Operational Axioms for Quantum Mechanics Giacomo Mauro D'Ariano
D'Ariano, Giacomo Mauro
Operational Axioms for Quantum Mechanics Giacomo Mauro D'Ariano QUIT Group, Dipartimento di Fisica formulation of Quantum Mechanics in terms of complex Hilbert space is derived for finite dimensions, starting: 03.65.-w 1. INTRODUCTION Quantum Mechanics has been universally accepted as a general law of nature
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.
Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2015-01-01
One examines putative corrections to the Bell operator due to the noncommutativity in the phase-space. Starting from a Gaussian squeezed envelop whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics respectively, one concludes that, although the time evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations, noncommutativity versions of quantum mechnics remains as non-local as quantum mechanics itself.
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.
Deformed quantum mechanics and q-Hermitian operators
A. Lavagno
2008-08-14
Starting on the basis of the non-commutative q-differential calculus, we introduce a generalized q-deformed Schr\\"odinger equation. It can be viewed as the quantum stochastic counterpart of a generalized classical kinetic equation, which reproduces at the equilibrium the well-known q-deformed exponential stationary distribution. In this framework, q-deformed adjoint of an operator and q-hermitian operator properties occur in a natural way in order to satisfy the basic quantum mechanics assumptions.
NASA Astrophysics Data System (ADS)
Song, Jun; Zhou, Jun; Fan, Hong-Yi
2013-10-01
We study Hankel transformation of the induced entangled state representation by quantum mechanical operator algebraic method, the derivatives of functions and their ascending and lowering operators—studied by quantum mechanical operator algebraic method of the derivatives of functions.
Exact Heisenberg operator solutions for multi-particle quantum mechanics
Satoru Odake; Ryu Sasaki
2007-06-06
Exact Heisenberg operator solutions for independent `sinusoidal coordinates' as many as the degree of freedom are derived for typical exactly solvable multi-particle quantum mechanical systems, the Calogero systems based on any root system. These Heisenberg operator solutions also present the explicit forms of the annihilation-creation operators for various quanta in the interacting multi-particle systems. At the same time they can be interpreted as multi-variable generalisation of the three term recursion relations for multi-variable orthogonal polynomials constituting the eigenfunctions.
Exact Heisenberg operator solutions for multi-particle quantum mechanics
Odake, Satoru
2007-01-01
Exact Heisenberg operator solutions for independent `sinusoidal coordinates' as many as the degree of freedom are derived for typical exactly solvable multi-particle quantum mechanical systems, the Calogero systems based on any root system. These Heisenberg operator solutions also present the explicit forms of the annihilation-creation operators for various quanta in the interacting multi-particle systems. At the same time they can be interpreted as multi-variable generalisation of the three term recursion relations for multi-variable orthogonal polynomials constituting the eigenfunctions.
Exact Heisenberg operator solutions for multiparticle quantum mechanics
NASA Astrophysics Data System (ADS)
Odake, Satoru; Sasaki, Ryu
2007-08-01
Exact Heisenberg operator solutions for independent "sinusoidal coordinates" as many as the degree of freedom are derived for typical exactly solvable multiparticle quantum mechanical systems, the Calogero systems [J. Math. Phys. 12, 419 (1971)] based on any root system. These Heisenberg operator solutions also present the explicit forms of the annihilation-creation operators for various quanta in the interacting multiparticle systems. At the same time they can be interpreted as multivariable generalization of the three term recurrence relations for multivariable orthogonal polynomials constituting the eigenfunctions.
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.
Isometric operators, isospectral Hamiltonians, and supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Pursey, D. L.
1986-04-01
Isometric operators are used to provide a unified theory of the three established procedures for generating one-parameter families of isospectral Hamiltonians. All members of the same family of isospectral Hamiltonians are unitarily equivalent, and the unitary transformations between them form a group isomorphic with the additive group of real numbers. The theory is generalized by including the parameter identifying a member of an isospectral family as a new variable. The unitary transformations within a family correspond to translations in the parameter space. The generator of infinitesimal translations represents a conserved quantity in the extended theory. Isometric operators are then applied to the development of models of supersymmetric quantum mechanics. In addition to the standard models based on the Darboux procedure, I show how to construct models based on the Abraham-Moses and Pursey procedures. The formalism shows that the Nieto ambiguity present in all models of supersymmetric quantum mechanics can be interpreted as a renormalization of the ground state of the supersymmetric system. This allows a generalization of supersymmetric quantum mechanics analogous to that developed for systems of isospectral Hamiltonians.
Duality, Mechanical Wave Theory, New Quantum Operators and Nonlinear Equations in Quantum Theory
Yi-Fang Chang
2010-08-17
Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various mechanical equations, and may be derive some new results. It is called the mechanical wave theory. From this we derive new operators which represent more physical quantities. Further, we propose some nonlinear equations and their solutions, which may be probably applied to quantum theory.
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.
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…
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.
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'
Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics
Satoru Odake; Ryu Sasaki
2006-05-25
The annihilation-creation operators $a^{(\\pm)}$ are defined as the positive/negative frequency parts of the exact Heisenberg operator solution for the `sinusoidal coordinate'. Thus $a^{(\\pm)}$ are hermitian conjugate to each other and the relative weights of various terms in them are solely determined by the energy spectrum. This unified method applies to most of the solvable quantum mechanics of single degree of freedom including those belonging to the `discrete' quantum mechanics.
Unified theory of annihilation-creation operators for solvable ('discrete') quantum mechanics
Odake, Satoru; Sasaki, Ryu
2006-10-15
The annihilation-creation operators a{sup ({+-})} are defined as the positive/negative frequency parts of the exact Heisenberg operator solution for the 'sinusoidal coordinate'. Thus a{sup ({+-})} are hermitian conjugate to each other and the relative weights of various terms in them are solely determined by the energy spectrum. This unified method applies to most of the solvable quantum mechanics of single degree of freedom including those belonging to the 'discrete' quantum mechanics.
Unified theory of annihilation-creation operators for solvable (``discrete'') quantum mechanics
NASA Astrophysics Data System (ADS)
Odake, Satoru; Sasaki, Ryu
2006-10-01
The annihilation-creation operators a(±) are defined as the positive/negative frequency parts of the exact Heisenberg operator solution for the "sinusoidal coordinate". Thus a(±) are hermitian conjugate to each other and the relative weights of various terms in them are solely determined by the energy spectrum. This unified method applies to most of the solvable quantum mechanics of single degree of freedom including those belonging to the "discrete" quantum mechanics.
Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics
Odake, S; Odake, Satoru; Sasaki, Ryu
2006-01-01
The annihilation-creation operators $a^{(\\pm)}$ are defined as the positive/negative frequency parts of the exact Heisenberg operator solution for the `sinusoidal coordinate'. Thus $a^{(\\pm)}$ are hermitian conjugate to each other and the relative weights of various terms in them are solely determined by the energy spectrum. This unified method applies to most of the solvable quantum mechanics of single degree of freedom including those belonging to the `discrete' quantum mechanics.
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)
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.
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)
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
Costa, Bruno G. da
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…
Annihilation and creation operators in non-Hermitian supersymmetric quantum mechanics
Znojil, M
2000-01-01
Harmonic oscillators with a centrifugal spike are analysed, via a non-Hermitian regularization, within a complexified SUSY quantum mechanics. The formalism enables us to construct the factorized creation and annihilation operators. We show how the real though, generically, non-equidistant spectrum complies with the current SUSY-type isospectrality and degeneracy in an unusual way.
Annihilation and creation operators in non-Hermitian supersymmetric quantum mechanics
Miloslav Znojil
2001-04-15
Harmonic oscillators with a centrifugal spike are analysed, via a non-Hermitian regularization, within a complexified SUSY quantum mechanics. The formalism enables us to construct the factorized creation and annihilation operators. We show how the real though, generically, non-equidistant spectrum complies with the current SUSY-type isospectrality and degeneracy in an unusual way.
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).
Satoru Odake; Ryu Sasaki
2008-02-07
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.
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.
NASA Astrophysics Data System (ADS)
Odake, S.; Sasaki, R.
2008-04-01
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 Schrödinger equation. Various reductions (restrictions) of the symmetry algebra of the Askey-Wilson system are explored in detail.
Testing Nonassociative Quantum Mechanics
NASA Astrophysics Data System (ADS)
Bojowald, Martin; Brahma, Suddhasattwa; Büyükçam, Umut
2015-11-01
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to nonassociative algebras. Their quantum physics has remained obscure. This Letter presents the first derivation of potentially testable physical results in nonassociative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.
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)].
Natural star-products on symplectic manifolds and related quantum mechanical operators
Maciej Blaszak; Ziemowit Domanski
2013-11-13
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.
NASA Astrophysics Data System (ADS)
Fan, Hong-Yi; Yuan, Hong-Chun
2010-07-01
As a natural and important extension of Fan's paper (Fan Hong-Yi 2010 Chin. Phys. B 19 040305) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation this paper finds a new two-fold complex integration transformation about the Wigner operator ? (?, ?) (in its entangled form) in phase space quantum mechanics, and its inverse transformation. In this way, some operator ordering problems regarding to (a†1 - a2) and (a†1 - a2) can be solved and the contents of phase space quantum mechanics can be enriched, where ai, a†i are bosonic creation and annihilation operators, respectively.
Natural star-products on symplectic manifolds and related quantum mechanical operators
B?aszak, Maciej Doma?ski, Ziemowit
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
Fan Hongyi; Lu Hailiang . E-mail: luhailiang@sjtu.edu.cn; Fan Yue
2006-02-15
Newton-Leibniz integration rule only applies to commuting functions of continuum variables, while operators made of Dirac's symbols (ket versus bra, e.g., |q>quantum mechanics are usually not commutative. Therefore, integrations over the operators of type |><| cannot be directly performed by Newton-Leibniz rule. We invented an innovative technique of integration within an ordered product (IWOP) of operators that made the integration of non-commutative operators possible. The IWOP technique thus bridges this mathematical gap between classical mechanics and quantum mechanics, and further reveals the beauty and elegance of Dirac's symbolic method and transformation theory. Various applications of the IWOP technique, including constructing the entangled state representations and their applications, are presented.
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
J. LaChapelle
2015-08-10
We propose $Sp(8,\\mathbb{R})$ and $SO(9,\\mathbb{R})$ as dynamical groups for closed quantum systems. Restricting here to $Sp(8,\\mathbb{R})$, the quantum theory is constructed and investigated. The functional Mellin transform plays a prominent role in defining the quantum theory as it provides a bridge between the quantum algebra of observables and the algebra of operators on Hilbert spaces furnishing unitary representations that are induced from a distinguished parabolic subgroup of $Sp(8,\\mathbb{R})$. As well, the parabolic subgroup furnishes a fiber bundle construction that models what can be described as a matrix quantum gauge theory. The formulation is strictly quantum mechanics: no a priori space-time is assumed and the only geometrical input comes from the group manifold. But, what appears on the surface to be a fairly simple model, turns out to have a capacious structure suggesting some surprising physical interpretations.
A Velocity Field and Operator for Spinning Particles in (Nonrelativistic) Quantum Mechanics
NASA Astrophysics Data System (ADS)
Salesi, Giovanni; Recami, Erasmo
1998-05-01
Starting from the formal expressions of the hydrodynamical (or “local”) quantities employed in the applications of Clifford algebras to quantum mechanics, we introduce— in terms of the ordinary tensorial language—a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, we also propose a new (nonrelativistic) velocity operator for a spin-{1/2} particle. This operator appears as the sum of the ordinary part p/ m describing the mean motion (the motion of the center-of-mass), and of a second part associated with the so-called Zitterbewegung, which is the spin “internal” motion observed in the center-of-mass frame (CMF). This spin component of the velocity operator is nonzero not only in the Pauli theoretical framework, i.e., in the presence of external electromagnetic fields with a nonconstant spin function, but also in the Schrödinger case, when the wavefunction is a spin eigenstate. Thus, one gets even in the latter case a decomposition of the velocity field for the Madelung fluid into two distinct parts, which constitutes the nonrelativistic analogue of the Gordon decomposition for the Dirac current. Explicit calculations are presented for the velocity field in the particular cases of the hydrogen atom, of a spherical well potential, and of an electron in a uniform magnetic field. We find, furthermore, that the Zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In the presence of a nonuniform spin vector (Pauli case) we have, besides the component of the local velocity normal to the spin (present even in the Schrödinger theory), also a component which is parallel to the curl of the spin vector.
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
Zhang, Xiao; Wei, Chaozhen; Liu, Yingming; Luo, Maokang
2014-11-15
In this paper we use Dirac function to construct a fractional operator called fractional corresponding operator, which is the general form of momentum corresponding operator. Then we give a judging theorem for this operator and with this judging theorem we prove that R–L, G–L, Caputo, Riesz fractional derivative operator and fractional derivative operator based on generalized functions, which are the most popular ones, coincide with the fractional corresponding operator. As a typical application, we use the fractional corresponding operator to construct a new fractional quantization scheme and then derive a uniform fractional Schrödinger equation in form. Additionally, we find that the five forms of fractional Schrödinger equation belong to the particular cases. As another main result of this paper, we use fractional corresponding operator to generalize fractional quantization scheme by using Lévy path integral and use it to derive the corresponding general form of fractional Schrödinger equation, which consequently proves that these two quantization schemes are equivalent. Meanwhile, relations between the theory in fractional quantum mechanics and that in classic quantum mechanics are also discussed. As a physical example, we consider a particle in an infinite potential well. We give its wave functions and energy spectrums in two ways and find that both results are the same.
NASA Astrophysics Data System (ADS)
Murdin, P.
2000-11-01
A development of quantum theory that was initiated in the 1920s by Werner Heisenberg (1901-76) and Erwin Schrödinger (1887-1961). The theory drew on a proposal made in 1925 Prince Louis de Broglie (1892-1987), that particles have wavelike properties (the wave-particle duality) and that an electron, for example, could in some respects be regarded as a wave with a wavelength that depended on its mo...
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
Osborn, T A
1997-01-01
The Moyal--Weyl description of quantum mechanics provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in \\hbar. Its semiclassical expansion `coefficients,' acting on symbols that represent observables, are simple, globally defined differential operators constructed in terms of the classical flow. Two methods of constructing this expansion are discussed. The first introduces a cluster-graph expansion for the symbol of an exponentiated operator, which extends Groenewold's formula for the Weyl product of symbols. This Poisson bracket based cluster expansion determines the Jacobi equations for the semiclassical expansion of `quantum trajectories.' Their Green function solutions construct the regular \\hbar\\downarrow0 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 \\hbar coefficients recursively. The Heisenberg--...
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.
Odake, Satoru
2011-01-01
A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, the unified theory of exact and quasi-exact solvability based on the sinusoidal coordinates, the infinite families of new orthogonal (the exceptional) polynomials. Two new infinite families of orthogonal polynomials, the X_\\ell Meixner-Pollaczek and the X_\\ell Meixner polynomials are reported.
Satoru Odake; Ryu Sasaki
2011-08-11
A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, the unified theory of exact and quasi-exact solvability based on the sinusoidal coordinates, the infinite families of new orthogonal (the exceptional) polynomials. Two new infinite families of orthogonal polynomials, the X_\\ell Meixner-Pollaczek and the X_\\ell Meixner polynomials are reported.
NASA Astrophysics Data System (ADS)
Odake, Satoru; Sasaki, Ryu
2011-09-01
A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorized Hamiltonians, the general structure of the solution spaces of the Schrödinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schrödinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, the unified theory of exact and quasi-exact solvability based on the sinusoidal coordinates, and the infinite families of new orthogonal (the exceptional) polynomials. Two new infinite families of orthogonal polynomials, the X? Meixner-Pollaczek and the X? Meixner polynomials, are reported.
Phase space quantum mechanics - Direct
Nasiri, S.; Sobouti, Y.; Taati, F.
2006-09-15
Conventional approach to quantum mechanics in phase space (q,p), is to take the operator based quantum mechanics of Schroedinger, or an equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of noncommuting observables. Further conceptual and practical merits of the formalism are demonstrated throughout the text.
Coexistence of quantum operations
Heinosaari, Teiko; Stano, Peter; Ziman, Mario
2009-01-01
Quantum operations are used to describe the observed probability distributions and conditional states of the measured system. In this paper, we address the problem of their joint measurability (coexistence). We derive two equivalent coexistence criteria. The two most common classes of operations - Luders operations and conditional state preparators - are analyzed. It is shown that Luders operations are coexistent only under very restrictive conditions, when the associated effects are either proportional to each other, or disjoint.
Coexistence of quantum operations
Teiko Heinosaari; Daniel Reitzner; Peter Stano; Mario Ziman
2009-08-21
Quantum operations are used to describe the observed probability distributions and conditional states of the measured system. In this paper, we address the problem of their joint measurability (coexistence). We derive two equivalent coexistence criteria. The two most common classes of operations - Luders operations and conditional state preparators - are analyzed. It is shown that Luders operations are coexistent only under very restrictive conditions, when the associated effects are either proportional to each other, or disjoint.
Pseudospectra in non-Hermitian quantum mechanics
NASA Astrophysics Data System (ADS)
Krej?i?ík, D.; Siegl, P.; Tater, M.; Viola, J.
2015-10-01
We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.
Quantum noise in ideal operational amplifiers
Jean-Michel Courty; Francesca Grassia; Serge Reynaud
1998-11-24
We consider a model of quantum measurement built on an ideal operational amplifier operating in the limit of infinite gain, infinite input impedance and null output impedance and with a feddback loop. We evaluate the intensity and voltage noises which have to be added to the classical amplification equations in order to fulfill the requirements of quantum mechanics. We give a description of this measurement device as a quantum network scattering quantum fluctuations from input to output ports.
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.
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...
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.
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.
