Operational measurements in quantum mechanics
NASA Astrophysics Data System (ADS)
Kocha?ski, Piotr; Wódkiewicz, Krzysztof
1997-10-01
The operational approach to quantum measurements is formulated in terms of a phase space propensity and the corresponding positive operator-valued measure. This general approach is illustrated by an operational measurement of the position and momentum of a particle, and by an operational Malus measurement of spin phases.
On the geometry of the energy operator in quantum mechanics
Carlos Tejero Prieto; Raffaele Vitolo
2014-08-26
We analyze the different ways to define the energy operator in geometric theories of quantum mechanics. In some formulations the operator contains the scalar curvature as a multiplicative term. We show that such term can be canceled or added with an arbitrary constant factor, both in the mainstream Geometric Quantization and in the Covariant Quantum Mechanics, developed by Jadczyk and Modugno with several contributions from many authors.
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.
Extended SUSY quantum mechanics, intertwining operators and coherent states
F. Bagarello
2009-04-01
We propose an extension of {\\em supersymmetric quantum mechanics} which produces a family of isospectral hamiltonians. Our procedure slightly extends the idea of intertwining operators. Several examples of the construction are given. Further, we show how to build up vector coherent states of the Gazeau-Klauder type associated to our hamiltonians.
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.
NASA Astrophysics Data System (ADS)
Choi, Taeseung
2015-03-01
A relativistic spin operator is the difference between the total and the orbital angular momentum. As the unique position operator for a localized state, the remarkable Newton-Wigner position operator, which has all the desirable commutation relations of a position operator, can give a proper spin operator. Historically, the three important spin operators proposed by Bogolubov et al., Pryce, and Foldy-Woutheysen, respectively were investigated to manifest a spin operator corresponding to the Newton-Wigner position operator. We clarify a unique spin operator in relativistic quantum mechanics, which can be described by using the Dirac Hamiltonian.
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.
Operational dynamic modeling transcending quantum and classical mechanics.
Bondar, Denys I; Cabrera, Renan; Lompay, Robert R; Ivanov, Misha Yu; Rabitz, Herschel A
2012-11-01
We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories. PMID:23215365
Operational Dynamic Modeling Transcending Quantum and Classical Mechanics
NASA Astrophysics Data System (ADS)
Bondar, Denys I.; Cabrera, Renan; Lompay, Robert R.; Ivanov, Misha Yu.; Rabitz, Herschel A.
2012-11-01
We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.
The modern tools of quantum mechanics (A tutorial on quantum states, measurements, and operations)
Matteo G. A. Paris
2012-10-13
This tutorial is devoted to review the modern tools of quantum mechanics, which are suitable to describe states, measurements, and operations of realistic, not isolated, systems in interaction with their environment, and with any kind of measuring and processing devices. We underline the central role of the Born rule and and illustrate how the notion of density operator naturally emerges, together the concept of purification of a mixed state. In reexamining the postulates of standard quantum measurement theory, we investigate how they may formally generalized, going beyond the description in terms of selfadjoint operators and projective measurements, and how this leads to the introduction of generalized measurements, probability operator-valued measures (POVM) and detection operators. We then state and prove the Naimark theorem, which elucidates the connections between generalized and standard measurements and illustrates how a generalized measurement may be physically implemented. The "impossibility" of a joint measurement of two non commuting observables is revisited and its canonical implementations as a generalized measurement is described in some details. Finally, we address the basic properties, usually captured by the request of unitarity, that a map transforming quantum states into quantum states should satisfy to be physically admissible, and introduce the notion of complete positivity (CP). We then state and prove the Stinespring/Kraus-Choi-Sudarshan dilation theorem and elucidate the connections between the CP-maps description of quantum operations, together with their operator-sum representation, and the customary unitary description of quantum evolution. We also address transposition as an example of positive map which is not completely positive, and provide some examples of generalized measurements and quantum operations.
Juan Sebastián Ardenghi; Mario Castagnino; Olimpia Lombardi
2010-12-05
The general aim of this paper is to extend the Modal-Hamiltonian interpretation of quantum mechanics to the case of relativistic quantum mechanics with gauge U(1) elds. In this case we propose that the actual- valued observables are the Casimir operators of the Poincar\\'e group and of the group U(1) of the internal symmetry of the theory. Moreover, we also show that the magnitudes that acquire actual values in the relativistic and in the non-relativistic cases are correctly related through the adequate limit.
Basic quantum mechanical concepts from the operational viewpoint
D N Klyshko
1998-01-01
The physical meaning of the basic quantum mechanical concepts (such as the wave function, reduction, state preparation and measurement, the projection postulate, and the uncertainty principle) is clarified using realistic experimental procedures and employing classical analogies whenever possible. Photon polarization measurement and particle coordinate and momentum measurement are considered as examples, as also are Einstein–Podolsky–Rosen correlations, Aharonov–Bohm effects, quantum teleportation,
Overcoming Misconceptions in Quantum Mechanics with the Time Evolution Operator
ERIC Educational Resources Information Center
Quijas, P. C. Garcia; Aguilar, L. M. Arevalo
2007-01-01
Recently, there have been many efforts to use the research techniques developed in the field of physics education research to improve the teaching and learning of quantum mechanics. In particular, part of this research is focusing on misconceptions held by students. For instance, a set of misconceptions is associated with the concept of stationary…
Quantum Mechanical Operators and Commutation C I. Bra-Ket Notation
Simons, Jack
Quantum Mechanical Operators and Commutation C I. Bra-Ket Notation It is conventional to represent notation, which is referred to as 'Dirac' or 'bra-ket' notation, can be summarized as follows: A as a 'bra'
Physical Properties as Modal Operators in the Topos Approach to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Freytes, H.; Domenech, G.; de Ronde, C.
