Townsend, John S.
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.
Quantum mechanics of cluster melting
Beck, T.L.; Doll, J.D.; Freeman, D.L.
1989-05-15
We present here prototype studies of the effects of quantum mechanics on the melting of clusters. Using equilibrium path integral methods, we examine the melting transition for small rare gas clusters. Argon and neon clusters are considered. We find the quantum-mechanical effects on the melting and coexistence properties of small neon clusters to be appreciable.
Invariance in adelic quantum mechanics
Branko Dragovich
2006-12-07
Adelic quantum mechanics is form invariant under an interchange of real and p-adic number fields as well as rings of p-adic integers. We also show that in adelic quantum mechanics Feynman's path integrals for quadratic actions with rational coefficients are invariant under changes of their entries within nonzero rational numbers.
QUANTUM MECHANICS WITHOUT STATISTICAL POSTULATES
G. GEIGER; ET AL
2000-11-01
The Bohmian formulation of quantum mechanics describes the measurement process in an intuitive way without a reduction postulate. Due to the chaotic motion of the hidden classical particle all statistical features of quantum mechanics during a sequence of repeated measurements can be derived in the framework of a deterministic single system theory.
Timelines and Quantum Time Operators
NASA Astrophysics Data System (ADS)
Moyer, Curt A.
2015-04-01
The failure of conventional quantum theory to recognize time as an observable and to admit time operators is addressed. Instead of focusing on the existence of a time operator for a given Hamiltonian, we emphasize the role of the Hamiltonian as the generator of translations in time to construct time states. Taken together, these states constitute what we call a timeline. Such timelines are adequate for the representation of any physical state, and appear to exist even for the semi-bounded and discrete Hamiltonian systems ruled out by Pauli's theorem. However, the step from a timeline to a valid time operator requires additional assumptions that are not always met. Still, this approach illuminates the issues surrounding the construction of time operators, and establishes timelines as legitimate alternatives to the familiar coordinate and momentum bases of standard quantum theory.
Quantum mechanics as applied mathematical statistics
Skala, L., E-mail: Lubomir.Skala@mff.cuni.cz [Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2 (Czech Republic); University of Waterloo, Department of Applied Mathematics, Waterloo, Ontario, Canada N2L 3G1 (Canada); Cizek, J. [Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2 (Czech Republic); University of Waterloo, Department of Applied Mathematics, Waterloo, Ontario, Canada N2L 3G1 (Canada); Kapsa, V. [Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2 (Czech Republic)
2011-05-15
Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.
Bananaworld: Quantum Mechanics for Primates
Jeffrey Bub
2013-01-08
This is intended to be a serious paper, in spite of the title. The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, since a theory of information is essentially a theory of probabilistic correlations. To make this clear, it suffices to consider measurements of two binary-valued observables, x with outcomes a = 0 or 1, performed by Alice in a region A, and y with outcomes b = 0 or 1 performed by Bob in a separated region B --or, to emphasize the banality of the phenomena, two ways of peeling a banana, resulting in one of two tastes. The imagined bananas of Bananaworld are non-standard, with operational or phenomenal probabilistic correlations for peelings and tastes that lie outside the polytope of local correlations. The 'no go' theorems tell us that we can't shoe-horn these correlations into a classical correlation polytope, which has the structure of a simplex, by supposing that something has been left out of the story, without giving up fundamental principles that define what we mean by a physical system. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are shown to be generic features of correlations that lie outside the local correlation polytope. As far as the conceptual problems are concerned, we might as well talk about bananas.
Quantum morphology operations based on quantum representation model
NASA Astrophysics Data System (ADS)
Yuan, Suzhen; Mao, Xia; Li, Tian; Xue, Yuli; Chen, Lijiang; Xiong, Qingxu
2015-05-01
Quantum morphology operations are proposed based on the novel enhanced quantum representation model. Two kinds of quantum morphology operations are included: quantum binary and grayscale morphology operations. Dilation and erosion operations are fundamental to morphological operations. Consequently, we focus on quantum binary and flat grayscale dilation and erosion operations and their corresponding circuits. As the basis of designing of binary morphology operations, three basic quantum logic operations AND, OR, and NOT involving two binary images are presented. Thus, quantum binary dilation and erosion operations can be realized based on these logic operations supplemented by quantum measurement operations. As to the design of flat grayscale dilation and erosion operations, the searching for maxima or minima in a certain space is involved; here, we use Grover's search algorithm to get these maxima and minima. With respect that the grayscale is represented by quantum bit string, the quantum bit string comparator is used as an oracle in Grover's search algorithm. In these quantum morphology operations, quantum parallelism is well utilized. The time complexity analysis shows that quantum morphology operations' time complexity is much lower or equal to the classical morphology operations.
Classical and Quantum Mechanical Waves
NSDL National Science Digital Library
Riley, Lewis
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.
Topological Strings from Quantum Mechanics
Alba Grassi; Yasuyuki Hatsuda; Marcos Marino
2014-11-27
We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized theta function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P2, local P1xP1 and local F1. In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.
Quantum Mechanics Of Consciousness
Rajat Kumar Pradhan
2009-07-29
A phenomenological approach using the states of spin-like observables is developed to understand the nature of consciousness and the totality of experience. The three states of consciousness are taken to form the triplet of eigenstates of a spin-one entity and are derived as the triplet resulting from the composition of two spins by treating the subject and the object as interacting two-state, spin-half systems with external and internal projections. The state of deep sleep is analysed in the light of this phenomenological approach and a novel understanding of the status of the individual consciousness in this state is obtained. The resulting fourth state i.e. the singlet state is interpreted to correspond to the superconscious state of intuitive experience and is justified by invoking the concept of the universal consciousness as the underlying source of all individual states of experience. It is proposed that the individual experiences result from the operations of four individualizing observables which project out the individual from the universal. The one-to-one correspondence between the individual and the universal states of experience is brought out and their identity in the fourth state is established by showing that all individualizing quantum numbers become zero in this state leaving no trace of any individuality.
Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
F G Scholtz; L Gouba; A Hafver; C M Rohwer
2008-12-15
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the standard quantum mechanical interpretation based on Positive Operator Valued Measures, provides a sufficient framework for the consistent interpretation of this quantum system. The implications of this formalism for rotational and time reversal symmetry are discussed. The formalism is applied to the free particle and harmonic oscillator in two dimensions and the physical signatures of non commutativity are identified.
Decoherence in quantum mechanics and quantum cosmology
NASA Technical Reports Server (NTRS)
Hartle, James B.
1992-01-01
A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.
Quantum Image Morphology Processing Based on Quantum Set Operation
NASA Astrophysics Data System (ADS)
Zhou, Ri-Gui; Chang, Zhi-bo; Fan, Ping; Li, Wei; Huan, Tian-tian
2015-06-01
Set operation is the essential operation of mathematical morphology, but it is difficult to complete the set operation quickly on the electronic computer. Therefore, the efficiency of traditional morphology processing is very low. In this paper, by adopting the method of the combination of quantum computation and image processing, though multiple quantum logical gates and combining the quantum image storage, quantum loading scheme and Boyer search algorithm, a novel quantum image processing method is proposed, which is the morphological image processing based on quantum set operation. The basic operations, such as erosion and dilation, are carried out for the images by using the quantum erosion algorithm and quantum dilation algorithm. Because the parallel capability of quantum computation can improve the speed of the set operation greatly, the image processing gets higher efficiency. The runtime of our quantum algorithm is . As a result, this method can produce better results.
D'Ariano, G M; Lo Presti, P
2001-05-01
Quantum operations describe any state change allowed in quantum mechanics, including the evolution of an open system or the state change due to a measurement. We present a general method based on quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation. As input the method needs only a single entangled state. The feasibility of the technique for the electromagnetic field is shown, and the experimental setup is illustrated based on homodyne tomography of a twin beam. PMID:11328133
Quantum Phase and Quantum Phase Operators: Some Physics and Some History
Michael Martin Nieto
1993-04-08
After reviewing the role of phase in quantum mechanics, I discuss, with the aid of a number of unpublished documents, the development of quantum phase operators in the 1960's. Interwoven in the discussion are the critical physics questions of the field: Are there (unique) quantum phase operators and are there quantum systems which can determine their nature? I conclude with a critique of recent proposals which have shed new light on the problem.
Quantum duality, unbounded operators, and inductive limits
Dosi, Anar [Middle East Technical University Northern Cyprus Campus, Guzelyurt, KKTC, Mersin 10 (Turkey)
2010-06-15
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.
A Quantum Mechanical Travelling Salesman
Ravindra N. Rao
2011-08-23
A quantum simulation of a travelling salesman is described. A vector space for a graph is defined together with a sequence of operators which transform a special initial state into a superposition states representing Hamiltonian tours. The quantum amplitude for any tour is a function of the classical cost of travelling along the edges in that tour. Tours with the largest quantum amplitude may be different than those with the smallest classically-computed cost.
Geometric formulation of quantum mechanics
Hoshang Heydari
2015-03-01
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical and non-linear theory defined on a symplectic geometry. However, after invention of general relativity, we are convinced that geometry is physical and affect us in all scale. Hence the geometric formulation of quantum mechanics sought to give a unified picture of physical systems based on its underling geometrical structures, e.g., now, the states are represented by points of a symplectic manifold with a compatible Riemannian metric, the observable are real-valued functions on the manifold, and quantum evolution is governed by the symplectic flow that is generated by a Hamiltonian function. In this work we will give a compact introduction to main ideas of geometric formulation of quantum mechanics. We will provide the reader with the details of geometrical structures of both pure and mixed quantum states. We will also discuss and review some important applications of geometric quantum mechanics.
Noninertial quantum mechanical fluctuations
H. C. Rosu
2001-11-05
Zero point quantum fluctuations as seen from non-inertial reference frames are of interest for several reasons. In particular, because phenomena such as Unruh radiation (acceleration radiation) and Hawking radiation (quantum leakage from a black hole) depend intrinsically on both quantum zero-point fluctuations and some appropriate notion of an accelerating vacuum state, any experimental test of zero-point fluctuations in non-inertial frames is implicitly a test of the foundations of quantum field theory, and the Unruh and Hawking effects
Communication: quantum mechanics without wavefunctions.
Schiff, Jeremy; Poirier, Bill
2012-01-21
We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications-theoretical, computational, and interpretational-are discussed. PMID:22280737
Communication: Quantum mechanics without wavefunctions
Schiff, Jeremy; Poirier, Bill
2012-01-21
We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications--theoretical, computational, and interpretational--are discussed.
Quantum Mechanics as Quantum Information (and only a little more)
Fuchs, Christopher A.
Quantum Mechanics as Quantum Information (and only a little more) Christopher A. Fuchs Computing identify one element of quantum mechanics that I would not label a subjective term in the theory 1973 Foundations of Quantum Mechanics and Ordered Linear Spaces, Marburg, Germany 1974 Quantum
Quantum mechanics from invariance principles
NASA Astrophysics Data System (ADS)
Moldoveanu, Florin
2015-07-01
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.
Fuzzy quantum logic II. The logics of unsharp quantum mechanics
NASA Astrophysics Data System (ADS)
Cattaneo, Gianpiero
1993-10-01
A survey of the main results of the Italian group about the logics of unsharp quantum mechanics is presented. In particular partial ordered structures playing with respect to effect operators (linear bounded operators F on a Hilbert space ? such that ????, 0?????2) the role played by orthomodular posets with respect to orthogonal projections (corresponding to “sharp” effects) are analyzed. These structures are generally characterized by the splitting of standard orthocomplementation on projectors into two nonusual orthocomplementations (a fuzzy-like and an intuitionistic-like) giving rise to different kinds of Brouwer-Zadeh (BZ) posets: de Morgan BZ posets, BZ* posets, and BZ3 posets. Physically relevant generalizations of ortho-pair semantics (paraconsistent, regular paraconsistent, and minimal quantum logics) are introduced and their relevance with respect to the logic of unsharp quantum mechanics are discussed.
Time and the foundations of quantum mechanics
NASA Astrophysics Data System (ADS)
Pashby, Thomas
Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain kinds of `time observables' to find a representation within quantum theory, including clock operators (which provide the means to measure the passage of time) and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on re ection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantum mechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack.
NASA Astrophysics Data System (ADS)
Fan, Hong-yi
2008-02-01
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
Quantum mechanics & the big world
Jasper van Wezel
2007-01-01
Quantum Mechanics is one of the most successful\\u000aphysical theories of the last century. It explains physical\\u000aphenomena from the smallest to the largest lengthscales.\\u000aDespite this triumph, quantum mechanics is often perceived\\u000aas a mysterious theory, involving superposition states that are\\u000aalien to our everyday Big World.\\u000aThe construction of a future quantum computer relies on\\u000aour ability to
Bush, John W. M.
Some two centuries before the quantum revolution, Newton (1) suggested that corpuscles of light generate waves in an aethereal medium like skipping stones generate waves in water, with their motion then being affected by ...
Quantum Mechanics and The Big World
Wezel van Jasper
2007-01-01
Quantum Mechanics is one of the most successful physical theories of the last century. It explains physicalphenomena from the smallest to the largest lengthscales. Despite this triumph, quantum mechanics is often perceived as a mysterious theory, involving superposition states that are alien to our everyday Big World.In Quantum Mechanics and The Big World the connection between Quantum Mechanics and the
Quantum Mechanics Joachim Burgdorfer and Stefan Rotter
Rotter, Stefan
1 1 Quantum Mechanics Joachim Burgd¨orfer and Stefan Rotter 1.1 Introduction 3 1.2 Particle and Quantization 8 1.5 Angular Momentum in Quantum Mechanics 9 1.6 Formalism of Quantum Mechanics 12 1.7 Solution Quantization 33 1.9.3 Gutzwiller Trace Formula 34 1.10 Conceptual Aspects of Quantum Mechanics 35 1
QUANTUM MECHANICS AND REAL Department of Mathematics
Penrose, Oliver
QUANTUM MECHANICS AND REAL EVENTS O.Penrose Department of Mathematics Heriot-Watt University into the evolution of a quantum-mechanical system, without altering the usual laws of quantum mechanics in any way Although quantum mechanics is wonderfully successful for predicting the results of experiments done
Ambiguous Discrimination of General Quantum Operations
NASA Astrophysics Data System (ADS)
Li, Lü-Jun
2014-12-01
We consider the problem of discriminating general quantum operations. Using the definition of mapping operator to vector, and by some calculating skills, we derive an explicit formulation as a new bound on the minimum-error probability for ambiguous discrimination between arbitrary m quantum operations. This formulation consists only of Kraus-operators, the dimension, and the priori probabilities of the discriminated quantum operations, and is independent of input states. To some extent, we further generalize the bounds on the minimum-error probability for discriminating mixed states to quantum operations.
Noncommutative Poisson boundaries of unital quantum operations
Lim, Bunrith Jacques
2010-05-15
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.
NSDL National Science Digital Library
Galvez, Enrique
This web site, authored by Enrique Galvez and Charles Holbrow of Colgate University, outlines a project to develop 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, and an article on the project are provided.
ERIC Educational Resources Information Center
DeWitt, Bryce S.
1970-01-01
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)
Quantum Mechanics: Fundamentals
A Whitaker
2004-01-01
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
Adding control to arbitrary unknown quantum operations.
Zhou, Xiao-Qi; Ralph, Timothy C; Kalasuwan, Pruet; Zhang, Mian; Peruzzo, Alberto; Lanyon, Benjamin P; O'Brien, Jeremy L
2011-01-01
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. PMID:21811242
Optimal guidance law in quantum mechanics
Yang, Ciann-Dong, E-mail: cdyang@mail.ncku.edu.tw; Cheng, Lieh-Lieh, E-mail: leo8101@hotmail.com
2013-11-15
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.
Quantum Mechanics on the Hypercube
E. G. Floratos; S. Nicolis
2000-06-01
We construct quantum evolution operators on the space of states, that is represented by the vertices of the n-dimensional unit hypercube. They realize the metaplectic representation of the modular group SL(2,Z(2^n)). By construction this representation acts in a natural way on the coordinates of the non-commutative 2-torus,T^2, and thus is relevant for noncommutative field theories as well as theories of quantum space-time.
QUANTUM CHAOS, CLASSICAL RANDOMNESS, AND BOHMIAN MECHANICS
Goldstein, Sheldon
QUANTUM CHAOS, CLASSICAL RANDOMNESS, AND BOHMIAN MECHANICS Detlef DË? urr* ,+ , Sheldon Goldstein of quantum theory, Bohmian mechanics, in which ``quantum chaos'' also arises solely from the dynamical law. Moreover, this occurs in a manner far simpler than in the classical case. KEY WORDS: Quantum chaos; quantum
Bohmian Mechanics and Quantum Information
Sheldon Goldstein
2009-07-14
Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of quantum mechanics, Bohmian mechanics, is concerned, not with information but with the behavior of an objective microscopic reality given by particles and their positions. What I would like to do here is to examine whether, and to what extent, the importance of information, observation, and the like in quantum theory can be understood from a Bohmian perspective. I would like to explore the hypothesis that the idea that information plays a special role in physics naturally emerges in a Bohmian universe.
Quantum Mechanics (QM) Measurement Package
NSDL National Science Digital Library
Belloni, Mario
This set of tutorial worksheets, based on the OSP Quantum Mechanics Simulations, help students explore the effects of position, momentum, and energy measurements on quantum state wavepackets. The probabilistic change in the wavefunction upon measurements and the time propagation of the states are illustrated. Similar worksheets are available for measurements of single and superpositions of energy eigenstates. The worksheets can be run online or downloaded as a pdf (attached).
Y. C. Huang; F. C. Ma; N. Zhang
2005-06-13
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new general continuous eigenvalue equation and a general discrete eigenvalue equation in quantum mechanics, and discover that a eigenvalue of quantum mechanics is just an extreme value of an operator in possibility distribution, the eigenvalue f is just classical observable quantity. A general classical statistical uncertain relation is further given, the general classical statistical uncertain relation is generally generalized to quantum uncertainty principle, the two lost conditions in classical uncertain relation and quantum uncertainty principle, respectively, are found. We generally expound the relations among uncertainty principle, singularity and condensed matter stability, discover that quantum uncertainty principle prevents from the appearance of singularity of the electromagnetic potential between nucleus and electrons, and give the failure conditions of quantum uncertainty principle. Finally, we discover that the classical limit of quantum mechanics is classical statistical mechanics, the classical statistical mechanics may further be degenerated to classical mechanics, and we discover that only saying that the classical limit of quantum mechanics is classical mechanics is mistake. As application examples, we deduce both Shrodinger equation and state superposition principle, deduce that there exist decoherent factor from a general mathematical representation of state superposition principle, and the consistent difficulty between statistical interpretation of quantum mechanics and determinant property of classical mechanics is overcome.
Quantum secret sharing schemes and reversibility of quantum operations
Ogawa, Tomohiro; Sasaki, Akira; Iwamoto, Mitsugu; Yamamoto, Hirosuke
2005-09-15
Quantum secret sharing schemes encrypting a quantum state into a multipartite entangled state are treated. The lower bound on the dimension of each share given by Gottesman [Phys. Rev. A 61, 042311 (2000)] is revisited based on a relation between the reversibility of quantum operations and the Holevo information. We also propose a threshold ramp quantum secret sharing scheme and evaluate its coding efficiency.
The Quantum Mechanical Arrows of Time
NASA Astrophysics Data System (ADS)
Hartle, James B.
The familiar textbook quantum mechanics of laboratory measurements incorporates a quantum mechanical arrow of time—the direction in time in which state vector reduction operates. This arrow is usually assumed to coincide with the direction of the thermodynamic arrow of the quasiclassical realm of everyday experience. But in the more general context of cosmology we seek an explanation of all observed arrows, and the relations between them, in terms of the conditions that specify our particular universe. This paper investigates quantum mechanical and thermodynamic arrows in a time-neutral formulation of quantum mechanics for a number of model cosmologies in fixed background spacetimes. We find that a general universe may not have well defined arrows of either kind. When arrows are emergent they need not point in the same direction over the whole of spacetime. Rather they may be local, pointing in different directions in different spacetime regions. Local arrows can therefore be consistent with global time symmetry. [Editors note: for a video of the talk given by Prof. Hartle at the Aharonov-80 conference in 2012 at Chapman University, see http://quantum.chapman.edu/talk-15.
Quantum Chaos: Spectral Analysis of Floquet Operators
James Matthew McCaw
2005-03-23
The Floquet operator, defined as the time-evolution operator over one period, plays a central role in the work presented in this thesis on periodically perturbed quantum systems. Knowledge of the spectral nature of the Floquet operator gives us information on the dynamics of such systems. The work presented here on the spectrum of the Floquet operator gives further insight into the nature of chaos in quantum mechanics. After discussing the links between the spectrum, dynamics and chaos and pointing out an ambiguity in the physics literature, I present a number of new mathematical results on the existence of different types of spectra of the Floquet operator. I characterise the conditions for which the spectrum remains pure point and then, on relaxing these conditions, show the emergence of a continuous spectral component. The nature of the continuous spectrum is further analysed, and shown to be singularly continuous. Thus, the dynamics of these systems are a candidate for classification as chaotic. A conjecture on the emergence of a continuous spectral component is linked to a long standing number-theoretic conjecture on the estimation of finite exponential sums.
New Potentials for Old: The Darboux Transformation in Quantum Mechanics
ERIC Educational Resources Information Center
Williams, Brian Wesley; Celius, Tevye C.
2008-01-01
The Darboux transformation in quantum mechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics…
Do Free Quantum-Mechanical Wave Packets Always Spread?
ERIC Educational Resources Information Center
Klein, James R.
1980-01-01
The spreading or shrinking of free three-dimensional quantum-mechanical wave packets is addressed. A seeming paradox concerning the time evolution operator and nonspreading wave packets is discussed, and the necessity of taking into account the appropriate mathematical structure of quantum mechanics is emphasized. Teaching implications are given.…
Quantum Mechanical Earth: Where Orbitals Become Orbits
ERIC Educational Resources Information Center
Keeports, David
2012-01-01
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…
Quantum Channels, Kraus Operators, POVMs Robert B. Griffiths
Griffiths, Robert B.
qitd411 Quantum Channels, Kraus Operators, POVMs Robert B. Griffiths Version of 4 Feb. 2010 = Consistent Quantum Theory by Griffiths (Cambridge, 2002) QCQI = Quantum Computation and Quantum Information
Perturbation theory for quantum-mechanical observables
J. D. Franson; Michelle M. Donegan
2002-01-28
The quantum-mechanical state vector is not directly observable even though it is the fundamental variable that appears in Schrodinger's equation. In conventional time-dependent perturbation theory, the state vector must be calculated before the experimentally-observable expectation values of relevant operators can be computed. We discuss an alternative form of time-dependent perturbation theory in which the observable expectation values are calculated directly and expressed in the form of nested commutators. This result is consistent with the fact that the commutation relations determine the properties of a quantum system, while the commutators often have a form that simplifies the calculation and avoids canceling terms. The usefulness of this method is illustrated using several problems of interest in quantum optics and quantum information processing.
Kowalevski top in quantum mechanics
Matsuyama, A., E-mail: spamatu@ipc.shizuoka.ac.jp
2013-09-15
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.