Dissipative and quantum mechanics
Roumen Tsekov
2015-06-08
Three existing interpretations of quantum mechanics, given by Heisenberg, Bohm and Madelung, are examined to describe dissipative quantum systems as well. It is found that the Madelung quantum hydrodynamics is the only correct approach. A new stochastic reinterpretation of the quantum mechanics is proposed, which represents the microscopic face of the Madelung hydrodynamics. The main idea is that the vacuum fluctuates permanently, which explains the probabilistic character of the quantum mechanics. Thus, it is an objective theory independent of the human beings and their measurements. The effect of the thermal fluctuations in the surrounding is also accounted for via a heuristic Langevin equation with two random forces. Some statistical characteristics of these quantum and thermal noises are determined by reproducing known results for the system phase-space dynamics.
Self-adjoint extensions of operators and the teaching of quantum mechanics
Guy Bonneau; Jacques Faraut; Galliano Valent
2001-03-28
For the example of the infinitely deep well potential, we point out some paradoxes which are solved by a careful analysis of what is a truly self-adjoint operator. We then describe the self-adjoint extensions and their spectra for the momentum and the Hamiltonian operators in different physical situations. Some consequences are worked out, which could lead to experimental checks.
Kapustin, Anton
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.
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.
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.
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)
Simons, Jack
Chapter 20 Many physical properties of a molecule can be calculated as expectation values of a corresponding quantum mechanical operator. The evaluation of other properties can be formulated in terms perturbation. I. Calculations of Properties Other Than the Energy There are, of course, properties other than
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.
Uniqueness results by covariance in covariant quantum mechanics
JanyÂ?ka, Josef
Uniqueness results by covariance in covariant quantum mechanics Josef JanyÅ¸ska 1 , Marco Modugno 2 is the covariant quantum mechanics of a scalar quantum particle in a curved spacetime which is fibred over absolute beginning of quantum mechanics the quantum operators associated with classical quantisable functions
Giddings, Steven B.
2008-10-15
If gravity respects quantum mechanics, it is important to identify the essential postulates of a quantum framework capable of incorporating gravitational phenomena. Such a construct likely requires elimination or modification of some of the 'standard' postulates of quantum mechanics, in particular, those involving time and measurement. This paper proposes a framework that appears sufficiently general to incorporate some expected features of quantum gravity. These include the statement that space and time may only emerge approximately and relationally. One perspective on such a framework is as a sort of generalization of the S-matrix approach to dynamics. Within this framework, more dynamical structure is required to fully specify a theory; this structure is expected to lack some of the elements of local quantum field theory. Some aspects of this structure are discussed, both in the context of scattering of perturbations about a flat background, and in the context of cosmology.
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
Fan Hongyi
2008-06-15
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.
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.
BOOK REVIEW: Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Antoine, J.-P.
2004-01-01
The aim of relativistic quantum mechanics is to describe the finer details of the structure of atoms and molecules, where relativistic effects become nonnegligible. It is a sort of intermediate realm, between the familiar nonrelativistic quantum mechanics and fully relativistic quantum field theory, and thus it lacks the simplicity and elegance of both. Yet it is a necessary tool, mostly for quantum chemists. Pilkuhn's book offers to this audience an up-to-date survey of these methods, which is quite welcome since most previous textbooks are at least ten years old. The point of view of the author is to start immediately in the relativistic domain, following the lead of Maxwell's equations rather than classical mechanics, and thus to treat the nonrelativistic version as an approximation. Thus Chapter 1 takes off from Maxwell's equations (in the noncovariant Coulomb gauge) and gradually derives the basic aspects of Quantum Mechanics in a rather pedestrian way (states and observables, Hilbert space, operators, quantum measurement, scattering,. Chapter 2 starts with the Lorentz transformations, then continues with the Pauli spin equation and the Dirac equation and some of their applications (notably the hydrogen atom). Chapter 3 is entitled `Quantum fields and particles', but falls short of treating quantum field theory properly: only creation/annihilation operators are considered, for a particle in a box. The emphasis is on two-electron states (the Pauli principle, the Foldy--Wouthuysen elimination of small components of Dirac spinors, Breit projection operators. Chapter 4 is devoted to scattering theory and the description of relativistic bound states. Chapter 5, finally, covers hyperfine interactions and radiative corrections. As we said above, relativistic quantum mechanics is by nature limited in scope and rather inelegant and Pilkuhn's book is no exception. The notation is often heavy (mostly noncovariant) and the mathematical level rather low. The central topic is the description of atoms and molecules, including relativistic effects. The author fulfils this program in a reasonable way and offers a valuable tool to the targeted audience. I am not overly enthusiastic about the end result, but I might be prejudiced. Clearly, going further would require the full power of quantum field theory, but this is clearly beyond the scope of the book.
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.
Quantum mechanics without measurements
Robert B. Griffiths
2006-12-08
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic probabilities in quantum theory requires setting up appropriate sample spaces taking proper account of quantum incompatibility. When this is done the Schrodinger equation can be used to calculate probabilities independent of whether a system is or is not being measured, and the results usually ascribed to wave function collapse are obtained in a less misleading way through conditional probabilities. Toy models that include measurement apparatus as part of the total quantum system make this approach accessible to students. Some comments are made about teaching this material.
Quantum Techniques for Stochastic Mechanics
John C. Baez; Jacob Biamonte
2015-10-22
Some ideas from quantum theory are just beginning to percolate back to classical probability theory. For example, there is a widely used and successful theory of "chemical reaction networks", which describes the interactions of molecules in a stochastic rather than quantum way. Computer science and population biology use the same ideas under a different name: "stochastic Petri nets". But if we look at these theories from the perspective of quantum theory, they turn out to involve creation and annihilation operators, coherent states and other well-known ideas - but in a context where probabilities replace amplitudes. We explain this connection as part of a detailed analogy between quantum mechanics and stochastic mechanics. We use this analogy to present new proofs of two major results in the theory of chemical reaction networks: the deficiency zero theorem and the Anderson-Craciun-Kurtz theorem. We also study the overlap of quantum mechanics and stochastic mechanics, which involves Hamiltonians that can generate either unitary or stochastic time evolution. These Hamiltonians are called "Dirichlet forms", and they arise naturally from electrical circuits made only of resistors.
Grassmann Matrix Quantum Mechanics
Anninos, Dionysios; Monten, Ruben
2015-01-01
We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kahler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit. We discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.
Grassmann Matrix Quantum Mechanics
Dionysios Anninos; Frederik Denef; Ruben Monten
2015-12-11
We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kahler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit. We discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.
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.
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.
PHYSICS 482, QUANTUM MECHANICS II Introductory Quantum Mechanics contd.
Akerib, Daniel S.
PHYSICS 482, QUANTUM MECHANICS II Introductory Quantum Mechanics contd. 1. Time dependent methods. Quantum Many-body physics: 1. Variational principle, simple applications. 2. Many body wave, ferromagnetism of the electron gas, Wigner crystals and quantum phase transitions. 4. Second quantization
Timothy J. Hollowood
2015-11-03
In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950's development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrodinger cat states are the norm rather than curiosities generated in physicists' laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr's quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.
From Quantum Mechanics to Thermodynamics?
Steinhoff, Heinz-Jürgen
From Quantum Mechanics to Thermodynamics? Dresden, 22.11.2004 Jochen Gemmer Universit¨at Osnabr Description? Quantum Mechanics i¯h t = (- ¯h2 2m + V ) Classical Mechanics: m d2 dt2 x = - V Thermodynamics: dU = TdS - pdV dS dt > 0 #12;Fundamental Law or Emergent Description? Quantum Mechanics i
Habib, S; Greenbaum, B; Jacobs, K; Shizume, K; Sundaram, B; Habib, Salman; Bhattacharya, Tanmoy; Greenbaum, Benjamin; Jacobs, Kurt; Shizume, Kosuke; Sundaram, Bala
2005-01-01
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our starting point here is that a complete dynamical description requires a full understanding of the evolution of measured systems, necessary to explain actual experimental results. This is of course true, both classically and quantum mechanically. Because the evolution of the physical state is now conditioned on measurement results, the dynamics of such systems is intrinsically nonlinear even at the level of distribution functions. Due to this feature, the physically more complete treatment reveals the existence of dynamical regimes -- such as chaos -- that have no direct counterpart in the linear (unobserved) case. Moreover, this treatment allows for understanding how an effective classical behavior can result from the dynamics of an observed quantum system, both at the level of t...
Nicolaidis, Argyris
2012-01-01
We suggest that the inner syntax of Quantum Mechanics is relational logic, a form of logic developed by C. S. Peirce during the years 1870 - 1880. The Peircean logic has the structure of category theory, with relation serving as an arrow (or morphism). At the core of the relational logical system is the law of composition of relations. This law leads to the fundamental quantum rule of probability as the square of an amplitude. Our study of a simple discrete model, extended to the continuum, indicates that a finite number of degrees of freedom can live in phase space. This "granularity" of phase space is determined by Planck's constant h. We indicate also the broader philosophical ramifications of a relational quantum mechanics.
Argyris Nicolaidis
2012-11-09
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.
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.
Fan Hongyi
2008-02-15
We show that the technique of integration within normal ordering of operators [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480-494] applied to tackling Newton-Leibniz integration over ket-bra projection operators, can be generalized to the technique of integration within Weyl ordered product (IWWOP) of operators. The Weyl ordering symbol is introduced to find the Wigner operator's Weyl ordering form {delta}(p,q) = {delta}(p - P){delta}(q - Q) , and to find operators' Weyl ordered expansion formula. A remarkable property is that Weyl ordering of operators is covariant under similarity transformation, so it has many applications in quantum statistics and signal analysis. Thus the invention of the IWWOP technique promotes the progress of Dirac's symbolic method.
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.
Testing non-associative quantum mechanics
Bojowald, Martin; Buyukcam, Umut
2015-01-01
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to non-associative algebras. Their quantum physics has remained obscure. This letter presents the first derivation of potentially testable physical results in non-associative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.
Testing non-associative quantum mechanics
Martin Bojowald; Suddhasattwa Brahma; Umut Buyukcam
2015-10-26
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to non-associative algebras. Their quantum physics has remained obscure. This letter presents the first derivation of potentially testable physical results in non-associative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.
Three Pictures of Quantum Mechanics
Olszewski Jr., Edward A.
Three 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 the Stage: Quantum Mechanics in Five Minutes #12;The Wave Function Â· A particle or system is described
Habib, Salman; Bhattacharya, Tanmoy; Greenbaum, Benjamin; Jacobs, Kurt; Shizume, Kosuke; Sundaram, Bala
2005-06-01
The relationship between chaos and quantum mechanics has been somewhat uneasy--even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our starting point here is that a complete dynamical description requires a full understanding of the evolution of measured systems, necessary to explain actual experimental results. This is of course true, both classically and quantum mechanically. Because the evolution of the physical state is now conditioned on measurement results, the dynamics of such systems is intrinsically nonlinear even at the level of distribution functions. Due to this feature, the physically more complete treatment reveals the existence of dynamical regimes--such as chaos--that have no direct counterpart in the linear (unobserved) case. Moreover, this treatment allows for understanding how an effective classical behavior can result from the dynamics of an observed quantum system, both at the level of trajectories as well as distribution functions. Finally, we have the striking prediction that time-series from measured quantum systems can be chaotic far from the classical regime, with Lyapunov exponents differing from their classical values. These predictions can be tested in next-generation experiments. PMID:15980320
Salman Habib; Tanmoy Bhattacharya; Benjamin Greenbaum; Kurt Jacobs; Kosuke Shizume; Bala Sundaram
2005-05-11
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our starting point here is that a complete dynamical description requires a full understanding of the evolution of measured systems, necessary to explain actual experimental results. This is of course true, both classically and quantum mechanically. Because the evolution of the physical state is now conditioned on measurement results, the dynamics of such systems is intrinsically nonlinear even at the level of distribution functions. Due to this feature, the physically more complete treatment reveals the existence of dynamical regimes -- such as chaos -- that have no direct counterpart in the linear (unobserved) case. Moreover, this treatment allows for understanding how an effective classical behavior can result from the dynamics of an observed quantum system, both at the level of trajectories as well as distribution functions. Finally, we have the striking prediction that time-series from measured quantum systems can be chaotic far from the classical regime, with Lyapunov exponents differing from their classical values. These predictions can be tested in next-generation experiments.
Time Asymmetric Quantum Mechanics
Arno R. Bohm; Manuel Gadella; Piotr Kielanowski
2011-09-03
The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone--von Neumann theorem, the solutions of the dynamical equations, the Schr\\"odinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width $\\Gamma$ and exponentially decaying states of lifetime $\\tau=\\frac{\\hbar}{\\Gamma}$ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution $t_{0}\\leq tbig bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.
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.
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.
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 #12;Does Anyone Understand Quantum Mechanics? "No One Understands Quantum Mechanics" "I think
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.
Quantum mechanics and the generalized uncertainty principle
Bang, Jang Young; Berger, Micheal S.
2006-12-15
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.
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.
Multiparty Operational Quantum Mutual Information
Asutosh Kumar
2015-04-27
Mutual information is the reciprocal information that is common to or shared by two or more parties. Quantum mutual information (QMI) for bipartite quantum systems is non-negative, and bears the interpretation of total correlation between the two subsystems.This may, however, be no longer true for three or more party quantum systems. It is possible that three-party QMI can be negative. That QMI can assume negative value is confronting, and we give operational definition of QMI which is non-negative. We then define multiparty operational quantum discord, and give some examples. Interestingly, we observe that quantum discord increases when measurement is performed on larger number of subsystems. Consequently, the symmetric version of quantum discord, which involves measurement on all parties, reveals the maximal quantumness. This raises question on the interpretation of measured mutual information as classical correlation.
Nonlinear friction in quantum mechanics
Roumen Tsekov
2013-03-10
The effect of nonlinear friction forces in quantum mechanics is studied via dissipative Madelung hydrodynamics. A new thermo-quantum diffusion equation is derived, which is solved for the particular case of quantum Brownian motion with a cubic friction. It is extended also by a chemical reaction term to describe quantum reaction-diffusion systems with nonlinear friction as well.
Hollowood, Timothy J
2015-01-01
In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950's development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrodinger cat states are the norm rather than curiosities generat...
Bohmian quantum mechanics with quantum trajectories
NASA Astrophysics Data System (ADS)
Jeong, Yeuncheol
The quantum trajectory method in the hydrodynamical formulation of Madelung-Bohm-Takabayasi quantum mechanics is an example of showing the cognitive importance of scientific illustrations and metaphors, especially, in this case, in computational quantum chemistry and electrical engineering. The method involves several numerical schemes of solving a set of hydrodynamical equations of motion for probability density fluids, based on the propagation of those probability density trajectories. The quantum trajectory method gives rise to, for example, an authentic quantum electron transport theory of motion to, among others, classically-minded applied scientists who probably have less of a commitment to traditional quantum mechanics. They were not the usual audience of quantum mechanics and simply choose to use a non-Copenhagen type interpretation to their advantage. Thus, the metaphysical issues physicists had a trouble with are not the main concern of the scientists. With the advantages of a visual and illustrative trajectory, the quantum theory of motion by Bohm effectively bridges quantum and classical physics, especially, in the mesoscale domain. Without having an abrupt shift in actions and beliefs from the classical to the quantum world, scientists and engineers are able to enjoy human cognitive capacities extended into the quantum mechanical domain.
Pragmatic Information in Quantum Mechanics
Juan G. Roederer
2015-12-16
An objective definition of pragmatic information and the consideration of recent results about information processing in the human brain can help overcome some traditional difficulties with the interpretation of quantum mechanics. Rather than attempting to define information ab initio, I introduce the concept of interaction between material bodies as a primary concept. Two distinct categories can be identified: 1) Interactions which can always be reduced to a superposition of physical interactions (forces) between elementary constituents; 2) Interactions between complex bodies which cannot be reduced to a superposition of interactions between parts, and in which patterns and forms (in space and/or time) play the determining role. Pragmatic information is then defined as the correspondence between a given pattern and the ensuing pattern-specific change. I will show that pragmatic information is a biological concept that plays no active role in the purely physical domain; it only does so when a living organism intervenes. The consequences for the foundations of both classical and quantum physics are important and will be discussed in detail. Since by its very definition pragmatic information (the one our brain uses to represent, think about and react to the outside world)cannot operate in the quantum domain, it is advisable to refrain from using it in our mental representation of what is happening 'inside' a quantum system. Although the theoretical framework developed for quantum mechanics handles mathematical entities specifically attributed to a quantum system, the only truly pragmatic information it can provide relates to macroscopic effects on the environment (natural, or artificial as in a measurement instrument) with which the system interacts.
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.
Outline of Quantum Mechanics William G. Faris 1
Ueltschi, Daniel
Contents Outline of Quantum Mechanics William G. Faris 1 Inequalities for SchrÂ¨odinger Operators is the goal of the present lecture notes. They include an excellent introduction to quantum mechanics been de- veloped over the years for, and because of, quantum mechanics. These are the subject of two
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.
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.
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.
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.
QUANTUM MECHANICS IN PHASE SPACE BRIAN C. HALL
is that the quantum mechanically important operators, in cluding Schr¨odinger operators, can be representeddefined set of creation and annihilation operators, and a natural ground state (or vacuum state). Between anyQUANTUM MECHANICS IN PHASE SPACE BRIAN C. HALL Abstract. This paper concerns the generalized Segal
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.
Bender, Carl M; DeKieviet, Maarten; Klevansky, S P
2013-04-28
PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics. PMID:23509390
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.
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.
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.
Scan Quantum Mechanics: Quantum Inertia Stops Superposition
Gato-Rivera, Beatriz
2015-01-01
A novel interpretation of the quantum mechanical superposition is put forward. Quantum systems scan all possible available states and switch randomly and very rapidly among them. The longer they remain in a given state, the larger the probability of the system to be found in that state during a measurement. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia $I_q$ reaches a critical value $I_{cr}$ for an observable, the switching among the different eigenvalues of that observable stops and the corresponding superposition comes to an end. Consequently, increasing the mass, temperature, gravitational force, etc. of a quantum system increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. The process could be reversible decreasing the size, temperature, gravitational force, etc. leading to...