2014-12-01
In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras. It allows us to introduce a classical type study of the mentioned properties.
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.
Quantum-Mechanical Position Operator in Extended Systems
Raffaele Resta; Fisica Teorica; Strada Costiera
1998-01-01
The position operator (defined within the Schrödinger representation in the standard way) becomes meaningless when periodic boundary conditions are adopted for the wave function, as usual in condensed matter physics. I show how to define the position expectation value by means of a simple many-body operator acting on the wave function of the extended system. The relationships of the present
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.
Vincent Buonomano
2002-10-07
We take Co-Operative Phenomena as a common physical conceptual base to speculate on the existence of a medium and the properties that it must have to physically understand some of the problems in Special Relativity, Gravitation and Quantum Mechanics.
Classical optics representation of the quantum mechanical translation operator via ABCD matrices
NASA Astrophysics Data System (ADS)
Ornigotti, Marco; Aiello, Andrea
2013-07-01
The ABCD matrix formalism describing paraxial propagation of optical beams across linear systems is generalized to arbitrary beam trajectories. As a by-product of this study, a one-to-one correspondence between the extended ABCD matrix formalism presented here and the quantum mechanical translation operator is established.
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)].
NSDL National Science Digital Library
De Raedt, Hans
This website contains a number of descriptions of quantum mechanical phenomena, using 3D animations to illustrate the physics. The goal is to introduce basic concepts and phenomena using simulations rather than complex mathematics. The time-dependence of quantum systems is a focus of this material.
A. L. Stewart; G. Scolarici; L. Solombrino
1963-01-01
We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with respect to a uniquely defined positive scalar product in a infinite dimensional (right) quaternionic Hilbert space. According to such results we obtain two alternative descriptions of a quantum
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 5 problems LAST NAME FIRST NAME #12 with the effective electron mass at the band edges. #12;Applied quantum mechanics 3 (c) Write a computer program
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 8 problems LAST NAME FIRST NAME #12;Applied quantum mechanics 3 (b) If the electron is in a semiconductor and has an effective mass m * 0.07 m
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 1 problems LAST NAME FIRST NAME #12 happens to the beat frequency if the airplane moves in an arc? #12;Applied quantum mechanics 3 Problem 1
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 10 problems LAST NAME FIRST NAME #12 ( ) L/( )= L/ #12;Applied quantum mechanics 3 (d) Use the results of (b) an (c) to draw the electron
Quantum Mechanics II (Undergraduate)
Nickrent, Daniel L.
Quantum Mechanics II (Undergraduate) Applications of Quantum Mechanics Spring, 2014 Physics 440 TEXTBOOK: Introduction to Quantum Mechanics (Second Edition), by David J. Griffiths, and QUNET's wikibook to apply quantum mechanics to some fundamental and important problems such as: better understanding
Loss mechanisms of quantum cascade lasers operating close to optical phonon frequencies
NASA Astrophysics Data System (ADS)
Castellano, F.; Bismuto, A.; Amanti, M. I.; Terazzi, R.; Beck, M.; Blaser, S.; Bächle, A.; Faist, J.
2011-05-01
The extension of the operating frequency of Quantum Cascade Lasers (QCL) into the 20-50 ?m regime is a desirable goal as it would bridge the gap between mid-infrared and THz devices. Coherent light emitters in this spectral range are also needed for spectroscopy and radio astronomy applications. Since little attention has been devoted to the subject in the past, we investigate the dominant loss mechanisms of QCLs in this spectral range. We report on an InGaAs/InAlAs QCL in an InP dielectric waveguide emitting at 23 ?m wavelength whose electroluminescence spectrum shows an anomalous low-frequency cut which prevents laser action at low electric field. We also observe similar line shape in other GaAs/AlGaAs devices. The spectral features are analyzed and explained in terms of refractive index anomalies induced by phonon resonances.
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 6 problems LAST NAME FIRST NAME #12 --- and that for a Poisson distribution of such photons #12; 1 2 n ---------------- Applied quantum mechanics 3 (c) Apply conditions is the quantum mechanical result m t 2 2 d d x xd d V x = the same Newton's second law in which
Fan Hongyi [CCAST (World Laboratory), P.O. Box 8730, Beijing 100080 (China); Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026 (China); Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 (China); Lu Hailiang [Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 (China)]. E-mail: luhailiang@sjtu.edu.cn; Fan Yue [Intel Corporation 2200 Mission College Blvd., Santa Clara, CA 95052-8119 (United States)
2006-02-15
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.