Using quantum mechanics to synthesize electronic devices
NASA Astrophysics Data System (ADS)
Schmidt, Petra; Levi, Anthony
2005-03-01
Adaptive quantum design [1] has been used to explore the possibility of creating new classes of electronic semiconductor devices. We show how non-equilibrium electron transmission through a synthesized conduction band potential profile can be used to obtain a desired current - voltage characteristic. We illustrate our methodology by designing a two-terminal linear resistive element in which current is limited by quantum mechanical transmission through a potential profile and power is dissipated non-locally in the electrodes. As electronic devices scale to dimensions in which the physics of operation is dominated by quantum mechanical effects, classical designs fail to deliver the desired functionality. Our device synthesis approach is a way to realize device functionality that may not otherwise be achieved. [1] Y.Chen, R.Yu, W.Li, O.Nohadani, S.Haas, A.F.J. Levi, Journal of Applied Physics, Vol.94, No.9, p6065, 2003
CPT and Quantum Mechanics Tests with Kaons
Jose Bernabeu; John Ellis; Nick E. Mavromatos; Dimitri V. Nanopoulos; Joannis Papavassiliou
2006-07-28
In this review we first discuss the theoretical motivations for possible CPT violation and deviations from ordinary quantum-mechanical behavior of field-theoretic systems in the context of an extended class of quantum-gravity models. Then we proceed to a description of precision tests of CPT symmetry using mainly neutral kaons. We emphasize the possibly unique role of neutral meson factories in providing specific tests of models where the quantum-mechanical CPT operator is not well-defined, leading to modifications of Einstein-Podolsky-Rosen particle correlators. Finally, we present tests of CPT, T, and CP using charged kaons, and in particular K_l4 decays, which are interesting due to the high statistics attainable in experiments.
QUANTUM MECHANICS. Quantum squeezing of motion in a mechanical resonator.
Wollman, E E; Lei, C U; Weinstein, A J; Suh, J; Kronwald, A; Marquardt, F; Clerk, A A; Schwab, K C
2015-08-28
According to quantum mechanics, a harmonic oscillator can never be completely at rest. Even in the ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. Using microwave frequency radiation pressure, we have manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state. We also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. Our results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion. PMID:26315431
Minkowski Space and Quantum Mechanics
NASA Astrophysics Data System (ADS)
O'Hara, Paul
A paradigm shift distinguishes general relativity from classical mechanics. In general relativity the energy-momentum tensor is the effective cause of the ontological space-time curvature and vice-versa, while in classical physics, the structure of space-time is treated as an accidental cause, serving only as a backdrop against which the laws of physics unfold. This split in turn is inherited by quantum mechanics, which is usually developed by changing classical (including special relativity) Hamiltonians into quantum wave equations.
Quantum groups, coherent states, squeezing and lattice quantum mechanics
E. Celeghini; S. De Martino; S. De Siena; M. Rasetti; G. Vitiello
1996-04-04
By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg algebra, $q$-WH, into the theory of entire analytic functions. The $q$--WH algebra operators are realized in terms of finite difference operators in the $z$ plane. In order to exhibit the relevance of our study, several applications to different cases of physical interest are discussed: squeezed states and the relation between coherent states and theta functions on one side, lattice quantum mechanics and Bloch functions on the other, are shown to find a deeper mathematical understanding in terms of $q$-WH. The r\\^ole played by the finite difference operators and the relevance of the lattice structure in the completeness of the coherent states system suggest that the quantization of the WH algebra is an essential tool in the physics of discretized (periodic) systems.
The length operator in Loop Quantum Gravity
Eugenio Bianchi
2008-09-11
The dual picture of quantum geometry provided by a spin network state is discussed. From this perspective, we introduce a new operator in Loop Quantum Gravity - the length operator. We describe its quantum geometrical meaning and derive some of its properties. In particular we show that the operator has a discrete spectrum and is diagonalized by appropriate superpositions of spin network states. A series of eigenstates and eigenvalues is presented and an explicit check of its semiclassical properties is discussed.
Quantum mechanical spectral engineering by scaling intertwining
D. J. Fernandez C.; H. C. Rosu
2001-08-22
Using the concept of spectral engineering we explore the possibilities of building potentials with prescribed spectra offered by a modified intertwining technique involving operators which are the product of a standard first-order intertwiner and a unitary scaling. In the same context we study the iterations of such transformations finding that the scaling intertwining provides a different and richer mechanism in designing quantum spectra with respect to that given by the standard intertwining
Atomic quantum transistor based on swapping operation
Sergey A. Moiseev; Sergey N. Andrianov; Eugene S. Moiseev
2011-08-31
We propose an atomic quantum transistor based on exchange by virtual photons between two atomic systems through the control gate-atom. The quantum transistor is realized in two QED cavities coupled in nano-optical scheme. We have found novel effect in quantum dynamics of coupled three-node atomic system which provides control-SWAP(\\theta) processes in quantum transistor operation. New possibilities of quantum entanglement in an example of bright and dark qubit states have been demonstrated for quantum transport in the atomic chain. Potentialities of the proposed nano-optical design for quantum computing and fundamental issues of multi-atomic physics are also discussed.
Quantum Logical Operations on Encoded Qubits
Wojciech Hubert Zurek; Raymond Laflamme
1996-05-14
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 one bit errors which either preexisted or occurred in course of operation. The logical operations we consider allow one to cary out the vast majority of the steps in the quantum factoring algorithm. Thus, our results help bring quantum factoring and other quantum computations closer to reality
Remarks on osmosis, quantum mechanics, and gravity
Carroll, Robert
2011-01-01
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.
Remarks on osmosis, quantum mechanics, and gravity
Robert Carroll
2011-04-03
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.
Remarks on Osmosis, Quantum Mechanics, and Gravity
NASA Astrophysics Data System (ADS)
Carroll, Robert
2012-05-01
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.
Renormalization group in quantum mechanics
Polony, J. [Laboratory of Theoretical Physics, Louis Pasteur University, 3 rue de l`Universite, 67084 Strasbourg Cedex (France)] [Laboratory of Theoretical Physics, Louis Pasteur University, 3 rue de l`Universite, 67084 Strasbourg Cedex (France); [Department of Atomic Physics, Lorand Eoelvos University, Puskin u 5-7, 1088 Budapest (Hungary)
1996-12-01
The running coupling constants are introduced in quantum mechanics and their evolution is described with the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The Hamiltonian and the Lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models. Copyright {copyright} 1996 Academic Press, Inc.
To the nonlinear quantum mechanics
Miroslav Pardy
2001-11-20
The Schroedinger equation with the nonlinear term is derived by the natural generalization of the hydrodynamical model of quantum mechanics. The nonlinear term appears to be logically necessary because it enables explanation of the classical limit of the wave function, the collaps of the wave function and solves the Schroedinger cat paradox.
What quantum computers may tell us about quantum mechanics
Monroe, Christopher
17 What quantum computers may tell us about quantum mechanics Christopher R. Monroe University computing and storage media are being miniaturized to the atomic scale, is beginning to confront quantum of Michigan, Ann Arbor Quantum mechanics occupies a unique position in the history of science. It has sur
The quantum field theory interpretation of quantum mechanics
Alberto C. de la Torre
2015-03-02
It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.
Algorithmic Information Theoretic Issues in Quantum Mechanics
Algorithmic Information Theoretic Issues in Quantum Mechanics Gavriel Segre - PHD thesis October 20 of qubits one has to give up the Hilbert- Space Axiomatization of Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 III The road for quantum algorithmic randomness 104 5 The irreducibility of quantum probability
Quantum-proof randomness extractors via operator space theory
Mario Berta; Omar Fawzi; Volkher B. Scholz
2015-02-17
Quantum-proof randomness extractors are an important building block for classical and quantum cryptography as well as for device independent randomness amplification and expansion. It is known that some constructions are quantum-proof whereas others are provably not [Gavinsky {\\it et al.}, STOC'07]. We argue that the theory of operator spaces offers a natural framework for studying to what extent extractors are secure against quantum adversaries: we first phrase the definition of extractors as a bounded norm condition between normed spaces, and then show that the presence of quantum adversaries corresponds to a completely bounded norm condition between operator spaces. From this we show that very high min-entropy extractors as well as extractors with small output are always (approximately) quantum-proof. We also study a generalization of extractors called randomness condensers. Again, we phrase the definition of condensers as a bounded norm condition and the definition of quantum-proof condensers as a completely bounded norm condition. Seeing condensers as bipartite graphs, we then find that the bounded norm condition corresponds to an instance of a well studied combinatorial problem, called bipartite densest subgraph. Furthermore, using the characterization in terms of operator spaces, we can associate to any condenser a Bell inequality (two-player game) such that classical and quantum strategies are in one-to-one correspondence with classical and quantum attacks on the condenser. Hence, we get for every quantum-proof condenser a Bell inequality that can not be violated by quantum mechanics.
Probable Inference and Quantum Mechanics
Grandy, W. T. Jr. [Department of Physics and Astronomy, University of Wyoming, Laramie, WY 82070 (United States)
2009-12-08
In its current very successful interpretation the quantum theory is fundamentally statistical in nature. Although commonly viewed as a probability amplitude whose (complex) square is a probability, the wavefunction or state vector continues to defy consensus as to its exact meaning, primarily because it is not a physical observable. Rather than approach this problem directly, it is suggested that it is first necessary to clarify the precise role of probability theory in quantum mechanics, either as applied to, or as an intrinsic part of the quantum theory. When all is said and done the unsurprising conclusion is that quantum mechanics does not constitute a logic and probability unto itself, but adheres to the long-established rules of classical probability theory while providing a means within itself for calculating the relevant probabilities. In addition, the wavefunction is seen to be a description of the quantum state assigned by an observer based on definite information, such that the same state must be assigned by any other observer based on the same information, in much the same way that probabilities are assigned.
Scattering in the Euclidean formulation of relativistic quantum mechanics
NASA Astrophysics Data System (ADS)
Polyzou, Wayne
2013-10-01
Euclidean relativistic quantum mechanics is a formulation of relativistic quantum mechanics based on the Osterwalder-Schrader reconstruction theorem that exploits the logical independence of locality from the rest of the axioms of Euclidean field theory. I discuss the properties of Euclidean Green functions necessary for the existence of Møller wave operators and the construction of these wave operators in this formalism. Supported by the US Department of Energy, Grant - DE-AC02-81ER40038.
Quantum mechanics of black holes.
Witten, Edward
2012-08-01
The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely. PMID:22859480
Correspondence Truth and Quantum Mechanics
Vassilios Karakostas
2015-04-07
The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either 'true' or 'false', describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of 'no go' theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton 'uniqueness theorem' is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a particular observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The conceptual implications of the resulting account are traced down and analyzed at length. In this light, the traditional conception of correspondence truth may be viewed as a species or as a limit case of the more generic proposed scheme of contextual correspondence when the non-explicit specification of a context of discourse poses no further consequences.
Is Pseudo-Hermitian Quantum Mechanics an Indefinite-Metric Quantum Theory?
Ali Mostafazadeh
2003-08-05
With a view to eliminate an important misconception in some recent publications, we give a brief review of the notion of a pseudo-Hermitian operator, outline pseudo-Hermitian quantum mechanics, and discuss its basic difference with the indefinite-metric quantum mechanics. In particular, we show that the answer to the question posed in the title is a definite No.
Quantum mechanics with respect to different reference frames
Mangiarotti, L.; Sardanashvily, G.
2007-08-15
Geometric (Schroedinger) quantization of nonrelativistic mechanics with respect to different reference frames is considered. In classical nonrelativistic mechanics, a reference frame is represented by a connection on a configuration space fibered over a time axis R. Under quantization, it yields a connection on the quantum algebra of Schroedinger operators. The operators of energy with respect to different reference frames are examined.
Quantum mechanics with respect to different reference frames
L. Mangiarotti; G. Sardanashvily
2007-03-29
Geometric (Schrodinger) quantization of nonrelativistic mechanics with respect to different reference frames is considered. In classical nonrelativistic mechanics, a reference frame is represented by a connection on a configuration space fibered over a time axis. Under quantization, it yields a connection on the quantum algebra of Schrodinger operators. The operators of energy with respect to different reference frames are examined.
Quantum Mechanical Reflection Resonances
Erica Caden; Robert Gilmore
2006-10-27
Resonances in the reflection probability amplitude r(E) can occur in energy ranges in which the reflection probability R(E)=|r(E)|^2 is 1. They occur as the phase phi(E) defined by r(E) = t*(E)/t(E) = 1e^{i 2phi(E)} undergoes a rapid change of pi radians. During this transition the phase angle exhibits a Lorentzian profile in that d(phi(E))/dE ~= 1/[(E-E_0)^2+(hbar*gamma/2)^2]. The energy E_0 identifies the location of a quasi-bound state, gamma measures the lifetime of this state, and t(E) is a matrix element of the transfer operator. Methods for computing and measuring these resonances are proposed.
Ideal quantum clocks and operator time
Walter Gessner
2013-05-04
In the framework of any quantum theory in the Schroedinger picture a general operator time concept is given. For this purpose certain systems are emphasized as ideal quantum clocks. Their definition follows heuristically from a common property of ideal clocks and from general postulates of traditional quantum theory. Any such ideal quantum clock allows the definition of a symmetric time operator T. T and the Hamiltonian H necessarily satisfy the time-energy uncertainty relation. The argument of Pauli against the existence of any time operator does not strike, because T is symmetric but not selfadjoint.
Private Quantum Subsystems and Quasiorthogonal Operator Algebras
Jeremy Levick; Tomas Jochym-O'Connor; David Kribs; Raymond Laflamme; Rajesh Pereira
2015-10-04
We generalize a recently discovered example of a private quantum subsystem to find private subsystems for Abelian subgroups of the $n$-qubit Pauli group, which exist in the absence of private subspaces. In doing so, we also connect these quantum privacy investigations with the theory of quasiorthogonal operator algebras through the use of tools from group theory and operator theory.
NONEQUILIBRIUM QUANTUM STATISTICAL MECHANICS AND THERMODYNAMICS #
NONEQUILIBRIUM QUANTUM STATISTICAL MECHANICS AND THERMODYNAMICS # Walid K. Abou Salem + Institut f nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and di#erent reversible and irreversible thermodynamic processes are studied from the point of view of quantum statistical mechanics
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Review of Quantum Mechanics In general, particles
Visualizing quantum mechanics in phase space
Heiko Bauke; Noya Ruth Itzhak
2011-01-11
We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner function formalism resembles the mathematical language of classical mechanics of non-interacting particles. Thus, it allows a more direct comparison between classical and quantum dynamical features.
129 Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
129 Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We's equation of motion in mechanics. The initial condtions to solve the Newton's equation of motion
221B Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
221B Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics We the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We's equation of motion in mechanics. The initial condtions to solve the Newton's equation of motion
221B Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
221B Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics We the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We, similarly to the Newton's equation of motion in mechanics. The initial condtions to solve the Newton
Quantum Mechanics and Representation Theory Columbia University
Woit, Peter
Quantum Mechanics and Representation Theory Peter Woit Columbia University Texas Tech, November 21 2013 Peter Woit (Columbia University) Quantum Mechanics and Representation Theory November 2013 1 / 30, 1967 Peter Woit (Columbia University) Quantum Mechanics and Representation Theory November 2013 2 / 30
Improving student understanding of quantum mechanics
NASA Astrophysics Data System (ADS)
Singh, Chandralekha
2015-04-01
Learning quantum mechanics is challenging for many students. We are investigating the difficulties that upper-level students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) and tools for peer-instruction. Many of the QuILTs employ computer simulations to help students visualize and develop better intuition about quantum phenomena. We will discuss the common students' difficulties and research-based tools we are developing to bridge the gap between quantitative and conceptual aspects of quantum mechanics and help students develop a solid grasp of quantum concepts. Support from the National Science Foundation is gratefully acknowledged.
Quantum Mechanics Of Consciousness
Pradhan, Rajat Kumar
2009-01-01
A phenomenological approach using the states of spin-like observables is developed to understand the nature of consciousness and the totality of experience. The three states of consciousness are taken to form the triplet of eigenstates of a spin-one entity and are derived as the triplet resulting from the composition of two spins by treating the subject and the object as interacting two-state, spin-half systems with external and internal projections. The state of deep sleep is analysed in the light of this phenomenological approach and a novel understanding of the status of the individual consciousness in this state is obtained. The resulting fourth state i.e. the singlet state is interpreted to correspond to the superconscious state of intuitive experience and is justified by invoking the concept of the universal consciousness as the underlying source of all individual states of experience. It is proposed that the individual experiences result from the operations of four individualizing observables which pro...
Paradoxical Reflection in Quantum Mechanics
Pedro L. Garrido; Sheldon Goldstein; Jani Lukkarinen; Roderich Tumulka
2011-05-03
This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast, classical particles get reflected only at upward steps. The conditions for this effect are that the wave length is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. This phenomenon is suggested by non-normalizable solutions to the time-independent Schroedinger equation, and we present evidence, numerical and mathematical, that it is also indeed predicted by the time-dependent Schroedinger equation. Furthermore, this paradoxical reflection effect suggests, and we confirm mathematically, that a quantum particle can be trapped for a long time (though not forever) in a region surrounded by downward potential steps, that is, on a plateau.
Larkin, Teresa L.
Conceptual Development of Quantum Mechanics: Experiences with the Visual Quantum Mechanics using a portion of the materials developed by the Visual Quantum Mechanics (VQM) project1 as part of our recent efforts to investigate student understanding of basic quantum mechanics concepts. The VQM
Erasing Quantum Coherence: An Operational Approach
Uttam Singh; Manabendra Nath Bera; Avijit Misra; Arun Kumar Pati
2015-06-26
Despite being one of the hallmarks of quantum physics, there is a lack of operational interpretations of quantum coherence. Here we provide an operational interpretation of coherence of a quantum system, in terms of the amount of noise that is to be injected in order to fully decohere it. In particular, we show that in the asymptotic limit, the minimum amount of noise that is required to fully decohere a quantum system, is equal to the relative entropy of coherence. This quantifies the erasure cost of quantum coherence. We employ the entropy exchanged between system and environment during the decohering operation and the memory required to store the information about the decohering operation as the quantifiers of noise. We show that both the quantifiers yield the same cost of erasing coherence in the asymptotic limit. The relative entropy of coherence, hence, is endowed with a thermodynamical and operational interpretation.
A quantum genetic algorithm with quantum crossover and mutation operations
NASA Astrophysics Data System (ADS)
SaiToh, Akira; Rahimi, Robabeh; Nakahara, Mikio
2013-11-01
In the context of evolutionary quantum computing in the literal meaning, a quantum crossover operation has not been introduced so far. Here, we introduce a novel quantum genetic algorithm that has a quantum crossover procedure performing crossovers among all chromosomes in parallel for each generation. A complexity analysis shows that a quadratic speedup is achieved over its classical counterpart in the dominant factor of the run time to handle each generation.
Quantum mechanics and the psyche
NASA Astrophysics Data System (ADS)
Galli Carminati, G.; Martin, F.
2008-07-01
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.
Z Theory and its Quantum-Relativistic Operators
Pietro Giorgio Zerbo
2006-02-08
The view provided by Z theory, based on its quantum-relativistic operators, is an integrated picture of the micro and macro quantities relationships. The axiomatic formulation of the theory is presented in this paper. The theory starts with the existence of the wave function, the existence of three fundamental constants h, c and G as well as the physical quantity Rc (the radius of the space-time continuum) plus the definition of a general form for the quantum-relativistic functional operators. Using such starting point the relationships between relativity, quantum mechanics and cosmological quantities can be clarified.
Statistical Mechanics and Quantum Cosmology
B. L. Hu
1995-11-29
Statistical mechanical concepts and processes such as decoherence, correlation, and dissipation can prove to be of basic importance to understanding some fundamental issues of quantum cosmology and theoretical physics such as the choice of initial states, quantum to classical transition and the emergence of time. Here we summarize our effort in 1) constructing a unified theoretical framework using techniques in interacting quantum field theory such as influence functional and coarse-grained effective action to discuss the interplay of noise, fluctuation, dissipation and decoherence; and 2) illustrating how these concepts when applied to quantum cosmology can alter the conventional views on some basic issues. Two questions we address are 1) the validity of minisuperspace truncation, which is usually assumed without proof in most discussions, and 2) the relevance of specific initial conditions, which is the prevailing view of the past decade. We also mention how some current ideas in chaotic dynamics, dissipative collective dynamics and complexity can alter our view of the quantum nature of the universe.
Quantum Mechanics in symmetry language
Houri Ziaeepour
2014-09-17
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better understood in this view. In particular, the abstract concept of symmetry provides a basis-independent definition for observables. Moreover, we show that the apparent projection/collapse of the state as the final step of measurement or decoherence is the result of breaking of symmetries. This phenomenon is comparable with a phase transition by spontaneous symmetry breaking, and makes the process of decoherence and classicality a natural fate of complex systems consisting of many interacting subsystems. Additionally, we demonstrate that the property of state space as a vector space representing symmetries is more fundamental than being an abstract Hilbert space, and its $L2$ integrability can be obtained from the imposed condition of being a representation of a symmetry group and general properties of probability distributions.
The Transactional Interpretation of Quantum Mechanics and Quantum Nonlocality
John G. Cramer
2015-02-28
Quantum nonlocality is discussed as an aspect of the quantum formalism that is seriously in need of interpretation. The Transactional Interpretation of quantum mechanics, which describes quantum processes as transactional "handshakes" between retarded $\\psi$ waves and advanced $\\psi*$ waves, is discussed. Examples of the use of the Transactional Interpretation in resolving quantum paradoxes and in understanding the counter-intuitive aspects of the formalism, particularly quantum nonlocality, are provided.
Braiding Operator via Quantum Cluster Algebra
Kazuhiro Hikami; Rei Inoue
2014-09-13
We construct a braiding operator in terms of the quantum dilogarithm function based on the quantum cluster algebra. We show that it is a q-deformation of the R-operator for which hyperbolic octrahedron is assigned. Also shown is that, by taking q to be a root of unity, our braiding operator reduces to the Kashaev R-matrix up to a simple gauge-transformation.
On a commutative ring structure in quantum mechanics
Shigeki Matsutani
2009-10-10
In this article, I propose a concept of the $p$-on which is modelled on the multi-photon absorptions in quantum optics. It provides a commutative ring structure in quantum mechanics. Using it, I will give an operator representation of the Riemann $\\zeta$ function.
NASA Astrophysics Data System (ADS)
Lin, Li-Hua
2010-05-01
We describe a scheme for the generation of macroscopic quantum-interference states for a collection of trapped ions by a single geometric phase operation. In the scheme the vibrational mode is displaced along a circle with the radius proportional to the number of ions in a certain ground electronic state. For a given interaction time, the vibrational mode returns to the original state, and the ionic system acquires a geometric phase proportional to the area of the circle, evolving from a coherent state to a superposition of two coherent states. The ions undergo no electronic transitions during the operation. Taking advantage of the inherent fault-tolerant feature of the geometric operation, our scheme is robust against decoherence.
Effective equations for the quantum pendulum from momentous quantum mechanics
Hernandez, Hector H.; Chacon-Acosta, Guillermo
2012-08-24
In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.
Quantum mechanical light harvesting mechanisms in photosynthesis
NASA Astrophysics Data System (ADS)
Scholes, Gregory
2012-02-01
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).
Game Theory in Categorical Quantum Mechanics
Ali Nabi Duman
2014-05-17
Categorical quantum mechanics, which examines quantum theory via dagger-compact closed categories, gives satisfying high-level explanations to the quantum information procedures such as Bell-type entanglement or complementary observables (\\cite{AC}, \\cite{Co}, \\cite{Co2}). Inspired by the fact that Quantum Game Theory can be seen as branch of quantum information, we express Quantum Game Theory procedures using the topological semantics provided by Categorical Quantum Mechanics. We also investigate Bayesian Games with correlation from this novel point of view while considering the connection between Bayesian game theory and Bell non-locality investigated recently by Brunner and Linden \\cite{BL}.
An approach to nonstandard quantum mechanics
Andreas Raab
2006-12-27
We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to non-relativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the M{\\o}ller wave operators and the S-Matrix.
Bell trajectories for revealing quantum control mechanisms
Eric Dennis; Herschel Rabitz
2003-01-01
The dynamics induced while controlling quantum systems by optimally shaped laser pulses have often been difficult to understand in detail. A method is presented for quantifying the importance of specific sequences of quantum transitions involved in the control process. The method is based on a ``beable'' formulation of quantum mechanics due to John Bell that rigorously maps the quantum evolution
Iyengar, Srinivasan S.