Galilei general relativistic quantum mechanics revisited
JanyÂ?ka, Josef
Galilei general relativistic quantum mechanics revisited Arkadiusz Jadczyk Institute of Theoretical of Galilei relativistic quantum mechanics. The main concepts used are GalileiÂNewton spaceÂtime, Newtonian : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 22 1.9 Classical particle mechanics : : : : : : : : : : : : : : : : : : : : : : : : 22 2 Quantum
Quantum Mechanics 1 for graduate students
Course 606 Quantum Mechanics 1 for graduate students Fall 2010 Instructor Valery Pokrovsky 1 electromagnetic field. Gauge invariance. Landau levels. 7. Semiclassical approximation. 8. Quantum mechanics. Scattering. The main textbook is E. Merzbacher, Quantum Mechanics, third edition, Wiley. Additional
Quantum mechanics as applied mathematical statistics
Skala, L.; Cizek, J.; Kapsa, V.
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.
Quantum Mechanics as Classical Physics
Charles Sebens
2015-04-02
Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds.
Coherent states in noncommutative quantum mechanics
Ben Geloun, J.; Scholtz, F. G.
2009-04-15
Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position uncertainty relation, obey a Poisson distribution, and possess a flat geometry. Using the natural isometry between the quantum Hilbert space of Hilbert-Schmidt operators and the tensor product of the classical configuration space and its dual, we reveal the inherent vector feature of these states.
Classical explanations of results of quantum mechanics
NASA Astrophysics Data System (ADS)
Giese, Albrecht
2015-09-01
We present a particle model which was developed to explain special relativity by classical means. This model is also able to account for physical processes that are normally attributed to quantum mechanics. The model is able to describe several well-known QM processes by means of classical calculations, making them accessible to the imagination. An essential difference compared with the Standard Model of present-day particle physics is the fact that, in the model presented, particles are viewed as being extended rather than point-like. In addition, the strong force is shown to be the universal force operating in all particles. Also, the photon, which quantum mechanics views as being nothing but a quantum of energy, can be understood to have an internal structure. The model presented here is not merely a different way of explaining physics with similar results; in contrast to quantum mechanics, it has the ability to provide deeper insights into physical processes.
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.
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.
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.
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 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.
Foundations of Quantum Mechanics and Quantum Computation
NASA Astrophysics Data System (ADS)
Aspect, Alain; Leggett, Anthony; Preskill, John; Durt, Thomas; Pironio, Stefano
2013-03-01
I ask the question: What can we infer about the nature and structure of the physical world (a) from experiments already done to test the predictions of quantum mechanics (b) from the assumption that all future experiments will agree with those predictions? I discuss existing and projected experiments related to the two classic paradoxes of quantum mechanics, named respectively for EPR and Schrödinger's Cat, and show in particular that one natural conclusion from both types of experiment implies the abandonment of the concept of macroscopic counterfactual definiteness.
Generalizations of Quantum Mechanics
Philip Pearle; Antony Valentini
2005-10-14
We review realistic models that reproduce quantum theory in some limit and yield potentially new physics outside that limit. In particular, we consider deterministic hidden-variables theories (such as the pilot-wave model) and their extension to 'quantum nonequilibrium', and we consider the continuous spontaneous localization model of wave function collapse. Other models are briefly discussed.
Quantum mechanical description of waveguides
Zhi-Yong Wang; Cai-Dong Xiong; Bing He
2008-05-12
In this paper, applying the spinor representation of the electromagnetic field, we present a quantum-mechanical description of waveguides. As an example of application, a potential qubit generated via photon tunneling is discussed.
Free will and quantum mechanics
Antonio Di Lorenzo
2011-05-05
A simple example is provided showing that violation of free will allows to reproduce the quantum mechanical predictions, and that the Clauser-Horne parameter can take the maximum value 4 for a proper choice.
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.
Quantum mechanics from invariance principles
Florin Moldoveanu
2015-10-25
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 inequalities.
Quantum mechanics for relativistic bosons
Soon-Tae Hong
2015-11-12
We construct a relativistic quantum mechanics for a boson. To do this we exploit two component wave functions in Dirac type equations of motion. In our formalism we fix the pathological aspect of particle probability density which appears in Klein-Gordon theory. Our solutions possess a negative solution as well as a positive one. We also formulate a diagonal Hamiltonian of the relativistic quantum mechanics for the boson.
Superadiabatic Control of Quantum Operations
Jonathan Vandermause; Chandrasekhar Ramanathan
2015-12-15
Adiabatic pulses are used extensively to enable robust control of quantum operations. We introduce a new approach to adiabatic control that uses the superadiabatic quality or Q-factor as a performance metric to design robust, high fidelity pulses. Our approach permits the systematic design of quantum control schemes to maximize the adabaticity of a unitary operation in a given time interval, given the available control resources. We numerically examine the interplay between adiabaticity, fidelity and robustness of the resulting pulses for the case of single-qubit inversion, and demonstrate the improved robustness of superadiabatic pulses. We introduce a numerical search strategy to implement a broader class of adiabatic operations, including multi-qubit adiabatic uni- taries, and demonstrate the utility of the technique by designing control waveforms that adiabatically implement a two-qubit entangling gate for a model system.
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 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.
Models of Damped Oscillators in Quantum Mechanics
Ricardo Cordero-Soto; Erwin Suazo; Sergei K. Suslov
2009-06-04
We consider several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schroedinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time-evolution of the expectation values of the energy related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator.
A Euclidean formulation of relativistic quantum mechanics
Philip Kopp; Wayne Polyzou
2011-06-21
In this paper we discuss a formulation of relativistic quantum mechanics that uses Euclidean Green functions or generating functionals as input. This formalism has a close relation to quantum field theory, but as a theory of linear operators on a Hilbert space, it has many of the advantages of quantum mechanics. One interesting feature of this approach is that matrix elements of operators in normalizable states on the physical Hilbert space can be calculated directly using the Euclidean Green functions without performing an analytic continuation. The formalism is summarized in this paper. We discuss the motivation, advantages and difficulties in using this formalism. We discuss how to compute bound states, scattering cross sections, and finite Poincare transformations without using analytic continuation. A toy model is used to demonstrate how matrix elements of exp(-beta H) in normalizable states can be used to construct-sharp momentum transition matrix elements.
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.
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 in Insulators
Aeppli, G.
2009-08-20
Atomic physics is undergoing a large revival because of the possibility of trapping and cooling ions and atoms both for individual quantum control as well as collective quantum states, such as Bose-Einstein condensates. The present lectures start from the 'atomic' physics of isolated atoms in semiconductors and insulators and proceed to coupling them together to yield magnets undergoing quantum phase transitions as well as displaying novel quantum states with no classical analogs. The lectures are based on: G.-Y. Xu et al., Science 317, 1049-1052 (2007); G. Aeppli, P. Warburton, C. Renner, BT Technology Journal, 24, 163-169 (2006); H. M. Ronnow et al., Science 308, 392-395 (2005) and N. Q. Vinh et al., PNAS 105, 10649-10653 (2008).
Scan Quantum Mechanics: Quantum Inertia Stops Superposition
Beatriz Gato-Rivera
2015-12-11
A novel interpretation of the quantum mechanical superposition is put forward. Quantum systems scan all possible available states and switch randomly and very rapidly among them. The longer they remain in a given state, the larger the probability of the system to be found in that state during a measurement. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia $I_q$ reaches a critical value $I_{cr}$ for an observable, the switching among the different eigenvalues of that observable stops and the corresponding superposition comes to an end. Consequently, increasing the mass, temperature, gravitational force, etc. of a quantum system increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. The process could be reversible decreasing the size, temperature, gravitational force, etc. Entanglement can only occur between quantum systems, not between a quantum system and a classical one, because an exact synchronization between the switchings of the systems involved must be established in the first place and classical systems do not have any switchings to start with. Future experiments might determine the critical inertia $I_{cr}$ corresponding to different observables. In addition, our proposal implies a new radiation mechanism in strong gravitational fields, giving rise to non-thermal emission, that could contribute to neutron star formation and provides new insight into the information loss paradox and the firewall. Superconductivity, superfluidity, Bose-Einstein condensates, and any other physical phenomena at very low temperatures must be reanalyzed in the light of this interpretation, as well as mesoscopic systems in general.
V. A. Fateev; R. De Pietri; E. Onofri
2004-07-13
A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an exact eigenfunction expansion; these can be associated to Riemannian symmetric spaces of rank one with positive, negative or vanishing curvature. For all other cases an accurate semiclassical approximation is derived, based on the identification of the operators with a peculiar Schroedinger-like operator.
Quantum duality, unbounded operators, and inductive limits
Dosi, Anar
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.
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics) New Particles anti-particles (combining special relativity and quantum mechanics pions (mediator/momentum/mass discrepancy must fit inside the quantum mechanical uncertainty p, E E2 - p2 c2 = 0 Thursday, May 7, 2009 #12
Chem 793 Quantum Mechanics I Chemistry 793
Chem 793 Quantum Mechanics I Chemistry 793 Quantum Mechanics I Fall 2000 Course outline 1 formulation. · Constants of the motion. 2. Probability in classical and quantum mechanics · Probability University #12;Chem 793 Quantum Mechanics I 7. Separable problems in 2D and 3D · Direct product functions
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
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics, 2009 #12;Quantum Mechanics: Measurement and Uncertainty Thursday, May 7, 2009 #12;Puzzle: The Stern it. Quantum mechanics understanding: the particle exists in a state without definite position
Hierarchies of incoherent quantum operations
Alexander Streltsov; Swapan Rana; Manabendra Nath Bera; Maciej Lewenstein
2015-09-29
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 general, we show that the larger class of separable incoherent operations (SI) has a simple mathematical form, yet still preserving the main features of LICC. We apply these results to the task of assisted coherence distillation, where the aim is to locally extract maximally coherent states. For all pure states and certain mixed states we observe a collapse of all classes: the distillation rate is always the same. It remains open if the distillation rate can be different for general mixed states, and if the intersection of LOCC and SI is equivalent to LICC. We also introduce the task of incoherent teleportation and show that perfect incoherent teleportation of one qubit is possible with one singlet and two bits of classical communication. The approach presented here opens new ways to study the resource theory of coherence in distributed scenarios.
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)
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
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 of Michigan, Ann Arbor Quantum mechanics occupies a unique position in the history of science. It has sur successes of quantum mechanics, its foundations are often questioned, owing to the glaring difficulties
Optimal guidance law in quantum mechanics
Yang, Ciann-Dong Cheng, Lieh-Lieh
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.
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics with constant velocity with respect to each other (These are inertial reference frames) Newton's Laws (mechanics
Entanglement and Disentanglement in Relativistic Quantum Mechanics
Johnson, Kent
Entanglement and Disentanglement in Relativistic Quantum Mechanics Jeffrey A. Barrett March 31 the quantum measurement problem.1 1 Relativistic Quantum Mechanics and Entanglement Work on the conceptual quantum mechanics and of the entangled states of spacelike separated systems requires a concrete
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 MECHANICS AND DUALISM JEFFREY A. BARRETT
Johnson, Kent
QUANTUM MECHANICS AND DUALISM JEFFREY A. BARRETT Abstract. The quantum measurement problem has led, and in a no-collapse formulation of quantum mechanics, a strong variety of dualism provides a way to account with Eugene Wigner's understanding of the standard collapse formulation of quantum mechanics. Two years prior
Horizon Quantum Mechanics: a hitchhiker's guide to quantum black holes
R. Casadio; A. Giugno; O. Micu
2015-12-13
It is congruous with the quantum nature of the world to view the space-time geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the space-time manifold as a purely theoretical arena, where quantum states are defined, with the additional freedom of changing coordinates like any other symmetry. Observables, including positions and distances, should then be described by suitable operators acting on such quantum states. In principle, the top-down (canonical) quantisation of Einstein-Hilbert gravity falls right into this picture, but is notoriously very involved. The complication stems from allowing all the classical canonical variables that appear in the (presumably) fundamental action to become quantum observables acting on the "superspace" of all metrics, regardless of whether they play any role in the description of a specific physical system. On can instead revisit the more humble "minisuperspace" approach and choose the gravitational observables not simply by imposing some symmetry, but motivated by their proven relevance in the (classical) description of a given system. In particular, this review focuses on compact, spherically symmetric, quantum mechanical sources, in order to determine the probability they are black holes rather than regular particles. The gravitational radius is therefore lifted to the status of a quantum mechanical operator acting on the "horizon wave-function", the latter being determined by the quantum state of the source. This formalism is then applied to several sources with a mass around the fundamental scale, which are viewed as natural candidates of quantum black holes.
Quantum statistical mechanics, L-series, Anabelian Geometry
Marcolli, Matilde
Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Beijing, August 2013 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12;joint work with Gunther Cornelissen General philosophy: Zeta functions are counting devices: spectra of operators with spectral
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.…
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…
Kowalevski top in quantum mechanics
Matsuyama, A.
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.
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
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.
Iyengar, Srinivasan S.
Quantum Mechanics Course Number: C668 C668: Special topics in physical chemistry: Advanced Quantum@gmail.com Chemistry, Indiana University i c 2014, Srinivasan S. Iyengar (instructor) #12;Quantum Mechanics Course Mechanics by J. J. Sakurai · Quantum Mechanics in Chemistry by Schatz and Ratner · Introduction to Quantum
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.
Quantum Mechanics in Noncommutative space
Veronika Gáliková; Samuel Ková?ik; Peter Prešnajder
2015-12-09
This paper provides an examination of how are prediction of standard quantum mechanic (QM) affected by introducing a noncommutative (NC) structure into the configuration space of the considered system (electron in the Coulomb potential in the present case). The parameter controlling the extent of modification is denoted as {\\lambda}. The coordinates in the NC space are realized via creation and annihilation operators acting in an auxiliary Fock space, this one being chosen in such a way that the rotational invariance of the system remains intact also in NCQM. Analog of Schr\\"odinger equation for hydrogen atom is found and analytically solved, both for bound states and scattering. The exact formulas for NC corrections are given. None of the NC predictions contradicts experimentally verified QM results, since in the correspondence limit {\\lambda} -> 0 both QM and NCQM coincide. Highly surprising feature of the NC version is the existence of bound states for repulsive potential at ultra-high energies. However, these disappear from the Hilbert space in the mentioned limit. The whole problem is solved also using a method analogous to that of Pauli. Besides rotational invariance, the dynamical symmetry related to the conservation of NC analog of Laplace-Runge-Lenz vector is being used and the results obtained this way are in the full agreement with those given by "Schr\\"odinger-like" approach. The presented NC deformation of QM preserves all those mysterious properties of the Coulomb system that made it a distinguished key-stone of the modern physics.
Quantum Mechanics in Noncommutative space
Veronika Gáliková; Samuel Ková?ik; Peter Prešnajder
2015-10-15
This paper provides an examination of how are prediction of standard quantum mechanic (QM) affected by introducing a noncommutative (NC) structure into the configuration space of the considered system (electron in the Coulomb potential in the present case). The parameter controlling the extent of modification is denoted as {\\lambda}. The coordinates in the NC space are realized via creation and annihilation operators acting in an auxiliary Fock space, this one being chosen in such a way that the rotational invariance of the system remains intact also in NCQM. Analog of Schr\\"odinger equation for hydrogen atom is found and analytically solved, both for bound states and scattering. The exact formulas for NC corrections are given. None of the NC predictions contradicts experimentally verified QM results, since in the correspondence limit {\\lambda} -> 0 both QM and NCQM coincide. Highly surprising feature of the NC version is the existence of bound states for repulsive potential at ultra-high energies. However, these disappear from the Hilbert space in the mentioned limit. The whole problem is solved also using a method analogous to that of Pauli. Besides rotational invariance, the dynamical symmetry related to the conservation of NC analog of Laplace-Runge-Lenz vector is being used and the results obtained this way are in the full agreement with those given by "Schr\\"odinger-like" approach. The presented NC deformation of QM preserves all those mysterious properties of the Coulomb system that made it a distinguished key-stone of the modern physics.
Quantum mechanics of 4-derivative theories
Salvio, Alberto
2015-01-01
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantisation. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalisable wave functions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm.
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.
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Mechanical Particle Physics General Relativistic Quantum Gravity increasing speed decreasing size increasing Extra Dimensions Strings and the Strong Force Thursday, June 4, 2009 #12;The Higgs Mechanism Summary
Faster than Hermitian quantum mechanics.
Bender, Carl M; Brody, Dorje C; Jones, Hugh F; Meister, Bernhard K
2007-01-26
Given an initial quantum state |psi(I)> and a final quantum state |psi(F)>, there exist Hamiltonians H under which |psi(I)> evolves into |psi(F)>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time tau? For Hermitian Hamiltonians tau has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, tau can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from |psi(I)> to |psi(F)> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing. PMID:17358747
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
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.
Creation mechanism of quantum accelerator modes
Summy, G. S.
We investigate the creation mechanism of quantum accelerator modes which are attributed to the existence of the stability islands in an underlying pseudoclassical phase space of the quantum delta-kicked accelerator. Quantum ...
Nonlinear entangled state representation in quantum mechanics
NASA Astrophysics Data System (ADS)
Fan, Hongyi; Cheng, Hailing
2002-03-01
We develop Dirac's representation theory in quantum mechanics by constructing the nonlinear entangled state | ?> nl and its non-Hermite conjugate state nl??| with continuum variable. By virtue of the technique of integration within an ordered product of operators we show that | ?> nl and nl??| make up an orthonormal and complete representation. From | ?> nl we also deduce another kind of entangled states. Application of | ?> nl in studying two-mode squeezed state is demonstrated.
QUICK QUANTUM MECHANICS ---Introduction ---
Jackson, Andrew D.
of Classical Mechanics After Newton found his equations of motion, physicists knew they would have to wait are completely equivalent to Newton's laws. 2 A generalized coordinate can be, e.g., a Cartesian coordinate the behaviour of all of the generalized coordinates, q(t), subject to initial boundary conditions. Since Newton
Hermeneutics, Underdetermination and Quantum Mechanics.
ERIC Educational Resources Information Center
Cushing, James T.
1995-01-01
States that the existence of an essential underdetermination in the interpretation of the formalism of quantum mechanics, in spite of the widespread belief that logic and empirical considerations alone demand an indeterministic world view in physics, legitimizes the analysis of hermeneutics in science education. (LZ)
Renormalization group in quantum mechanics
Polony, J.