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 6 problems LAST NAME FIRST NAME #12 of the system. (b) Find . (c) Find and show that . Under what conditions is the quantum mechanical result( ) td d A t( ) t A td d A /= A B i 2 --- A^ B^,[ ] A^ B^ Et 2 --- n n 1 2 --- #12;Applied quantum
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
Nonuniqueness of the {C} operator in {P} {T}-symmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Bender, Carl M.; Gianfreda, Mariagiovanna
2013-07-01
The {C} operator in {PT}-symmetric quantum mechanics satisfies a system of three simultaneous algebraic operator equations, {C}^2=1, [ {C}, {PT}]=0, and [ {C},H]=0. These equations are difficult to solve exactly, so perturbative methods have been used in the past to calculate {C}. The usual approach has been to express the Hamiltonian as H = H0 + ?H1, and to seek a solution for {C} in the form {C}=e^Q {P}, where Q = Q(q, p) is odd in the momentum p, even in the coordinate q, and has a perturbation expansion of the form Q = ?Q1 + ?3Q3 + ?5Q5 + ???. (In previous work it has always been assumed that the coefficients of even powers of ? in this expansion would be absent because their presence would violate the condition that Q(p, q) is odd in p.) In an earlier paper it was argued that the {C} operator is not unique because the perturbation coefficient Q1 is nonunique. Here, the nonuniqueness of {C} is demonstrated at a more fundamental level: it is shown that the perturbation expansion for Q actually has the more general form Q = Q0 + ?Q1 + ?2Q2 + ??? in which all powers and not just odd powers of ? appear. For the case in which H0 is the harmonic-oscillator Hamiltonian, Q0 is calculated exactly and in closed form and it is shown explicitly to be nonunique. The results are verified by using powerful summation procedures based on analytic continuation. It is also shown how to calculate the higher coefficients in the perturbation series for Q.
REVIEWS OF TOPICAL PROBLEMS: Basic quantum mechanical concepts from the operational viewpoint
D. N. Klyshko
1998-01-01
The physical meaning of the basic quantum mechanical concepts (such as the wave function, reduction, state preparation and measurement, the projection postulate, and the uncertainty principle) is clarified using realistic experimental procedures and employing classical analogies whenever possible. Photon polarization measurement and particle coordinate and momentum measurement are considered as examples, as also are Einstein-Podolsky-Rosen correlations, Aharonov-Bohm effects, quantum teleportation,
REVIEWS OF TOPICAL PROBLEMS: Basic quantum mechanical concepts from the operational viewpoint
NASA Astrophysics Data System (ADS)
Klyshko, D. N.
1998-09-01
The physical meaning of the basic quantum mechanical concepts (such as the wave function, reduction, state preparation and measurement, the projection postulate, and the uncertainty principle) is clarified using realistic experimental procedures and employing classical analogies whenever possible. Photon polarization measurement and particle coordinate and momentum measurement are considered as examples, as also are Einstein-Podolsky-Rosen correlations, Aharonov-Bohm effects, quantum teleportation, etc. Various nonclassicality criteria of quantum models, including photon antibunching and the violation of the Bell inequality, are discussed.
Speculation on Quantum Mechanics and the Operation of Life Giving Catalysts
NASA Astrophysics Data System (ADS)
Haydon, Nathan; McGlynn, Shawn E.; Robus, Olin
2011-02-01
The origin of life necessitated the formation of catalytic functionalities in order to realize a number of those capable of supporting reactions that led to the proliferation of biologically accessible molecules and the formation of a proto-metabolic network. Here, the discussion of the significance of quantum behavior on biological systems is extended from recent hypotheses exploring brain function and DNA mutation to include origins of life considerations in light of the concept of quantum decoherence and the transition from the quantum to the classical. Current understandings of quantum systems indicate that in the context of catalysis, substrate-catalyst interaction may be considered as a quantum measurement problem. Exploration of catalytic functionality necessary for life's emergence may have been accommodated by quantum searches within metal sulfide compartments, where catalyst and substrate wave function interaction may allow for quantum based searches of catalytic phase space. Considering the degree of entanglement experienced by catalytic and non catalytic outcomes of superimposed states, quantum contributions are postulated to have played an important role in the operation of efficient catalysts that would provide for the kinetic basis for the emergence of life.
Principles of Fractional Quantum Mechanics
Nick Laskin
2010-09-28
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum mechanics, hermiticity of the Hamilton operator, parity conservation law and the current density. Applications of fractional quantum mechanics cover dynamics of a free particle, new representation for a free particle quantum mechanical kernel, infinite potential well, bound state in {\\delta}-potential well, linear potential, fractional Bohr atom and fractional oscillator. We also review fundamentals of the L\\'evy path integral approach to fractional statistical mechanics.
NASA Astrophysics Data System (ADS)
Nucci, M. C.; Leach, P. G. L.
2014-10-01
Superintegrable systems are characterised by the possession of many symmetries and integrals. We use the simple harmonic oscillator as an example and examine the relationship between the Noetherian integrals of a given Lagrangian as quantum operators and the Lie symmetries of the corresponding Schrödinger Equation.
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
NASA Astrophysics Data System (ADS)
Zhang, Xiao; Wei, Chaozhen; Liu, Yingming; Luo, Maokang
2014-11-01
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.