Quantum Mechanics Course Number: C668 C668: Special topics in physical chemistry: Advanced Quantum will rationalize "complicated ideas" in quantum mechanics using physically in- tuitive arguments (I think@gmail.com Chemistry, Indiana University i c 2014, Srinivasan S. Iyengar (instructor) #12;Quantum Mechanics Course
Imperfect Cloning Operations in Algebraic Quantum Theory
NASA Astrophysics Data System (ADS)
Kitajima, Yuichiro
2015-01-01
No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal -imperfect cloning operation which tolerates a finite loss of fidelity in the cloned state, and show that an individual system's algebra of observables is abelian if and only if there is a universal -imperfect cloning operation in the case where the loss of fidelity is less than . Therefore in this case no universal -imperfect cloning operation is possible in algebraic quantum theory.
Quantum Mechanics: Structures, Axioms and Paradoxes
Aerts, Diederik
Quantum Mechanics: Structures, Axioms and Paradoxes Diederik Aerts Center Leo Apostel, Brussels present an analysis of quantum mechanics and its problems and para- doxes taking into account the results that have been obtained during the last two decades by investigations in the field of `quantum structures re
Quantum-Mechanical by Seth Lloyd
Robins, Gabriel
Quantum-Mechanical Computers by Seth Lloyd Quantum-mechanical computers, if they can be constructed have. HYDROGEN ATOMS could be used to store bits of information in a quantum computer. An atom in its and its excited state, the electron will jump from one state to the other. 98 Scientific American
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Particle Interaction Summary quantum
Quantum Mechanical Observers and Time Reparametrization Symmetry
Eiji Konishi
2012-12-20
We propose that the degree of freedom of measurement by quantum mechanical observers originates in the Goldstone mode of the spontaneously broken time reparametrization symmetry. Based on the classification of quantum states by their non-unitary temporal behavior as seen in the measurement processes, we describe the concepts of the quantum mechanical observers via the time reparametrization symmetry.
Nonlinear backreaction in a quantum mechanical SQUID
J. F. Ralph; T. D. Clark; M. J. Everitt; P. Stiffell
2001-08-30
In this paper we discuss the coupling between a quantum mechanical superconducting quantum interference device (SQUID) and an applied static magnetic field. We demonstrate that the backreaction of a SQUID on the applied field can interfere with the ability to bias the SQUID at values of the static (DC) magnetic flux at, or near to, transitions in the quantum mechanical SQUID.
Quantum mechanics on York slices
Roser, Philipp
2015-01-01
For some time the York time parameter has been identified as a candidate for a physically meaningful time in cosmology. An associated Hamiltonian may be found by solving the Hamiltonian constraint for the momentum conjugate to the York time variable, although an explicit solution can only be found in highly symmetric cases. The Poisson structure of the remaining variables is not canonical. Here we quantise this dynamics in an anisotropic minisuperspace model via a natural extension of canonical quantisation. The resulting quantum theory has no momentum representation. Instead the position basis takes a fundamental role. We illustrate how the quantum theory and the modified representation of its momentum operators lead to a consistent theory in the presence of the constraints that arose during the Hamiltonian reduction. We are able to solve for the eigenspectrum of the Hamiltonian. Finally we discuss how far the results of this model extend to the general non-homogeneous case, in particular perturbation theory...
Quantum mechanics: Myths and facts
H. Nikolic
2007-04-16
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
Quantum walks in the density operator picture
Chaobin Liu
2015-06-08
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal state is described by density operators. To formulate the unitary evolution, we define reflections in the tensor product of an internal Hilbert space and a spatial Hilbert space. We then construct unitary channels that govern the evolution of the system in the graph. The discrete dynamics of the system (called quantum walks) is obtained by iterating the unitary channel on the density operator of the quantum system. It turns out that in this framework, the action of the unitary channel on a density operator is described by the usual matrix multiplication.
Treating time travel quantum mechanically
NASA Astrophysics Data System (ADS)
Allen, John-Mark A.
2014-10-01
The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilizing the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their nonlinearity and time-travel paradoxes. In particular, the "equivalent circuit model"—which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory—is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of alternate theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features—such as time-travel paradoxes, the ability to distinguish nonorthogonal states with certainty, and the ability to clone or delete arbitrary pure states—that are present with D-CTCs and P-CTCs. The problems with nonlinear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.
Treating Time Travel Quantum Mechanically
John-Mark A. Allen
2014-10-10
The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilising the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their non-linearity and time travel paradoxes. In particular, the "equivalent circuit model"---which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory---is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of new theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features---such as time travel paradoxes, the ability to distinguish non-orthogonal states with certainty, and the ability to clone or delete arbitrary pure states---that are present with D-CTCs and P-CTCs. The problems with non-linear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.
Correspondence Truth and Quantum Mechanics
Karakostas, Vassilios
2015-01-01
The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either 'true' or 'false', describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of 'no go' theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton 'uniqueness theorem' is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state...
The Arrow of Time in Rigged Hilbert Space Quantum Mechanics
Robert C. Bishop
2005-06-22
Arno Bohm and Ilya Prigogine's Brussels-Austin Group have been working on the quantum mechanical arrow of time and irreversibility in rigged Hilbert space quantum mechanics. A crucial notion in Bohm's approach is the so-called preparation/registration arrow. An analysis of this arrow and its role in Bohm's theory of scattering is given. Similarly, the Brussels-Austin Group uses an excitation/de-excitation arrow for ordering events, which is also analyzed. The relationship between the two approaches is initially discussed focusing on their semi-group operators and time arrows. Finally a possible realist interpretation of the rigged Hilbert space formulation of quantum mechanics is considered.
Depicting qudit quantum mechanics and mutually unbiased qudit theories
André Ranchin
2014-12-30
We generalize the ZX calculus to quantum systems of dimension higher than two. The resulting calculus is sound and universal for quantum mechanics. We define the notion of a mutually unbiased qudit theory and study two particular instances of these theories in detail: qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits. The calculus allows us to analyze the structure of qudit stabilizer quantum mechanics and provides a geometrical picture of qudit stabilizer theory using D-toruses, which generalizes the Bloch sphere picture for qubit stabilizer quantum mechanics. We also use our framework to describe generalizations of Spekkens toy theory to higher dimensional systems. This gives a novel proof that qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits are operationally equivalent in three dimensions. The qudit pictorial calculus is a useful tool to study quantum foundations, understand the relationship between qubit and qudit quantum mechanics, and provide a novel, high level description of quantum information protocols.
Hilbert Space Quantum Mechanics Robert B. Griffiths
Griffiths, Robert B.
qitd114 Hilbert Space Quantum Mechanics Robert B. Griffiths Version of 16 January 2014 Contents 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 References: CQT = Consistent Quantum Theory by Griffiths (Cambridge, 2002), Ch. 2; Ch. 3; Ch. 4
Errors and paradoxes in quantum mechanics
D. Rohrlich
2007-08-28
Errors and paradoxes in quantum mechanics, entry in the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, ed. F. Weinert, K. Hentschel, D. Greenberger and B. Falkenburg (Springer), to appear
Entropic Fluctuations in Quantum Statistical Mechanics
Jaksic, Vojkan
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.7 Quantum hypothesis testingEntropic Fluctuations in Quantum Statistical Mechanics An Introduction V. JAKSI Â´Ca , Y. OGATAb , Y 1.9 Large time limit I: Scattering theory
Propagators in polymer quantum mechanics
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
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.
Entropy, Stochastic Matrices, and Quantum Operations
Lin Zhang
2013-02-22
The goal of the present paper is to derive some conditions on saturation of (strong) subadditivity inequality for the stochastic matrices. The notion of relative entropy of stochastic matrices is introduced by mimicking quantum relative entropy. Some properties of this concept are listed and the connection between the entropy of the stochastic quantum operations and that of stochastic matrices are discussed.
Improved lattice actions for supersymmetric quantum mechanics
Sebastian Schierenberg; Falk Bruckmann
2012-10-19
We analyze the Euclidean version of supersymmetric quantum mechanics on the lattice by means of a numerical path integral. We consider two different lattice derivatives and improve the actions containing them with respect to supersymmetry by systematically adding interaction terms with non-zero extent. To quantize this improvement, we measure boson and fermion masses and Ward identities for the naive as well as the improved models. The masses are degenerate in all models, but the magnitude of the Ward identities decreases significantly for both derivative operators using the improved actions. This is a clear sign that the breaking of supersymmetry due to lattice artifacts is reduced.
Non-representative quantum mechanical weak values
B. E. Y. Svensson
2015-03-06
The operational definition of a weak value for a quantum mechanical system involves the limit of the weak measurement strength tending to zero. I study how this limit compares to the situation for the undisturbed (no weak measurement) system. Under certain conditions, which I investigate, this limit is discontinuous in the sense that it does not merge smoothly to the Hilbert space description of the undisturbed system. Hence, in these discontinuous cases, the weak value does not represent the undisturbed system. As a result, conclusions drawn from such weak values regarding the properties of the studied system cannot be upheld. Examples are given.
Path integral in energy representation in quantum mechanics
P. Putrov
2007-08-30
In this paper we develop the alternative path-integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is Laplace transform of a evolution operator) in a form which has a sense of ``the sum over paths'' but it is much more better defined than the usual functional integral. We investigate this representation from various directions and compare such approach to quantum mechanics with the standard ones.
An extended phase space for Quantum Mechanics
C. Lopez
2015-09-23
The standard formulation of Quantum Mechanics violates locality of interactions and the action reaction principle. An alternative formulation in an extended phase space could preserve both principles, but Bell's theorems show that a distribution of probability in a space of local variables can not reproduce the quantum correlations. An extended phase space is defined in an alternative formulation of Quantum Mechanics. Quantum states are represented by a complex va\\-lued distribution of amplitude, so that Bell's theorems do not apply.
Quantum selfish gene (biological evolution in terms of quantum mechanics)
Yuri I. Ozhigov
2013-12-07
I propose to treat the biological evolution of genoms by means of quantum mechanical tools. We start with the concept of meta- gene, which specifies the "selfish gene" of R.Dawkins. Meta- gene encodes the abstract living unity, which can live relatively independently of the others, and can contain a few real creatures. Each population of living creatures we treat as the wave function on meta- genes, which module squared is the total number of creatures with the given meta-gene, and the phase is the sum of "aspirations" to change the classical states of meta- genes. Each individual life thus becomes one of possible outcomes of the virtual quantum measurement of this function. The evolution of genomes is described by the unitary operator in the space of psi-functions or by Kossovsky-Lindblad equation in the case of open biosystems. This operator contains all the information about specific conditions under which individuals are, and how "aspirations" of their meta- genes may be implemented at the biochemical level. We show the example of quantum description of the population with two parts of meta-gene: "wolves" and "deer", which can be simultaneously in the same abstract living unity. "Selfish gene" reconciled with the notion of individuality of alive beings that gives possibility to consider evolutionary scenarios and their possible physical causes from the single position.
Moyal Quantum Mechanics: The Semiclassical Heisenberg Dynamics
NASA Astrophysics Data System (ADS)
Osborn, T. A.; Molzahn, F. H.
1995-07-01
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 ? 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 ? 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 ? ? 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 ? coefficients recursively. In contrast to the WKB approximation for propagators, the Heisenberg-Weyl description of evolution involves no essential singularity in ?, no Hamilton-Jacobi equation to solve for the action, and no multiple trajectories, caustics, or Maslov indices.
Homework 5, Quantum Mechanics 501, Rutgers December 7, 2014
Gustafsson, Torgny
Homework 5, Quantum Mechanics 501, Rutgers December 7, 2014 1) A beam of composite particles spin operators with corresponding orbital angular momentum operators, i.e., Sx Lx and S2 L2 . Write was orbital angular momentum operatore Lx. Give the x, y, z dependence of such wave func- tions. Hint: First
Propagators in Polymer Quantum Mechanics
Ernesto Flores-González; Hugo A. Morales-Técotl; Juan D. Reyes
2013-02-07
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 Schr\\"odinger propagators in the limit of small parameter $\\mu_0$, the length scale introduced in the polymer dynamics and which plays a role analog of that of Planck length in Quantum Gravity.
Quantum mechanics without state vectors
NASA Astrophysics Data System (ADS)
Weinberg, Steven
2014-10-01
Because the state vectors of isolated systems can be changed in entangled states by processes in other isolated systems, keeping only the density matrix fixed, it is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying only on density matrices. The density matrix is defined here by the formula giving the mean values of physical quantities, which implies the same properties as the usual definition in terms of state vectors and their probabilities. This change in the description of physical states opens up a large variety of new ways that the density matrix may transform under various symmetries, different from the unitary transformations of ordinary quantum mechanics. Such new transformation properties have been explored before, but so far only for the symmetry of time translations into the future, treated as a semigroup. Here, new transformation properties are studied for general symmetry transformations forming groups, not just semigroups. Arguments that such symmetries should act on the density matrix as in ordinary quantum mechanics are presented, but all of these arguments are found to be inconclusive.
Heisenberg and the Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Camilleri, Kristian
2011-09-01
Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.
Heisenberg and the Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Camilleri, Kristian
2009-02-01
Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.
Quantum Mechanics and Closed Timelike Curves
Florin Moldoveanu
2007-04-23
General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal region of space-time are investigated. If the correspondence principle is true, then all generalizations of quantum mechanics on acausal manifolds are not renormalizable. Therefore quantum mechanics can only be defined on global hyperbolic manifolds and all general relativity solutions exhibiting time travel are unphysical.
New length operator for loop quantum gravity
Ma Yongge [Department of Physics, Beijing Normal University, Beijing 100875 (China); Soo Chopin; Yang Jinsong [Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan (China)
2010-06-15
An alternative expression for the length operator in loop quantum gravity is presented. The operator is background independent, symmetric, positive semidefinite, and well defined on the kinematical Hilbert space. The expression for the regularized length operator can moreover be understood both from a simple geometrical perspective as the average of a formula relating the length to area, volume and flux operators, and also consistently as the result of direct substitution of the densitized triad operator with the functional derivative operator into the regularized expression of the length. Both these derivations are discussed, and the origin of an undetermined overall factor in each case is also elucidated.
Simulation of n-qubit quantum systems. III. Quantum operations
NASA Astrophysics Data System (ADS)
Radtke, T.; Fritzsche, S.
2007-05-01
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.
The Stability of Matter in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Lieb, Elliott H.; Seiringer, Robert
2009-11-01
Preface; 1. Prologue; 2. Introduction to elementary quantum mechanics and stability of the first kind; 3. Many-particle systems and stability of the second kind; 4. Lieb-Thirring and related inequalities; 5. Electrostatic inequalities; 6. An estimation of the indirect part of the Coulomb energy; 7. Stability of non-relativistic matter; 8. Stability of relativistic matter; 9. Magnetic fields and the Pauli operator; 10. The Dirac operator and the Brown-Ravenhall model; 11. Quantized electromagnetic fields and stability of matter; 12. The ionization problem, and the dependence of the energy on N and M separately; 13. Gravitational stability of white dwarfs and neutron stars; 14. The thermodynamic limit for Coulomb systems; References; Index.
Quantum Mechanics Dung-Hai Lee
Murayama, Hitoshi
Quantum Mechanics Dung-Hai Lee Summer 2000 #12;Contents 1 A brief reminder of linear Algebra 3 1.5 Bell's inequality . . . . . . . . . . . . . . . . . . . . . . . 20 3 Quantum dynamics 23 3 . . . . . . . . . . . . . . . . . . . 43 3.12 Classical approximation . . . . . . . . . . . . . . . . . . 45 3.13 Quantum statistical
A framework for fast quantum mechanical algorithms
Lov K. Grover
1998-01-01
Summary A framework is presented for the design and analy- sis of quantum mechanical algorithms, the step quantum search algorithm is an immediate consequence of this framework. It leads to several other search-type applications - an example is presented where the Walsh- Hadamard (W-H) transform of the quantum search algo- rithm is replaced by another transform tailored to the parameters
Causal localizations in relativistic quantum mechanics
NASA Astrophysics Data System (ADS)
Castrigiano, Domenico P. L.; Leiseifer, Andreas D.
2015-07-01
Causal localizations describe the position of quantum systems moving not faster than light. They are constructed for the systems with finite spinor dimension. At the center of interest are the massive relativistic systems. For every positive mass, there is the sequence of Dirac tensor-localizations, which provides a complete set of inequivalent irreducible causal localizations. They obey the principle of special relativity and are fully Poincaré covariant. The boosters are determined by the causal position operator and the other Poincaré generators. The localization with minimal spinor dimension is the Dirac localization. Thus, the Dirac equation is derived here as a mere consequence of the principle of causality. Moreover, the higher tensor-localizations, not known so far, follow from Dirac's localization by a simple construction. The probability of localization for positive energy states results to be described by causal positive operator valued (PO-) localizations, which are the traces of the causal localizations on the subspaces of positive energy. These causal Poincaré covariant PO-localizations for every irreducible massive relativistic system were, all the more, not known before. They are shown to be separated. Hence, the positive energy systems can be localized within every open region by a suitable preparation as accurately as desired. Finally, the attempt is made to provide an interpretation of the PO-localization operators within the frame of conventional quantum mechanics attributing an important role to the negative energy states.
Mechanical momentum in nonequilibrium quantum electrodynamics
Michel de Haan
2006-10-23
The reformulation of field theory in which self-energy processes are no longer present [Annals of Physics, {\\bf311} (2004), 314.], [ Progr. Theor. Phys., {\\bf 109} (2003), 881.], [Trends in Statistical Physics {\\bf 3} (2000), 115.] provides an adequate tool to transform Swinger-Dyson equations into a kinetic description outside any approximation scheme. Usual approaches in quantum electrodynamics (QED) are unable to cope with the mechanical momentum of the electron and replace it by the canonical momentum. The use of that unphysical momentum is responsible for the divergences that are removed by the renormalization procedure in the $S$-matrix theory. The connection between distribution functions in terms of the canonical and those in terms of the mechanical momentum is now provided by a dressing operator [Annals of Physics, {\\bf314} (2004), 10] that allows the elimination of the above divergences, as the first steps are illustrated here.
NASA Astrophysics Data System (ADS)
Oss, Stefano; Rosi, Tommaso
2015-04-01
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many reasons why quantum mechanical systems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called "common sense" based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.
Quantum mechanics without potential function
NASA Astrophysics Data System (ADS)
Alhaidari, A. D.; Ismail, M. E. H.
2015-07-01
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schrödinger equation, which is solved for the wavefunction, bound states energy spectrum, and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which is written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states, and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and three-parameter systems.
Quantum mechanics without potential function
A. D. Alhaidari; M. E. H. Ismail
2015-06-26
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\\"odinger equation, which is solved for the wave function, bound states energy spectrum and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which is written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and there-parameter systems.
Characterizations of fixed points of quantum operations
Li Yuan [College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062 (China)
2011-05-15
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.
Kindergarten Quantum Mechanics lectures notes
Coecke, B
2005-01-01
These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in quant-ph/0402130 and [4]) which subsumes my Logic of Entanglement quant-ph/0402014. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes quant-ph/0506132. In a last section we provide some pointers to the body of technical literature on the subject.
Stochastic Theory of Quantum Mechanics
Maurice J. M. L. O. Godart
2014-03-31
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the classical trajectories of the particles are identical to the sample functions of a diffusion Markov process, whose conditional probability density is proposed as a substitute for the wave function. The Schroedinger equation and the so-called Nelson equations are used to determine the diffusion tensor and the drift vectors characteristic of such a process. It is then possible to write down the forward and backward Kolmogorov equations that are used to determine the conditional probability density, as well as the Fokker-Planck equation that is used to determine the normal probability density. This method is applied to several simple cases and the results obtained are compared with those of the orthodox theory. Among the most important differences let us mention that any system evolving freely from any original state returns spontaneously to its ground state, that the definitions of the particles velocities and momenta are impossible because the sample functions of a diffusion Markov process nowhere possess a derivative with respect to time and that the so-called collapse of the wave function is a mere mirage explained by the updating choice between new and older initial conditions in the resolution of partial differential equations. We finally attempt to extend the proposed theory to the domain of the relativistic quantum mechanics. It is promising but is clearly unfinished because it has not been possible up to now to solve the Nelson and Kolmogorov equations, except in the very simple case of a free particle.
Tests of CPT and Quantum Mechanics: experiment
NASA Astrophysics Data System (ADS)
Ambrosino, F.; Antonelli, A.; Antonelli, M.; Bacci, C.; Barva, M.; Beltrame, P.; Bencivenni, G.; Bertolucci, S.; Bini, C.; Bloise, C.; Bocchetta, S.; Bocci, V.; Bossi, F.; Bowring, D.; Branchini, P.; Bulychjov, S. A.; Caloi, R.; Campana, P.; Capon, G.; Capussela, T.; Carboni, G.; Ceradini, F.; Cervelli, F.; Chi, S.; Chiefari, G.; Ciambrone, P.; Conetti, S.; De Lucia, E.; De Santis, A.; De Simone, P.; De Zorzi, G.; Dell'Agnello, S.; Denig, A.; Di Domenico, A.; Di Donato, C.; Di Falco, S.; Di Micco, B.; Doria, A.; Dreucci, M.; Farilla, A.; Felici, G.; Ferrari, A.; Ferrer, M. L.; Finocchiaro, G.; Fiore, S.; Forti, C.; Franzini, P.; Gatti, C.; Gauzzi, P.; Giovannella, S.; Gorini, E.; Graziani, E.; Incagli, M.; Kluge, W.; Kulikov, V.; Lacava, F.; Lanfranchi, G.; Lee-Franzini, J.; Leone, D.; Martemianov, M.; Martini, M.; Massarotti, P.; Matsyuk, M.; Mei, W.; Meola, S.; Messi, R.; Miscetti, S.; Moulson, M.; Müller, S.; Murtas, F.; Napolitano, M.; Nguyen, F.; Palutan, M.; Pasqualucci, E.; Passalacqua, L.; Passeri, A.; Patera, V.; Perfetto, F.; Pontecorvo, L.; Primavera, M.; Santangelo, P.; Santovetti, E.; Saracino, G.; Schamberger, R. D.; Sciascia, B.; Sciubba, A.; Scuri, F.; Sfiligoi, I.; Sibidanov, A.; Spadaro, T.; Spiriti, E.; Tabidze, M.; Testa, M.; Tortora, L.; Valente, P.; Valeriani, B.; Venanzoni, G.; Veneziano, S.; Ventura, A.; Ventura, S.; Versaci, R.; Villella, I.; Xu, G.; KLOE Collaboration
2007-05-01
Neutral kaons provide one of the systems most sensitive to quantum mechanics and CPT violation. Models predicting quantum mechanics violation, also related to CPT violation, have been tested at the CPLEAR and KLOE experiments. In this report results of CPLEAR obtained by studying the time evolution of single and two entangled kaons are reviewed. New or improved limits on decoherence and CPT violation parameters have been obtained by KLOE studying the quantum interference in the channel ??KK?????. No deviations from the expectations of quantum mechanics and CPT symmetry have been observed.
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Relativity (Why it makes sense) Thursday, May 7
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification that is naturally solved by string theory Strings vibrating in a variety of ways give rise to particles of different
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification from the interaction energy Thursday, June 4, 2009 #12;String Theory: A different kind of unification
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Friday, June 19, 2009 #12;String Theory Origins We introduced string theory as a possible solution to our
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Scattering Summary the best way to study
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Review of Relativity The laws of physics
Quaternionic Formulation of Supersymmetric Quantum Mechanics
Seema Rawat; O. P. S. Negi
2007-03-18
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions. Supercharges, superpartner Hamiltonians and energy eigenvalues are discussed and it has been shown that the results are consistent with the results of quantum mechanics.