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.
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
Probable Inference and Quantum Mechanics
NASA Astrophysics Data System (ADS)
Grandy, W. T.
2009-12-01
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 rôle 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.
Quantum Mechanics of Black Holes
NASA Astrophysics Data System (ADS)
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.
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
Star Products for Relativistic Quantum Mechanics
P. Henselder
2007-05-24
The star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. We want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in the proper time formulation.
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.
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.
Lecture Notes in Quantum Mechanics Doron Cohen
Cohen, Doron
Lecture Notes in Quantum Mechanics Doron Cohen Department of Physics, Ben-Gurion University, Beer-Sheva 84105, Israel These are the lecture notes of quantum mechanics courses that are given by DC at Ben · Spherical geometry, phase shifts · Cross section, optical theorem, resonances Quantum mechanics in practice
Lecture Notes in Quantum Mechanics Doron Cohen
Cohen, Doron
Lecture Notes in Quantum Mechanics Doron Cohen Department of Physics, Ben-Gurion University, Beer-Sheva 84105, Israel (arXiv:quant-ph/0605180) These are the lecture notes of quantum mechanics courses · Spherical geometry, phase shifts · Cross section, optical theorem, resonances Quantum mechanics in practice
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 classical to quantum mechanics . . . . . . . . . . . 47 3.14.1 Route I . . . . . . . . . . . . . . . . . . . . . 53 4 Symmetry in quantum mechanics 57 4.1 General discussions
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
Causal Structure in Categorical Quantum Mechanics
Murawski, Andrzej
Causal Structure in Categorical Quantum Mechanics Raymond Lal Christ Church University of Oxford mechanics is a way of formalising the structural features of quantum theory using category theory. It uses. In particular, categorical quantum mechanics provides a graphical calculus that exposes the information flow
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
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.
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Particle Interaction Summary quantum mechanics and special relativity together imply the existence of anti-particles forces are mediated
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: 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 a genuine incomplete- ness of standard quantum mechanics, however not an incompleteness that means
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.
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
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.
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.
Quantum mechanics without statistical postulates
H. Geiger; G. Obermair; Ch. Helm
1999-05-21
The Bohmian formulation of quantum mechanics is used in order to describe the measurement process in an intuitive way without a reduction postulate in the framework of a deterministic single system theory. Thereby the motion of the hidden classical particle is chaotic during almost all nontrivial measurement processes. For the correct reproduction of experimental results, it is further essential that the distribution function $P(x)$ of the results of a position measurement is identical with $|\\Psi|^2$ of the wavefunction $\\Psi$ of the single system under consideration. It is shown that this feature is not an additional assumption, but can be derived strictly from the chaotic motion of a single system during a sequence of measurements, providing a completely deterministic picture of the statistical features of quantum mechanics.
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.
Quantum Phase Operator and Phase States
Xin Ma; William Rhodes
2015-11-09
A proper Hermitian phase operator is formulated for the quantum harmonic oscillator. The phase operator satisfies trigonometric identities with appropriate behavior in time evolution. Its eigenstates are expressed in terms of Gegenbauer ultraspherical polynomials in the number state representation.
On reconciling quantum mechanics and local realism
Donald A. Graft
2013-09-04
A necessary and natural change in our application of quantum mechanics to separated systems is shown to reconcile quantum mechanics and local realism. An analysis of separation and localization justifies the proposed change in application of quantum mechanics. An important EPRB experiment is reconsidered and it is seen that when it is correctly interpreted it supports local realism. This reconciliation of quantum mechanics with local realism allows the axiom sets of quantum mechanics, probability, and special relativity to be joined in a consistent global axiom set for physics.
The quantum-mechanical inhomogeneous symplectic group
NASA Astrophysics Data System (ADS)
Wünsche, A.
2002-02-01
The structure of the quantum-mechanical inhomogeneous symplectic group ISp(2,C) in single boson mode is discussed and, in addition to its most common realization by quadratic combinations of the boson annihilation and creation operators, other nonlinear realizations are considered. The most basic disentanglement relations of the separation of squeezing (including rotation) and displacement operators are derived using a three-dimensional fundamental representation. The phase factors are determined using a special approach involving transformation of the inhomogeneous quadratic form in the boson operators to a central point together with special normal- and antinormal-ordering relations. In appendix B, the most basic formulae of operator disentanglement are collected together and special cases of the derived relations are considered.
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.
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.
A quantum genetic algorithm with quantum crossover and mutation operations
Akira SaiToh; Robabeh Rahimi; Mikio Nakahara
2013-11-22
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 which 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.
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}.
Faster than Hermitian Quantum Mechanics
Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.; Meister, Bernhard K.
2007-01-26
Given an initial quantum state vertical bar {psi}{sub I}> and a final quantum state vertical bar {psi}{sub F}>, there exist Hamiltonians H under which vertical bar {psi}{sub I}> evolves into vertical bar {psi}{sub F}>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time {tau}? For Hermitian Hamiltonians {tau} has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, {tau} can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from vertical bar {psi}{sub I}> to vertical bar {psi}{sub F}> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.
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.
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.
Teaching Quantum Mechanics on an Introductory Level.
ERIC Educational Resources Information Center
Muller, Rainer; Wiesner, Hartmut
2002-01-01
Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)
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.
Sensible Quantum Mechanics:. are Probabilities Only in the Mind?
NASA Astrophysics Data System (ADS)
Page, Don N.
Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so that it contains nothing probabilistic except conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by expectation values of positive-operator-valued awareness operators. Ratios of the measures for these sets of perceptions can be interpreted as frequency-type probabilities for many actually existing sets. These probabilities generally cannot be given by the ordinary quantum “probabilities” for a single set of alternatives. Probabilism, or ascribing probabilities to unconscious aspects of the world, may be seen to be an aesthemamorphic myth.
BOOK REVIEWS: Quantum Mechanics: Fundamentals
NASA Astrophysics Data System (ADS)
Whitaker, A.
2004-02-01
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 a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Quantum mechanics was already solidly established by 1966, but this second edition gives an indication of progress made and changes in perspective over the last thirty-five years, and also recognises the very substantial increase in knowledge of quantum theory obtained at the undergraduate level. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Their practical importance has now been fully recognised, and a substantial account of them is provided in the new book. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. John Bell’s work of the mid-1960s has led to genuine theoretical and experimental achievement, which has facilitated the development of quantum optics and quantum information theory. Gottfried’s 1966 book played a modest part in this development. When Bell became increasingly irritated with the standard theoretical approach to quantum measurement, Viki Weisskopf repeatedly directed him to Gottfried’s book. Gottfried had devoted a chapter of his book to these matters, titled ‘The Measurement Process and the Statistical Interpretation of Quantum Mechanics’. Gottfried considered the von Neumann or Dirac ‘collapse of state-vector’ (or ‘reduction postulate’ or ‘projection postulate’) was unsatisfactory, as he argued that it led inevitably to the requirement to include ‘consciousness’ in the theory. He replaced this by a more mathematically and conceptually sophisticated treatment in which, following measurement, the density matrix of the correlated measured and measuring systems, rho, is replaced by hat rho, in which the interference terms from rho have been removed. rho represents a pure state, and hat rho a mixture, but Gottfried argued that they are ‘indistinguishable’, and that we may make our replacement, ‘safe in the knowledge that the error will never be found’. Now our combined state is represented as a mixture, it is intuitive, Gottfried argued, to interpret it in a probabilistic way, |cm|2 being the probability of obtaining the mth measurement result. Bell liked Gottfried’s treatment little more than the cruder ‘collapse’ idea of von Neumann, and when, shortly before Bell’s death, his polemical article ‘Against measurement’ was published in the August 1990 issue of Physics World (pages 33-40), his targets included, not only Landau and Lifshitz’s classic Quantum Mechanics, pilloried for its advocacy of old-fashioned collapse, and a paper by van Kampen in Physica, but also Gottfried’s approach. Bell regarded his replacement of rho by hat rho as a ‘butchering’ of the density matrix, and considered, in any case, that even the butchered density matrix should represent co-existence of different terms, not a set of probabilities. Gottfried has replied to Bell ( Physics World, October 1991, pages 34-40; Nature 405, 533-36 (2000)). He has also become a major commentator on Bell’s work, for example editing the section on quantum foundations in the World Scientific edition of Bell’s collected works. Thus it is exceedingly interesting to disco
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 29 1.8.3 Resonances 30 1.9 Semiclassical Mechanics 31 1.9.1 The WKB Approximation 31 1.9.2 The EBK
Non-relativistic Quantum Mechanics versus Quantum Field Theories
Antonio Pineda
2007-05-29
We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.
Quantum Mechanics: Myths and Facts
NASA Astrophysics Data System (ADS)
Nikoli?, Hrvoje
2007-11-01
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.
NASA Astrophysics Data System (ADS)
Rapoport, Diego L.
2011-01-01
In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to the commutator of the True and False operators of matrix logic, still with a quantum superposed state related to a Moebius surface, and as the physical field at the basis of Spencer-Brown's primitive distinction in the protologic of the calculus of distinction. In this setting, paradox, self-reference, depth, time and space, higher-order non-dual logic, perception, spin and a time operator, the Klein bottle, hypernumbers due to Musès which include non-trivial square roots of ±1 and in particular non-trivial nilpotents, quantum field operators, the transformation of cognition to spin for two-state quantum systems, are found to be keenly interwoven in a world conception compatible with the philosophical approach taken for basis of this article. The Klein bottle is found not only to be the topological in-formation for self-reference and paradox whose logical counterpart in the calculus of indications are the paradoxical imaginary time waves, but also a classical-quantum transformer (Hadamard's gate in quantum computation) which is indispensable to be able to obtain a complete multivalued logical system, and still to generate the matrix extension of classical connective Boolean logic. We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation, generates the matrix logic which supersedes the classical logic of connectives and which has for particular subtheories fuzzy and quantum logics. Thus, from a primitive distinction in the vacuum plane and the axioms of the calculus of distinction, we can derive by incorporating paradox, the world conception succinctly described above.
Operation-triggered quantum clock synchronization
NASA Astrophysics Data System (ADS)
Yue, Jie-Dong; Zhang, Yu-Ran; Fan, Heng
2015-09-01
We present a quantum clock synchronization scheme of multiple parties which uses operation as the trigger to start the evolution of the initial state. In comparison, the existing protocols use measurement to start the evolution. We show that our protocol links the problem to a multiple-phase estimation problem, such that we have provided a general framework for the study of quantum clock synchronization. We can use the Fisher information to give the precision of the synchronization, and we explicitly show that the Heisenberg scale of synchronization is achieved in the two-party case. We prove that the measurement-triggered quantum clock synchronization is included in the operation-triggered quantum clock synchronization, so the operation-triggered quantum clock synchronization is, in general, more powerful than measurement-triggered quantum clock synchronization. We show that our protocol is very efficient in synchronizing a clock to the average time of other clocks.
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.
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.
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.
Distinguishability, classical information of quantum operations
Dong Yang
2005-04-09
A basic property of distinguishability is that it is non-increasing under further quantum operations. Following this, we generalize two measures of distinguishability of pure states--fidelity and von Neumann entropy, to mixed states as self-consistent measures. Then we extend these two measures to quantum operations. The information-theoretic point of the generalized Holevo quantity of an ensemble of quantum operations is constructed. Preferably it is an additive measure. The exact formula for SU(2) ensemble is presented. With the aid of the formula, we show Jozsa-Schlienz paradox that states as a whole are less distinguishable while all pairwise are more distinguishable in an ensemble of quantum states, also occurs in an ensemble of quantum operations, even in the minimal dimensional case SU(2) ensemble.
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
Propagators in polymer quantum mechanics
Flores-González, Ernesto Morales-Técotl, Hugo A. Reyes, Juan D.
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.
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.
Non-representative Quantum Mechanical Weak Values
NASA Astrophysics Data System (ADS)
Svensson, B. E. Y.
2015-09-01
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.
Non-representative Quantum Mechanical Weak Values
NASA Astrophysics Data System (ADS)
Svensson, B. E. Y.
2015-12-01
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.
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.
The Konigsberg Interpretation Of Quantum Mechanics?
Horner, Jack K.
THE KÖNIGSBERG INTERPRETATION OF QUANTUM MECHANICS? Jack K. Horner It is surely a truism that the science and philos ophy of an age influence one another; and this century has been no exception: the rise of quantum theory in particular profoundly threatened... against this criterion to show that the rejoinder must, if cogent, assume B. 1. The EPR argument. The object of the EPR argu ment Ts to show that the quantum theory fails to describe "completely" certain quantum-mechanical events. Provided...
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.
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.
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.
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.
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.
Supersymmetric Quantum Mechanics For Atomic Electronic Systems
NASA Astrophysics Data System (ADS)
Markovich, Thomas; Biamonte, Mason; Kouri, Don
2012-02-01
We employ our new approach to non-relativistic supersymmetric quantum mechanics (SUSY-QM), (J. Phys. Chem. A 114, 8202(2010)) for any number of dimensions and distinguishable particles, to treat the hydrogen atom in full three-dimensional detail. In contrast to the standard one-dimensional radial equation SUSY-QM treatment of the hydrogen atom, where the superpotential is a scalar, in a full three-dimensional treatment, it is a vector which is independent of the angular momentum quantum number. The original scalar Schr"odinger Hamiltonian operator is factored into vector ``charge'' operators: Q and Q^. Using these operators, the first sector Hamiltonian is written as H1= Q^.Q + E0^1. The second sector Hamiltonian is a tensor given by H2= Q Q^ + E0^11 and is isospectral with H1. The second sector ground state, ?0^(2), can be used to obtain the excited state wave functions of the first sector by application of the adjoint charge operator. We then adapt the aufbau principle to show this approach can be applied to treat the helium atom.
Bohmian particle trajectories contradict quantum mechanics
Michael Zirpel
2009-03-23
The Bohmian interpretation of quantum mechanics adds particle trajectories to the wave function and ensures that the probability distribution of the particle positions agrees with quantum mechanics at any time. This is not sufficient to avoid contradictions with quantum mechanics. There are correlations between particle positions at different times which cannot be reproduced with real particle trajectories. A simple rearrangement of an experimental test of the Bell-CHSH inequality demonstrates this.
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.
Quantum Mechanics and Closed Timelike Curves
Moldoveanu, Florin
2007-01-01
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.
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.
GRADUATE QUANTUM MECHANICS: 502 Spring 2002 Solutions to assignment 3.
Coleman, Piers
creation and annihilation operators, you may confirm that = u+ a + b 2 + v+ a + b 2 2 #12; = u- a - b 2GRADUATE QUANTUM MECHANICS: 502 Spring 2002 Solutions to assignment 3. 1. (Solution to Sakurai py m (3) are the annihilation operators for modes in the x and y directions, respectively
Introduction to Quantum Mechanics, Spring 2015 Problem Set 9
Woit, Peter
. Problem 2: Show that the linear transformation of annihilation and creation operators a a = a + a a (aIntroduction to Quantum Mechanics, Spring 2015 Problem Set 9 Due Thursday, February 5 Problem 1 state | , compute |Q| 1 #12;and |P| Show that coherent states are not eigenstates of the number operator
GRADUATE QUANTUM MECHANICS: 502 Spring 2002 Solutions to assignment 3.
Coleman, Piers
) in terms of the original creation and annihilation operators, you may confirm that # = u+ #18; a + b # 2GRADUATE QUANTUM MECHANICS: 502 Spring 2002 Solutions to assignment 3. 1. (Solution to Sakurai x m# #17; b = r m# 2â?¢h #16; y + i p y m# #17; (3) are the annihilation operators for modes in the x
Introduction to Quantum Mechanics, Spring 2015 Problem Set 12
Woit, Peter
involving products of annihilation and creation operators, can you write this interaction term as a momentum space integral involving products of annihilation and creation operators (in terms of the FourierIntroduction to Quantum Mechanics, Spring 2015 Problem Set 12 Due Tuesday, March 24 Problem 1
Introduction to Quantum Mechanics, Fall 2014 Problem Set 1
Woit, Peter
the representation (, C3 ) this gives on the vector space C3 of complex valued functions on the set of 3 elements (asIntroduction to Quantum Mechanics, Fall 2014 Problem Set 1 Due Tuesday, September 16 Problem 1 mechanical system with state space H = C3 and Hamilto- nian operator H = 0 1 0 1 0 0 0 0 2 Solve the Schr
NASA Astrophysics Data System (ADS)
Courbage, M.
1982-04-01
We study some mathematical problems posed in nonequilibrium statistical mechanics and subdynamics theory developed by Prigogine and coworkers. We study in the superspace of the Hilbert-Schmidt operators the solution of the Liouville-von Neumann equation. The application in this frame of the spectral deformation methods yields expression of analytic continuations of a class of matrix elements of the resolvent of the Liouville-von Neumann operator, and this allows the analytic continuation of the collision and destruction operators. However, it is impossible to obtain simultaneously analytic continuation of the creation operator in this frame. The above results will be used in the second part of the article in order to study the pseudo-Markovian equation.
Extending quantum mechanics entails extending special relativity
S. Aravinda; R. Srikanth
2015-09-21
The complementarity of signaling and local randomness in the resources required to simulate singlet statistics is a fundamental feature of quantum nonlocality, that unifies a number results. Here we generalize the complementarity 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.
The representation of numbers in quantum mechanics.
Benioff, P.; Physics
2002-12-01
Earlier work on modular arithmetic of k-ary representations of length L of the natural numbers in quantum mechanics is extended here to k-ary representations of all natural numbers, and to integers and rational numbers. Since the length L is indeterminate, representations of states and operators using creation and annihilation operators for bosons and fermions are defined. Emphasis is on definitions and properties of operators corresponding to the basic operations whose properties are given by the axioms for each type of number. The importance of the requirement of efficient implementability for physical models of the axioms is emphasized. Based on this, successor operations for each value of j corresponding to addition of k {l_brace}j-1{r_brace} if j>0 and k {l_brace}j{r_brace} if j<0 are defined. It follows from the efficient implementability of these successors, which is the case for all computers, that implementation of the addition and multiplication operators, which are defined in terms of polynomially many iterations of the successors, should be efficient. This is not the case for definitions based on the successor for j=1 only. This is the only successor defined in the usual axioms of arithmetic.