Bohmian mechanics contradicts quantum mechanics
Neumaier, Arnold
Bohmian mechanics contradicts quantum mechanics Arnold Neumaier Institut fur Mathematik, Universit://solon.cma.univie.ac.at/#24;neum/ Abstract. It is shown that, for a harmonic oscillator in the ground state, Bohmian mechanics and quantum mechanics predict values of opposite sign for certain time correlations. The discrepancy can
Metric Operator in Pseudo-Hermitian Quantum Mechanics and the Imaginary Cubic Potential
Ali Mostafazadeh
2006-07-26
We present a systematic perturbative construction of the most general metric operator (and positive-definite inner product) for quasi-Hermitian Hamiltonians of the standard form, H= p^2/2 + v(x), in one dimension. We show that this problem is equivalent to solving an infinite system of iteratively decoupled hyperbolic partial differential equations in (1+1)-dimensions. For the case that v(x) is purely imaginary, the latter have the form of a nonhomogeneous wave equation which admits an exact solution. We apply our general method to obtain the most general metric operator for the imaginary cubic potential, v(x)=i \\epsilon x^3. This reveals an infinite class of previously unknown CPT- as well as non-CPT-inner products. We compute the physical observables of the corresponding unitary quantum system and determine the underlying classical system. Our results for the imaginary cubic potential show that, unlike the quantum system, the corresponding classical system is not sensitive to the choice of the metric operator. As another application of our method we give a complete characterization of the pseudo-Hermitian canonical quantization of a free particle moving in real line that is consistent with the usual choice for the quantum Hamiltonian. Finally we discuss subtleties involved with higher dimensions and systems having a fixed length scale.
Quantum Mechanics Measurements, Mutually
Gruner, Daniel S.
Quantum Mechanics Measurements, Mutually Unbiased Bases and Finite Geometry Or why six is the first) #12;Quantum Mechanics for Dummies Finite dimensional quantum states are represented by trace one,1 -icS1,1[ ] #12;Quantum systems evolve and are measured. The evolution of a quantum system using
Applied quantum mechanics 1 Applied Quantum Mechanics
Levi, Anthony F. J.
Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 5 problems LAST NAME FIRST NAME #12 + --------------------------------------------- k = t 10/= t 1= Ek 2t kxL( ) 2t 2kxL( )cos+cos= t 10/= t 1= t 0.2= #12;Applied quantum mechanics 3 (c) Write a computer program to plot the electron density of states for a square lat- tice
Nikolai Laskin
2000-01-01
A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Lévy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Lévy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and
Biorthogonal quantum mechanics
NASA Astrophysics Data System (ADS)
Brody, Dorje C.
2014-01-01
The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called ‘biorthogonal quantum mechanics’, is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems.
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
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 ...
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.
NASA Astrophysics Data System (ADS)
Laskin, Nikolai
2000-06-01
A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Levy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrodinger equation has been discovered. The new relationship between the energy and the momentum of the non-relativistic fractional quantum-mechanical particle has been found, and the Levy wave packet has been introduced into quantum mechanics. We have derived a free particle quantum-mechanical propagator using Fox's H-function. A fractional generalization of the Heisenberg uncertainty relation has been established. We also discuss the relationships between fractional and the well-known Feynman path integrals approaches to quantum mechanics.
Phase Space Quantum Mechanics - Direct
S. Nasiri; Y. Sobouti; F. Taati
2006-05-15
Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of non commuting observables. Further conceptual and practical merits of the formalism are demonstrated throughout the text.
Phase space quantum mechanics - Direct
Nasiri, S.; Sobouti, Y.; Taati, F. [Institute for Advanced Studies in Basic Sciences, Zanjan, 45195-1159 (Iran, Islamic Republic of) and Department of Physics, Zanjan University, Zanjan (Iran); Institute for Advanced Studies in Basic Sciences, Zanjan, 45195-1159 (Iran, Islamic Republic of); Institute for Advanced Studies in Basic Sciences, Zanjan, 45195-1159 (Iran, Islamic Republic of) and Department of Physics, University of Kurdistan, D-78457 Sanadaj (Iran)
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.
NON-COMMUTATIVE SPHERES AND NUMERICAL QUANTUM MECHANICS
Arveson, William
NON-COMMUTATIVE SPHERES AND NUMERICAL QUANTUM MECHANICS basic issues that arise when one attempts to mo* *del quantum mechanical systems on a computer, quantum mechanics. Contributed to the proceedings of a NATO conference on operator algebras, ma
Fractals and quantum mechanics
NASA Astrophysics Data System (ADS)
Laskin, Nick
2000-12-01
A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Lévy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Lévy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrödinger equation has been discovered. The new relationship between the energy and the momentum of the nonrelativistic fractional quantum-mechanical particle has been established, and the Lévy wave packet has been introduced into quantum mechanics. The equation for the fractional plane wave function has been found. We have derived a free particle quantum-mechanical kernel using Fox's H-function. A fractional generalization of the Heisenberg uncertainty relation has been found. As physical applications of the fractional quantum mechanics we have studied a free particle in a square infinite potential well, the fractional "Bohr atom" and have developed a new fractional approach to the QCD problem of quarkonium. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum mechanics.