Quantum mechanics in complex systems
NASA Astrophysics Data System (ADS)
Hoehn, Ross Douglas
This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown. These nodes are spaced far enough from each other to minimized the electronic repulsion of the electrons, while still providing adequate enough attraction so as to bind the excess elections into orbitals. We have found that even with relativistic considerations these species are stably bound within the field. It was also found that performing the dimensional scaling calculations for systems within the confines of laser fields to be a much simpler and more cost-effective method than the supporting D=3 SCF method. The dimensional scaling method is general and can be extended to include relativistic corrections to describe the stability of simple molecular systems in super-intense laser fields. Chapter 3, we delineate the model, and aspects therein, of inelastic electron tunneling and map this model to the protein environment. G protein-coupled receptors (GPCRs) constitute a large family of receptors that sense molecules outside of a cell and activate signal transduction pathways inside the cell. Modeling how an agonist activates such a receptor is important for understanding a wide variety of physiological processes and it is of tremendous value for pharmacology and drug design. Inelastic electron tunneling spectroscopy (IETS) has been proposed as the mechanism by which olfactory GPCRs are activated by an encapsulated agonist. In this note we apply this notion to GPCRs within the mammalian nervous system using ab initio quantum chemical modeling. We found that non-endogenous agonists of the serotonin receptor share a singular IET spectral aspect both amongst each other and with the serotonin molecule: a peak that scales in intensity with the known agonist activities. We propose an experiential validation of this model by utilizing lysergic acid dimethylamide (DAM-57), an ergot derivative, and its isotopologues in which hydrogen atoms are replaced by deuterium. If validated our theory may provide new avenues for guided drug design and better in silico prediction of efficacies. Our final chapter, explores methods which may be explored to assist in the early instructio
Phase-space contraction and quantum operations
Garcia-Mata, Ignacio; Spina, Maria Elena [Departamento de Fisica, Comision Nacional de Energia Atomica. Av del Libertador 8250 (1429), Buenos Aires (Argentina); Saraceno, Marcos [Departamento de Fisica, Comision Nacional de Energia Atomica. Av del Libertador 8250 (1429), Buenos Aires (Argentina); Escuela de Ciencia y Tecnologia, Universidad Nacional de San Martin. Alem 3901 (B1653HIM), Villa Ballester (Argentina); Carlo, Gabriel [Center for Nonlinear and Complex Systems, Universita degli Studi dell'Insubria and Instituto Nazionale per la Fisica della Materia, Unita di Como, Via Valleggio 11, 22100 Como (Italy)
2005-12-15
We give a criterion to differentiate between dissipative and diffusive quantum operations. It is based on the classical idea that dissipative processes contract volumes in phase space. We define a quantity that can be regarded as 'quantum phase space contraction rate' and which is related to a fundamental property of quantum channels: nonunitality. We relate it to other properties of the channel and also show a simple example of dissipative noise composed with a chaotic map. The emergence of attractor-like structures is displayed.
Imperfect cloning operations in algebraic quantum theory
Yuichiro Kitajima
2014-09-30
No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal $\\epsilon$-imperfect cloning operation which tolerates a finite loss $\\epsilon$ of fidelity in the cloned state, and show that an individual system's algebra of observables is Abelian if and only if there is a universal $\\epsilon$-imperfect cloning operation in the case where the loss of fidelity is less than 1/4. Therefore, in this case no universal $\\epsilon$-imperfect cloning operation is possible in algebraic quantum theory.
An entropic picture of emergent quantum mechanics
D. Acosta; P. Fernandez de Cordoba; J. M. Isidro; J. L. G. Santander
2011-09-20
Quantum mechanics emerges a la Verlinde from a foliation of space by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantised in units of Boltzmann's constant k. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on space. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant h from Boltzmann's constant k.
Level shift operators for open quantum systems
Marco Merkli
2006-01-07
Level shift operators describe the second order displacement of eigenvalues under perturbation. They play a central role in resonance theory and ergodic theory of open quantum systems at positive temperatures. We exhibit intrinsic properties of level shift operators, properties which stem from the structure of open quantum systems at positive temperatures and which are common to all such systems. They determine the geometry of resonances bifurcating from eigenvalues of positive temperature Hamiltonians and they relate the Gibbs state, the kernel of level shift operators, and zero energy resonances. We show that degeneracy of energy levels of the small part of the open quantum system causes the Fermi Golden Rule Condition to be violated and we analyze ergodic properties of such systems.
The Multiverse Interpretation of Quantum Mechanics
Raphael Bousso; Leonard Susskind
2011-07-22
We argue that the many-worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics. Decoherence - the modern version of wave-function collapse - is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the "environment". In fact decoherence is absent in the complete description of any region larger than the future light-cone of a measurement event. However, if one restricts to the causal diamond - the largest region that can be causally probed - then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment. We argue that the global multiverse is a representation of the many-worlds (all possible decoherent causal diamond histories) in a single geometry. We propose that it must be possible in principle to verify quantum-mechanical predictions exactly. This requires not only the existence of exact observables but two additional postulates: a single observer within the universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite. In causal diamonds with finite surface area, holographic entropy bounds imply that no exact observables exist, and both postulates fail: experiments cannot be repeated infinitely many times; and decoherence is not completely irreversible, so outcomes are not definite. We argue that our postulates can be satisfied in "hats" (supersymmetric multiverse regions with vanishing cosmological constant). We propose a complementarity principle that relates the approximate observables associated with finite causal diamonds to exact observables in the hat.
Quantum selfish gene (biological evolution in terms of quantum mechanics)
Ozhigov, Yuri I
2014-01-01
I propose to treat the biological evolution of genoms by means of quantum mechanical tools. We start with the concept of meta- gene, which specifies the "selfish gene" of R.Dawkins. Meta- gene encodes the abstract living unity, which can live relatively independently of the others, and can contain a few real creatures. Each population of living creatures we treat as the wave function on meta- genes, which module squared is the total number of creatures with the given meta-gene, and the phase is the sum of "aspirations" to change the classical states of meta- genes. Each individual life thus becomes one of possible outcomes of the virtual quantum measurement of this function. The evolution of genomes is described by the unitary operator in the space of psi-functions or by Kossovsky-Lindblad equation in the case of open biosystems. This operator contains all the information about specific conditions under which individuals are, and how "aspirations" of their meta- genes may be implemented at the biochemical lev...
Quantum Mechanics associated with a Finite Group
Robert W. Johnson
2006-04-20
I describe, in the simplified context of finite groups and their representations, a mathematical model for a physical system that contains both its quantum and classical aspects. The physically observable system is associated with the space containing elements fxf for f an element in the regular representation of a given finite group G. The Hermitian portion of fxf is the Wigner distribution of f whose convolution with a test function leads to a mathematical description of the quantum measurement process. Starting with the Jacobi group that is formed from the semidirect product of the Heisenberg group with its automorphism group SL(2,F{N}) for N an odd prime number I show that the classical phase space is the first order term in a series of subspaces of the Hermitian portion of fxf that are stable under SL(2,F{N}). I define a derivative that is analogous to a pseudodifferential operator to enable a treatment that parallels the continuum case. I give a new derivation of the Schrodinger-Weil representation of the Jacobi group. Keywords: quantum mechanics, finite group, metaplectic. PACS: 03.65.Fd; 02.10.De; 03.65.Ta.
Some Novel Thought Experiments Involving Foundations of Quantum Mechanics and Quantum Information
Omid Akhavan
2004-02-19
In this thesis, we have proposed some novel thought experiments involving foundations of quantum mechanics and quantum information theory, using quantum entanglement property. Concerning foundations of quantum mechanics, we have suggested some typical systems including two correlated particles which can distinguish between the two famous theories of quantum mechanics, i.e. the standard and Bohmian quantum mechanics, at the individual level of pair of particles. Meantime, the two theories present the same predictions at the ensemble level of particles. Regarding quantum information theory, two theoretical quantum communication schemes including quantum dense coding and quantum teleportation schemes have been proposed by using entangled spatial states of two EPR particles shared between two parties. It is shown that the rate of classical information gain in our dense coding scheme is greater than some previously proposed multi-qubit protocols by a logarithmic factor dependent on the dimension of Hilbert space. The proposed teleportation scheme can provide a complete wave function teleportation of an object having other degrees of freedom in our three-dimensional space, for the first time. All required unitary operators which are necessary in our state preparation and Bell state measurement processes are designed using symmetric normalized Hadamard matrix, some basic gates and one typical conditional gate, which are introduced here for the first time.
NASA Astrophysics Data System (ADS)
Huang, Ling-Yun; Ye, Tian-Yu
2015-08-01
In this paper, a kind of quantum dialogue (QD) protocols without information leakage assisted by quantum operation is proposed. The participant in charge of preparation can automatically know the collapsed states after quantum operation performed on the prepared quantum states. The other participant is able to know the collapsed states derived from the prepared quantum states through quantum measurement. The information leakage problem is avoided by means of imposing auxiliary quantum operation on the prepared quantum states.
Improving students' understanding of quantum mechanics
NASA Astrophysics Data System (ADS)
Zhu, Guangtian
2011-12-01
Learning physics is challenging at all levels. Students' difficulties in the introductory level physics courses have been widely studied and many instructional strategies have been developed to help students learn introductory physics. However, research shows that there is a large diversity in students' preparation and skills in the upper-level physics courses and it is necessary to provide scaffolding support to help students learn advanced physics. This thesis explores issues related to students' common difficulties in learning upper-level undergraduate quantum mechanics and how these difficulties can be reduced by research-based learning tutorials and peer instruction tools. We investigated students' difficulties in learning quantum mechanics by administering written tests and surveys to many classes and conducting individual interviews with a subset of students. Based on these investigations, we developed Quantum Interactive Learning Tutorials (QuILTs) and peer instruction tools to help students build a hierarchical knowledge structure of quantum mechanics through a guided approach. Preliminary assessments indicate that students' understanding of quantum mechanics is improved after using the research-based learning tools in the junior-senior level quantum mechanics courses. We also designed a standardized conceptual survey that can help instructors better probe students' understanding of quantum mechanics concepts in one spatial dimension. The validity and reliability of this quantum mechanics survey is discussed.
Quantum Mechanical Models Of The Fermi Shuttle
Sternberg, James [University of Tennessee, Department of Physics and Astronomy, Knoxville TN 37996 (United States)
2011-06-01
The Fermi shuttle is a mechanism in which high energy electrons are produced in an atomic collision by multiple collisions with a target and a projectile atom. It is normally explained purely classically in terms of the electron's orbits prescribed in the collision. Common calculations to predict the Fermi shuttle use semi-classical methods, but these methods still rely on classical orbits. In reality such collisions belong to the realm of quantum mechanics, however. In this paper we discuss several purely quantum mechanical calculations which can produce the Fermi shuttle. Being quantum mechanical in nature, these calculations produce these features by wave interference, rather than by classical orbits.
Quantum chaos and operator fidelity metric
Paolo Giorda; Paolo Zanardi
2009-03-06
We show that the recently introduced operator fidelity metric provides a natural tool to investigate the cross-over to quantum chaotic behaviour. This metric is an information-theoretic measure of the global stability of a unitary evolution against perturbations. We use random matrix theory arguments to conjecture that the operator fidelity metric can be used as an "order parameter" to discriminates phases with regular behaviour from quantum chaotic ones. A numerical study of the onset of chaotic in the Dicke model is given in order to support the conjecture
Quantum chaos and operator fidelity metric.
Giorda, Paolo; Zanardi, Paolo
2010-01-01
We show that the recently introduced operator fidelity metric provides a natural tool to investigate the crossover to quantum chaotic behavior. This metric is an information-theoretic measure of the global stability of a unitary evolution against perturbations. We use random matrix theory arguments to conjecture that the operator fidelity metric can be used to discriminate phases with regular behavior from quantum chaotic ones. A numerical study of the onset of chaotic in the Dicke model is given in order to support the conjecture. PMID:20365506
Conditional phase shift for quantum CCNOT operation
NASA Astrophysics Data System (ADS)
Miroshnichenko, G. P.; Trifanov, A. I.
2013-03-01
We suggest the improvement of description methods for quantum phase gate implementation based on cavity QED. Qubits are encoded into two lowest Fock states. Three qubit phase transformation is resulted from the interaction between Rydberg atom and three modes of cavity electromagnetic field. Evolution of conditional field states after atom measurement is described by Kraus operators. We show that one of these operators corresponds to conditional evolution without quantum jumps and is very convenient for phase gate implementation. Also we describe cavity based generating EPR pair from certain initially disentangled state.
Polymer Quantum Mechanics and its Continuum Limit
Alejandro Corichi; Tatjana Vukasinac; Jose A. Zapata
2007-08-22
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle and a simple cosmological model.
Polymer quantum mechanics and its continuum limit
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A.
2007-08-15
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.
Quantum mechanical version of the classical Liouville theorem
NASA Astrophysics Data System (ADS)
Xie, Chuan-Mei; Fan, Hong-Yi
2013-03-01
In terms of the coherent state evolution in phase space, we present a quantum mechanical version of the classical Liouville theorem. The evolution of the coherent state from |z> to |sz - rz*> corresponds to the motion from a point z (q,p) to another point sz - rz* with |s|2 - |r|2 = 1. The evolution is governed by the so-called Fresnel operator U(s,r) that was recently proposed in quantum optics theory, which classically corresponds to the matrix optics law and the optical Fresnel transformation, and obeys group product rules. In other words, we can recapitulate the Liouville theorem in the context of quantum mechanics by virtue of coherent state evolution in phase space, which seems to be a combination of quantum statistics and quantum optics.
Superconformal Quantum Mechanics from M2-branes
Tadashi Okazaki
2015-03-12
We discuss the superconformal quantum mechanics arising from the M2-branes. We begin with a comprehensive review on the superconformal quantum mechanics and emphasize that conformal symmetry and supersymmetry in quantum mechanics contain a number of exotic and enlightening properties which do not occur in higher dimensional field theories. We see that superfield and superspace formalism is available for $\\mathcal{N}\\le 8$ superconformal mechanical models. We then discuss the M2-branes with a focus on the world-volume descriptions of the multiple M2-branes which are superconformal three-dimensional Chern-Simons matter theories. Finally we argue that the two topics are connected in M-theoretical construction by considering the multiple M2-branes wrapped around a compact Riemann surface and study the emerging IR quantum mechanics. We establish that the resulting quantum mechanics realizes a set of novel $\\mathcal{N}\\ge 8$ superconformal quantum mechanical models which have not been reached so far. Also we discuss possible applications of the superconformal quantum mechanics to mathematical physics.
Entropic characterization of quantum operations
Wojciech Roga; Mark Fannes; Karol Zyczkowski
2011-01-21
We investigate decoherence induced by a quantum channel in terms of minimal output entropy and of map entropy. The latter is the von Neumann entropy of the Jamiolkowski state of the channel. Both quantities admit q-Renyi versions. We prove additivity of the map entropy for all q. For the case q = 2, we show that the depolarizing channel has the smallest map entropy among all channels with a given minimal output Renyi entropy of order two. This allows us to characterize pairs of channels such that the output entropy of their tensor product acting on a maximally entangled input state is larger than the sum of the minimal output entropies of the individual channels. We conjecture that for any channel {\\Phi}1 acting on a finite dimensional system there exists a class of channels {\\Phi}2 sufficiently close to a unitary map such that additivity of minimal output entropy for {\\Psi}1 x {\\Psi}2 holds.
Factorization in the quantum mechanics with the generalized uncertainty principle
NASA Astrophysics Data System (ADS)
Chung, Won Sang
2015-07-01
In this paper, we discuss the quantum mechanics with the generalized uncertainty principle (GUP) where the commutation relation is given by [x?,p?] = i?(1 + ?p? + ?p?2). For this algebra, we obtain the eigenfunction of the momentum operator. We also study the GUP corrected quantum particle in a box. Finally, we apply the factorization method to the harmonic oscillator in the presence of a minimal observable length and obtain the energy eigenvalues by applying the perturbation method.
CPT and Quantum Mechanics Tests with Kaons: Theory
Nick E. Mavromatos
2006-07-28
In this talk I review theoretical motivations for possible CPT Violation and deviations from ordinary quantum mechanical behavior of field theoretic systems in some quantum gravity models, and I describe the relevant precision tests using neutral and charged Kaons. I emphasize the possibly unique role of neutral-meson factories in providing specific tests of models in which the CPT operator is not well-defined, leading to modifications of Einstein-Podolsky-Rosen (EPR) particle correlators.
Logical operator tradeoff for local quantum codes
NASA Astrophysics Data System (ADS)
Haah, Jeongwan; Preskill, John
2011-03-01
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. NSF PHY-0803371, DOE DE-FG03-92-ER40701, NSA/ARO W911NF-09-1-0442, and KFAS.
A quantum-mechanical Maxwell's demon
Seth Lloyd
1996-12-12
A Maxwell's demon is a device that gets information and trades it in for thermodynamic advantage, in apparent (but not actual) contradiction to the second law of thermodynamics. Quantum-mechanical versions of Maxwell's demon exhibit features that classical versions do not: in particular, a device that gets information about a quantum system disturbs it in the process. In addition, the information produced by quantum measurement acts as an additional source of thermodynamic inefficiency. This paper investigates the properties of quantum-mechanical Maxwell's demons, and proposes experimentally realizable models of such devices.
Operator approach to quantum optomechanics
C. Ventura-Velázquez; B. M. Rodríguez-Lara; H. M. Moya-Cessa
2014-11-26
We study the mirror-field interaction in several frameworks: when it is driven, when it is affected by an environment and when a two-level atom is introduced in the cavity. By using operator techniques we show how these problems may be either solved or how the Hamiltonians involved, via sets of unitary transformations, may be taken to known Hamiltonians for which there exist approximate solutions.
Operator approach to quantum optomechanics
NASA Astrophysics Data System (ADS)
Ventura-Velázquez, C.; Rodríguez-Lara, B. M.; Moya-Cessa, H. M.
2015-06-01
We study the mirror-field interaction in several frameworks: when it is driven, when it is affected by an environment, and when a two-level atom is introduced in the cavity. By using operator techniques, we show either how these problems may be solved or how the Hamiltonians involved, via sets of unitary transformations, may be taken to known Hamiltonians for which there exist approximate solutions.
The ZX-calculus is complete for stabilizer quantum mechanics
Miriam Backens
2013-07-26
The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics, meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer quantum mechanics, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations.
Aalok Pandya
2008-09-08
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics could prove to be valuable for larger objectives such as understanding of gravity.
The volume operator in covariant quantum gravity
You Ding; Carlo Rovelli
2010-04-22
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular, the geometrical observable giving the area of a surface has been shown to be the same as the one in loop quantum gravity. Here we discuss the volume observable. We derive the volume operator in the covariant theory, and show that it matches the one of loop quantum gravity, as does the area. We also reconsider the implementation of the constraints that defines the model: we derive in a simple way the boundary Hilbert space of the theory from a suitable form of the classical constraints, and show directly that all constraints vanish weakly on this space.
Riemann hypothesis and quantum mechanics
NASA Astrophysics Data System (ADS)
Planat, Michel; Solé, Patrick; Omar, Sami
2011-04-01
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
Quantum Mechanical Basis of Vision
Chakravarthi, Ramakrishna; Devi, A R Usha
2008-01-01
The two striking components of retina, i.e., the light sensitive neural layer in the eye, by which it responds to light are (the three types of) color sensitive Cones and color insensitive Rods (which outnumber the cones 20:1). The interaction between electromagnetic radiation and these photoreceptors (causing transitions between cis- and trans- states of rhodopsin molecules in the latter) offers a prime example of physical processes at the nano-bio interface. After a brief review of the basic facts about vision, we propose a quantum mechanical model (paralleling the Jaynes-Cummings model (JCM) of interaction of light with matter) of early vision describing the interaction of light with the two states of rhodopsin mentioned above. Here we model the early essential steps in vision incorporating, separately, the two well-known features of retinal transduction (converting light to neural signals): small numbers of cones respond to bright light (large number of photons) and large numbers of rods respond to faint ...
The Linguistic Interpretation of Quantum Mechanics
Shiro Ishikawa
2012-04-17
About twenty years ago, we proposed the mathematical formulation of Heisenberg's uncertainty principle, and further, we concluded that Heisenberg's uncertainty principle and EPR-paradox are not contradictory. This is true, however we now think that we should have argued about it under a certain firm interpretation of quantum mechanics. Recently we proposed the linguistic quantum interpretation (called quantum and classical measurement theory), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics, in other words, quantum philosophy). In fact, we can consider that traditional philosophies have progressed toward quantum philosophy. In this paper, we first review the linguistic quantum interpretation, and further, clarify the relation between EPR-paradox and Heisenberg's uncertainty principle. That is, the linguistic interpretation says that EPR-paradox is closely related to the fact that syllogism does not generally hold in quantum physics. This fact should be compared to the non-locality of Bell's inequality.
A discrete spacetime model for quantum mechanics
Antonio Sciarretta
2015-06-02
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schroedinger equation or complex wavefunctions. Unlike the standard QM picture, the proposed model only uses integer-valued quantities and arithmetic operations. In particular, it assumes a discrete spacetime under the form of an euclidean lattice. The proposed approach describes individual particle trajectories as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to the particles during their preparation, or stored in the lattice sites they visit during the walk. Non-relativistic QM predictions, particularly selfinterference, are retrieved as probability distributions of similarly-prepared ensembles of particles. Extension to interacting particles is discussed but not detailed in this paper.
Quantum-mechanical suppression of bremsstrahlung
Becker-Szendy, R. [Stanford Linear Accelerator Center, Menlo Park, CA (United States); Anthony, P. [Stanford Linear Accelerator Center, Menlo Park, CA (United States)]|[Lawrence Livermore National Lab., CA (United States); Bosted, P. [American Univ., Washington, DC (United States)] [and others
1993-12-01
We have studied quantum-mechanical suppression of bremsstrahlung of low-energy 1-500 MeV photons from high-energy 25 GeV electrons. We measured the LPM effect, where multiple scattering of the radiating electron destroys coherence required for the emission of low-energy photons, and the dielectric effect, where the emitted photon traveling in the radiator medium interferes with itself. For the experiment, the collaboration developed a novel method of extracting a parasitic low-intensity high-energy electron beam into the fixed target area during normal SLC operation of the accelerator. The results agree quantitatively with Migdal`s calculation of the LPM effect. Surface effects, for which there is no satisfactory theoretical prediction, are visible at low photon energies. For very thin targets, the suppression disappears, as expected. Preliminary results on dielectric suppression of bremsstrahlung are in qualitative agreement with the expectation.
Four-dimensional understanding of quantum mechanics
Jarek Duda
2009-10-14
In this paper I will try to convince that quantum mechanics does not have to lead to indeterminism, but is just a natural consequence of four-dimensional nature of our world - that for example particles shouldn't be imagined as 'moving points' in space, but as their trajectories in the spacetime like in optimizing action formulation of Lagrangian mechanics. There will be analyzed simplified model - Boltzmann distribution among trajectories occurs to give quantum mechanic like behavior - for example electron moving in proton's potential would make some concrete trajectory which average exactly to the probability distribution of the quantum mechanical ground state. We will use this model to build intuition about quantum mechanics and discuss its generalizations to get some effective approximation of physics. We will see that topological excitations of the simplest model obtained this way already creates known from physics particle structure, their decay modes and electromagnetic/gravitational interactions between them.
Four-dimensional understanding of quantum mechanics
Duda, Jarek
2009-01-01
In this paper I will try to convince that quantum mechanics does not have to lead to indeterminism, but is just a natural consequence of four-dimensional nature of our world - that for example particles shouldn't be imagined as 'moving points' in space, but as their trajectories in the spacetime like in optimizing action formulation of Lagrangian mechanics. There will be analyzed simplified model - Boltzmann distribution among trajectories occurs to give quantum mechanic like behavior - for example electron moving in proton's potential would make some concrete trajectory which average exactly to the probability distribution of the quantum mechanical ground state. We will use this model to build intuition about quantum mechanics and discuss its generalizations to get some effective approximation of physics. We will see that topological excitations of the simplest model obtained this way already creates known from physics particle structure, their decay modes and electromagnetic/gravitational interactions betwe...