Landsman, N.P. "Klaas"
(H), for some Hilbert space H. Another key example is A = C0(X), the space of all continuous complex- valuedAlgebraic quantum mechanics Algebraic quantum mechanics is an abstraction and generalization of the Hilbert space formulation of quantum mechanics due to von Neumann [5]. In fact, von Neumann himself played
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.
Bohmian Mechanics and the Quantum Revolution
Sheldon Goldstein
1995-12-26
This is a review-essay on ``Speakable and Unspeakable in Quantum Mechanics'' by John Bell and ``The Undivided Universe: An Ontological Interpretation of Quantum Mechanics'' by David Bohm and Basil Hiley. The views of these authors concerning the character of quantum theory and quantum reality---and, in particular, their approaches to the issues of nonlocality, the possibility of hidden variables, and the nature of and desiderata for a satisfactory scientific explanation of quantum phenomena---are contrasted, with each other and with the orthodox approach to these issues.
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.
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.
Moyal Quantum Mechanics: The Semiclassical Heisenberg Dynamics
T. A. Osborn; F. H. Molzahn
1994-09-21
The Moyal--Weyl description of quantum mechanics provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in $\\hbar$. Its semiclassical expansion `coefficients,' acting on symbols that represent observables, are simple, globally defined differential operators constructed in terms of the classical flow. Two methods of constructing this expansion are discussed. The first introduces a cluster-graph expansion for the symbol of an exponentiated operator, which extends Groenewold's formula for the Weyl product of symbols. This Poisson bracket based cluster expansion determines the Jacobi equations for the semiclassical expansion of `quantum trajectories.' Their Green function solutions construct the regular $\\hbar\\downarrow0$ 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 $\\hbar$ coefficients recursively. The Heisenberg--Weyl description of evolution involves no essential singularity in $\\hbar$, no Hamilton--Jacobi equation to solve for the action, and no multiple trajectories, caustics or Maslov indices.
Negative Observations in Quantum Mechanics
D. M. Snyder
1999-12-06
In quantum mechanics, it is possible to make observations that affect physical entities without there being a physical interaction between the observer and the physical entity measured. Epstein (1945) and Renninger (1960) discussed this situation, and Renninger called this type of observation a "negative observation." Empirical research on electron shelving supports the possibility of negative observations (Bergquist, Hulet, Itano, and Wineland, 1986; Nagourney, Sandberg, and Dehmelt, 1986; Sauter, Neuhauser, Blatt, and Toschek, 1986). Two scenarios are presented that emphasize the role of human observation in negative observations. The first is modeled after the two hole gedankenexperiments of Feynman, Leighton, and Sands (1965) and portrays negative observations in a non-technical manner. The second scenario allows for quantifying the affect on physical entities of negative observations in a simple fashion. In addition, various issues related to negative observation are discussed, including an objection that might be raised. The Schrodinger cat gedankenexperiment is discussed briefly as well.
Kindergarten Quantum Mechanics: Lecture Notes
Coecke, Bob
2006-01-04
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 which subsumes my Logic of Entanglement. For a survey on the 'what', the 'why' and the 'hows' I refer to a previous set of lecture notes. In a last section we provide some pointers to the body of technical literature on the subject.
Pragmatic Information in Quantum Mechanics
Roederer, Juan G
2015-01-01
An objective definition of pragmatic information and the consideration of recent results about information processing in the human brain can help overcome some traditional difficulties with the interpretation of quantum mechanics. Rather than attempting to define information ab initio, I introduce the concept of interaction between material bodies as a primary concept. Two distinct categories can be identified: 1) Interactions which can always be reduced to a superposition of physical interactions (forces) between elementary constituents; 2) Interactions between complex bodies which cannot be reduced to a superposition of interactions between parts, and in which patterns and forms (in space and/or time) play the determining role. Pragmatic information is then defined as the correspondence between a given pattern and the ensuing pattern-specific change. I will show that pragmatic information is a biological concept that plays no active role in the purely physical domain; it only does so when a living organism ...
NONEQUILIBRIUM QUANTUM STATISTICAL MECHANICS AND THERMODYNAMICS #
NONEQUILIBRIUM QUANTUM STATISTICAL MECHANICS AND THERMODYNAMICS # Walid K. Abou Salem + Institut f recent progress in deriving the fundamental laws of thermodynamics (0 th , 1 st and 2 nd Âlaw) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and di#erent reversible
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 Friday, June 19, 2009 #12;String Theory Origins We introduced string theory as a possible solution to our
Quantum Mechanics with a Little Less Mystery
ERIC Educational Resources Information Center
Cropper, William H.
1969-01-01
Suggests the "route of the inquiring mind in presenting the esoteric quantum mechanical postulates and concepts in an understandable form. Explains that the quantum mechanical postulates are but useful mathematical forms to express thebroader principles of superposition and correspondence. Briefly describes some of the features which makes the…
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.
Random Matrix theory approach to Quantum mechanics
K. V. S. Shiv Chaitanya
2015-01-27
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of random matrix theory. This study helps in identify the potential appear in the joint probability distribution function in the random matrix theory as a super potential. This approach allows to extend the random matrix theory to the newly discovered exceptional polynomials.
Coherent state operators in loop quantum gravity
NASA Astrophysics Data System (ADS)
Alesci, Emanuele; Dapor, Andrea; Lewandowski, Jerzy; Mäkinen, Ilkka; Sikorski, Jan
2015-11-01
We present a new method for constructing operators in loop quantum gravity. The construction is an application of the general idea of "coherent state quantization," which allows one to associate a unique quantum operator with every function on a classical phase space. Using the heat kernel coherent states of Hall and Thiemann, we show how to construct operators corresponding to functions depending on holonomies and fluxes associated with a fixed graph. We construct the coherent state versions of the fundamental holonomy and flux operators, as well as the basic geometric operators of area, angle, and volume. Our calculations show that the corresponding canonical operators are recovered from the coherent state operators in the limit of large spins.
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
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.
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.
Exactly and quasi-exactly solvable `discrete' quantum mechanics
Ryu Sasaki
2010-04-27
Brief introduction to the discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators, dynamical symmetry algebras including the $q$-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable Hamiltonians in one-dimensional `discrete' quantum mechanics is presented. It reproduces all the known ones whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and quasi-exactly solvable ones are constructed. The sinusoidal coordinate plays an essential role.
Exactly and quasi-exactly solvable `discrete' quantum mechanics
Sasaki, Ryu
2010-01-01
Brief introduction to the discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators, dynamical symmetry algebras including the $q$-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable Hamiltonians in one-dimensional `discrete' quantum mechanics is presented. It reproduces all the known ones whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and quasi-exactly solvable ones are constructed. The sinusoidal coordinate plays an essential role.
Exactly and quasi-exactly solvable 'discrete' quantum mechanics.
Sasaki, Ryu
2011-03-28
A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role. PMID:21320918
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.
The formal path integral and quantum mechanics
Theo Johnson-Freyd
2010-09-05
Given an arbitrary Lagrangian function on \\RR^d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by "Feynman diagrams," although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a "Fubini theorem" expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous-quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by "cutting and pasting" and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic "formal path integral" for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.
The formal path integral and quantum mechanics
Johnson-Freyd, Theo
2010-11-15
Given an arbitrary Lagrangian function on R{sup d} and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.
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.
Implementation of the quantum-walk step operator in lateral quantum dots
NASA Astrophysics Data System (ADS)
van Hoogdalem, K. A.; Blaauboer, M.
2009-09-01
We propose a physical implementation of the step operator of the discrete quantum walk for an electron in a one-dimensional chain of quantum dots. The operating principle of the step operator is based on locally enhanced Zeeman splitting and the role of the quantum coin is played by the spin of the electron. We calculate the probability of successful transfer of the electron in the presence of decoherence due to quantum charge fluctuations, modeled as a bosonic bath. We then analyze two mechanisms for creating locally enhanced Zeeman splitting based on, respectively, locally applied electric and magnetic fields and slanting magnetic fields. Our results imply that a success probability of >90% is feasible under realistic experimental conditions.
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.
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.
Statistical Structures Underlying Quantum Mechanics and Social Science
NASA Astrophysics Data System (ADS)
Wright, Ron
2007-08-01
Common observations of the unpredictability of human behavior and the influence of one question on the answer to another suggest social science experiments are probabilistic and may be mutually incompatible with one another, characteristics attributed to quantum mechanics (as distinguished from classical mechanics). This paper examines this superficial similarity in depth using the Foulis-Randall Operational Statistics language. In contradistinction to physics, social science deals with complex, open systems for which the set of possible experiments is unknowable and outcome interference is a graded phenomenon resulting from the ways the human brain processes information. It is concluded that social science is, in some ways, “less classical” than quantum mechanics, but that generalized “quantum” structures may provide appropriate descriptions of social science experiments. Specific challenges to extending “quantum” structures to social science are identified.
Phase-space contraction and quantum operations
Garcia-Mata, Ignacio; Spina, Maria Elena; Saraceno, Marcos; Carlo, Gabriel
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.
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.
Radon-Nikodym derivatives of quantum operations
Maxim Raginsky
2003-09-16
Given a completely positive (CP) map $T$, there is a theorem of the Radon-Nikodym type [W.B. Arveson, Acta Math. {\\bf 123}, 141 (1969); V.P. Belavkin and P. Staszewski, Rep. Math. Phys. {\\bf 24}, 49 (1986)] that completely characterizes all CP maps $S$ such that $T-S$ is also a CP map. This theorem is reviewed, and several alternative formulations are given along the way. We then use the Radon-Nikodym formalism to study the structure of order intervals of quantum operations, as well as a certain one-to-one correspondence between CP maps and positive operators, already fruitfully exploited in many quantum information-theoretic treatments. We also comment on how the Radon-Nikodym theorem can be used to derive norm estimates for differences of CP maps in general, and of quantum operations in particular.
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.
Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology
Gell-Mann, Murray; Gell-Mann, Murray; Hartle, James B.
1993-01-01
We investigate the origin of the arrow of time in quantum mechanics in the context of quantum cosmology. The ``Copenhagen'' quantum mechanics of measured subsystems incorporates a fundamental arrow of time. Extending discussions of Aharonov, Bergmann and Lebovitz, Griffiths, and others we investigate a generalized quantum mechanics for cosmology that utilizes both an initial and a final density matrix to give a time-neutral formulation without a fundamental arrow of time. Time asymmetries can arise for particular universes from differences between their initial and final conditions. Theories for both would be a goal of quantum cosmology. A special initial condition and a final condition of indifference would be sufficient to explain the observed time asymmetries of the universe. In this essay we ask under what circumstances a completely time symmetric universe, with T-symmetric initial and final condition, could be consistent with the time asymmetries of the limited domain of our experience. We discuss the ap...
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.
Faster quantum searching with almost arbitrary operators
Avatar Tulsi
2015-03-19
Grover search algorithm drives a quantum system from an initial state to a desired final state by using selective phase inversions of these two states. In (1), we studied a generalization of Grover algorithm which relaxes the assumption of the efficient implementation of the selective phase inversion of the initial state, also known as diffusion operator. This assumption is known to become a serious handicap in cases of physical interest (2,3,4,5). Our general search algorithm works with almost arbitrary diffusion operator with only restriction of having the initial state as one of its eigenstates. The price that we pay for using arbitrary operator is an increase in the number of oracle queries by a factor of order of B, where B is a characteristic of the eigenspectrum of diffusion operator and it can be large in some situations. Here we show that by using quantum fourier transform, we can regain the optimal query complexity of Grover algorithm without losing the freedom of using arbitrary diffusion operators for quantum searching. However, the total number of operators required by algorithm is still order of B times more than that of Grover algorithm. So our algorithm offers advantage only if oracle operator is computationally more expensive than diffusion operator, which is true in most search problems.
Irreversibility and Measurement in Quantum Mechanics
D. M. Snyder
2000-02-28
Irreversibility is often considered to characterize measurements in quantum mechanics. Fundamental problems with this characterization are addressed. First, whether a measurement is made in quantum mechanics is an arbitrary decision on the part of the experimenter concerning how the experimental circumstances are structured. Second, how is irreversibility that occurs in making a measurement explained in terms of a neurophysiological mechanism where a macroscopic measuring instrument is not required in principle to make the measurement, as in macroscopic quantum tunneling? Third, how does irreversibility characterize a negative observation where there is no physical interaction in the measurement process?
The formal path integral and quantum mechanics
Johnson-Freyd, Theo
2010-01-01
Given an arbitrary Lagrangian function on \\RR^d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by "Feynman diagrams," although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a "Fubini theorem" expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous-quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by "cutting and pasting" and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic "formal path integral" for the nonrelativistic qu...
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 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
Why space has three dimensions: A quantum mechanical explanation
NASA Astrophysics Data System (ADS)
Marcer, Peter; Schempp, Walter
2000-05-01
The theoretical physics of a quantum mechanical model of space, relativistic quantum holography, is described. It specifies three dimensions, such as is validated by the nature of our spatial experience, but where additionally, quantum non-locality, which Feynman described as the only mystery of quantum theory, is made manifest by means of observable phase relationships. For example, synchronicity between events, and other phenomena such as are described by the geometric/Berry phase, etc., which are outside the bounds of classical explanation. It can therefore be hypothesized: a) that we live in a entirely quantum mechanical world/universe and not a classical mechanical one (where quantum phenomena are confined to the microscopic scale) as is the current generally held scientific view, b) that three spatial dimensions are a fundamental consequence of quantum mechanics, c) that quantum holography is a natural candidate to explain quantum gravity, such that mass/inertia concerns not the eigenvalues of some operator, but rather the observable gauge invariant phases of a state vector, postulated to be that of the universe itself, as a whole, and d) that this model provides a natural explanation in terms of relativistic quantum signal processing of any each individual's perception and cognition will be of a three dimensional world, defined similarly in relation to each individual's quantum state vector, describing its mind/body and associated gauge invariant phases or mindset, which have observable consequences, such that mental processes and events can cause neural events and processes! These testable hypotheses, if validated, will have profound implications for our understanding, radically changing our scientific perspective on the world, as we enter the new millennium. .
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.
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
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.
Introduction to Quantum Mechanics, Spring 2015 Problem Set 14
Woit, Peter
in three dimensions, find the quadratic functions Lj on the phase space of complex valued functions on R3 Problem 3: For the complex-valued scalar field theory, show that the charge operator Q has the followingIntroduction to Quantum Mechanics, Spring 2015 Problem Set 14 Due Tuesday, April 21 Problem 1: Show
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.
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
Tensor Fields in Relativistic Quantum Mechanics
Valeriy V. Dvoeglazov
2015-11-21
We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We discuss corresponding massless limits. We analize the quantum field theory taking into account the mass dimensions of the notoph and the photon. Next, we deduced the gravitational field equations from relativistic quantum mechanics.
Tensor Fields in Relativistic Quantum Mechanics
Dvoeglazov, Valeriy V
2015-01-01
We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We discuss corresponding massless limits. We analize the quantum field theory taking into account the mass dimensions of the notoph and the photon. Next, we deduced the gravitational field equations from relativistic quantum mechanics.
Alternative Approach to Noncommutative Quantum Mechanics on a Curved Space
Nakamura, M
2015-01-01
Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator method. Imposing the additional constraints to eliminate the reduntant degrees of freedom, the noncommutative quantum system with noncommutativity among the coordinates on the curved space is exactly constructed. Then, it is shown that the resultant Hamiltonian contains the quantum corrections in the exact form. We further discuss the additional constraints to realize the noncommutativities both of coordinates and momenta on the curved space.
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.
On the Birth of Quantum Mechanics.
ERIC Educational Resources Information Center
Singh, C. P.
1991-01-01
An event that created a revolution in physics, the birth of quantum mechanics, is discussed. The rich, complex, dramatic as well as touching story of fights and contradictions between two groups of great scientists is described. (Author)
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.
Student Difficulties in Learning Quantum Mechanics.
ERIC Educational Resources Information Center
Johnston, I. D.; Crawford, K.; Fletcher, P. R.
1998-01-01
Reports on a preliminary project that uses a phenomenographic approach to explore the ways in which a small number of fundamental ideas are conceptualized by students who are judged to have mastered quantum mechanics material. (DDR)
Quantum mechanical stabilization of Minkowski signature wormholes
Visser, M.
1989-05-19
When one attempts to construct classical wormholes in Minkowski signature Lorentzian spacetimes violations of both the weak energy hypothesis and averaged weak energy hypothesis are encountered. Since the weak energy hypothesis is experimentally known to be violated quantum mechanically, this suggests that a quantum mechanical analysis of Minkowski signature wormholes is in order. In this note I perform a minisuperspace analysis of a simple class of Minkowski signature wormholes. By solving the Wheeler-de Witt equation for pure Einstein gravity on this minisuperspace the quantum mechanical wave function of the wormhole is obtained in closed form. The wormhole is shown to be quantum mechanically stabilized with an average radius of order the Planck length. 8 refs.
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)
Lee, Sang-Bong
1993-09-01
Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaotic nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover`s and Kubo-Fox-Keizer`s approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty.
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.
Quantum mechanical effects on the shock Hugoniot
Bennett, B.I. ); Liberman, D.A. )
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.
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.
Linear Logic for Generalized Quantum Mechanics Vaughan Pratt
Pratt, Vaughan
Linear Logic for Generalized Quantum Mechanics Vaughan Pratt Dept. of Computer Science Stanford connection to quantum mechanics. 1 Motivation VLSI designers will eventually need to reckon with quantum with a deduction theorem or currying principle. Quantum logic as a faithful abstraction of quantum mechanics must
Dynamical phase transitions in quantum mechanics
NASA Astrophysics Data System (ADS)
Rotter, Ingrid
2012-02-01
The nucleus is described as an open many-body quantum system with a non-Hermitian Hamilton operator the eigenvalues of which are complex, in general. The eigenvalues may cross in the complex plane (exceptional points), the phases of the eigenfunctions are not rigid in approaching the crossing points and the widths bifurcate. By varying only one parameter, the eigenvalue trajectories usually avoid crossing and width bifurcation occurs at the critical value of avoided crossing. An analog spectroscopic redistribution takes place for discrete states below the particle decay threshold. By this means, a dynamical phase transition occurs in the many-level system starting at a critical value of the level density. Hence the properties of the low-lying nuclear states (described well by the shell model) and those of highly excited nuclear states (described by random ensembles) differ fundamentally from one another. The statement of Niels Bohr on the collective features of compound nucleus states at high level density is therefore not in contradiction to the shell-model description of nuclear (and atomic) states at low level density. Dynamical phase transitions are observed experimentally in different quantum mechanical systems by varying one or two parameters.