Fractals and quantum mechanics.
Laskin, Nick
2000-12-01
A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Levy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrodinger equation has been discovered. The new relationship between the energy and the momentum of the nonrelativistic fractional quantum-mechanical particle has been established, and the Levy wave packet has been introduced into quantum mechanics. The equation for the fractional plane wave function has been found. We have derived a free particle quantum-mechanical kernel using Fox's H-function. A fractional generalization of the Heisenberg uncertainty relation has been found. As physical applications of the fractional quantum mechanics we have studied a free particle in a square infinite potential well, the fractional "Bohr atom" and have developed a new fractional approach to the QCD problem of quarkonium. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum mechanics. (c) 2000 American Institute of Physics. PMID:12779428
NSDL National Science Digital Library
Mabuchi, Hideo
This web site contains resources for a comprehensive quantum mechanics course designed for graduate and advanced undergraduate students at Cal Tech. The course has been revised to include quantum information science, and prepares students for a course in quantum computation. Lecture notes, a syllabus, homework problems with solutions, and exam solutions are available.
Chapin, Kimberly R.
1997-01-01
to describe the quantum mechanical system The first, matrix mechanics, was presented by Heisenberg [31-33] in 1925. The second, wave mechanics, was presented by Schrodinger [34-37] a year later. In 1926, Schrodmger [38] demonstrated the equivalence... can jump &om one state to another. The result is a discontinuous variation in time (i. e. the tune atom) [42]. Throughout the development of quantum mechanics, this atomistic view of time surfaces again and again, For example, In 1925, J. J...
Introduction to Quantum Mechanics
NSDL National Science Digital Library
The Concord Consortium
2011-12-12
The microscopic world is full of phenomena very different from what we see in everyday life. Some of those phenomena can only be explained using quantum mechanics. This activity introduces basic quantum mechanics concepts about electrons that are essential to understanding modern and future technology, especially nanotechnology. Start by exploring probability distribution, then discover the behavior of electrons with a series of simulations.
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.
Okazaki, Tadashi
2015-01-01
We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the BLG-model and the ABJM-model compactified on a torus are N = 16 and N = 12 superconformal gauged quantum mechanics. After integrating out the auxiliary gauge fields we find OSp(16|2) and SU(1,1|6) quantum mechanics from the reduced systems. The curved Riemann surface is taken as a holomorphic curve in a Calabi-Yau space to preserve supersymmetry and we present a prescription of the topological twisting. We find the N = 8 superconformal gauged quantum mechanics that may describe the motion of two wrapped M2-branes in a K3 surface.
Emergent Quantum Mechanics and Emergent Symmetries
Gerard't Hooft; Gerard t
2007-01-01
Quantum mechanics is ‘emergent’ if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present in the underlying deterministic system. Such theories allow for a natural explanation of the existence of gauge equivalence classes (gauge orbits), including the equivalence classes
Covariant quantum mechanics and quantum symmetries
JanyÂ?ka, Josef
Covariant quantum mechanics and quantum symmetries Josef JanyÅ¸ska 1 , Marco Modugno 2 , Dirk Saller: quantum mechanics, classical mechanics, general relativity, infinitesimal symmetries. 2000 MSC: 81P99, 81Q Introduction 2 2 Covariant quantum mechanics 5 2.1 Classical background
Quantum mechanical effects from deformation theory
Much, A. [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)] [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)
2014-02-15
We consider deformations of quantum mechanical operators by using the novel construction tool of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a role. Furthermore, a quantum plane can be defined by using the deformation techniques. This in turn gives an experimentally verifiable effect.
Quantum mechanics from classical statistics
Wetterich, C. [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)], E-mail: c.wetterich@thphys.uni-heidelberg.de
2010-04-15
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.
Laskin
2000-09-01
A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Levy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and statistical mechanics have been developed via our fractional path integral approach. A fractional generalization of the Schrodinger equation has been found. A relationship between the energy and the momentum of the nonrelativistic quantum-mechanical particle has been established. The equation for the fractional plane wave function has been obtained. We have derived a free particle quantum-mechanical kernel using Fox's H function. A fractional generalization of the Heisenberg uncertainty relation has been established. Fractional statistical mechanics has been developed via the path integral approach. A fractional generalization of the motion equation for the density matrix has been found. The density matrix of a free particle has been expressed in terms of the Fox's H function. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum and statistical mechanics. PMID:11088808
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.
Kapustin, Anton [California Institute of Technology, Pasadena, California 91125 (United States)] [California Institute of Technology, Pasadena, California 91125 (United States)
2013-06-15
We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.
Quantum mechanics and brain uncertainty.