A Possible Operational Motivation for the Orthocomplementation in Quantum Structures
NASA Astrophysics Data System (ADS)
D'Hooghe, Bart
2010-11-01
In the foundations of quantum mechanics Gleason’s theorem dictates the uniqueness of the state transition probability via the inner product of the corresponding state vectors in Hilbert space, independent of which measurement context induces this transition. We argue that the state transition probability should not be regarded as a secondary concept which can be derived from the structure on the set of states and properties, but instead should be regarded as a primitive concept for which measurement context is crucial. Accordingly, we adopt an operational approach to quantum mechanics in which a physical entity is defined by the structure of its set of states, set of properties and the possible (measurement) contexts which can be applied to this entity. We put forward some elementary definitions to derive an operational theory from this State-COntext-Property (SCOP) formalism. We show that if the SCOP satisfies a Gleason-like condition, namely that the state transition probability is independent of which measurement context induces the change of state, then the lattice of properties is orthocomplemented, which is one of the ‘quantum axioms’ used in the Piron-Solèr representation theorem for quantum systems. In this sense we obtain a possible physical meaning for the orthocomplementation widely used in quantum structures.
Dynamics of Quantum Phase Transitions: Quantum Kibble-Zurek Mechanism
NASA Astrophysics Data System (ADS)
Dziarmaga, Jacek
2015-07-01
Ideally, in an adiabatic quantum computation or quantum state preparation, a simple ground state of an initial Hamiltonian is evolved adiabatically to an interesting ground state of a final Hamiltonian. Unfortunately, the simple and the interesting are often different enough to be separated by a quantum phase transition. Due to a vanishing energy gap between the ground state and excited states at the critical point, near the transition the adiabaticity is bound to fail. This failure is quantified by a quantum version of the Kibble-Zurek mechanism (KZM). In these notes I introduce KZM in its general textbook form, based on adiabatic/impulse approximation, and then support the picture by an exact solution of the integrable transverse field quantum Ising chain and an approximate one of the non-integrable Bose-Hubbard model. The last model illustrates typical problems with adiabatic quantum state preparation that are encoutered in atomic quantum simulators.
Slowest local operators in quantum spin chains
NASA Astrophysics Data System (ADS)
Kim, Hyungwon; Banuls, Mari Carmen; Cirac, Ignacio; Hastings, Matthew; Huse, David
2015-03-01
We numerically construct slowly relaxing local operators in a nonintegrable spin-1/2 chain. Restricting the support of the operator to M consecutive spins along the chain, we exhaustively search for the operator that minimizes the Frobenius norm of the commutator with the Hamiltonian and show that the Frobenius norm bounds the time scale of relaxation of the operator. We find operators with significantly slower relaxation than the slowest simple ``hydrodynamic'' mode due to energy diffusion. Using both exhaustive search and tensor network techniques, we find similar slowly relaxing operators for a Floquet spin chain and for quantum circuits on spin chains; these systems are hydrodynamically ``trivial,'' with no conservation laws restricting their dynamics. We argue that such slow relaxation may be a generic feature following from locality and unitarity.
Extending quantum mechanics entails extending special relativity
S. Aravinda; R. Srikanth
2015-06-09
The complementarity of signaling and local randomness in the resources required to simulate singlet statistics is generalized here by relaxing the assumption of free will in the choice of measurement settings. The complementarity implies that under the assumption of full free will, simulation resources with reduced randomness will be signaling. It would appear at first sight that an ontological extension based on such a simulation protocol would contradict no-signaling and free will. We prove that this is not so, by constructing such an extension through the "oblivious embedding" of the protocol in a Newtonian spacetime. Relativistic or other intermediate spacetimes are ruled out as the locus of the embedding because they would permit the violation of no-signaling at the operational level by virtue of hidden influence inequalities. This implies that predictively superior extensions of quantum mechanics (QM) must be Lorentz non-covariant. However, the operational theory reproduced by the extensions will be compatible with no-signaling and Lorentz covariance. This clarifies why in principle there is no obstacle to the compatibility of extensions of QM such as Bohmian mechanics and GRW-type collapse theories with special relativity. Certain arguments against the extendability of QM, due to Conway and Kochen (2009) and Colbeck and Renner (2012), are attributed to their assumption that the spacetime of the extensions has Minkowskian causal structure.
Playing Games with Quantum Mechanics
Simon J. D. Phoenix; Faisal Shah Khan
2012-02-22
We present a perspective on quantum games that focuses on the physical aspects of the quantities that are used to implement a game. If a game is to be played, it has to be played with objects and actions that have some physical existence. We call such games playable. By focusing on the notion of playability for games we can more clearly see the distinction between classical and quantum games and tackle the thorny issue of what it means to quantize a game. The approach we take can more properly be thought of as gaming the quantum rather than quantizing a game and we find that in this perspective we can think of a complete quantum game, for a given set of preferences, as representing a single family of quantum games with many different playable versions. The versions of Quantum Prisoners Dilemma presented in the literature can therefore be thought of specific instances of the single family of Quantum Prisoner's Dilemma with respect to a particular measurement. The conditions for equilibrium are given for playable quantum games both in terms of expected outcomes and a geometric approach. We discuss how any quantum game can be simulated with a classical game played with classical coins as far as the strategy selections and expected outcomes are concerned.
Quantum Mechanical Search and Harmonic Perturbation
Jie-Hong R. Jiang; Dah-Wei Chiou; Cheng-En Wu
2007-09-14
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some important technology advances, such as masers, lasers, nuclear magnetic resonance, etc., originated from it. Here we add quantum computation to this list with a theoretical demonstration. Based on harmonic perturbation, a quantum mechanical algorithm is devised to search the ground state of a given Hamiltonian. The intrinsic complexity of the algorithm is continuous and parametric in both time T and energy E. More precisely, the probability of locating a search target of a Hamiltonian in N-dimensional vector space is shown to be 1/(1+ c N E^{-2} T^{-2}) for some constant c. This result is optimal. As harmonic perturbation provides a different computation mechanism, the algorithm may suggest new directions in realizing quantum computers.
Quantum Mechanical Methods for Biomolecular Simulations
NASA Astrophysics Data System (ADS)
Wong, Kin-Yiu; Song, Lingchun; Xie, Wangshen; Major, Dan T.; Lin, Yen-Lin; Cembran, Alessandro; Gao, Jiali
We discuss quantum mechanical methods for the description of the potential energy surface and for the treatment of nuclear quantum effects in chemical and biological applications. Two novel electronic structure methods are described, including an electronic structure-based explicit polarization (X-Pol) force field and an effective Hamiltonian molecular orbital and valence bond (EH-MOVB) theory. In addition, we present two path integral techniques to treat nuclear quantum effects, which include an analytical pathintegral method based on Kleinert’s variational perturbation theory, and integrated pathintegral free-energy perturbation and umbrella sampling (PI-FEP/UM) simulation. Studies have shown that quantum mechanics can be applied to biocatalytic systems in a variety of ways and scales. We hope that the methods presented in this article can further expand the scope of quantum mechanical applications to biomolecular systems
Visual Quantum Mechanics: Online Interactive Programs
NSDL National Science Digital Library
The Visual Quantum Mechanics project, from the Physics Education Group of Kansas State University's Department of Physics, develops innovative ways to "introduce quantum physics to high school and college students who do not have a background in modern physics or higher level math." Funded by the National Science Foundation, this resource for educators provides interactive computer visualizations and animations that introduce quantum mechanics. The interactive programs (which require Shockwave) include a spectroscopy lab suite, a probability illustrator, an energy band creator, quantum tunneling, a color creator (a Java version is also available), a wave function sketcher, a wave packet explorer, an energy diagram explorer, a diffraction suite, and a hydrogen spectroscopy program. These online demonstrations should prove to be excellent visual, hands-on teaching aids when introducing concepts involving quantum mechanics. Users can download Shockwave at the site.
Taming the zoo of supersymmetric quantum mechanical models
NASA Astrophysics Data System (ADS)
Smilga, A. V.
2013-05-01
We show that in many cases nontrivial and complicated supersymmetric quantum mechanical (SQM) models can be obtained from the simple model describing free dynamics in flat complex space by two operations: (i) Hamiltonian reduction and (ii) similarity transformation of the complex supercharges. We conjecture that it is true for any SQM model.
Hidden algebra method (quasi-exact-solvability in quantum mechanics)
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
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.
Lagrangian Approaches of Dirac and Feynman to Quantum Mechanics
Y. G. Yi
2006-03-23
A unified exposition of the Lagrangian approach to quantum mechanics is presented, embodying the main features of the approaches of Dirac and of Feynman. The arguments of the exposition address the relation of the Lagrangian approach to the Hamiltonian operator and how the correspondence principle fits into each context.
Photon quantum mechanics and beam splitters
NASA Astrophysics Data System (ADS)
Holbrow, C. H.; Galvez, E.; Parks, M. E.
2002-03-01
We are developing materials for classroom teaching about the quantum behavior of photons in beam splitters as part of a project to create five experiments that use correlated photons to exhibit nonclassical quantum effects vividly and directly. Pedagogical support of student understanding of these experiments requires modification of the usual quantum mechanics course in ways that are illustrated by the treatment of the beam splitter presented here.
Strange Bedfellows: Quantum Mechanics and Data Mining
Weinstein, Marvin; /SLAC
2009-12-16
Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.
Strange Bedfellows: Quantum Mechanics and Data Mining
NASA Astrophysics Data System (ADS)
Weinstein, Marvin
2010-02-01
Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.
Destruction of states in quantum mechanics
P. Caban; J. Rembielinski; K. A. Smolinski; Z. Walczak
2002-03-19
A description of destruction of states on the grounds of quantum mechanics rather than quantum field theory is proposed. Several kinds of maps called supertraces are defined and used to describe the destruction procedure. The introduced algorithm can be treated as a supplement to the von Neumann-Lueders measurement. The discussed formalism may be helpful in a description of EPR type experiments and in quantum information theory.
Can quantum mechanics help distributed computing?
Anne Broadbent; Alain Tapp
2009-11-30
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 survey is on communication complexity but we also address other distributed tasks.
Strange Bedfellows: Quantum Mechanics and Data Mining
Marvin Weinstein
2009-11-03
Last year, in 2008, I gave a talk titled {\\it Quantum Calisthenics}. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.
Quantum Channels, Kraus Operators, POVMs Robert B. Griffiths
Griffiths, Robert B.
qitd412 Quantum Channels, Kraus Operators, POVMs Robert B. Griffiths Version of 22 March 2012 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 References: CQT = Consistent Quantum Theory by R. B. Griffiths (Cambridge, 2002) QCQI = Quantum
Decoherent quantum walks driven by a generic coin operation
G. Abal; R. Donangelo; F. Severo; R. Siri
2007-08-09
We consider the effect of different unitary noise mechanisms on the evolution of a quantum walk (QW) on a linear chain with a generic coin operation: (i) bit-flip channel noise, restricted to the coin subspace of the QW, and (ii) topological noise caused by randomly broken links in the linear chain. Similarities and differences in the respective decoherent dynamics of the walker as a function of the probability per unit time of a decoherent event taking place are discussed.
Superconformal Quantum Mechanics from M2-branes
Okazaki, Tadashi
2015-01-01
We discuss the superconformal quantum mechanics arising from the M2-branes. We begin with a comprehensive review on the superconformal quantum mechanics and emphasize that conformal symmetry and supersymmetry in quantum mechanics contain a number of exotic and enlightening properties which do not occur in higher dimensional field theories. We see that superfield and superspace formalism is available for $\\mathcal{N}\\le 8$ superconformal mechanical models. We then discuss the M2-branes with a focus on the world-volume descriptions of the multiple M2-branes which are superconformal three-dimensional Chern-Simons matter theories. Finally we argue that the two topics are connected in M-theoretical construction by considering the multiple M2-branes wrapped around a compact Riemann surface and study the emerging IR quantum mechanics. We establish that the resulting quantum mechanics realizes a set of novel $\\mathcal{N}\\ge 8$ superconformal quantum mechanical models which have not been reached so far. Also we discus...
Control landscapes for open system quantum operations
NASA Astrophysics Data System (ADS)
Wu, Re-Bing; Rabitz, Herschel
2012-12-01
The reliable realization of control operations is a key component of quantum information applications. In practice, meeting this goal is very demanding for open quantum systems. This paper investigates the landscape defined as the fidelity J between the desired and achieved quantum operations with an open system. The goal is to maximize J as a functional of the control variables. We specify the complete set of critical points of the landscape function in the so-called kinematic picture. An associated Hessian analysis of the landscape reveals that, upon the satisfaction of a particular controllability criterion, the critical topology is dependent on the particular environment, but no false traps (i.e. suboptimal solutions) exist. Thus, a gradient-type search algorithm should not be hindered in searching for the ultimate optimal solution with such controllable systems. Moreover, the maximal fidelity is proven to coincide with Uhlmann’s fidelity between the environmental initial states associated with the achieved and desired quantum operations, which provides a generalization of Uhlmann’s theorem in terms of Kraus maps.
Local quantum mechanics with finite Planck mass
M Kozlowski; J. Marciak -Kozlowska; M. pelc
2007-04-20
In this paper the motion of quantum particles with initial mass m is investigated. The quantum mechanics equation is formulated and solved. It is shown that the wave function contains the component which is depended on the gravitation fine structure constant
Operational quantum theory without predefined time
Ognyan Oreshkov; Nicolas J. Cerf
2014-12-25
The current operational formulation of quantum theory is based on the concept of operation with an input and an output system, which assumes a prior notion of time and is asymmetric under time reversal. But in certain contexts, such as those involving gravity, time is expected to be dynamical and not predefined. Here, we propose an operational formulation of quantum theory without any predefined notion of time. It is based on a generalization of the concept of operation motivated by an epistemic approach: an operation is a description of knowledge about the events in a given region, which can be updated conditionally on information obtained from that region. Each such region has a set of boundary systems, which by definition provide the sole means of information exchange between the events in the region and the events in other regions. Separate operations can be connected in networks through their boundary systems with no directionality assumed for the connections, which generalizes the standard circuit picture. The events associated with an operation are described by positive semidefinite operators on the Hilbert spaces of the boundary systems, while the connections between regions are described by entangled states that encode a nontrivial physical symmetry. A simple rule provides the joint probabilities for the events in a network of operations. We discuss how it may be possible to understand the emergence of a causal structure from properties of the operators on the boundaries of compact space-time regions. The framework allows for indefinite causal order, timelike loops, and other acausal structures. As part of this work, we obtain a generalization of Wigner's theorem, which is based on the preservation of probabilities of actual events and thus puts the concept of time reversal symmetry on operational grounds. It contains the possibility for a new class of symmetry transformations.
Supersymmetric q-deformed quantum mechanics
Traikia, M. H.; Mebarki, N.
2012-06-27
A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.
Fundamental Quantum Mechanics--A Graphic Presentation
ERIC Educational Resources Information Center
Wise, M. N.; Kelley, T. G.
1977-01-01
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)
Quantum mechanical streamlines. I - Square potential barrier
NASA Technical Reports Server (NTRS)
Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.
1974-01-01
Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.
Beyond Quantum Mechanics and General Relativity
Andrea Gregori
2010-02-24
In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.
Quantum Ergodicity and the Analysis of Semiclassical Pseudodifferential Operators
Felix Wong
2014-10-11
This undergraduate thesis is concerned with developing the tools of differential geometry and semiclassical analysis needed to understand the the quantum ergodicity theorem of Schnirelman (1974), Zelditch (1987), and Colin de Verdi\\`ere (1985) and the quantum unique ergodicity conjecture of Rudnick and Sarnak (1994). The former states that, on any Riemannian manifold with negative curvature or ergodic geodesic flow, the eigenfunctions of the Laplace-Beltrami operator equidistribute in phase space with density 1. Under the same assumptions, the latter states that the eigenfunctions induce a sequence of Wigner probability measures on fibers of the Hamiltonian in phase space, and these measures converge in the weak-* topology to the uniform Liouville measure. If true, the conjecture implies that such eigenfunctions equidistribute in the high-eigenvalue limit with no exceptional "scarring" patterns. This physically means that the finest details of chaotic Hamiltonian systems can never reflect their quantum-mechanical behaviors, even in the semiclassical limit. The main contribution of this thesis is to contextualize the question of quantum ergodicity and quantum unique ergodicity in an elementary analytic and geometric framework. In addition to presenting and summarizing numerous important proofs, such as Colin de Verdi\\`ere's proof of the quantum ergodicity theorem, we perform graphical simulations of certain billiard flows and expositorily discuss several themes in the study of quantum chaos.
Relationship Between Quantum Walk and Relativistic Quantum Mechanics
C. M. Chandrashekar; Subhashish Banerjee; R. Srikanth
2010-06-26
Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This paper revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled form of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schrodinger form. By showing the coin to be a means to make the walk reversible, and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modelled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of quantum walk, maximum speed of the walk propagation and the earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two state system to which the study can be extended.
Relationship between quantum walks and relativistic quantum mechanics
Chandrashekar, C. M.; Banerjee, Subhashish; Srikanth, R.
2010-06-15
Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This article revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled forms of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schroedinger form. By showing the coin to be a means to make the walk reversible and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modeled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. The Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of the quantum walk, the maximum speed of walk propagation, and earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two-state system to which the study can be extended.
Some mutant forms of quantum mechanics
NASA Astrophysics Data System (ADS)
Takeuchi, Tatsu; Chang, Lay Nam; Lewis, Zachary; Minic, Djordje
2012-12-01
We construct a 'mutant' form of quantum mechanics on a vector space over the finite Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discretized quantum mechanics cannot be reproduced with any hidden variable theory. An alternative 'mutation' is also suggested.
Nonequilibrium quantum statistical mechanics and thermodynamics
Walid K. Abou Salem
2006-01-23
The purpose of this work is to discuss recent progress in deriving the fundamental laws of thermodynamics (0th, 1st and 2nd-law) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and different reversible and irreversible thermodynamic processes are studied from the point of view of quantum statistical mechanics. Special emphasis is put on new adiabatic theorems for steady states close to and far from equilibrium, and on investigating cyclic thermodynamic processes using an extension of Floquet theory.
Quantum mechanical effects on the shock Hugoniot
Bennett, B.I. (Los Alamos National Lab., NM (USA)); Liberman, D.A. (Lawrence Livermore National Lab., CA (USA))
1991-01-01
Calculations of the locus of shock Hugoniot states of aluminum, using two equations of state that either omit or include a quantum mechanical treatment for the material's electronic excitations, will be presented. The difference between the loci will be analyzed in the context of a comparison between an ab initio quantum mechanical model and a semiclassical treatment of the electronic states. The theoretical results are compared with high pressure (4--300 Mbars) data. 5 refs., 2 figs.
2T Physics and Quantum Mechanics
W. Chagas-Filho
2008-02-20
We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit described by the same Hamiltonian. One of these formulations is used as a basis for a complementation of the usual quantum mechanics when in the presence of gravity.
Quantum mechanics in de Sitter space
Subir Ghosh; Salvatore Mignemi
2011-01-25
We consider some possible phenomenological implications of the extended uncertainty principle, which is believed to hold for quantum mechanics in de Sitter spacetime. The relative size of the corrections to the standard results is however of the order of the ratio between the length scale of the quantum mechanical system and the de Sitter radius, and therefore exceedingly small. Nevertheless, the existence of effects due to the large scale curvature of spacetime in atomic experiments has a theoretical relevance.
Some Mutant Forms of Quantum Mechanics
Tatsu Takeuchi; Lay Nam Chang; Zachary Lewis; Djordje Minic
2012-08-28
We construct a `mutant' form of quantum mechanics on a vector space over the finite Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discretized quantum mechanics cannot be reproduced with any hidden variable theory. An alternative `mutation' is also suggested.
Some Mutant Forms of Quantum Mechanics
Takeuchi, Tatsu; Lewis, Zachary; Minic, Djordje
2013-01-01
We construct a `mutant' form of quantum mechanics on a vector space over the finite Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discretized quantum mechanics cannot be reproduced with any hidden variable theory. An alternative `mutation' is also suggested.
Quantum Semiotics: A Sign Language for Quantum Mechanics
Prashant
2006-01-01
Semiotics is the language of signs which has been used effectively in various disciplines of human scientific endeavor. It gives a beautiful and rich structure of language to express the basic tenets of any scientific discipline. In this article we attempt to develop from first principles such an axiomatic structure of semiotics for Quantum Mechanics. This would be a further enrichment to the already existing well understood mathematical structure of Quantum Mechanics but may give new insights and understanding to the theory and may help understand more lucidly the fundamentality of Nature which Quantum Theory attempts to explain.
Qubit-Programmable Operations on Quantum Light Fields
Marco Barbieri; Nicolò Spagnolo; Franck Ferreyrol; Rémi Blandino; Brian J. Smith; Rosa Tualle-Brouri
2014-12-01
Engineering quantum operations is one of the main abilities we need for developing quantum technologies and designing new fundamental tests. Here we propose a scheme for realising a controlled operation acting on a travelling quantum field, whose functioning is determined by an input qubit. This study introduces new concepts and methods in the interface of continuous- and discrete-variable quantum optical systems.
CLNS 96/1399 Peculiarities of Quantum Mechanics
CLNS 96/1399 Peculiarities of Quantum Mechanics: Origins and Meaning Yuri F. Orlov Floyd R. Newman, specifically quantum, features of quantum mechanics --- quan tum nonlocality, indeterminism, interference are quantum observables themselves and are represented in quantum mechanics by density matrices of pure states
On a New Form of Quantum Mechanics (II)
N. Gorobey; A. Lukyanenko; I. Lukyanenko
2009-12-16
The correspondence of a new form of quantum mechanics based on a quantum version of the action principle, which was proposed earlier [arXiv:0807.3508], with the ordinary quantum mechanics is established. New potentialities of the quantum action principle in the interpretation of quantum mechanics are considered.
Information Security and Quantum Mechanics: Security of Quantum Protocols
P. Oscar Boykin
2002-10-28
The problem of security of quantum key protocols is examined. In addition to the distribution of classical keys, the problem of encrypting quantum data and the structure of the operators which perform quantum encryption is studied. It is found that unitary bases are central to both encryption of quantum information, as well as the generation of states used in generalized quantum key distribution (which are called mutually unbiased bases). A one-to-one correspondence between certain unitary bases and mutually unbiased bases is found. Finally, a new protocol for making anonymous classical broadcasts is given along with a security proof. An experimental procedure to implement this protocol is also given. In order to prove these new results, some new bounds for accessible information of quantum sources are obtained.
A modified Lax-Phillips scattering theory for quantum mechanics
NASA Astrophysics Data System (ADS)
Strauss, Y.
2015-07-01
The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.
Hidden time interpretation of quantum mechanics and "no protocol" argument
P. V. Kurakin
2007-11-15
Previously suggested hidden time interpretation of quantum mechanics allows to reproduce the same predictions as standard quantum mechanics provides, since it is based on Feynman many - paths formulation of QM. While new experimental consequences of this interpretation are under investigation, some advantages can be enumerated. (1) The interpretation is much field theoretic - like in classical sense, so it is local in mathematical sense, though quantum (physical) non-locality is preserved. (2) The interpretation is based on one type of mathematical objects, rather than two different (Hilbert space vectors and operators). (3) The interpretation, as it was argued, overcomes the problem of hidden variables in a radically new way, with no conflict to Bell's theorem. Recently an important argument against hidden variables - like formulations of quantum theory was risen - "no protocol" argument. It is argued in the paper, that hidden time interpretation successfully overcomes this argument.