Mechanical equivalent of quantum heat engines
NASA Astrophysics Data System (ADS)
Arnaud, Jacques; Chusseau, Laurent; Philippe, Fabrice
2008-06-01
Quantum heat engines employ as working agents multilevel systems instead of classical gases. We show that under some conditions quantum heat engines are equivalent to a series of reservoirs at different altitudes containing balls of various weights. A cycle consists of picking up at random a ball from one reservoir and carrying it to the next, thereby performing or absorbing some work. In particular, quantum heat engines, employing two-level atoms as working agents, are modeled by reservoirs containing balls of weight 0 or 1. The mechanical model helps us prove that the maximum efficiency of quantum heat engines is the Carnot efficiency. Heat pumps and negative temperatures are considered.
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.
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.
The information entropy of quantum mechanical states
Alexander Stotland; Andrei A. Pomeransky; Eitan Bachmat; Doron Cohen
2004-05-24
It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the latter is problematic from quantum information point of view. Consequently we introduce a new definition of entropy that reflects the inherent uncertainty of quantum mechanical states. We derive for it an explicit expression, and discuss some of its general properties. We distinguish between the minimum uncertainty entropy of pure states, and the excess statistical entropy of mixtures.
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.
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.
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
Chaotic Evolution in Quantum Mechanics
Asher Peres
1995-08-11
A quantum system is described, whose wave function has a complexity which increases exponentially with time. Namely, for any fixed orthonormal basis, the number of components required for an accurate representation of the wave function increases exponentially.
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
Huang, Yi-Zhi
Quantum Hall systems Representation theory of vertex operator algebras Applications The end Quantum Science, CAS #12;Quantum Hall systems Representation theory of vertex operator algebras Applications quantum computation 2 Representation theory of vertex operator algebras Vetrex operator algebras, modules
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).
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...
Cryptographic Distinguishability Measures for Quantum Mechanical States
Christopher A. Fuchs; Jeroen van de Graaf
1998-04-03
This paper, mostly expository in nature, surveys four measures of distinguishability for quantum-mechanical states. This is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography. Each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions: namely, the probability of an identification error, the Kolmogorov distance, the Bhattacharyya coefficient, and the Shannon distinguishability (as defined through mutual information). These measures have a long history of use in statistical pattern recognition and classical cryptography. We obtain several inequalities that relate the quantum distinguishability measures to each other, one of which may be crucial for proving the security of quantum cryptographic key distribution. In another vein, these measures and their connecting inequalities are used to define a single notion of cryptographic exponential indistinguishability for two families of quantum states. This is a tool that may prove useful in the analysis of various quantum cryptographic protocols.
Quantum Mechanics, Nonlinear Dynamics, and Correlated Statistical Mechanics
NASA Astrophysics Data System (ADS)
McHarris, Wm. C.
2007-02-01
Many of the so-called paradoxes of orthodox quantum mechanics can be shown to have parallel, more logical interpretations in the realm of nonlinear dynamics and chaos theory. Among these are violations of Bell-type inequalities, which in comparing "classical" mechanics with quantum mechanics implicitly compare uncorrelated and correlated statistics. During the past decade research in the field of nonextensive thermodynamics (including Tsallis entropy) has demonstrated the existence of many statistical correlations in classical, nonlinear systems. When such correlations exist, the conventional classical upper limit on statistical correlations in Bell-type experiments can easily be raised to overlap with quantum mechanical predictions involving correlated states such as the Bell singlet state, a favorite for deriving Bell inequalities. Thus, arguments based on experimental violations of Bell-type inequalities, which rule out the existence of "local reality," become moot. Perhaps quantum mechanics does have a deterministic, ontological basis, albeit one based in nonlinear dynamics and chaos theory. If so, deterministic chaos could provide Einstein's longed-for fundamental determinism, but because chaotic systems must be interpreted statistically, this also fits in quite well with the ideas of Bohr — Einstein and Bohr both could have been correct! It should be emphasized that the concept of nonlinear dynamics and chaos underpinning quantum mechanics does not involve hidden variables, nor does the fact that chaos is deterministic interlope on the existence of free will.
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.
The Möbius Symmetry of Quantum Mechanics
Alon E. Faraggi; Marco Matone
2015-02-16
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 M\\"obius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global M\\"obius 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 M\\"obius 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.
e measure of all things: quantum mechanics and the soul
Halvorson, Hans
e measure of all things: quantum mechanics and the soul Hans Halvorson Introduction e twentieth and our place in the universe). e introduction of quantum mechanics may be the greatest scienti c around quantum mechanics. For example, some claim that quantum mechanics proves that the universe
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
Chem 7940 Quantum Mechanics II Spring 2013 Chemistry 7940
Chem 7940 Quantum Mechanics II Spring 2013 Chemistry 7940 Quantum Mechanics II Spring 2013. (Confucius) We shall refer to a variety of sources. You should have a standard quantum mechanics text investigation of foundational issues in quantum mechanics. See also the article by Zeilinger [31
Chem 7940 Quantum Mechanics II Spring 2013 Chemistry 7940
Chem 7940 Quantum Mechanics II Spring 2013 Chemistry 7940 Quantum Mechanics II Spring 2013 Course with classical mechanics. · Relaxation and decoherence. · Generalized measurements, quantum information theory of the path integral. · Path integral formulation of quantum statistical mechanics: polymer beads, and all
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.
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.
Operational meaning of quantum measures of recovery
Tom Cooney; Christoph Hirche; Ciara Morgan; Jonathan P. Olson; Kaushik P. Seshadreesan; Mark M. Wilde
2015-12-16
Several information measures have recently been defined which capture the notion of "recoverability" of a tripartite quantum state. In particular, the fidelity of recovery quantifies how well one can recover a system $A$ of a tripartite state, defined on systems $ABC$, by acting on system $C$ alone. The relative entropy of recovery is an associated measure in which the fidelity is replaced by relative entropy. The fact that state recoverability plays a key role in applications such as quantum key distribution and error correction suggests that we should try to understand the property of recoverability in more detail. In this paper, we provide concrete operational interpretations of the aforementioned recovery measures in terms of a computational decision problem and a hypothesis testing scenario, each of which is connected to the notion of recovery. Specifically, we show that the fidelity of recovery is equal to the maximum probability with which a computationally unbounded quantum prover can convince a computationally bounded quantum verifier that a given quantum state is recoverable. This places the associated decision problem in QIP and establishes it as hard for QSZK (a class of problems believed to be difficult to solve even for a quantum computer). We also prove that the regularized relative entropy of recovery is equal to the optimal Type II error exponent when trying to distinguish many copies of a tripartite state from a recovered version of this state, such that the Type I error is constrained to be no larger than a specified constant.
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.
Mechanical Resonators for Quantum Optomechanics Experiments at Room Temperature
Norte, Richard A; Gröblacher, Simon
2015-01-01
All quantum optomechanics experiments to date operate at cryogenic temperatures, imposing severe technical challenges and fundamental constraints. Here we present a novel design of on-chip mechanical resonators which exhibit fundamental modes with frequencies $f$ and mechanical quality factors $Q_\\mathrm{m}$ sufficient to enter the optomechanical quantum regime at room temperature. We overcome previous limitations by designing ultra-thin, high-stress silicon nitride membranes, with tensile stress in the resonators' clamps close to the ultimate yield strength of the material. By patterning a photonic crystal on the SiN membranes, we observe reflectivities greater than 99%. These on-chip resonators have remarkably low mechanical dissipation, with $Q_\\mathrm{m}$$\\sim$$10^8$, which makes them a unique platform for experiments towards the observation of massive quantum behavior at room temperature.
Mechanical Resonators for Quantum Optomechanics Experiments at Room Temperature
Richard A. Norte; Joao P. Moura; Simon Gröblacher
2015-11-19
All quantum optomechanics experiments to date operate at cryogenic temperatures, imposing severe technical challenges and fundamental constraints. Here we present a novel design of on-chip mechanical resonators which exhibit fundamental modes with frequencies $f$ and mechanical quality factors $Q_\\mathrm{m}$ sufficient to enter the optomechanical quantum regime at room temperature. We overcome previous limitations by designing ultra-thin, high-stress silicon nitride membranes, with tensile stress in the resonators' clamps close to the ultimate yield strength of the material. By patterning a photonic crystal on the SiN membranes, we observe reflectivities greater than 99%. These on-chip resonators have remarkably low mechanical dissipation, with $Q_\\mathrm{m}$$\\sim$$10^8$, which makes them a unique platform for experiments towards the observation of massive quantum behavior at room temperature.
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.
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.
Bibliographic guide to the foundations of quantum mechanics and quantum information
Adan Cabello
2004-11-15
This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, web sites, etc.), sorted alphabetically and (some of them) classified by subject, on foundations of quantum mechanics and quantum information. Specifically, it covers hidden variables (``no-go'' theorems, experiments), interpretations of quantum mechanics, entanglement, quantum effects (quantum Zeno effect, quantum erasure, ``interaction-free'' measurements, quantum ``non-demolition'' measurements), quantum information (cryptography, cloning, dense coding, teleportation), and quantum computation.
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.
How to teach Quantum Mechanics
Oliver Passon
2004-04-22
In the spirit and style of John S. Bell's well known paper on How to Teach Special Relativity it is argued, that a ``Bohmian pedagogy''provides a very useful tool to illustrate the relation between classical and quantum physics and illuminates the peculiar features of the latter.
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?".
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…
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.
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.
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.
Standard Quantum Limit for Probing Mechanical Energy Quantization
Corbitt, Thomas R.
We derive a standard quantum limit for probing mechanical energy quantization in a class of systems with mechanical modes parametrically coupled to external degrees of freedom. To resolve a single mechanical quantum, it ...
Epistemology of quantum mechanics: the Växjö viewpoint
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
2011-09-01
This paper summarizes the experience of the Växjö series of conferences - the longest series of conferences on foundations of quantum mechanics. One of the main lessons of this series is that the present state of development of quantum theory does not exclude a possibility to elaborate a local realistic interpretation. One of such interpretations, the Växjö interpretation, combines realism and contextuality. And it became recognized worldwide.
Boundary Operators in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Esposito, Giampiero
The fundamental laws of physics can be derived from the requirement of invariance under suitable classes of transformations on the one hand, and from the need for a well-posed mathematical theory on the other hand. As a part of this programme, the present paper shows under which conditions the introduction of pseudodifferential boundary operators in one-loop Euclidean quantum gravity is compatible both with their invariance under infinitesimal diffeomorphisms and with the requirement of a strongly elliptic theory. Suitable assumptions on the kernel of the boundary operator make it therefore possible to overcome problems resulting from the choice of purely local boundary conditions.
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 that proves that two separated quantum entities cannot be described by means of standard quantum mechanics of this result indicates a failure of standard quantum mechanics, and not just some peculiar shortcoming due
The Linearity of Quantum Mechanics at Stake: The Description of Separated Quantum Entities
Aerts, Diederik
The Linearity of Quantum Mechanics at Stake: The Description of Separated Quantum Entities Diederik entity cannot be described by standard quantum mechanics. More precisely, it was shown that two with the superposition principle, which means that sep- arated quantum entities put the linearity of quantum mechanics
Philosophy of Quantum Mechanics Quantum theory is arguably the most accurate scientific theory ever
Callender, Craig
1 PHIL 245: Philosophy of Quantum Mechanics Quantum theory is arguably the most accurate scientific: yes, but youll have to learn some simple quantum mechanics. A good test is whether youre able to get through the chapter on the quantum formalism in #12;2 Alberts Quantum Mechanics and Experience. Well go
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.
Realism and Objectivism in Quantum Mechanics
Vassilios Karakostas
2012-03-01
The present study attempts to provide a consistent and coherent account of what the world could be like, given the conceptual framework and results of contemporary quantum theory. It is suggested that standard quantum mechanics can, and indeed should, be understood as a realist theory within its domain of application. It is pointed out, however, that a viable realist interpretation of quantum theory requires the abandonment or radical revision of the classical conception of physical reality and its traditional philosophical presuppositions. It is argued, in this direction, that the conceptualization of the nature of reality, as arising out of our most basic physical theory, calls for a kind of contextual realism. Within the domain of quantum mechanics, knowledge of 'reality in itself', 'the real such as it truly is' independent of the way it is contextualized, is impossible in principle. In this connection, the meaning of objectivity in quantum mechanics is analyzed, whilst the important question concerning the nature of quantum objects is explored.
Presenting Nonreflexive Quantum Mechanics: Formalism and Metaphysics
Krause, Decio
2015-01-01
Nonreflexive quantum mechanics is a formulation of quantum theory based on a non-classical logic termed \\ita{nonreflexive logic} (a.k.a. `non-reflexive'). In these logics, the standard notion of identity, as encapsulated in classical logic and set theories, does not hold in full. The basic aim of this kind of approach to quantum mechanics is to take seriously the claim made by some authors according to whom quantum particles are \\ita{non-individuals} in some sense, and also to take into account the fact that they may be absolutely indistinguishable (or indiscernible). The nonreflexive formulation of quantum theory assumes these features of the objects already at the level of the underlying logic, so that no use is required of symmetrization postulates or other mathematical devices that serve to pretend that the objects are indiscernible (when they are not: all objects that obey classical logic are \\ita{individuals} in a sense). Here, we present the ideas of the development of nonreflexive quantum mechanics an...
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
Green's Functions and Their Applications to Quantum Mechanics
Morrow, James A.
Green's Functions and Their Applications to Quantum Mechanics Jeff Schueler June 2, 2011 Contents 1 Green's Functions in Quantum Mechanics and Many-body Theory 8 3.1 Time Independent Green's Fuctions, specifically in how they apply to quantum mechan- ics. I plan to introduce some of the fundamentals of quantum
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.
Quantum mechanics and consciousness: fact and fiction
Ulrich Mohrhoff
2014-08-03
This article was written in response to a request from an editor of American Vedantist. It is shown that the idea that consciousness is essential to understanding quantum mechanics arises from logical fallacies. This may be welcome news to those who share the author's annoyance at consciousness being dragged into discussions of physics, but beware: The same fallacies may underlie the reader's own way of making sense of quantum mechanics. The article ends up embracing a Vedantic world view, for two reasons. For one, such a world view seems to the author to be the most sensible alternative to a materialistic one. For another, quantum mechanics is inconsistent with a materialistic world view but makes perfect sense within a Vedantic framework of thought.
Phase space propagators for quantum operators
Ozorio de Almeida, A.M.; Brodier, O. . E-mail: ozorio@cbpf.br
2006-08-15
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.
Estimates on Functional Integrals of Quantum Mechanics and Non-Relativistic Quantum Field Theory
Gonzalo A. Bley; Lawrence E. Thomas
2015-12-26
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form $E\\left[\\exp(A_T)\\right]$, the (effective) action $A_T$ being a function of particle trajectories up to time $T$. The estimates in turn yield rigorous lower bounds for ground state energies, via the Feynman-Kac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is first illustrated in familiar quantum mechanical settings: for the hydrogen atom, for a Schr\\"odinger operator with $1/|x|^2$ potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.
Estimates on Functional Integrals of Quantum Mechanics and Non-Relativistic Quantum Field Theory
Gonzalo A. Bley; Lawrence E. Thomas
2015-12-01
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form $E\\left[\\exp(A_T)\\right]$, the (effective) action $A_T$ being a function of particle trajectories up to time $T$. The estimates in turn yield rigorous lower bounds for ground state energies, via the Feynman-Kac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is first illustrated in familiar quantum mechanical settings: for the hydrogen atom, for a Schr\\"odinger operator with $1/|x|^2$ potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.
To Enjoy the Morning Flower in the Evening -- Where is the Subtlety of Quantum Mechanics?
Guang-jiong Ni
1998-04-05
Why does the $i=\\sqrt{-1}$ appear essentially in the quantum mechanics? Why are there operators and noncommutativity (the uncertainty relation) in the quantum mechanics? Why are these two aspects closely related and indivisible? In probing these problems, a new point of view is proposed tentatively.
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.
Novel symmetries in N=2 supersymmetric quantum mechanical models
Malik, R.P.; Khare, Avinash
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.
The Central Mystery of Quantum Mechanics
Partha Ghose
2009-06-04
A critical re-examination of the double-slit experiment and its variants is presented to clarify the nature of what Feynmann called the ``central mystery'' and the ``only mystery'' of quantum mechanics, leading to an interpretation of complementarity in which a `wave {\\em and} particle' description rather than a `wave {\\em or} particle' description is valid for the {\\em same} experimental set up, with the wave culminating in the particle sequentially in time. This interpretation is different from Bohr's but is consistent with the von Neumann formulation as well as some more recent interpretations of quantum mechanics.
Two basic Uncertainty Relations in Quantum Mechanics
Angelow, Andrey
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.
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.
Basic Concepts for a Quantum Mechanical Theory of Events
Kim J. Bostroem
2005-03-21
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. As a key feature, the laws are formulated in terms of quantum events rather than of particle states. Temporal and spatial coordinates of a quantum event are treated on equal footing, namely as self-adjoint operators on a Hilbert space. The theory is not based upon Lagrangian or Hamiltonian mechanics, and breaks with the concept of a continuously flowing time. The physical object under consideration is a spinless particle exposed to an external potential. The theory also accounts for particle-antiparticle pair creation and annihilation, and is therefore not a single-particle theory in the usual sense. The Maxwell equations are derived as a straightforward consequence of certain fundamental commutation relations. In the non-relativistic limit and in the limit of vanishing time uncertainty, the Schr\\"odinger equation of a spinless particle exposed to an external electromagnetic field is obtained.