Macgregor, Ronald J
2006-09-01
This paper argues that molecular governing structures (such as receptors, gating molecules, or ionic channels) which operate pervasively in the brain, often with small number particle systems (as, for example, at the surfaces of membranes, synaptic clefts, or macromolecules), may plausibly be vehicles for the transmutation of quantum mechanical fluctuations to normal-level neural signaling. PMID:17125159
A mathematical theory for deterministic quantum mechanics
Gerard't Hooft
2007-01-01
Classical, i.e. deterministic theories underlying quantum mechanics are considered, and it is shown how an apparent quantum mechanical Hamiltonian can be defined in such theories, being the operator that generates evolution in time. It includes various types of interactions. An explanation must be found for the fact that, in the real world, this Hamiltonian is bounded from below. The mechanism
A Criterion for Holism in Quantum Mechanics
Seevinck, Michiel
A Criterion for Holism in Quantum Mechanics M.P Seevinck Utrecht University, The Netherlands, June 2003. 1 #12; Motivation · The question whether or not quantum mechanics (QM) gives rise to some mechanics a holistic theory (if so), and other physical theories not (if so). · I propose an operational
A Criterion for Holism in Quantum Mechanics
Seevinck, Michiel
A Criterion for Holism in Quantum Mechanics # M.P Seevinck # # Utrecht University, The Netherlands, June 2003. # 1 #12; # Motivation # . The question whether or not quantum mechanics (QM) gives rise mechanics a holistic theory (if so), and other physical theories not (if so). . I propose an operational
Ontology and Quantum Mechanics
N. D. Hari Dass
2014-06-19
The issue of ontology in quantum mechanics, or equivalently the issue of the reality of the wave function is critically examined within standard quantum theory. It is argued that though no strict ontology is possible within quantum theory, ingenious measurement schemes may still make the notion of a \\emph{FAPP Ontology} i.e ontology for all practical purposes (a phrase coined by John Bell), meaningful and useful.
Fan Hongyi [Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 (China); Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026 (China)], E-mail: fhym@sjtu.edu.cn
2008-06-15
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.
W G Unruh
2006-01-01
Quantum mechanics is one of the most successful theoretical structures in all of science. Developed between 1925-26 to explain the optical spectrum of atoms, the theory over the succeeding 80 years has been extended, first to quantum field theories, gauge field theories, and now even string theory. It is used every day by thousands of physicists to calculate physical phenomena
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.
Orthodox Quantum Mechanics Free from Paradoxes
Rodrigo Medina
2005-08-02
A formulation of quantum mechanics based on an operational definition of state is presented. This formulation, which includes explicitly the macroscopic systems, assumes the probabilistic interpretation and is nevertheless objective. The classical paradoxes of quantum mechanics are analyzed and their origin is found to be the fictitious properties that are usually attributed to quantum-mechanical states. The hypothesis that any mixed state can always be considered as an incoherent superposition of pure states is found to contradict quantum mechanics. A solution of EPR paradox is proposed. It is shown that entanglement of quantum states is compatible with realism and locality of events, but implies non-local encoding of information.
Supersymmetry in quantum mechanics
Avinash Khare
1997-01-01
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical\\u000a problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable. In\\u000a this lecture I review the theoretical formulation of supersymmetric quantum mechanics and discuss many of its applications.\\u000a I show that the well-known exactly solvable
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.
The parity operator in quantum optical metrology
Christopher C. Gerry; Jihane Mimih
2010-01-01
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
QUANTUM MECHANICS II Physics 342
Rosner, Jonathan L.
QUANTUM MECHANICS II Physics 342 KPTC 103 9:00 Â 10:20 a.m. 1 Tues., Thurs. Â 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
Histories Approach to Quantum Mechanics
Tulsi Dass
2005-01-27
These lecture notes cover the important developments in histories approach to quantum mechanics with overall content and emphasis somewhat different from other reviews and books on the subject.The idea of Houtappel, Van Dam and Wigner of employing objects based on primitive concepts of physical theories is discussed in some detail and the fact that histories are such objects is emphasized. Application of histories formalism to the problem of understanding the quasiclassical domain is treated in some detail. Other topics discussed include generalized histories-based quantum mechanics and its application to the quantum mechanics of space-time,generalization of the notion of time sequences employing partial semigroups,quasitemporal structures, history projection operator (HPO) formalism, the algebraic scheme of Isham and Linden, an axiomatic scheme for quasitemporal histories-based theories and symmetries and conservation laws in histories-based theories.
Principles of a 2nd Quantum Mechanics
Mioara Mugur-Schächter
2014-10-23
A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this representation as a reference-and-imbedding-structure, the foundations of an intelligible reconstruction of the Hilbert-Dirac formulation of Quantum Mechanics is developed. Inside this reconstruction the measurement problem as well as the other major problems raised by the quantum mechanical formalism, dissolve.
NSDL National Science Digital Library
Zollman, Dean
The Kansas State University Visual Quantum Mechanics project is developing instructional materials about quantum physics for high school and college students. Instructional units and/or courses are being created for high school and college non-science students, pre-medical and biology students, and science and engineering majors. Each set of the teaching-learning materials integrates interactive visualizations with inexpensive materials and written documents in an activity-based environment.
Quantum mechanics on a real Hilbert space
Jan Myrheim
1999-01-01
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics, keeping the same set of physical states, but admitting more general observables. The standard time reversal operator involves complex conjugation, in
Quantum computation with noisy operations
Ying Li
2015-06-11
In this paper, we show how to use low-fidelity operations to control the dynamics of quantum systems. Noisy operations usually drive a system to evolve into a mixed state and damage the coherence. Sometimes frequent noisy operations result in the coherent evolution of a subsystem, and the dynamics of the subsystem is controlled by tuning noisy operations. Based on this, we find that universal quantum computation can be carried out by low-fidelity (fidelity $<90\\%$) operations.