Quantum Mechanics, Common Sense and the Black Hole Information Paradox
Ulf H. Danielsson; Marcelo Schiffer
1993-05-14
The purpose of this paper is to analyse, in the light of information theory and with the arsenal of (elementary) quantum mechanics (EPR correlations, copying machines, teleportation, mixing produced in sub-systems owing to a trace operation, etc.) the scenarios available on the market to resolve the so-called black-hole information paradox. We shall conclude that the only plausible ones are those where either the unitary evolution of quantum mechanics is given up, in which information leaks continuously in the course of black-hole evaporation through non-local processes, or those in which the world is polluted by an infinite number of meta-stable remnants.
Quantum Information Theory and the Foundations of Quantum Mechanics
Christopher Gordon Timpson
2004-12-08
This thesis is a contribution to the debate on the implications of quantum information theory for the foundations of quantum mechanics. In Part 1, the logical and conceptual status of various notions of information is assessed. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; however it is maintained that in both settings `information' functions as an abstract noun, hence does not refer to a particular or substance (the worth of this point is illustrated in application to quantum teleportation). The claim that `Information is Physical' is assessed and argued to face a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. The reflections of Bruckner and Zeilinger (2001) and Deutsch and Hayden (2000) on the nature of information in quantum mechanics are critically assessed and some results presented on the characterization of entanglement in the Deutsch-Hayden formalism. Some philosophical aspects of quantum computation are discussed and general morals drawn concerning the nature of quantum information theory. In Part II, following some preliminary remarks, two particular information-theoretic approaches to the foundations of quantum mechanics are assessed in detail. It is argued that Zeilinger's (1999) Foundational Principle is unsuccessful as a foundational principle for quantum mechanics. The information-theoretic characterization theorem of Clifton, Bub and Halvorson (2003) is assessed more favourably, but the generality of the approach is questioned and it is argued that the implications of the theorem for the traditional foundational problems in quantum mechanics remains obscure.
Testing foundations of quantum mechanics with photons
Peter Shadbolt; Jonathan C. F. Matthews; Anthony Laing; Jeremy L. O'Brien
2015-01-15
The foundational ideas of quantum mechanics continue to give rise to counterintuitive theories and physical effects that are in conflict with a classical description of Nature. Experiments with light at the single photon level have historically been at the forefront of tests of fundamental quantum theory and new developments in photonics engineering continue to enable new experiments. Here we review recent photonic experiments to test two foundational themes in quantum mechanics: wave-particle duality, central to recent complementarity and delayed-choice experiments; and Bell nonlocality where recent theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different photonics experiments.
Interpretations of Quantum Mechanics: a critical survey
Caponigro, Michele
2008-01-01
This brief survey analyzes the epistemological implications about the role of observer in the interpretations of Quantum Mechanics. As we know, the goal of most interpretations of quantum mechanics is to avoid the apparent intrusion of the observer into the measurement process. In the same time, there are implicit and hidden assumptions about his role. In fact, most interpretations taking as ontic level one of these fundamental concepts as information, physical law and matter bring us to new problematical questions. We think, that no interpretation of the quantum theory can avoid this intrusion until we do not clarify the nature of observer.
Interpretations of Quantum Mechanics: a critical survey
Michele Caponigro
2008-11-24
This brief survey analyzes the epistemological implications about the role of observer in the interpretations of Quantum Mechanics. As we know, the goal of most interpretations of quantum mechanics is to avoid the apparent intrusion of the observer into the measurement process. In the same time, there are implicit and hidden assumptions about his role. In fact, most interpretations taking as ontic level one of these fundamental concepts as information, physical law and matter bring us to new problematical questions. We think, that no interpretation of the quantum theory can avoid this intrusion until we do not clarify the nature of observer.
Deformation quantization: Quantum mechanics lives and works in phase space
NASA Astrophysics Data System (ADS)
Zachos, Cosmas K.
2014-09-01
Wigner's 1932 quasi-probability Distribution Function in phase-space, his first paper in English, is a special (Weyl) representation of the density matrix. It has been useful in describing quantum flows in semiclassical limits; quantum optics; nuclear and physics; decoherence (eg, quantum computing); quantum chaos; "Welcher Weg" puzzles; molecular Talbot-Lau interferometry; atomic measurements. It is further of great importance in signal processing (time-frequency analysis). Nevertheless, a remarkable aspect of its internal logic, pioneered by H. Groenewold and J. Moyal, has only blossomed in the last quarter-century: It furnishes a third, alternate, formulation of Quantum Mechanics, independent of the conventional Hilbert Space (the gold medal), or Path Integral (the silver medal) formulations, and perhaps more intuitive, since it shares language with classical mechanics: one need not choose sides between coordinate or momentum space variables, since it is formulated simultaneously in terms of position and momentum. This bronze medal formulation is logically complete and self-standing, and accommodates the uncertainty principle in an unexpected manner, so that it offers unique insights into the classical limit of quantum theory. The observables in this formulation are cnumber functions in phase space instead of operators, with the same interpretation as their classical counterparts, only now composed together in novel algebraic ways using star products. One might then envision an imaginary world in which this formulation of quantum mechanics had preceded the conventional Hilbert-space formulation, and its own techniques and methods had arisen independently, perhaps out of generalizations of classical mechanics and statistical mechanics. A sampling of such intriguing techniques and methods has already been published in C. K. Zachos, Int Jou Mod Phys A17 297-316 (2002), and T. L. Curtright, D. B. Fairlie, and C. K. Zachos, A Concise Treatise on Quantum Mechanics in Phase Space, (Imperial Press & World Scientific, 2014).
Uncertainty in quantum mechanics: faith or fantasy?
Penrose, Roger
2011-12-13
The word 'uncertainty', in the context of quantum mechanics, usually evokes an impression of an essential unknowability of what might actually be going on at the quantum level of activity, as is made explicit in Heisenberg's uncertainty principle, and in the fact that the theory normally provides only probabilities for the results of quantum measurement. These issues limit our ultimate understanding of the behaviour of things, if we take quantum mechanics to represent an absolute truth. But they do not cause us to put that very 'truth' into question. This article addresses the issue of quantum 'uncertainty' from a different perspective, raising the question of whether this term might be applied to the theory itself, despite its unrefuted huge success over an enormously diverse range of observed phenomena. There are, indeed, seeming internal contradictions in the theory that lead us to infer that a total faith in it at all levels of scale leads us to almost fantastical implications. PMID:22042902
Macroscopic quantum mechanics in a classical spacetime.
Yang, Huan; Miao, Haixing; Lee, Da-Shin; Helou, Bassam; Chen, Yanbei
2013-04-26
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
Quantum Field Theory for Mathematicians Hamiltonian Mechanics and Symplectic Geometry
Woit, Peter
Quantum Field Theory for Mathematicians · Hamiltonian Mechanics and Symplectic Geometry Integral Quantization Supersymmetric Quantum Mechanics Introduction to Scattering Theory · Classical Field Theory · Relativistic Fields, Poincar´e Group and Wigner Classification · Free Quantum Fields
Point form relativistic quantum mechanics and relativistic SU(6)
NASA Technical Reports Server (NTRS)
Klink, W. H.
1993-01-01
The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.
Avoiding Negative Probabilities in Quantum Mechanics
Nyambuya, Golden Gadzirayi
2013-01-01
As currently understood since its discovery, the bare Klein-Gordon theory consists of negative quantum probabilities which are considered to be physically meaningless if not outright obsolete. Despite this annoying setback, these negative probabilities are what led the great Paul Dirac in 1928 to the esoteric discovery of the Dirac Equation. The Dirac Equation led to one of the greatest advances in our understanding of the physical world. In this reading, we ask the seemingly senseless question, "Do negative probabilities exist in quantum mechanics?" In an effort to answer this question, we arrive at the conclusion that depending on the choice one makes of the quantum probability current, one will obtain negative probabilities. We thus propose a new quantum probability current of the Klein-Gordon theory. This quantum probability current leads directly to positive definite quantum probabilities. Because these negative probabilities are in the bare Klein-Gordon theory, intrinsically a result of negative energie...
Chemistry 6491: Quantum Mechanics Requirements and Grading Scheme
Sherrill, David
to quantum mechanics: Scope and applicability of quantum mechanics The Schr¨odinger equation (B) LinearChemistry 6491: Quantum Mechanics Requirements and Grading Scheme Problem sets 30% First test 20 and receive an overall passing grade. Topics Unit I: Fundamentals of Quantum Mechanics (A) Introduction
Quantum Mechanics Summary/Review Spring 2009 Compton Lecture Series
Quantum Mechanics Summary/Review Spring 2009 Compton Lecture Series: From Quantum Mechanics one component at a time. · Planck's constant determines the scale at which quantum mechanical effects could get rid of quantum mechanical effects The "wavelength" of particles given by h mv would all
Conformal quantum mechanics and holographic quench
Järvelä, Jarkko; Keski-Vakkuri, Esko
2015-01-01
Recently, there has been much interest in holographic computations of two-point non-equilibrium Green functions from AdS-Vaidya backgrounds. In the strongly coupled quantum field theory on the boundary, the dual interpretation of the background is an equilibration process called a holographic quench. The two dimensional AdS-Vaidya spacetime is a special case, dual to conformal quantum mechanics. We study how the quench is incorporated into a Hamiltonian $H + \\theta(t) \\Delta H$ and into correlation functions. With the help of recent work on correlation functions in conformal quantum mechanics, we first rederive the known two point functions, and then compute non-equilibrium 3- and 4-point functions. We also compute the 3-point function Witten diagram in the two-dimensional AdS-Vaidya background, and find agreement with the conformal quantum mechanics result.
The Möbius symmetry of quantum mechanics
NASA Astrophysics Data System (ADS)
Faraggi, Alon E.; Matone, Marco
2015-07-01
The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under D-dimensional Mobius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global Mobius transformations implies that spatial space is compact. Furthermore, it implies energy quantisation and undefinability of quantum trajectories without assuming any prior interpretation of the wave function. The approach may be viewed as conventional quantum mechanics with the caveat that spatial space is compact, as dictated by the Möbius symmetry, with the classical limit corresponding to the decompactification limit. Correspondingly, there exists a finite length scale in the formalism and consequently an intrinsic regularisation scheme. Evidence for the compactness of space may exist in the cosmic microwave background radiation.
New methods for quantum mechanical reaction dynamics
Thompson, W.H. [Univ. of California, Berkeley, CA (United States). Dept. of Chemistry]|[Lawrence Berkeley Lab., CA (United States)
1996-12-01
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.
Statistical mechanics based on fractional classical and quantum mechanics
Korichi, Z.; Meftah, M. T.
2014-03-15
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.
Realization of near-deterministic arithmetic operations and quantum state engineering
Mark Um; Junhua Zhang; Dingshun Lv; Yao Lu; Shuoming An; Jing-Ning Zhang; Hyunchul Nha; M. S. Kim; Kihwan Kim
2015-06-24
Quantum theory is based on a mathematical structure totally different from conventional arithmetic. Due to the symmetric nature of bosonic particles, annihilation or creation of single particles translates a quantum state depending on how many bosons are already in the given quantum system. This proportionality results in a variety of non-classical features of quantum mechanics including the bosonic commutation relation. The annihilation and creation operations have recently been implemented in photonic systems. However, this feature of quantum mechanics does not preclude the possibility of realizing conventional arithmetic in quantum systems. We implement conventional addition and subtraction of single phonons for a trapped \\Yb ion in a harmonic potential. In order to realize such operations, we apply the transitionless adiabatic passage scheme on the anti-Jaynes-Cummings coupling between the internal energy states and external motion states of the ion. By performing the operations on superpositions of Fock states, we realize the hybrid computation of classical arithmetic in quantum parallelism, and show that our operations are useful to engineer quantum states. Our single-phonon operations are nearly deterministic and robust against parameter changes, enabling handy repetition of the operations independently from the initial state of the atomic motion. We demonstrate the transform of a classical state to a nonclassical one of highly sub-Poissonian phonon statistics and a Gaussian state to a non-Gaussian state, by applying a sequence of the operations. The operations implemented here are the Susskind-Glogower phase operators, whose non-commutativity is also demonstrated.
Operational distance and fidelity for quantum channels Viacheslav P. Belavkina
Raginsky, Maxim
of quantum-mechanical systems, derived from the well-known fi- delity "generalized transition probability and in experiment, involve finding a set of quantum-mechanical states or channels that solve some sort be a complex separable Hilbert space associated to a quantum-mechanical system. Given a pair of density
On Effective Procedures in Analyzing of Quantum Operations and Processes
NASA Astrophysics Data System (ADS)
Jamio?kowski, Andrzej
2013-01-01
In this paper we discuss some constructive procedures which can be used in certain characterizations of quantum operations and quantum channels. In particular, an effective method of checking if a given quantum operation is irreducible or not is presented. Also the question of the existance of decoherence-free subspaces for a given quantum operation is discussed. Our methods make use of an explicit form of a fixed quantum operation in its Kraus representation. Some examples based on the theory of open quantum systems are discussed.
Phase space propagators for quantum operators
NASA Astrophysics Data System (ADS)
Ozorio de Almeida, A. M.; Brodier, O.
2006-08-01
The Heisenberg evolution of a given unitary operator corresponds classically to a fixed canonical transformation that is viewed through a moving coordinate system. The operators that form the bases of the Weyl representation and its Fourier transform, the chord representation are, respectively, unitary reflection and translation operators. Thus, the general semiclassical study of unitary operators allows us to propagate arbitrary operators, including density operators, i.e., the Wigner function. The various propagation kernels are different representations of the super-operators which act on the space of operators of a closed quantum system. We here present the mixed semiclassical propagator, that takes translation chords to reflection centres, or vice versa. In contrast to the centre-centre propagator that directly evolves Wigner functions, they are guaranteed to be caustic free, having a simple WKB-like universal form for a finite time, whatever the number of degrees of freedom. Special attention is given to the near-classical region of small chords, since this dominates the averages of observables evaluated through the Wigner function.
Introduction to nonequilibrium quantum statistical mechanics
Jaksic, Vojkan
statistical mechanics 3 8 FGR thermodynamics of the SEBB model 58 8.1 The weak coupling limitIntroduction to nonÂequilibrium quantum statistical mechanics W. Aschbacher 1 , V. JaksÅ¸iâ?? c 2 , Y, Germany 2 Department of Mathematics and Statistics McGill University 805 Sherbrooke Street West Montreal
Inertial and gravitational mass in quantum mechanics
E. Kajari; N. L. Harshman; E. M. Rasel; S. Stenholm; G. Süßmann; W. P. Schleich
2010-01-01
We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear\\u000a gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the spatial modulation of the corresponding energy wave function is determined by the third root of the product of the two masses. Moreover, the discrete
Quantum mechanics: last stop for reductionism
Gabriele Carcassi
2012-03-16
The state space of a homogeneous body is derived under two different assumptions: infinitesimal reducibility and irreducibility. The first assumption leads to a real vector space, used in classical mechanics, while the second one leads to a complex vector space, used in quantum mechanics.
From classical to quantum mechanics through optics
NASA Astrophysics Data System (ADS)
Masoliver, Jaume; Ros, Ana
2010-01-01
In this paper, we revise the main aspects of the 'Hamiltonian analogy': the fact that optical paths are completely analogous to mechanical trajectories. We follow Schrödinger's original idea and go beyond this analogy by changing over from the Hamilton's principal function S to the wavefunction ?. We thus travel from classical to quantum mechanics using optics as a guide. Unfortunately, and despite its mathematical beauty and simplicity, the connection between classical and quantum mechanics through optics is nowadays hardly known and mostly ignored in university education. The present work tries to fill this gap.
NASA Astrophysics Data System (ADS)
Aspelmeyer, Markus; Schwab, Keith
2008-09-01
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
Quantum Mechanics, Spacetime Locality, and Gravity
NASA Astrophysics Data System (ADS)
Nomura, Yasunori
2013-08-01
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.
Spectral triplets, statistical mechanics and emergent geometry in non-commutative quantum mechanics
F. G. Scholtz; B. Chakraborty
2012-10-12
We show that when non-commutative quantum mechanics is formulated on the Hilbert space of Hilbert-Schmidt operators (referred to as quantum Hilbert space) acting on a classical configuration space, spectral triplets as introduced by Connes in the context of non-commutative geometry arise naturally. A distance function as defined by Connes can therefore also be introduced. We proceed to give a simple and general algorithm to compute this function. Using this we compute the distance between pure and mixed states on quantum Hilbert space and demonstrate a tantalizing link between statistics and geometry.
ERIC Educational Resources Information Center
Oss, Stefano; Rosi, Tommaso
2015-01-01
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many…
Quantum mechanism of Biological Search
Younghun Kwon
2006-05-09
We wish to suggest an algorithm for biological search including DNA search. Our argument supposes that biological search be performed by quantum search.If we assume this, we can naturally answer the following long lasting puzzles such that "Why does DNA use the helix structure?" and "How can the evolution in biological system occur?".
BOOK REVIEWS: Quantum Mechanics: Fundamentals
Kurt Gottfri; Tung-Mow Yan
2004-01-01
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
Noncommutative unification of general relativity and 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
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.
Canonical Relational Quantum Mechanics from Information Theory
Joakim Munkhammar
2011-01-07
In this paper we construct a theory of quantum mechanics based on Shannon information theory. We define a few principles regarding information-based frames of reference, including explicitly the concept of information covariance, and show how an ensemble of all possible physical states can be setup on the basis of the accessible information in the local frame of reference. In the next step the Bayesian principle of maximum entropy is utilized in order to constrain the dynamics. We then show, with the aid of Lisi's universal action reservoir approach, that the dynamics is equivalent to that of quantum mechanics. Thereby we show that quantum mechanics emerges when classical physics is subject to incomplete information. We also show that the proposed theory is relational and that it in fact is a path integral version of Rovelli's relational quantum mechanics. Furthermore we give a discussion on the relation between the proposed theory and quantum mechanics, in particular the role of observation and correspondence to classical physics is addressed. In addition to this we derive a general form of entropy associated with the information covariance of the local reference frame. Finally we give a discussion and some open problems.
Testing the limits of quantum mechanical superpositions
Markus Arndt; Klaus Hornberger
2014-10-01
Quantum physics has intrigued scientists and philosophers alike, because it challenges our notions of reality and locality--concepts that we have grown to rely on in our macroscopic world. It is an intriguing open question whether the linearity of quantum mechanics extends into the macroscopic domain. Scientific progress over the last decades inspires hope that this debate may be decided by table-top experiments.
Classical Structures in Quantum Mechanics and Applications
Augusto Cesar Lobo; Clyffe de Assis Ribeiro
2012-12-21
The theory of Non-Relativistic Quantum Mechanics was created (or discovered) back in the 1920's mainly by Schr\\"odinger and Heisenberg, but it is fair enough to say that a more modern and unified approach to the subject was introduced by Dirac and Jordan with their (intrinsic) Transformation Theory. In his famous text book on quantum mechanics [1], Dirac introduced his well-known bra and ket notation and a view that even Einstein (who was, as well known, very critical towards the general quantum physical world-view) considered the most elegant presentation of the theory at that time[2]. One characteristic of this formulation is that the observables of position and momentum are truly treated equally so that an intrinsic phase-space approach seems a natural course to be taken. In fact, we may distinguish at least two different quantum mechanical approaches to the structure of the quantum phase space: The Weyl-Wigner (WW) formalism and the advent of the theory of Coherent States (CS). The Weyl-Wigner formalism has had many applications ranging from the discussion of the Classical/Quantum Mechanical transition and quantum chaos to signal analysis[3,4]. The Coherent State formalism had a profound impact on Quantum Optics and during the course of time has found applications in diverse areas such as geometric quantization, wavelet and harmonic analysis [5]. In this chapter we present a compact review of these formalisms (with also a more intrinsic and coordinate independent notation) towards some non-standard and up-to-date applications such as modular variables and weak values.
On Time. 6b: Quantum Mechanical Time
C. K. Raju
2008-08-09
The existence of small amounts of advanced radiation, or a tilt in the arrow of time, makes the basic equations of physics mixed-type functional differential equations. The novel features of such equations point to a microphysical structure of time. This corresponds to a change of logic at the microphysical level. We show that the resulting logic is a quantum logic. This provides a natural and rigorous explanation of quantum interference. This structured-time interpretation of quantum mechanics is briefly compared with various other interpretations of q.m.
Classical Limit of Relativistic Quantum Mechanical Equations in the Foldy-Wouthuysen Representation
A. J. Silenko
2013-02-08
It is shown that, under the Wentzel-Kramers-Brillouin approximation conditions, using the Foldy-Wouthuysen representation allows the problem of finding a classical limit of relativistic quantum mechanical equations to be reduced to the replacement of operators in the Hamiltonian and quantum mechanical equations of motion by the respective classical quantities.
CLNS 96/1443 Peculiarities of Quantum Mechanics
CLNS 96/1443 REVISED Peculiarities of Quantum Mechanics: Origins and Meaning 1 Yuri F. Orlov Floyd The most peculiar, specifically quantum, features of quantum mechanics --- quan tum nonlocality mechanics 1 This paper, to be presented to the Nordic Symposium on Basic Problems in Quantum Physics, June
Emergent quantum mechanics of finances
NASA Astrophysics Data System (ADS)
Nastasiuk, Vadim A.
2014-06-01
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.
Multichannel framework for singular quantum mechanics
Camblong, Horacio E.; Epele, Luis N.; Fanchiotti, Huner; García Canal, Carlos A.; Ordóñez, Carlos R.
2014-01-15
A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant (“asymptotic”) observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances. -- Highlights: •A multichannel framework is proposed for singular quantum mechanics and analogues. •The framework unifies several established approaches for singular potentials. •Singular points are treated as new scattering channels. •Nonunitary asymptotic behavior is subsumed in a unitary multichannel S-matrix. •Conformal quantum mechanics and the inverse quartic potential are highlighted.
Novel symmetries in N=2 supersymmetric quantum mechanical models
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
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.
Minimal Coupling and the Equivalence Principle in Quantum Mechanics
Claus Lämmerzahl
1998-07-28
The role of the Equivalence Principle (EP) in classical and quantum mechanics is reviewed. It is shown that the weak EP has a counterpart in quantum theory, a Quantum Equivalence Principle (QEP). This implies that also in the quantum domain the geometrisation of the gravitational interaction is an operational procedure similar to the procedure in classical physics. This QEP can be used for showing that it is only the usual Schr\\"odinger equation coupled to gravito--inertial fields which obeys our equivalence principle. In addition, the QEP applied to a generalised Pauli equation including spin results in a characterisation of the gravitational fields which can be identified with the Newtonian potential and with torsion. Also, in the classical limit it is possible to state beside the usual EP for the path an EP for the spin which again may be used for introducing torsion as a gravitational field.
Foundations of quantum physics: a general realistic and operational approach
Aerts, Diederik
Foundations of quantum physics: a general realistic and operational approach Diederik Aerts FUND of quantum physics: a general realistic and operational approach", International Journal of Theoretical examples in detail in the light of this formalism: a classical deterministic entity and a quantum entity
Quantum mechanics is a relativity theory
Léon Brenig
2006-08-02
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the Heisenberg inequalities invariant and form a group. They are related to dilatations of space variables provided the quantum potential is added to the classical Hamiltonian functional. The Schr\\"odinger equation appears to have a nonunitary and nonlinear companion acting in another time variable. Evolution in this time seems related to the state vector reduction.
Inertial and gravitational mass in quantum mechanics
E. Kajari; N. L. Harshman; E. M. Rasel; S. Stenholm; G. Süßmann; W. P. Schleich
2010-06-15
We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the spatial modulation of the corresponding energy wave function is determined by the third root of the product of the two masses. Moreover, the discrete energy spectrum of a particle constrained in its motion by a linear gravitational potential and an infinitely steep wall depends on the inertial as well as the gravitational mass with different fractional powers. This feature might open a new avenue in quantum tests of the universality of free fall.