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.
Space and time from quantum mechanics
NASA Astrophysics Data System (ADS)
Chew, G. F.
1992-09-01
Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over the collapse of the quantum-mechanical state vector when measurement is performed. Additionally, the pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as a coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.
Space and time from quantum mechanics
Chew, G.F.
1992-09-16
Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over collapse of the quantum-mechanical state vector when measurement is performed. Additionally, pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.
Scattering Relativity in Quantum Mechanics
Richard Shurtleff
2015-07-06
By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the particle field translated along one displacement, particle states are translated along a possibly different displacement. Arbitrary phase results. And particle momentum, a spin (1/2,1/2) quantity, is allowed to change when field and states are translated. It is shown that a path of extreme phase obeys a semiclassical equation for force with derived terms that can describe electromagnetism and gravitation.
Horizon Quantum Mechanics: a hitchhiker's guide to quantum black holes
Casadio, R; Micu, O
2015-01-01
It is congruous with the quantum nature of the world to view the space-time geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the space-time manifold as a purely theoretical arena, where quantum states are defined, with the additional freedom of changing coordinates like any other symmetry. Observables, including positions and distances, should then be described by suitable operators acting on such quantum states. In principle, the top-down (canonical) quantisation of Einstein-Hilbert gravity falls right into this picture, but is notoriously very involved. The complication stems from allowing all the classical canonical variables that appear in the (presumably) fundamental action to become quantum observables acting on the "superspace" of all metrics, regardless of whether they play any role in the description of a specific physical system. On can instead revisit the more humble "minisuperspace" approach and choose the gravitational observa...
Quantum mechanical studies of carbon structures
Bartelt, Norman Charles; Ward, Donald; Zhou, Xiaowang; Foster, Michael E.; Schultz, Peter A.; Wang, Bryan M.; McCarty, Kevin F.
2015-10-01
Carbon nanostructures, such as nanotubes and graphene, are of considerable interest due to their unique mechanical and electrical properties. The materials exhibit extremely high strength and conductivity when defects created during synthesis are minimized. Atomistic modeling is one technique for high resolution studies of defect formation and mitigation. To enable simulations of the mechanical behavior and growth mechanisms of C nanostructures, a high- fidelity analytical bond-order potential for the C is needed. To generate inputs for developing such a potential, we performed quantum mechanical calculations of various C structures.
Mechanically mediated microwave frequency conversion in the quantum regime
F. Lecocq; J. B. Clark; R. W. Simmonds; J. Aumentado; J. D. Teufel
2015-11-30
We report the observation of efficient and low-noise frequency conversion between two microwave modes, mediated by the motion of a mechanical resonator subjected to radiation pressure. We achieve coherent conversion of more than $10^{12}~\\mathrm{photons/s}$ with a $95\\mathrm{\\%}$ efficiency and a $14~\\mathrm{kHz}$ bandwidth. With less than $10^{-1}~\\mathrm{photons \\cdot s^{-1}\\cdot Hz^{-1}}$ of added noise, this optomechanical frequency converter is suitable for quantum state transduction. We show the ability to operate this converter as a tunable beam splitter, with direct applications for photon routing and communication through complex quantum networks.
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.
A new introductory quantum mechanics curriculum
NASA Astrophysics Data System (ADS)
Kohnle, Antje; Bozhinova, Inna; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth
2014-01-01
The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum-mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of the interpretive aspects of quantum mechanics and quantum information theory. This paper gives an overview of the resources available from the IOP website. The core text includes around 80 articles which are co-authored by leading experts, arranged in themes, and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is included in the resource. Solutions to activities are available to instructors. The resources can be used in a variety of ways, from being supplemental to existing courses to forming a complete programme.
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.
Can quantum mechanics fool the cosmic censor?
NASA Astrophysics Data System (ADS)
Matsas, G. E. A.; Richartz, M.; Saa, A.; da Silva, A. R. R.; Vanzella, D. A. T.
2009-05-01
We revisit the mechanism for violating the weak cosmic-censorship conjecture (WCCC) by overspinning a nearly-extreme charged black hole. The mechanism consists of an incoming massless neutral scalar particle, with low energy and large angular momentum, tunneling into the hole. We investigate the effect of the large angular momentum of the incoming particle on the background geometry and address recent claims that such a backreaction would invalidate the mechanism. We show that the large angular momentum of the incident particle does not constitute an obvious impediment to the success of the overspinning quantum mechanism, although the induced backreaction turns out to be essential to restoring the validity of the WCCC in the classical regime. These results seem to endorse the view that the “cosmic censor” may be oblivious to processes involving quantum effects.
Quantum statistical mechanics, L-series, Anabelian Geometry
Marcolli, Matilde
Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Adem Lectures, Mexico City, January 2011 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12 Mechanics, L-series and Anabelian Geometry, arXiv:1009.0736 Matilde Marcolli Quantum statistical mechanics
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.
Quantum mechanics and the time travel paradox
Pegg, D T
2005-01-01
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.
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.
Differentiable-path integrals in quantum mechanics
NASA Astrophysics Data System (ADS)
Koch, Benjamin; Reyes, Ignacio
2015-06-01
A method is presented which restricts the space of paths entering the path integral of quantum mechanics to subspaces of C?, by only allowing paths which possess at least ? derivatives. The method introduces two external parameters, and induces the appearance of a particular time scale ?D such that for time intervals longer than ?D the model behaves as usual quantum mechanics. However, for time scales smaller than ?D, modifications to standard formulation of quantum theory occur. This restriction renders convergent some quantities which are usually divergent in the time-continuum limit ? ? 0. We illustrate the model by computing several meaningful physical quantities such as the mean square velocity
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...
Quantum mechanics of time travel through post-selected teleportation
Maccone, Lorenzo
This paper discusses the quantum mechanics of closed-timelike curves (CTCs) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based ...
Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
Alexander A. Andrianov; Andrey V. Sokolov
2009-06-17
When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples.
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 mechanics of the damped harmonic oscillator
Blasone, Massimo
645 Quantum mechanics of the damped harmonic oscillator Massimo Blasone and Petr Jizba Abstract: We quantize the system of a damped harmonic oscillator coupled to its time- reversed image, known as Bateman of the simplest dissipative system -- the damped harmonic oscillator (DHO) -- is not an easy task [1], and indeed
quantum mechanics position and momentum Pigment Molecules
quantum mechanics position and momentum Pigment Molecules A typical pigment molecule has a photon of wavelength at the pigment molecule. What is the largest value of such that the photon can be absorbed by an electron in the pigment molecule? When the photon is absorbed, the electron must be able
Comparison of Classical and Quantum Mechanical Uncertainties.
ERIC Educational Resources Information Center
Peslak, John, Jr.
1979-01-01
Comparisons are made for the particle-in-a-box, the harmonic oscillator, and the one-electron atom. A classical uncertainty principle is derived and compared with its quantum-mechanical counterpart. The results are discussed in terms of the statistical interpretation of the uncertainty principle. (Author/BB)
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...
The inside observer in quantum mechanics
Mould, R.
1995-11-01
The {open_quotes}observer{close_quotes} in physics has always referred to someone who stands on the outside of a system looking in. In this paper an {open_quotes}inside observer{close_quotes} is defined, and an experiment is proposed that tests a given formulation of the problem of measurement in quantum mechanics.
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.
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
Interagency mechanical operations group numerical systems group
1997-09-01
This report consists of the minutes of the May 20-21, 1971 meeting of the Interagency Mechanical Operations Group (IMOG) Numerical Systems Group. This group looks at issues related to numerical control in the machining industry. Items discussed related to the use of CAD and CAM, EIA standards, data links, and numerical control.
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
Spin Glass: A Bridge between quantum computation and statistical mechanics
Masayuki Ohzeki
2012-04-24
We show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Second, we show another interesting technique to employ quantum nature, quantum annealing. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.
Toward an Information-based Interpretation of Quantum Mechanics and the Quantum-Classical Transition
Juan G. Roederer
2015-12-21
I will show how an objective definition of the concept of information and the consideration of recent results about information-processing in the human brain help clarify some fundamental and often counter-intuitive aspects of quantum mechanics. In particular, I will discuss entanglement, teleportation, non-interaction measurements and decoherence in the light of the fact that pragmatic information, the one our brain handles, can only be defined in the classical macroscopic domain; it does not operate in the quantum domain. This justifies viewing quantum mechanics as a discipline dealing with mathematical models and procedures aimed exclusively at predicting possible macroscopic changes and their likelihood that a given quantum system may cause when it interacts with its environment, including man-made devices such as measurement instruments. I will discuss the informational and neurobiological reasons of why counter-intuitive aspects arise whenever we attempt to construct mental images of the "inner workings" of a quantum system by forcing the concepts of classical information and time into the quantum domain; in this context I will examine the role of pragmatic information as a discriminator in the quantum-to-classical transition.
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.
The Compton effect: Transition to quantum mechanics
NASA Astrophysics Data System (ADS)
Stuewer, R. H.
2000-11-01
The discovery of the Compton effect at the end of 1922 was a decisive event in the transition to the new quantum mechanics of 1925-1926 because it stimulated physicists to examine anew the fundamental problem of the interaction between radiation and matter. I first discuss Albert Einstein's light-quantum hypothesis of 1905 and why physicists greeted it with extreme skepticism, despite Robert A. Millikan's confirmation of Einstein's equation of the photoelectric effect in 1915. I then follow in some detail the experimental and theoretical research program that Arthur Holly Compton pursued between 1916 and 1922 at the University of Minnesota, the Westinghouse Lamp Company, the Cavendish Laboratory, and Washington University that culminated in his discovery of the Compton effect. Surprisingly, Compton was not influenced directly by Einstein's light-quantum hypothesis, in contrast to Peter Debye and H.A. Kramers, who discovered the quantum theory of scattering independently. I close by discussing the most significant response to that discovery, the Bohr-Kramers-Slater theory of 1924, its experimental refutation, and its influence on the emerging new quantum mechanics.
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
Quantum statistical mechanics, L-series, Anabelian Geometry
Marcolli, Matilde
Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Colloquium, Harvard University, March 24, 2011 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12;joint work with Gunther Cornelissen General philosophy: Zeta functions are counting devices: spectra
Koch, Christof
1 The relation between quantum mechanics and higher brain functions: Lessons from quantum should be addressed. Email koch@klab.caltech.edu The relationship between quantum mechanics and higher-founded understanding of these issues is desirable. The role of quantum mechanics for the photons received by the eye
Probability and Quantum Symmetries. II. The Theorem of Noether in quantum mechanics
Zambrini, Jean-Claude
Probability and Quantum Symmetries. II. The Theorem of Noether in quantum mechanics S. Albeverio, a new rigorous, but not probabilistic, Lagrangian version of nonrelativistic quantum mechanics is given in SchrÃ¶dinger's Euclidean quantum mechanics."1 There, a proba- bilistic i.e., "Euclidean" generalization
Limits to the Universality of Quantum Mechanics
Brian D. Josephson
2011-10-08
Niels Bohr's arguments indicating the non-applicability of quantum methodology to the study of the ultimate details of life given in his book "Atomic physics and human knowledge" conflict with the commonly held opposite view. The bases for the usual beliefs are examined and shown to have little validity. Significant differences do exist between the living organism and the type of system studied successfully in the physics laboratory. Dealing with living organisms in quantum-mechanical terms with the same degree of rigour as is normal for non-living systems would seem not to be possible without considering also questions of the origins of life and of the universe.
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.
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.
The effectiveness of quantum operations for eavesdropping on sealed messages
Paul A Lopata; Thomas B Bahder
2007-04-04
A quantum protocol is described which enables a user to send sealed messages and that allows for the detection of active eavesdroppers. We examine a class of eavesdropping strategies, those that make use of quantum operations, and we determine the information gain versus disturbance caused by these strategies. We demonstrate this tradeoff with an example and we compare this protocol to quantum key distribution, quantum direct communication, and quantum seal protocols.
Macroscopic test of quantum mechanics versus stochastic electrodynamics S. Chaturvedi
Queensland, University of
Macroscopic test of quantum mechanics versus stochastic electrodynamics S. Chaturvedi School with quantum mechanics at the microscopic level, from the Bell inequalities 1 . Experimental tests at this level have decided in favor of quantum mechanics 2 , although there are still some experimental problems
Putnam looks at quantum mechanics (again and again) Christian Wthrich
WÃ¼thrich, Christian
1 Putnam looks at quantum mechanics (again and again) Christian WÃ¼thrich University of California Hilary Putnam (1965, 2005) has argued that from a realist perspective, quantum mechanics stands in need that quantum mechanics needs no interpretation and thus stands in tension with his claim of three years later
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…
Quantum Mechanics as a Science -Religion Bridge By Stanley Klein
Klein, Stanley
Quantum Mechanics as a Science - Religion Bridge By Stanley Klein (May 1, 2002) Stanley Klein and for fitting contact lenses. Klein's interest in quantum mechanics and brain research has led him to explore of more than 20 years, DUALITY, summarizes his theme that the duality of quantum mechanics provides
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
MSE 157: Quantum Mechanics of Nanoscale Materials Course Information
MSE 157: Quantum Mechanics of Nanoscale Materials Course Information Basic info Prof. Aaron to Quantum Mechanics by David Griffiths but we will make many diversions from this. This book is on reserve at the Engineering Library. Other recommended books for outside reading: Applied Quantum Mechanics by David Levi
The syllabus of the Course 624 Quantum Mechanics 2
The syllabus of the Course 624 Quantum Mechanics 2 Spring 2009. Instructor V.L. Pokrovsky. 1. Many-body quantum mechanics. Second quantization. Spin and statistics. Bose- Einstein condensation. 6's phase. Landau-Zener theory. Principal textbook: E. Merzbacher, Quantum Mechanics, 3-d edition, Wiley
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
A NOTE ON RELATION BETWEEN QUANTUM MECHANICS AND ALGEBRAIC INVARIANTS
A NOTE ON RELATION BETWEEN QUANTUM MECHANICS AND ALGEBRAIC INVARIANTS Alex A. Samoletov Department appeared in the quantum mechanics at its early period [4],[5] and then took clear form in the work [6 representation of quantum mechanics and the group of affine canonical transformations of the phase space. 2
-ALGEBRAIC FORMALISM OF QUANTUM MECHANICS JONATHAN JAMES GLEASON
May, J. Peter
THE C -ALGEBRAIC FORMALISM OF QUANTUM MECHANICS JONATHAN JAMES GLEASON Abstract. In this paper 7 6. Quantum Mechanics from the Ground Up 8 7. Closing Comments 17 8. Appendix: Definitions 18 of quantum mechan- ics (i.e., the states are elements of a separable Hilbert space and the observables self
JEFFREY A. BARRETT A QUANTUM-MECHANICAL ARGUMENT
Johnson, Kent
JEFFREY A. BARRETT A QUANTUM-MECHANICAL ARGUMENT FOR MINDÂBODY DUALISM ABSTRACT. I argue that a strong mindÂbody dualism is required of any formu- lation of quantum mechanics that satisfies. From the earliest formulation of the theory, physicists have thought that quantum mechanics has
Quantum interference between H + D2 quasiclassical reaction mechanisms
Quantum interference between H + D2 quasiclassical reaction mechanisms Pablo G. Jambrina1 , Diego the origin of that structure to the quantum interference between different quasiclassical mechanisms of the quasiclassical trajectory (QCT) method in which quantum mechanical (QM) binning is imposed on the results
Hidden Variables and Commutativity in Quantum Mechanics Benjamin Feintzeig
Johnson, Kent
Hidden Variables and Commutativity in Quantum Mechanics Benjamin Feintzeig Department of Logic takes up a suggestion that the reason we cannot find hidden variable theories for quantum mechanics theories for quantum mechanics, so the proposal for getting around Bell's Theorem fails. Contents 1
The Liar-paradox in a Quantum Mechanical Perspective
Aerts, Diederik
The Liar-paradox in a Quantum Mechanical Perspective Diederik Aerts, Jan Broekaert, Sonja Smets paradox in a quantum mechanical perspective", Foundations of Science, 4, 156. 1 #12;on the other side can be described in a meaningful way by the quantum mechanical formalism. The theories of chaos
Mathematical formalism of many-worlds quantum mechanics
Zeqian Chen
2015-06-09
We combine the ideas of Dirac's orthonormal representation, Everett's relative state, and 't Hooft's ontological basis to define the notion of a world for quantum mechanics. Mathematically, for a quantum system $\\mathcal{Q}$ with an associated Hilbert space $\\mathbb{H},$ a world of $\\mathcal{Q}$ is defined to be an orthonormal basis of $\\mathbb{H}.$ The evolution of the system is governed by Schr\\"{o}dinger's equation for the worlds of it. An observable in a certain world is a self-adjoint operator diagonal under the corresponding basis. Moreover, a state is defined in an associated world but can be uniquely extended to the whole system as proved recently by Marcus, Spielman, and Srivastava. Although the states described by unit vectors in $\\mathbb{H}$ may be determined in different worlds, there are the so-called topology-compact states which must be determined by the totality of a world. We can apply the Copenhagen interpretation to a world for regarding a quantum state as an external observation, and obtain the Born rule of random outcomes. Therefore, we present a mathematical formalism of quantum mechanics based on the notion of a world instead of a quantum state.
Huang, Yi-Zhi
Fractional quantum Hall states Anyons and representation theory Vertex operator (super / Quamtum Math Seminar #12;Fractional quantum Hall states Anyons and representation theory Vertex operator Fractional quantum Hall states and vertex operator algebras 2 Anyons and representation theory Anyons Modules
Kink mass quantum shifts from SUSY quantum mechanics
NASA Astrophysics Data System (ADS)
Izquierdo, Alberto Alonso; Guilarte, Juan Mateos; Plyushchay, Mikhail S.
2013-04-01
In this paper a new version of the DHN (Dashen-Hasslacher-Neveu) formula, which is used to compute the one-loop order kink mass correction in (1+1)-dimensional scalar field theory models, is constructed. The new expression is written in terms of the spectral data coming from the supersymmetric partner operator of the second-order small kink fluctuation operator and allows us to compute the kink mass quantum shift in new models for which this calculation was out of reach by means of the old formula.