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.
Fan Hongyi [Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026 (China); Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 (China)], E-mail: fhym@sjtu.edu.cn
2008-02-15
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.
QUANTUM MECHANICS I Physics 341
Rosner, Jonathan L.
QUANTUM MECHANICS I Physics 341 KPTC 103 9:00 Â 10:20 a.m. 1 Tues., Thurs. Â Fall Quarter 1999 mechanics at the graduate level. The text for Quantum mechanics I and II will be J. J. Sakurai and Jim Napolitano, Modern Quantum Mechanics, Second Edition (Addison- Wesley, 2011). We will cover the first three
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
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.
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.
Interpretation of quantum mechanics
Roland Omnès
1987-01-01
New axioms are proposed for the interpretation of quantum mechanics. They rest on a kind of calculus allowing to select meaningful physical statements and giving rules to check a given physical reasoning containing implications. Measurement theory is reformulated. Laboratoire associé au Centre National de la Recherche Scientifique.
Supersymmetry and quantum mechanics
Fred Cooper; Avinash Khare; Uday Sukhatme
1995-01-01
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of
Scattering in conformally invariant quantum mechanics
Oksak, A.I.
1986-08-01
The S matrix conformally invariant quantum mechanics is determined by the multiple valuedness of the representation of the conformal group (i.e., by the operator that realizes conformal rotation through angle 2..pi..).
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.
Epigenetics: Biology's Quantum Mechanics
Jorgensen, Richard A.
2011-01-01
The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene – the molecular biological view and the epigenetic view – are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider. PMID:22639577
Glenn Eric Johnson
2014-12-21
The quantum field theories (QFT) constructed in [1,2] include phenomenology of interest. The constructions approximate: scattering by $1/r$ and Yukawa potentials in non-relativistic approximations; and the first contributing order of the Feynman series for Compton scattering. To have a semi-norm, photon states are constrained to transverse polarizations and for Compton scattering, the constructed cross section deviates at large momentum exchanges from the cross section prediction of the Feynman rules. Discussion includes the incompatibility of canonical quantization with the constructed interacting fields, and the role of interpretations of quantum mechanics in realizing QFT.
Probabilistic Interpretation of Quantum Mechanics
Brigitte Falkenburg; Peter Mittelstaedt
The probabilistic interpretation of quantum mechanics is based on Born's 1926 papers and von Neumann's formal account of quantum\\u000a mechanics in ? Hilbert space. According to Max Born (1882–1970), the quantum mechanical ? wave function ? does not have any\\u000a direct physical meaning, whereas its square ???2 is a probability [1] ? Born rule, probability in quantum mechanics. According to
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.
Is quantum field theory a generalization of quantum mechanics?
A. V. Stoyanovsky
2009-01-01
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
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
Determinism Beneath Quantum Mechanics
Gerard't Hooft
Contrary to common belief, it is not difficult to construct deterministic\\u000amodels where stochastic behavior is correctly described by quantum mechanical\\u000aamplitudes, in precise accordance with the Copenhagen-Bohr-Bohm doctrine. What\\u000ais difficult however is to obtain a Hamiltonian that is bounded from below, and\\u000awhose ground state is a vacuum that exhibits complicated vacuum fluctuations,\\u000aas in the real world.
Euclidean Relativistic Quantum Mechanics
Philip Kopp; Wayne Polyzou
2013-01-28
We discuss a formulation of exactly Poincar\\'e invariant quantum mechanics where the input is model Euclidean Green functions or their generating functional. We discuss the structure of the models, the construction of the Hilbert space, the construction and transformation properties of single-particle states, and the construction of GeV scale transition matrix elements. A simple model is utilized to demonstrate the feasibility of this approach.
Relativity and quantum mechanics
Hüseyin Yilmaz
1982-01-01
Conditions under which quantum mechanics can be made compatible with the curved space-time of gravitation theories is investigated. A postulate is imposed in the formv=vg wherev is the kinematical Hamilton-Jacobi (geometric optic limit) velocity andvg is the group velocity of the waves. This imposes a severe condition on the possible coordinates in which the Schrödinger form (the coordinate realization) of
Can Quantum Mechanics Heal Classical Singularities?
NASA Astrophysics Data System (ADS)
Helliwell, T. M.; Konkowski, D. A.
2008-09-01
We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. We show that a large subset of classically singular spacetimes is nevertheless nonsingular quantum mechanically, in that the Hamiltonian operator is essentially self-adjoint so the evolution of quantum wave packets lacks the ambiguity associated with scattering off singularities.
Quantum mechanics and the generalized uncertainty principle
NASA Astrophysics Data System (ADS)
Bang, Jang Young; Berger, Micheal S.
2006-12-01
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 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.
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.