Two basic Uncertainty Relations in Quantum Mechanics
Angelow, Andrey [Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko chaussee, 1784 Sofia (Bulgaria)
2011-04-07
In the present article, we discuss two types of uncertainty relations in Quantum Mechanics-multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schroedinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics-Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.
Mossbauer neutrinos in quantum mechanics and quantum field theory
Joachim Kopp
2009-06-12
We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence, and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detection cross section, including localization and Lamb-Mossbauer terms, cannot be predicted in quantum mechanics and have to be put in by hand.
Using unitary operations to preserve quantum states in the presence of relaxation Benjamin Recht,
Recht, Ben
-unitary behavior is one of the biggest challenges facing the engineering of quantum information technology. Much property EtEs = Et+s (2) Electronic address: brecht@media.mit.edu Department of Mechanical EngineeringUsing unitary operations to preserve quantum states in the presence of relaxation Benjamin Recht
Combining Bohm and Everett: Axiomatics for a Standalone Quantum Mechanics
Kim Joris Boström
2012-10-03
A non-relativistic quantum mechanical theory is proposed that combines elements of Bohmian mechanics and of Everett's "many-worlds" interpretation. The resulting theory has the advantage of resolving known issues of both theories, as well as those of standard quantum mechanics. It has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Most importantly, the Born rule can be derived by straightforward application of the Laplacian rule, without reliance on a "quantum equilibrium hypothesis" that is crucial for Bohmian mechanics, and without reliance on a "branch weight" that is crucial for Everett-type theories. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett's approach, without being actually reducible to these. In particular, there is no "splitting of worlds", which is a typical feature of Everett-type theories. Altogether, the theory explains 1) the subjective occurrence of probabilities, 2) their quantitative value as given by the Born rule, 3) the identification of observables as self-adjoint operators on Hilbert space, and 4) the apparently random "collapse of the wavefunction" caused by the measurement, while still being an objectively deterministic theory.
Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory
Goldstein, Sheldon
Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory Detlef D of the Reviews of Modern Physics to submit a paper on the role of operators in quantum theory. That was 12 year; genuine measurement; hidden variables; Bohm's causal interpretation of quantum theory; pilot wave
Boundary dynamics and topology change in quantum mechanics
J. M. Pérez-Pardo; M. Barbero-Liñán; A. Ibort
2015-01-12
We show how to use boundary conditions to drive the evolution on a Quantum Mechanical system. We will see how this problem can be expressed in terms of a time-dependent Schr\\"{o}dinger equation. In particular we will need the theory of self-adjoint extensions of differential operators in manifolds with boundary. An introduction of the latter as well as meaningful examples will be given. It is known that different boundary conditions can be used to describe different topologies of the associated quantum systems. We will use the previous results to study how this topology change can be accomplished in a dynamical way.
Relations between multi-resolution analysis and quantum mechanics
F. Bagarello
2009-04-01
We discuss a procedure to construct multi-resolution analyses (MRA) of $\\Lc^2(\\R)$ starting from a given {\\em seed} function $h(s)$ which should satisfy some conditions. Our method, originally related to the quantum mechanical hamiltonian of the fractional quantum Hall effect (FQHE), is shown to be model independent. The role of a canonical map between certain canonically conjugate operators is discussed. This clarifies our previous procedure and makes much easier most of the original formulas, producing a convenient framework to produce examples of MRA.
F-theory Yukawa Couplings and Supersymmetric Quantum Mechanics
V. K. Oikonomou
2011-11-20
The localized fermions on the intersection curve $\\Sigma$ 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.
Macroscopic Quantum Mechanics in a Classical Spacetime
Huan Yang; Haixing Miao; Da-Shin Lee; Bassam Helou; Yanbei Chen
2013-04-23
We apply the many-particle Schr\\"{o}dinger-Newton equation, which describes the co-evolution of an many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schr\\"odinger-Newton equation for their centers of mass, which are degrees of freedom that can be monitored and manipulated at the quantum mechanical levels by state-of-the-art optoemchanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, we found that its quantum uncertainty evolves in a different frequency from its classical eigenfrequency --- with a difference that depends on the internal structure of the object, and can be observable using current technology. For several objects, the Schr\\"odinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet they do not allow quantum uncertainty to be transferred from one object to another through gravity.
NASA Astrophysics Data System (ADS)
Farenick, Douglas; Kozdron, Michael J.
2012-04-01
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.
Douglas Farenick; Michael J. Kozdron
2012-03-14
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values 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 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-Nikodym derivatives. This allows us to formulate and prove a quantum analogue of Bayes' rule.
Hidden algebra method (quasi-exact-solvability in quantum mechanics)
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
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.}
Quantum mechanics and the time travel paradox
David T. Pegg
2005-06-17
The closed causal chains arising from backward time travel do not lead to paradoxes if they are self consistent. This raises the question as to how physics ensures that only self-consistent loops are possible. We show that, for one particular case at least, the condition of self consistency is ensured by the interference of quantum mechanical amplitudes associated with the loop. If this can be applied to all loops then we have a mechanism by which inconsistent loops eliminate themselves.
Mechanism of the quantum speed-up
Giuseppe Castagnoli
2011-05-23
We explain the mechanism of the quantum speed-up - quantum algorithms requiring fewer computation steps than their classical equivalent - for a family of algorithms. 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 measurements the determination of correlated (thus redundant) measurement outcomes. Solving this problem explains the speed-up. All is like Alice, by reading the solution at the end of the algorithm, contributed to the initial choice of Bob, for 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 this 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. This yields a speed-up with respect to the classical case where, initially, Bob's choice is completely unknown to Alice.
Network implementation of covariant two-qubit quantum operations
J. Novotny; G. Alber; I. Jex
2007-01-09
A six-qubit quantum network consisting of conditional unitary gates is presented which is capable of implementing a large class of covariant two-qubit quantum operations. Optimal covariant NOT operations for one and two-qubit systems are special cases contained in this class. The design of this quantum network exploits basic algebraic properties which also shed new light onto these covariant quantum processes.
Stochastic Isometries in Quantum Mechanics
Paul Busch
2013-03-26
The class of stochastic maps, that is, linear, trace-preserving, positive maps between the self-adjoint trace class operators of complex separable Hilbert spaces plays an important role in the representation of reversible dynamics and symmetry transformations. Here a characterization of the isometric stochastic maps is given and possible physical applications are indicated.
Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics
NASA Astrophysics Data System (ADS)
Grössing, Gerhard
2015-10-01
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level...
A theory of emergent quantum mechanics
Ricardo Gallego Torromé
2015-08-12
Hamilton-Randers dynamical systems, a particular class of Hamiltonian dynamical systems, are considered as mathematical models for deterministic emergent quantum mechanics. We show that in such framework, local diffeomorphism invariance, reversibility of the effective quantum dynamics and an universal maximal bound for proper acceleration emerge in that class of classical, deterministic and local models. Starting from the elements of Hamilton-Randers spaces, a phenomenological Hilbert space is constructed and associated with the space of wave functions of quantum mechanics. A geometric description for a spontaneous reduction of the quantum states, based on the concentration of measure phenomena as it appears in asymptotic Banach theory and probability theory, is described in general terms. It is also shown how the same concentration of measure phenomena plays a remarkable role in showing conditions for the existence of stable vacua states for the matter Hamiltonian. Furthermore, it is discussed the emergence of a weak equivalence principle from very fundamental principles of mathematical analysis and the basic assumptions of Hamilton-Randers theory. This fact, together with the existence in the theory of a maximal speed and the property of diffeomorphism invariance of the interaction driving the reduction of the quantum state, suggest that the reduction of the quantum state is driven by a gravitational type interaction. Moreover, since such interaction appears only in the dynamical domain when localization happens, it must be associated with a classical interaction. We make the hypothesis that such identification is universal and that indeed gravity is a domain of the dynamics of Hamilton-Randers systems. Hence Hamilton-Randers theory provides an unification scheme where quantum mechanics and classical gravity are both emergent.
A proof of von Neumann's postulate in Quantum Mechanics
Conte, Elio [Department of Pharmacology and Human Physiology, TIRES-Center for Innovative Technologies for Signal Detection and Processing, Department of Physics, University of Bari (Italy) and School of Advanced International Studies for Applied Theoretical and Non Linear Methodologies of Physics, Bari (Italy)
2010-05-04
A Clifford algebraic analysis is explained. It gives proof of von Neumann's postulate on quantum measurement. It is of basic significance to explain the problem of quantum wave function reduction in quantum mechanics.
A tossed coin as quantum mechanical object
Soiguine, Alexander M
2013-01-01
Comprehensive and physically consistent model of a tossed coin is presented in terms of geometric algebra. The model clearly shows that there is nothing elementary particle specific in the half-spin quantum mechanical formalism. It also demonstrates what really is behind this formalism, feasibly reveals the probabilistic meaning of wave function.
Quantum Mechanics Studies of Cellobiose Conformations
Technology Transfer Automated Retrieval System (TEKTRAN)
Three regions of the Phi,Psi space of cellobiose were analyzed with quantum mechanics. A central region, in which most crystal structures are found, was covered by a 9 x 9 grid of 20° increments of Phi and Psi. Besides these 81 constrained minimizations, we studied two central sub-regions and two re...
Quantum mechanical model for Maya Blue
María E. Fuentes; Brisa Peña; César Contreras; Ana L. Montero; Russell Chianelli; Manuel Alvarado; Ramón Olivas; Luz M. Rodríguez; Héctor Camacho; Luis A. Montero-Cabrera
2008-01-01
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
Errata and Addenda Elements of Quantum Mechanics
Fayer, Michael D.
Errata and Addenda Elements of Quantum Mechanics Michael D. Fayer Oxford University Press If you find errors in the book, please email them to fayer@stanford.edu. Last update: October 13, 2014 Chapter radial distribution, which shows the relative probability of finding a
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-01
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. PMID:26124252
New Trajectory Interpretation of Quantum Mechanics
P. R. Holland
1998-01-01
It was shown by de Broglie and Bohm that the concept of a deterministic particle trajectory is compatible with quantum mechanics. It is demonstrated by explicit construction that there exists another more general deterministic trajectory interpretation. The method exploits an internal angular degree of freedom that is implicit in the Schrödinger equation, in addition to the particle position. The de
WEAK MEASUREMENT IN QUANTUM MECHANICS ABRAHAM NEBEN
Rosner, Jonathan L.
WEAK MEASUREMENT IN QUANTUM MECHANICS ABRAHAM NEBEN PHYS 342 Final Project March 10, 2011 Contents of Postselection 4 4. Impossible Spin Measurements 5 5. Hardy's Paradox 5 6. Controversy over Weak Measurement 8 7 of a Measurement of a Component of the Spin of a Spin-1/2 Particle Can Turn Out to be 100." [1] The topic
Quantum Mechanical Effects in Gravitational Collapse
Eric Greenwood
2010-01-12
In this thesis we investigate quantum mechanical effects to various aspects of gravitational collapse. These quantum mechanical effects are implemented in the context of the Functional Schr\\"odinger formalism. The Functional Schr\\"odinger formalism allows us to investigate the time-dependent evolutions of the quantum mechanical effects, which is beyond the scope of the usual methods used to investigate the quantum mechanical corrections of gravitational collapse. Utilizing the time-dependent nature of the Functional Schr\\"odinger formalism, we study the quantization of a spherically symmetric domain wall from the view point of an asymptotic and infalling observer, in the absence of radiation. To build a more realistic picture, we then study the time-dependent nature of the induced radiation during the collapse using a semi-classical approach. Using the domain wall and the induced radiation, we then study the time-dependent evolution of the entropy of the domain wall. Finally we make some remarks about the possible inclusion of backreaction into the system.
Is Quantum Mechanics needed to explain consciousness ?
Knud Thomsen
2007-11-13
In this short comment to a recent contribution by E. Manousakis [1] it is argued that the reported agreement between the measured time evolution of conscious states during binocular rivalry and predictions derived from quantum mechanical formalisms does not require any direct effect of QM. The recursive consumption analysis process in the Ouroboros Model can yield the same behavior.
Conventions in relativity theory and quantum mechanics
Karl Svozil
2001-10-09
The conventionalistic aspects of physical world perception are reviewed with an emphasis on the constancy of the speed of light in relativity theory and the irreversibility of measurements in quantum mechanics. An appendix contains a complete proof of Alexandrov's theorem using mainly methods of affine geometry.
Quantum statistical mechanics over function fields
Caterina Consani; Matilde Marcolli
2007-01-01
In this paper we construct a noncommutative space of “pointed Drinfeld modules” that generalizes to the case of function fields the noncommutative spaces of commensurability classes of Q-lattices. It extends the usual moduli spaces of Drinfeld modules to possibly degenerate level structures. In the second part of the paper we develop some notions of quantum statistical mechanics in positive characteristic
QBism and Locality in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Nauenberg, Michael
2015-03-01
A critique to the article by C.A. Fuchs, N.D. Mermin, and R.Schack, "An introduction to QBism with and application to the locality of quantum mechanics" that appeared in Am. J. Phys. 82 (8), 749-754 (2014)
The geometric semantics of algebraic quantum mechanics
John Alex Cruz Morales; Boris Zilber
2014-10-27
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
Quantum reference systems: reconciling locality with quantum mechanics
Gyula Bene
2000-08-30
The status of locality in quantum mechanics is analyzed from a nonstandard point of view. It is assumed that quantum states are relative, they depend on and are defined with respect to some bigger physical system which contains the former system as a subsystem. Hence, the bigger system acts as a reference system. It is shown that quantum mechanics can be reformulated in accordance with this new physical assumption. There is an important consequence of this dependence: states may not be comparable, i.e., they cannot be checked by suitable measurements simultaneously. This special circumstance is fully reflected mathematically by the theory. Especially, it is shown that certain joint probabilities (or the corresponding combined events) which play a vital role in any proof of Bell's theorem do not exist. The conclusion is that the principle of locality is fully valid in quantum mechanics, and one has to give up instead of locality an intuitively natural-looking feature of realism, namely, the comparability of existing states.
Consistent interpretations of quantum mechanics
Omnes, R. )
1992-04-01
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.
Applications of density matrix in the fractional quantum mechanics
Jianping Dong
2010-12-22
The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, and obtain the quantum pressure of the free electron gas. We also show the validity of the Hohenberg-Kohn theory in the space fractional quantum mechanics and generalize the density functional theory to the fractional quantum mechanics.
Gravitational Mass, Its Mechanics - What It Is; How It Operates
Roger Ellman
2006-03-06
The earlier paper, Inertial Mass, Its Mechanics - What It Is; How It Operates, developed the mechanics of inertial mass. The present paper is for the purpose of equivalently developing gravitation. The behavior of gravitation is well known, as described by Newton's Law of Gravitation. But just what gravitational mass is, how gravitational behavior comes about, what in material reality produces the effects of gravitational mass, has been little understood. The only extant hypotheses involve the unsuccessful efforts to develop "quantum gravitation" and to tie it into the rest of quantum mechanics, and the equally failed attempts to detect "gravitons" and "gravitational waves" in spite of very substantial efforts. From a starting point of only the limitation on the speed of light, the necessity of conservation, and the impossibility of an infinity in material reality, the present paper presents a new and comprehensive analysis of the phenomenon gravitational mass: - how it appears in particles, - how the Newtonian gravitational behavior arises from that, and - how the values of inertial mass and gravitational mass are identical, or, in other words, the mechanics of gravitational mass and gravitation.
Morozov, Alexandre V.
Comparison of Quantum Mechanics and Molecular Mechanics Dimerization Energy Landscapes for Pairs, quantum mechanical calculations on small molecule models, and molecular mechanics potential decomposition find reasonable qualitative agreement between molecular mechanics and quantum chemistry calculations
Towards bringing Quantum Mechanics and General Relativity together
Elemer E Rosinger
2005-12-16
Two questions are suggested as having priority when trying to bring together Quantum Mechanics and General Relativity. Both questions have a scope which goes well beyond Physics, and in particular Quantum Mechanics and General Relativity.
Nano, Quantum, and Statistical Mechanics and Thermodynamics: Educational Sites
NSDL National Science Digital Library
This collection of links provides access to web sites associated with nano, quantum, and statistical mechanics and thermodynamics. The links are arranged by type: basic principles (including classical thermodynamics), nano, quantum, and statistical mechanics, mathematical techniques, applications, and references.
The emergent Copenhagen interpretation of quantum mechanics
NASA Astrophysics Data System (ADS)
Hollowood, Timothy J.
2014-05-01
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.
Web-based Quantum Mechanics II Course
NSDL National Science Digital Library
Breinig, Marianne
This web site, authored by Marianne Breinig, is an entire web-based Quantum Mechanics II Course based at the University of Tennessee. It has instructional materials, in-class tutorials, simulations, links to other quantum resources, a discussion forum, homework assignments, and solutions. A schedule and syllabus are also included for easier implementation into a curriculum. Most of the tools on the website require a browser of Internet Explorer 4 or higher to function. This is a nice set of resources for students or instructors interested in physics.
Quantum mechanical coherence, resonance, and mind
Stapp, H.P.
1995-03-26
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.
A Primer on Resonances in Quantum Mechanics
Rosas-Ortiz, Oscar; Fernandez-Garcia, Nicolas [Departamento de Fisica, Cinvestav, AP 14-740, 07000 Mexico DF (Mexico); Cruz y Cruz, Sara [Departamento de Fisica, Cinvestav, AP 14-740, 07000 Mexico DF (Mexico); Seccion de Estudios de Posgrado e Investigacion, UPIITA-IPN, Av IPN 2508, CP 07340, Mexico DF (Mexico)
2008-11-13
After a pedagogical introduction to the concept of resonance in classical and quantum mechanics, some interesting applications are discussed. The subject includes resonances occurring as one of the effects of radiative reaction, the resonances involved in the refraction of electromagnetic waves by a medium with a complex refractive index, and quantum decaying systems described in terms of resonant states of the energy (Gamow-Siegert functions). Some useful mathematical approaches like the Fourier transform, the complex scaling method and the Darboux transformation are also reviewed.
A necessary and sufficient condition to play games in quantum mechanical settings
Sahin Kaya Ozdemir; Junichi Shimamura; Nobuyuki Imoto
2007-03-01
Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum measurement. By transferring two-player-two strategy (2x2) dilemma containing classical games into quantum realm, dilemmas can be resolved in quantum pure strategies if entanglement is distributed between the players who use quantum operations. Moreover, players receive the highest sum of payoffs available in the game, which are otherwise impossible in classical pure strategies. Encouraged by the observation of rich dynamics of physical systems with many interacting parties and the power of entanglement in quantum versions of 2x2 games, it became generally accepted that quantum versions can be easily extended to N-player situations by simply allowing N-partite entangled states. In this article, however, we show that this is not generally true because the reproducibility of classical tasks in quantum domain imposes limitations on the type of entanglement and quantum operators. We propose a benchmark for the evaluation of quantum and classical versions of games, and derive the necessary and sufficient conditions for a physical realization. We give examples of entangled states that can and cannot be used, and the characteristics of quantum operators used as strategies.
Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics
Gerhard Groessing
2013-04-12
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder's group on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schr\\"odinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level. It is further demonstrated both analytically and with the aid of computer simulations that our model provides explanations for various quantum effects such as double-slit or n-slit interference. We show the averaged trajectories emerging from our model to be identical to Bohmian trajectories, albeit without the need to invoke complex wave functions or any other quantum mechanical tool. Finally, the model provides new insights into the origins of entanglement, and, in particular, into the phenomenon of a "systemic" nonlocality.
Emergence of quantum mechanics from a sub-quantum statistical mechanics
NASA Astrophysics Data System (ADS)
Grössing, Gerhard
2014-07-01
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level. It is further demonstrated both analytically and with the aid of computer simulations that our model provides explanations for various quantum effects such as double-slit or n-slit interference. We show the averaged trajectories emerging from our model to be identical to Bohmian trajectories, albeit without the need to invoke complex wavefunctions or any other quantum mechanical tool. Finally, the model provides new insights into the origins of entanglement, and, in particular, into the phenomenon of a "systemic" non-locality.
How to Teach the Postulates of Quantum Mechanics without Enigma.
ERIC Educational Resources Information Center
Teixeira-Dias, Jose J. C.
1983-01-01
Shows how a statistical approach can help students accept postulates of quantum mechanics. The approach, which also makes students aware of the philosophical/humanistic implications of quantum mechanics, involves the following sequence: (1) important experiments in quantum mechanics; (2) conventional statistical interpretation; (3) mathematical…
Bicomplex Quantum Mechanics: I. The Generalized Schrodinger Equation
Rochon, Dominic
Bicomplex Quantum Mechanics: I. The Generalized SchrÂ¨odinger Equation D. Rochon1 and S. Tremblay2 D) #12;232 Bicomplex Quantum Mechanics: I. The Generalized ... D. Rochon & S. Tremblay Â· i0 i1 i2 j i0 i0 are commutative with some non-invertible elements situated on the "null cone". The extension of quantum mechanics
A Factor-Graph Representation of Probabilities in Quantum Mechanics
Loeliger, Hans-Andrea
A Factor-Graph Representation of Probabilities in Quantum Mechanics Hans-Andrea Loeliger ETH Zurich for statistical inference. So far, however, quantum mechanics (e.g., [8], [9]) has been standing apart. Despite categories. Indeed, it has often been emphasized that quantum mechanics is a generalization of probability
Noncommutative Quantum Mechanics on a Curved Space
M. Nakamura
2015-03-23
Starting with the first-order singular Lagrangian, the canonical structures of the noncommutative quantum system on a submanifold embedded in the higher-dimensional Euclidean space are investigated with the projection operator method (POM) and the Dirac-bracket formulation in the case of the derivative-type constraint. Using the successive projection procedure and the iterativity of the Dirac bracket, the noncommutative quantum system is constructed in the form including all orders of the noncommutativity-parameters. When the noncommutative quantum system is constrained to a curved space, the commutator algebra of the system is presented within the 1st-order approximation with respect to Dirac-const. and the noncommutativity-parameters.
Attosecond delays in photoionization: time and quantum mechanics
NASA Astrophysics Data System (ADS)
Maquet, Alfred; Caillat, Jérémie; Taïeb, Richard
2014-10-01
This article addresses topics regarding time measurements performed on quantum systems. The motivation is linked to the advent of ‘attophysics’ which makes feasible to follow the motion of electrons in atoms and molecules, with time resolution at the attosecond (1 as = 10?18 s) level, i.e. at the natural scale for electronic processes in these systems. In this context, attosecond ‘time-delays’ have been recently measured in experiments on photoionization and the question arises if such advances could cast a new light on the still active discussion on the status of the time variable in quantum mechanics. One issue still debatable is how to decide whether one can define a quantum time operator with eigenvalues associated to measurable ‘time-delays’, or time is a parameter, as it is implicit in the Newtonian classical mechanics. One objective of this paper is to investigate if the recent attophysics-based measurements could shed light on this parameter–operator conundrum. To this end, we present here the main features of the theory background, followed by an analysis of the experimental schemes that have been used to evidence attosecond ‘time-delays’ in photoionization. Our conclusion is that these results reinforce the view that time is a parameter which cannot be defined without reference to classical mechanics.
Semantics for a Quantum Programming Language by Operator Algebras
Kenta Cho
2014-12-30
This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces. We show that the opposite category of the category of W*-algebras and normal completely positive subunital maps is an elementary quantum flow chart category in the sense of Selinger. As a consequence, it gives a denotational semantics for Selinger's first-order functional quantum programming language QPL. The use of operator algebras allows us to accommodate infinite structures and to handle classical and quantum computations in a unified way.
A Study of Modifications to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Lewis, Zachary E.