Measurement and Fundamental Processes in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Jaeger, Gregg
2015-07-01
In the standard mathematical formulation of quantum mechanics, measurement is an additional, exceptional fundamental process rather than an often complex, but ordinary process which happens also to serve a particular epistemic function: during a measurement of one of its properties which is not already determined by a preceding measurement, a measured system, even if closed, is taken to change its state discontinuously rather than continuously as is usual. Many, including Bell, have been concerned about the fundamental role thus given to measurement in the foundation of the theory. Others, including the early Bohr and Schwinger, have suggested that quantum mechanics naturally incorporates the unavoidable uncontrollable disturbance of physical state that accompanies any local measurement without the need for an exceptional fundamental process or a special measurement theory. Disturbance is unanalyzable for Bohr, but for Schwinger it is due to physical interactions' being borne by fundamental particles having discrete properties and behavior which is beyond physical control. Here, Schwinger's approach is distinguished from more well known treatments of measurement, with the conclusion that, unlike most, it does not suffer under Bell's critique of quantum measurement. Finally, Schwinger's critique of measurement theory is explicated as a call for a deeper investigation of measurement processes that requires the use of a theory of quantum fields.
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 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.
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.
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.
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.)
A quantum mechanics glimpse to standard cosmology
Barbosa-Cendejas, N.; Reyes, M.
2010-07-12
In this work we present a connection between a standard cosmology model for inflation and quantum mechanics. We consider a time independent Schroedinger type equation derived from the equations of motion for a single scalar field in a flat space time with a FRW metric and a cosmological constant; the fact that the equation of motion is precisely a Schroedinger equation allows us to investigate on the algebraic relations between the two models and probe the consequences derived from this point of view.
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.
Supersymmetric Dissipative Quantum Mechanics from Superstrings
Luigi Cappiello; Giancarlo D'Ambrosio
2004-05-31
Following the approach of Callan and Thorlacius applied to the superstring, we derive a supersymmetric extension of the non-local dissipative action of Caldeira and Leggett. The dissipative term turns out to be invariant under a group of superconformal transformations. When added to the usual kinetic term, it provides an example of supersymmetric dissipative quantum mechanics. As a by-product of our analysis, an intriguing connection to the homeotic/hybrid fermion model, proposed for CPT violation in neutrinos, appears.
Supersymmetric Dissipative Quantum Mechanics from Superstrings
Cappiello, L; Cappiello, Luigi; Ambrosio, Giancarlo D'
2004-01-01
Following the approach of Callan and Thorlacius applied to the superstring, we derive a supersymmetric extension of the non-local dissipative action of Caldeira and Leggett. The dissipative term turns out to be invariant under a group of superconformal transformations. When added to the usual kinetic term, it provides an example of supersymmetric dissipative quantum mechanics. As a by-product of our analysis, an intriguing connection to the homeotic/hybrid fermion model, proposed for CPT violation in neutrinos, appears.
Using the Internet to teach Quantum Mechanics
NASA Astrophysics Data System (ADS)
Breinig, Marianne
1997-04-01
All instructional materials for a Quantum Mechanics course for graduate students in physics at the University of Tennessee are distributed over the Internet. Class notes, problems, and solutions are available in portable document format (PDF). A discussion forum allows students to post questions and to discuss class materials among themselves and with the instructor. Using an Internet connection to various computers in the classroom allows the introduction of numerical and visualization techniques in class.
Quantum Mechanics and Motion: A Modern Perspective
Gerald E. Marsh
2009-12-27
This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum, yields a world-line. If a force acts on the particle, its probability distribution is accordingly modified. This must also be true for macroscopic objects, although now the description is far more complicated by the structure of matter and associated surface physics.
Mona Lisa - ineffable smile of quantum mechanics
Slobodan Prvanovic
2003-02-25
The portrait of Mona Lisa is scrutinized with reference to quantum mechanics. The elements of different expressions are firstly recognized on her face. The contradictory details are then classified in two pictures that, undoubtedly representing distinct moods, confirm dichotomous character of the original. Consecutive discussion has lead to conclusion that the mysterious state Mona Lisa is in actually is coherent mixture - superposition, of cheerfulness and sadness.
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.
Grounding quantum probability in psychological mechanism.
Love, Bradley C
2013-06-01
Pothos & Busemeyer (P&B) provide a compelling case that quantum probability (QP) theory is a better match to human judgment than is classical probability (CP) theory. However, any theory (QP, CP, or other) phrased solely at the computational level runs the risk of being underconstrained. One suggestion is to ground QP accounts in mechanism, to leverage a wide range of process-level data. PMID:23673043
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.
Finite quantum mechanical model for the stock market
Liviu-Adrian Cotfas
2012-09-04
The price of a given stock is exactly known only at the time of sale when the stock is between the traders. If we know the price (owner) then we have no information on the owner (price). A more general description including cases when we have partial information on both price and ownership is obtained by using the quantum mechanics methods. The relation price-ownership is similar to the relation position-momentum. Our approach is based on the mathematical formalism used in the case of quantum systems with finite-dimensional Hilbert space. The linear operator corresponding to the ownership is obtained from the linear operator corresponding to the price by using the finite Fourier transform. In our idealized model, the Schrodinger type equation describing the time evolution of the stock price is solved numerically.
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}.
Emergent quantum mechanics as a classical, irreversible thermodynamics
Acosta, D; Isidro, J M; Santander, J L G
2012-01-01
We present an explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics as developed by Onsager, Prigogine et al. Our correspondence maps irreversible Gaussian Markov processes into the semiclassical approximation of quantum mechanics. Quantum-mechanical propagators are mapped into thermodynamical probability distributions. The Feynman path integral also arises naturally in this setup. The fact that quantum mechanics can be translated into thermodynamical language provides additional support for the conjecture that quantum mechanics is not a fundamental theory but rather an emergent phenomenon, i.e., an effective description of some underlying degrees of freedom.
Representation of complex rational numbers in quantum mechanics
Benioff, Paul
2005-09-15
A representation of complex rational numbers in quantum mechanics is described that is not based on logical or physical qubits. It stems from noting that the 0's in a product qubit state do not contribute to the number. They serve only as place holders. The representation is based on the distribution of four types of systems on an integer lattice. The four types, labeled as positive real, negative real, positive imaginary, and negative imaginary, are represented by creation and annihilation operators acting on the system vacuum state. Complex rational number states correspond to products of creation operators acting on the vacuum. Various operators, including those for the basic arithmetic operations, are described. The representation used here is based on occupation number states and is given for bosons and fermions.
Representation of complex rational numbers in quantum mechanics
NASA Astrophysics Data System (ADS)
Benioff, Paul
2005-09-01
A representation of complex rational numbers in quantum mechanics is described that is not based on logical or physical qubits. It stems from noting that the 0’s in a product qubit state do not contribute to the number. They serve only as place holders. The representation is based on the distribution of four types of systems on an integer lattice. The four types, labeled as positive real, negative real, positive imaginary, and negative imaginary, are represented by creation and annihilation operators acting on the system vacuum state. Complex rational number states correspond to products of creation operators acting on the vacuum. Various operators, including those for the basic arithmetic operations, are described. The representation used here is based on occupation number states and is given for bosons and fermions.
Quantum mechanics in structure-based drug design.
Peters, Martin B; Raha, Kaushik; Merz, Kenneth M
2006-05-01
In principle, quantum mechanics provides a more accurate representation of molecular systems than other modeling approaches. While this notion is not a matter of dispute, it has not yet been definitively demonstrated within the realm of structure-based drug design that the use of quantum mechanical methods over the use of classical modeling approaches is justified in consideration of the increase in expense associated with quantum mechanical methods. Demonstrating that quantum mechanics-based methods can be superior to simpler models, and resolving problems relating to estimating the effects of conformational entropy, will provide key areas of interest in the coming years for in silico structure-based drug design. Recent applications using quantum mechanical methods in structure-based drug design are reviewed herein, and applications ranging from scoring receptor-ligand interactions using quantum mechanics to the generation of quantitative structure-activity relationships using quantum mechanics-derived descriptors are discussed. PMID:16729734
Foundations of Physics, Vol . 29, No. 8, 1999 A Quantum Mechanical Supertask
known. The time evolution governed by the differential SchroÈ dinger equation can also a quantum state time evolution operator U(t) = exp( 2 iHt) and does not admit indeterminism, even. In standard applications of quantum mechanics, the time evolution governed by the SchroÈ dinger equation
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.
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.
From Cbits to Qbits: Teaching computer scientists quantum mechanics
N. David Mermin
2002-07-19
A strategy is suggested for teaching mathematically literate students, with no background in physics, just enough quantum mechanics for them to understand and develop algorithms in quantum computation and quantum information theory. Although the article as a whole addresses teachers of physics, well versed in quantum mechanics, the central pedagogical development is addressed directly to computer scientists and mathematicians, with only occasional asides to their teacher. Physicists uninterested in quantum pedagogy may be amused (or irritated) by some of the views of standard quantum mechanics that arise naturally from this unorthodox perspective.
O. Tapia
2014-04-02
Combining abstract to laboratory projected quantum states a general analysis of headline quantum phenomena is presented. Standard representation mode is replaced; instead quantum states sustained by elementary material constituents occupy its place. Renouncing to assign leading roles to language originated in classical physics when describing genuine quantum processes, together with sustainment concept most, if not all weirdness associated to Quantum Mechanics vanishes.
Neutrino oscillations: Quantum mechanics vs. quantum field theory
Akhmedov, Evgeny Kh.; Kopp, Joachim; ,
2010-01-01
A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
Neutrino oscillations: Quantum mechanics vs. quantum field theory
Evgeny Kh. Akhmedov; Joachim Kopp
2012-11-20
A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
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.
Mixing Quantum and Classical Mechanics Oleg V. Prezhdo \\Lambda
and a clearer picture of physical events. Applica tions of various quantumclassical approaches range fromMixing Quantum and Classical Mechanics Oleg V. Prezhdo \\Lambda Department of Chemistry quantumclassical system. The quantumclassical bracket entering the equation pre serves the Lie algebra
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.
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.
Probabilistic Quantum Logic Operations Using Polarizing Beam Splitters
T. B. Pittman; B. C. Jacobs; J. D. Franson
2001-07-22
It has previously been shown that probabilistic quantum logic operations can be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors. Here we describe the operation of several quantum logic operations of an elementary nature, including a quantum parity check and a quantum encoder, and we show how they can be combined to implement a controlled-NOT (CNOT) gate. All of these gates can be constructed using polarizing beam splitters that completely transmit one state of polarization and totally reflect the orthogonal state of polarization, which allows a simple explanation of each operation. We also describe a polarizing beam splitter implementation of a CNOT gate that is closely analogous to the quantum teleportation technique previously suggested by Gottesman and Chuang [Nature 402, p.390 (1999)]. Finally, our approach has the interesting feature that it makes practical use of a quantum-eraser technique.
Bohmian Mechanics and Quantum Field Theory Detlef Durr,1,
Goldstein, Sheldon
in the quantum field theory, the theory describes explicit creation and annihilation events: the world linesBohmian Mechanics and Quantum Field Theory Detlef D¨urr,1, Sheldon Goldstein,2, Roderich Tumulka: July 1, 2004) We discuss a recently proposed extension of Bohmian mechanics to quantum field theory
Faculty Disagreement about the Teaching of Quantum Mechanics
Colorado at Boulder, University of
Faculty Disagreement about the Teaching of Quantum Mechanics Michael Dubson1 , Steve Goldhaber1-level QM. We surveyed 27 faculty about their approaches to teaching QM, and reviewed 20 quantum textbooks (matter wave vs. information wave vs. something else). Keywords: upper-division quantum mechanics
Quantum mechanism helps agents combat with "bad" social choice rules
Wu, Haoyang
2010-01-01
Quantum strategies have been successfully applied in game theory for years. However, as a reverse problem of game theory, the theory of mechanism design is ignored by physicists. In this paper, we generalize the classical theory of mechanism design to a quantum domain. The main result is that by virtue of quantum mechanism, agents who satisfy a certain condition can combat with "bad" social choice rules instead of being restricted by the traditional mechanism design theory.
New Concept of Solvability in Quantum Mechanics
Miloslav Znojil
2013-02-08
In a pre-selected Hilbert space of quantum states the unitarity of the evolution is usually guaranteed via a pre-selection of the generator (i.e., of the Hamiltonian operator) in self-adjoint form. In fact, the simultaneous use of both of these pre-selections is overrestrictive. One should be allowed to make a given Hamiltonian self-adjoint only after an {\\em ad hoc} generalization of Hermitian conjugation. We argue that in the generalized, hidden-Hermiticity scenario with nontrivial metric, the current concept of solvability (meaning, most often, the feasibility of a non-numerical diagonalization of Hamiltonian) requires a generalization allowing for a non-numerical form of metric. A few illustrative solvable quantum models of this type are presented.
Adaptive Perturbation Theory I: Quantum Mechanics
Weinstein, Marvin; /SLAC
2005-10-19
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be treatable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, H, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. This paper introduces the method in the context of the pure anharmonic oscillator and then goes on to apply it to the case of tunneling between both symmetric and asymmetric minima. It concludes with an introduction to the extension of these methods to the discussion of a quantum field theory. A more complete discussion of this issue will be given in the second paper in this series, and it will show how to use the method of adaptive perturbation theory to non-perturbatively extract the structure of mass, wavefunction and coupling constant renormalization.
Burton, Geoffrey R.
Quantum Information Theory Quantum mechanics makes probabilistic predictions about experiments algebra and probability. Previous experience with quantum mechanics is helpful, but not required. Instead lead to the development of a theory of quantum information that generalises previous notions
Experimentally feasible measures of distance between quantum operations
Zbigniew Pucha?a; Jaros?aw Adam Miszczak; Piotr Gawron; Bart?omiej Gardas
2009-11-03
We present two measures of distance between quantum processes based on the superfidelity, introduced recently to provide an upper bound for quantum fidelity. We show that the introduced measures partially fulfill the requirements for distance measure between quantum processes. We also argue that they can be especially useful as diagnostic measures to get preliminary knowledge about imperfections in an experimental setup. In particular we provide quantum circuit which can be used to measure the superfidelity between quantum processes. As the behavior of the superfidelity between quantum processes is crucial for the properties of the introduced measures, we study its behavior for several families of quantum channels. We calculate superfidelity between arbitrary one-qubit channels using affine parametrization and superfidelity between generalized Pauli channels in arbitrary dimensions. Statistical behavior of the proposed quantities for the ensembles of quantum operations in low dimensions indicates that the proposed measures can be indeed used to distinguish quantum processes.
5.74 Introductory Quantum Mechanics II, Spring 2005
Tokmakoff, Andrei
Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...
5.74 Introductory Quantum Mechanics II, Spring 2003
Tokmakoff, Andrei
Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...
Lecture Script: Introduction to Computational Quantum Mechanics
Roman Schmied
2015-06-05
This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013 and in the Spring semester of 2015. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding analytical as well as numerical solutions and their visualization. Most of these calculations are too complicated to be done by hand. Even relatively simple problems, such as two interacting particles in a one-dimensional trap, do not have analytic solutions and require the use of computers for their solution and visualization. More complex problems scale exponentially with the number of degrees of freedom, and make the use of large computer simulations unavoidable. The course is taught using the Mathematica programming language; however, the concepts presented are readily translated to any other programming language.
Relativity and quantum mechanics: Jorgensen revisited
Bernhard Rothenstein
2007-03-25
We first define the functions which ensure the transformation of momentum and energy of a tardyon, the transformation of the wave vector and the frequency of the associated wave. Having done this, we show that they ensure the relativistic invariance of the quotient between momentum and wave vector and between energy and frequency if the product between particle velocity u and phase velocity w is a relativistic invariant (uw=c^2), a condition which is a natural combination of special relativity theory and quantum mechanics.
A New Formulation of Quantum Mechanics
Arbab I. Arbab; Faisal A. Yassein
2010-07-22
A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and Schrodinger probability density while keeping the Klein -Gordon and Schrodinger current unaltered. We have found time and space transformations under which Dirac's equation is invariant. The invariance of Maxwell's equations under these transformations shows that the electric and magnetic fields of a moving charged particle are perpendicular to the velocity of the propagating particle. This formulation agrees with the quaternionic formulation recently developed by Arbab.
Supersymmetric quantum mechanics and its applications
Sukumar, C.V.
2004-12-23
The Hamiltonian in Supersymmetric Quantum Mechanics is defined in terms of charges that obey the same algebra as that of the generators of supersymmetry in field theory. The consequences of this symmetry for the spectra of the component parts that constitute the supersymmetric system are explored. The implications of supersymmetry for the solutions of the Schroedinger equation, the Dirac equation, the inverse scattering theory and the multi-soliton solutions of the KdV equation are examined. Applications to scattering problems in Nuclear Physics with specific reference to singular potentials which arise from considerations of supersymmetry will be discussed.
Euclidean Quantum Mechanics and Universal Nonlinear Filtering
Bhashyam Balaji
2008-09-25
An important problem in applied science is the continuous nonlinear filtering problem, i.e., the estimation of a Langevin state that is observed indirectly. In this paper, it is shown that Euclidean quantum mechanics is closely related to the continuous nonlinear filtering problem. The key is the configuration space Feynman path integral representation of the fundamental solution of a Fokker-Planck type of equation termed the Yau Equation of continuous-continuous filtering. A corollary is the equivalence between nonlinear filtering problem and a time-varying Schr\\"odinger equation.
Wigner Measures in Noncommutative Quantum Mechanics
C. Bastos; N. C. Dias; J. N. Prata
2009-07-25
We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner measure, for a Gaussian to be a noncommutative Wigner measure, and derive certain properties of the marginal distributions which are not shared by ordinary Wigner measures. Moreover, we derive the Robertson-Schr\\"odinger uncertainty principle. Finally, we show explicitly how the set of noncommutative Wigner measures relates to the sets of Liouville and (commutative) Wigner measures.