In this work, the consequences of several modifications to quantum mechanics are examined. These modifications, motivated by string theory, fall into two categories: ones in which the canonical commutation relations between position and momentum are deformed and ones in which the space of states used are vector spaces over Galois fields instead of complex Hilbert spaces. The particular deformation of the canonical commutation relations used leads to a minimum value of the uncertainty in position which is interpreted as a minimum length scale. Both harmonic and anharmonic oscillators are studied in this framework with normalizable, positive energy eigenstates found in both cases. The quantum uncertainty relations and classical counterparts to these states are discussed. Creating modified quantum theories by replacing the Hilbert spaces of canonical quantum mechanics with vector spaces defined over several finite, Galois fields is accomplished. Correlation functions are calculated in these theories and the maximum values are shown to not behave as would be expected by the standard, Bell-like, bounding inequality theorems. The interpretations and implications of these theories are discussed.
Does quantum mechanics require non-locality?
Ghenadie N. Mardari
2014-10-29
Non-commutative properties of single quanta must violate the limit of Bell's theorem, but not the boundary of Tsirelson's theorem. This is a consequence of three basic principles: superposition (every quantum is in many states at the same time), correspondence (only the net state of interference is real), and uncertainty (conjugate variables have inversely proportional spectra). The two conditions have only been verified with entangled pairs of quanta. It is not possible to perform incompatible measurements on the same entity. Hence, the principles of quantum mechanics cannot be verified directly. At least one of them could be wrong. Though, as shown by EPR, this can only be true if non-locality is at work. In light of the latest developments in quantum theory, even that assumption is insufficient. Non-local effects are either unable to cross Bell's limit, or forced to violate Tsirelson's bound. New layers of hidden variables are required to maintain belief in action-at-a-distance, but the three principles cannot be rejected in any case. Therefore, quantum mechanics is immune to this challenge. The hypothesis of non-locality is superfluous.
Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime
Marco Cariglia
2003-12-21
In spacetimes admitting Yano tensors the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank two, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors.
Representations for a spins-first approach to quantum mechanics
NASA Astrophysics Data System (ADS)
Manogue, Corinne; Gire, Elizabeth; McIntyre, David; Tate, Janet
2012-02-01
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.
Quantum canonical ensemble: a projection operator approach
Wim Magnus; Fons Brosens
2015-05-19
Fixing the number of particles $N$, the quantum canonical ensemble imposes a constraint on the occupation numbers of single-particle states. The constraint particularly hampers the systematic calculation of the partition function and any relevant thermodynamic expectation value for arbitrary $N$ since, unlike the case of the grand-canonical ensemble, traces in the $N$-particle Hilbert space fail to factorize into simple traces over single-particle states. In this paper we introduce a projection operator that enables a constraint-free computation of the partition function and its derived quantities, at the price of an angular or contour integration. Being applicable to both bosonic and fermionic non-interacting systems in arbitrary dimensions, the projection operator approach provides closed-form expressions for the partition function $Z_N$ and the Helmholtz free energy $F_{\\! N}$ as well as for two- and four-point correlation functions. While appearing only as a secondary quantity in the present context, the chemical potential potential emerges as a by-product from the relation $\\mu_N = F_{\\! N+1} - F_{\\! N}$, as illustrated for a two-dimensional fermion gas with $N$ ranging between 2 and 500.
Quantum mechanics on phase space and teleportation
NASA Astrophysics Data System (ADS)
Messamah, Juba; Schroeck, Franklin E.; Hachemane, Mahmoud; Smida, Abdallah; Hamici, Amel H.
2015-03-01
The formalism of quantum mechanics on phase space is used to describe the standard protocol of quantum teleportation with continuous variables in order to partially investigate the interplay between this formalism and quantum information. Instead of the Wigner quasi-probability distributions used in the standard protocol, we use positive definite true probability densities which account for unsharp measurements through a proper wave function representing a non-ideal quantum measuring device. This is based on a result of Schroeck and may be taken on any relativistic or nonrelativistic phase space. The obtained formula is similar to a known formula in quantum optics, but contains the effect of the measuring device. It has been applied in three cases. In the first case, the two measuring devices, corresponding to the two entangled parts shared by Alice and Bob, are not entangled and described by two identical Gaussian wave functions with respect to the Heisenberg group. They lead to a probability density identical to the function which is analyzed and compared with the Wigner formalism. A new expression of the teleportation fidelity for a coherent state in terms of the quadrature variances is obtained. In the second case, these two measuring devices are entangled in a two-mode squeezed vacuum state. In the third case, two Gaussian states are combined in an entangled squeezed state. The overall observation is that the state of the measuring devices shared by Alice and Bob influences the fidelity of teleportation through their unsharpness and entanglement.
A Foundation Theory Of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Mould, Richard A.
2006-06-01
The nRules are empirical regularities that were discovered in macroscopic situations where the outcome is known. When they are projected theoretically into the microscopic domain they predict a novel ontology including the frequent collapse of an atomic wave function, thereby defining an nRule based foundation theory. Future experiments can potentially discriminate between this and other foundation theories of (non-relativistic) quantum mechanics. Important features of the nRules are: (1) they introduce probability through probability current rather than the Born rule, (2) they are valid independent of size (micro or macroscopic), (3) they apply to individual trials as well as to ensembles of trials. (4) they allow all observers to be continuously included in the system without ambiguity, (5) they account for the collapse of the wave function without introducing new or using old physical constants, and (6) in dense environments they provide a high frequency of stochastic localizations of quantum mechanical objects.
Fast method for quantum mechanical molecular dynamics
Niklasson, Anders M N
2012-01-01
With the continuous growth of processing power for scientific computing, first principles Born-Oppenheimer molecular dynamics (MD) simulations are becoming increasingly popular for the study of a wide range of problems in materials science, chemistry and biology. Nevertheless, the computational cost still remains prohibitively large in many cases, particularly in comparison to classical MD simulations using empirical force fields. Here we show how to circumvent the major computational bottleneck in Born-Oppenheimer MD simulations arising from the self-consistent-charge optimization. The optimization-free quantum mechanical MD method is demonstrated for density functional tight-binding theory. The molecular trajectories are almost indistinguishable from an "exact" microcanonical Born-Oppenheimer MD simulation even when linear scaling sparse matrix algebra is used. Our findings drastically reduce the computational gap between classical and quantum mechanical MD simulations.
Quantum Mechanics, Gravity, and the Multiverse
Yasunori Nomura
2012-07-30
The discovery of accelerating expansion of the universe has led us to take the dramatic view that our universe may be one of the many universes in which low energy physical laws take different forms: the multiverse. I explain why/how this view is supported both observationally and theoretically, especially by string theory and eternal inflation. I then describe how quantum mechanics plays a crucial role in understanding the multiverse, even at the largest distance scales. The resulting picture leads to a revolutionary change of our view of spacetime and gravity, and completely unifies the paradigm of the eternally inflating multiverse with the many worlds interpretation of quantum mechanics. The picture also provides a solution to a long-standing problem in eternal inflation, called the measure problem, which I briefly describe.
Quantum Mechanics, Gravity, and the Multiverse
Nomura, Yasunori
2012-01-01
The discovery of accelerating expansion of the universe has led us to take the dramatic view that our universe may be one of the many universes in which low energy physical laws take different forms: the multiverse. I explain why/how this view is supported both observationally and theoretically, especially by string theory and eternal inflation. I then describe how quantum mechanics plays a crucial role in understanding the multiverse, even at the largest distance scales. The resulting picture leads to a revolutionary change of our view of spacetime and gravity, and completely unifies the paradigm of the eternally inflating multiverse with the many worlds interpretation of quantum mechanics. The picture also provides a solution to a long-standing problem in eternal inflation, called the measure problem, which I briefly describe.
Quantum Mechanics, Gravity, and the Multiverse
NASA Astrophysics Data System (ADS)
Nomura, Yasunori
2012-04-01
The discovery of accelerating expansion of the universe has led us to take the dramatic view that our universe may be one of the many universes in which low energy physical laws take different forms: the multiverse. I explain why/how this view is supported both observationally and theoretically, especially by string theory and eternal inflation. I then describe how quantum mechanics plays a crucial role in understanding the multiverse, even at the largest distance scales. The resulting picture leads to a revolutionary change of our view of spacetime and gravity, and completely unifies the paradigm of the eternally inflating multiverse with the many worlds interpretation of quantum mechanics. The picture also provides a solution to a long-standing problem in eternal inflation, called the measure problem, which I briefly describe.
Beyond relativity and quantum mechanics: space physics
NASA Astrophysics Data System (ADS)
Lindner, Henry H.
2011-09-01
Albert Einstein imposed an observer-based epistemology upon physics. Relativity and Quantum Mechanics limit physics to describing and modeling the observer's sensations and measurements. Their "underlying reality" consists only of ideas that serve to model the observer's experience. These positivistic models cannot be used to form physical theories of Cosmic phenomena. To do this, we must again remove the observer from the center of physics. When we relate motion to Cosmic space instead of to observers and we attempt to explain the causes of Cosmic phenomena, we are forced to admit that Cosmic space is a substance. We need a new physics of space. We can begin by replacing Relativity with a modified Lorentzian-Newtonian model of spatial flow, and Quantum Mechanics with a wave-based theory of light and electrons. Space physics will require the reinterpretation of all known phenomena, concepts, and mathematical models.
The preparation of states in quantum mechanics
Juerg Froehlich; Baptiste Schubnel
2014-09-28
The important problem of how to prepare a quantum mechanical system, $S$, in a specific initial state of interest - e.g., for the purposes of some experiment - is addressed. Three distinct methods of state preparation are described. One of these methods has the attractive feature that it enables one to prepare $S$ in a preassigned initial state with certainty; i.e., the probability of success in preparing $S$ in a given state is unity. This method relies on coupling $S$ to an open quantum-mechanical environment, $E$, in such a way that the dynamics of $S \\vee E$ pulls the state of $S$ towards an "attractor", which is the desired initial state of $S$. This method is analyzed in detail.
On the consistent effect histories approach to quantum mechanics
NASA Astrophysics Data System (ADS)
Rudolph, Oliver
1996-11-01
A formulation of the consistent histories approach to quantum mechanics in terms of generalized observables (POV measures) and effect operators is provided. The usual notion of ``history'' is generalized to the notion of ``effect history.'' The space of effect histories carries the structure of a D-poset. Recent results of J. D. Maitland Wright imply that every decoherence functional defined for ordinary histories can be uniquely extended to a bi-additive decoherence functional on the space of effect histories. Omnès' logical interpretation is generalized to the present context. The result of this work considerably generalizes and simplifies the earlier formulation of the consistent effect histories approach to quantum mechanics communicated in a previous work of this author.
On the consistent effect histories approach to quantum mechanics
Rudolph, O.
1996-11-01
A formulation of the consistent histories approach to quantum mechanics in terms of generalized observables (POV measures) and effect operators is provided. The usual notion of {open_quote}{open_quote}history{close_quote}{close_quote} is generalized to the notion of {open_quote}{open_quote}effect history.{close_quote}{close_quote} The space of effect histories carries the structure of a {ital D}-poset. Recent results of J. D. Maitland Wright imply that every decoherence functional defined for ordinary histories can be uniquely extended to a bi-additive decoherence functional on the space of effect histories. Omn{grave e}s{close_quote} logical interpretation is generalized to the present context. The result of this work considerably generalizes and simplifies the earlier formulation of the consistent effect histories approach to quantum mechanics communicated in a previous work of this author. {copyright} {ital 1996 American Institute of Physics.}
Microscopic models of quantum jump super-operators
A. V. Dodonov; S. S. Mizrahi; V. V. Dodonov
2007-02-02
We discuss the quantum jump operation in an open system, and show that jump super-operators related to a system under measurement can be derived from the interaction of that system with a quantum measurement apparatus. We give two examples for the interaction of a monochromatic electromagnetic field in a cavity (the system) with 2-level atoms and with a harmonic oscillator (representing two different kinds of detectors). We show that derived quantum jump super-operators have `nonlinear' form which depends on assumptions made about the interaction between the system and the detector. A continuous transition to the standard Srinivas--Davies form of the quantum jump super-operatoris shown.
Hidden variables and nonlocality in quantum mechanics
NASA Astrophysics Data System (ADS)
Hemmick, Douglas Lloyd
1997-05-01
Most physicists hold a skeptical attitude toward a 'hidden variables' interpretation of quantum theory, despite David Bohm's successful construction of such a theory and John S. Bell's strong arguments in favor of the idea. The first reason for doubt concerns certain mathematical theorems (von Neumann's, Gleason's, Kochen and Specker's, and Bell's) which can be applied to the hidden variables issue. These theorems are often credited with proving that hidden variables are indeed 'impossible', in the sense that they cannot replicate the predictions of quantum mechanics. Many who do not draw such a strong conclusion nevertheless accept that hidden variables have been shown to exhibit prohibitively complicated features. The second concern is that the most sophisticated example of a hidden variables theory-that of David Bohm-exhibits non-locality, i.e., consequences of events at one place can propagate to other places instantaneously. However, neither the mathematical theorems in question nor the attribute of nonlocality detract from the importance of a hidden variables interpretation of quantum theory. Nonlocality is present in quantum mechanics itself, and is a required characteristic of any theory that agrees with the quantum mechanical predictions. We first discuss the earliest analysis of hidden variables-that of von Neumann's theorem-and review John S. Bell's refutation of von Neumann's 'impossibility proof'. We recall and elaborate on Bell's arguments regarding the theorems of Gleason, and Kochen and Specker. According to Bell, these latter theorems do not imply that hidden variables interpretations are untenable, but instead that such theories must exhibit contextuality, i.e., they must allow for the dependence of measurement results on the characteristics of both measured system and measuring apparatus. We demonstrate a new way to understand the implications of both Gleason's theorem and Kochen and Specker's theorem by noting that they prove a result we call 'spectral incompatibility'. We develop further insight into the concepts involved in these two theorems by investigating a special quantum mechanical experiment first described by David Albert. We review the Einstein-Podolsky-Rosen paradox, Bell's theorem, and Bell's later argument that these imply that quantum mechanics is irreducibly nonlocal. The paradox of Einstein, Podolsky, and Rosen was generalized by Erwin Schrodinger in the same paper where his famous 'cat paradox' appeared. We show that Schrodinger's conclusions can be derived using a simpler argument-one which makes clear the relationship between the quantum state and the 'perfect correlations' exhibited by the system. We use Schrodinger's EPR analysis to derive a wide variety of new quantum nonlocality proofs. These proofs share two important features with that of Greenberger, Horne, and Zeilinger. First, they are of a deterministic character, i.e., they are 'nonlocality without inequalities' proofs. Second, the quantum nonlocality results we develop may be experimentally verified so that one need only observe the 'perfect correlations' between the appropriate observables. This latter feature serves to contrast these proofs with EPR/Bell nonlocality, the laboratory confirmation of which demands not only the observation of perfect correlations, but also the observations required to test whether 'Bell's inequality' is violated. The 'Schrodinger nonlocality' proofs we give differ from the GHZ proof in that they apply to two-component composite systems, while the latter involves a composite system of at least three-components. In addition, some of the Schrodinger proofs involve classes of observables larger than that addressed in the GHZ proof. (Abstract shortened by UMI.)
Covariant quantum mechanics applied to noncommutative geometry
NASA Astrophysics Data System (ADS)
Astuti, Valerio
2015-08-01
We here report a result obtained in collaboration with Giovanni Amelino-Camelia, first shown in the paper [1]. Applying the manifestly covariant formalism of quantum mechanics to the much studied Snyder spacetime [2] we show how it is trivial in every physical observables, this meaning that every measure in this spacetime gives the same results that would be obtained in the flat Minkowski spacetime.
A tossed coin as quantum mechanical object
Alexander M. Soiguine
2014-08-28
Comprehensive and physically consistent model of a tossed coin is presented in terms of geometric algebra. The model clearly shows that there is nothing elementary particle specific in the half-spin quantum mechanical formalism. It also demonstrates what really is behind this formalism, feasibly reveals the probabilistic meaning of wave function and shows that arithmetic of packed objects, namely wave functions and Pauli matrices, reduces the amount of available information.
Chiral quantum mechanics (CQM) for antihydrogen systems
G. Van Hooydonk
2005-12-03
A first deception of QM on antiH already appears in one-center integrals for two-center systems (G. Van Hooydonk, physics/0511115). In reality, full QM is a theory for chiral systems but the QM establishment was wrong footed with a permutation of reference frames. With chiral quantum mechanics (CQM), the theoretical ban on natural antiH must be lifted as soon as possible.
Modern Quantum Mechanics Experiments for Undergraduates
NSDL National Science Digital Library
Beck, Mark
Authored by Mark Beck of Whitman College's Department of Physics, this site provides information about simplified quantum mechanics experiments such as the Grangier experiment and single photon interference. Included are a general description, an overview, course materials, experiments, external links and notes. Each experiment or lesson provides instructions and other need information such as images, charts or graphs. This series of resources could be used to enhance or create curricula in the field.
Collocation method for fractional quantum mechanics
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
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.
Physical Interpretations of Nilpotent Quantum Mechanics
Peter Rowlands
2010-04-09
Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit construction of vacuum. Physical interpretation of the nilpotent formalism is discussed with respect to boson and baryon structures, the mass-gap problem, zitterbewgung, Berry phase, renormalization, and related issues.
Hierarchy of temporal correlations in quantum mechanics
Shiladitya Mal; Archan S. Majumdar; Dipankar Home
2015-10-02
Temporal steering and violation of the Leggett-Garg inequality are two different ways of probing the violation of macro-realistic assumptions in quantum mechanics. It is shown here that under unitary evolution and projective measurements the two types of temporal correlations lead to similar results. However, their inequivalence is exhibited by formulating a task of secure key generation with different levels of trust on the devices. We further demonstrate the hierarchy between them by employing either generalized measurements, or noisy evolution.
Accessing quantum secrets via local operations and classical communication
Vlad Gheorghiu; Barry C. Sanders
2013-08-30
Quantum secret-sharing and quantum error-correction schemes rely on multipartite decoding protocols, yet the non-local operations involved are challenging and sometimes infeasible. Here we construct a quantum secret-sharing protocol with a reduced number of quantum communication channels between the players. Our scheme is based on embedding a classical linear code into a quantum error-correcting code. Our work paves the way towards the more general problem of simplifying the decoding of quantum error-correcting codes.
The Optimal Cloner for Mixed States as a Quantum Operation
NASA Astrophysics Data System (ADS)
Gardiner, John G.; van Huele, Jean-Francois S.
2012-10-01
The no-cloning theorem in quantum information says that it is impossible to produce two copies of an arbitrary quantum state. This precludes the possibility of a perfect universal quantum cloner, a process that could copy any quantum state perfectly. It is possible, however, to find optimal approximations of such a cloner. Using the formalism of quantum operations we obtain the optimal quantum cloner for arbitrary mixed states of a given purity and find that it is equivalent to the Buzek-Hillery optimal cloner for pure states. We also find the fidelity of this cloner as a function of the chosen purity.
Hunting for Snarks in Quantum Mechanics
Hestenes, David
2009-12-08
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}.
Failure of Standard Quantum Mechanics for the Description of Compound Quantum Entities
Aerts, Diederik
Failure of Standard Quantum Mechanics for the Description of Compound Quantum Entities Diederik for the description of compound quantum entities. International Journal of Theoretical Physics, 43, pp. 251264 1 #12
Hybrid protocol of remote implementations of quantum operations
Ning Bo Zhao; An Min Wang
2007-08-04
We propose a protocol of remote implementations of quantum operations by hybridizing bidirectional quantum state teleportation's (BQST) and Wang's one. The protocol is available for remote implemetations of quantum operations in the restricted sets specified in Sec. III. We also give the proof of the protocol and point out its optimization. As an extension, this hybrid protocol can be reduced to BQST and Wang protocols.
Classical-Operation-Based Deterministic Secure Quantum Communication
NASA Astrophysics Data System (ADS)
Liu, Zhi-Hao; Chen, Han-Wu; Wang, Dong; Xue, Xi-Ling
2014-06-01
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.
Bohmian mechanics in relativistic quantum mechanics, quantum field theory and string theory
H. Nikolic
2006-10-12
I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle trajectories, the problem of particle creation and destruction, the Bohmian interpretation of fermionic fields and the intrinsically Bohmian quantization of fields and strings based on the De Donder-Weyl covariant canonical formalism.
Quantum Mechanical Insights into Biological Processes at the Electronic Level
NASA Astrophysics Data System (ADS)
Alexandrova, Anastassia N.
The realm of biology is always governed by underlying electronic effects. These effects are often treated implicitly and may go nearly unnoticed in classical biomolecular simulations, such as Monte Carlo or molecular dynamics. It is important to remember, however, that these classical methods always operate on the single, ground electronic potential energy surface (PES). Furthermore, classical methods assume the classical behavior of the atomic nuclei, and thus rely on the so-called Born-Oppenheimer approximation (BAO) heavily used in quantum mechanics, as discussed in detail below. Due to the BAO, the ground PES can be obtained by finding the optimal electronic solution for every position of stationary classical nuclei. The combined electronic and nuclear energy as a function of nuclear coordinates in the PES. The Born-Oppenheimer PES is usually very close to the chemical reality. Parameters of classical force fields are optimized to reproduce this ground PES, either calculated quantum mechanically or derived from the experiment. Thus, electronic structure is always an active player in classical simulations through the parameters of the force field in use. However, when it comes to the assessment of the mechanism of a biochemical reaction that involves breaking and forming of covalent bonds, quantum mechanics is an almost exclusive reliable approach, with a prominent classical exception being the empirical valence bond method. Furthermore, there is a large class of biological processes that simply cannot be assessed without explicit quantum mechanical treatment. An obvious example is electron transfer in enzymes or DNA that plays a pivotal role in every oxidation or reduction event in living cells.
Bhomian Mechanics vs. Standard Quantum Mechanics: a Difference in Experimental Predictions
Artur Szczepanski
2010-02-08
Standard Quantum Mechanics (QM) predicts an anti-intuitive fenomenon here referred to as "quantum autoscattering", which is excluded by Bhomian Mechanics. The scheme of a gedanken experiment testing the QM prediction is briefly discussed.
To Principles of Quantum Mechanics Development
Dmitri Yerchuck; Alla Dovlatova; Felix Borovik; Yauhen Yerchak; Vyacheslav Stelmakh
2014-07-15
New insight to the principles of the quantum physics development is given. The correct ways for the construction of new versions of quantum mechanics on the second main postulate base are discussed. The conclusion on the status of the second main postulate is given. Its formulation in all textbooks has to be represented in the form of statement, since the hypothesis of Schr\\"odinger on the existance of the field scalar function, being to be observable quantity, just charge density, is strictly proved for the case of EM-field, the role of which is argued to be decisive for the dynamics of the atomic systems. It is shown, that the field scalar function, being to be the function the only of coordinates and time, actually describes the state of the system. The second main postulate in Schr\\"odinger formulation is mathematically strictly grounded, but in the popular probabilistic form used in modern textbooks on quantum theory it cannot be proved. The probabilistic theatise, proposed by Born is true in a number of special cases, quite correctly indicated by Dirac. The possible ways of the development of quantum theory, based on clear understanding of the origin of corpuscular-wave dualism are analysed.
Quantum mechanics with coordinate dependent noncommutativity
Kupriyanov, V. G.
2013-11-15
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.
Enhancing quantum correlation in open-system dynamics by reliable quantum operations
NASA Astrophysics Data System (ADS)
Shi, Jia Dong; Wang, Dong; Ma, Wen Chao; Ye, Liu
2015-06-01
We investigate the decoherence to generate quantum discord between two separable qubits of an unentangled mixed state and propose a series of feasible schemes to enhance quantum discord by means of reliable quantum operations. By combing our schemes with the previous proposal, one can note that the generated quantum discord can be greatly enhanced. Moreover, our success probability entirely depends on the quantum measurement strength.