The Mechanism of Quantum Computation
NASA Astrophysics Data System (ADS)
Castagnoli, Giuseppe
2008-08-01
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine whose coordinates are submitted to a nonfunctional relation representing all the problem constraints; moving an input part, reversibly and nondeterministically produces a solution through a many body interaction. The machine can be considered the many body generalization of another perfect machine, the bouncing ball model of reversible computation. The mathematical description of the machine’s motion, as it is, is applicable to quantum problem solving, an extension of the quantum algorithms that comprises the physical representation of the interdependence between the problem and the solution. The configuration space of the classical machine is replaced by the phase space of the quantum machine. The relation between the coordinates of the machine parts now applies to the populations of the reduced density operators of the parts of the computer register throughout state vector reduction. Thus, reduction produces the solution of the problem under a nonfunctional relation representing the problem-solution interdependence. At the light of this finding, the quantum speed up turns out to be “precognition” of the solution, namely the reduction of the initial ignorance of the solution due to backdating, to before running the algorithm, a part of the state vector reduction on the solution (a time-symmetric part in the case of unstructured problems); as such, it is bounded by state vector reduction through an entropic inequality. The computation mechanism under discussion might also explain the wholeness appearing in the introspective analysis of perception.
Abstract: Quantum mechanics provides a
Shahriar, Selim
Abstract: Quantum mechanics provides a mechanism for absolutely secure communication between remote parties. For distances greater than 100 kilometers direct quantum communication via optical fiber is not viable, due to fiber losses, and intermediate storage of the quantum information along the trans- mission
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.
Quantum Computation by Quantum Operations on Mixed States
Vasily E. Tarasov
2002-01-09
Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are quantum operations, not necessarily unitary. A mixed state (operator of density matrix) of n two-level quantum systems is considered as an element of $4^{n}$-dimensional operator Hilbert space. Unitary quantum gates and nonunitary quantum operations for n-qubit system are considered as generalized quantum gates acting on mixed state. In this paper we study universality for quantum computations by quantum operations on mixed states.
Octonic relativistic quantum mechanics
V. L. Mironov; S. V. Mironov
2008-04-22
In this paper we represent the generalization of relativistic quantum mechanics on the base of eght-component values "octons", generating associative noncommutative spatial algebra. It is shown that the octonic second-order equation for the eight-component octonic wave function, obtained from the Einshtein relation for energy and momentum, describes particles with spin of 1/2. It is established that the octonic wave function of a particle in the state with defined spin projection has the specific spatial structure in the form of octonic oscillator with two spatial polarizations: longitudinal linear and transversal circular. The relations between bispinor and octonic descriptions of relativistic particles are established. We propose the eight-component spinors, which are octonic generalisation of two-component Pauli spinors and four-component Dirac bispinors. It is shown that proposed eight-component spinors separate the states with different spin projection, different particle-antiparticle state as well as different polarization of the octonic oscillator. We demonstrate that in the frames of octonic relativistic quantum mechanics the second-order equation for octonic wave function can be reformulated in the form of the system of first-order equations for quantum fields, which is analogous to the system of Maxwell equations for the electromagnetic field. It is established that for the special type of wave functions the second-order equation can be reduced to the single first-order equation, which is analogous to the Dirac equation. At the same time it is shown that this first-order equation describes particles, which do not create quantum fields.
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
Gravitomagnetism in quantum mechanics
Adler, Ronald J.; Chen Pisin [Gravity Probe B, Hansen Laboratory for Experimental Physics, Stanford University, Stanford California 94309 (United States); Leung Center for Cosmology and Particle Astrophysics and Department of Physics and Graduate Institute of Astrophysics, National Taiwan University, Taipei, Taiwan 10617 and Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Menlo Park, California 94025 (United States)
2010-07-15
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.
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.
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.
Gamification of Quantum Mechanics Teaching
Ole Eggers Bjælde; Mads Kock Pedersen; Jacob Sherson
2015-06-26
In this small scale study we demonstrate how a gamified teaching setup can be used effectively to support student learning in a quantum mechanics course. The quantum mechanics games were research games, which were played during lectures and the learning was measured with a pretest/posttest method with promising results. The study works as a pilot study to guide the planning of quantum mechanics courses in the future at Aarhus University in Denmark.
Gamification of Quantum Mechanics Teaching
Bjælde, Ole Eggers; Sherson, Jacob
2015-01-01
In this small scale study we demonstrate how a gamified teaching setup can be used effectively to support student learning in a quantum mechanics course. The quantum mechanics games were research games, which were played during lectures and the learning was measured with a pretest/posttest method with promising results. The study works as a pilot study to guide the planning of quantum mechanics courses in the future at Aarhus University in Denmark.
NASA Astrophysics Data System (ADS)
Jones, Robert
2011-03-01
I do not agree with mind-body dualism. Today the consensus view is that thought and mind is a combination of processes like memory, generalization, comparison, deduction, organization, induction, classification, feature detection, analogy, etc. performed by computational machinery. (R. Jones, Trans. of the Kansas Acad. Sci., vol. 109, # 3/4, 2006 and www.robert-w-jones.com, philosopher, theory of thought) But I believe that quantum mechanics is a more plausible dualist theory of reality. The quantum mechanical wave function is nonphysical, it exists in a 3N space (for an N body system) not in (x,y,z,t) 4-space, and does not possess physical properties. But real physical things like energy (which do exist in our 4-space world) influence the wave function and the wave function, in its turn, influences real physical things, like where a particle can be found in 4-space. The coupling between the spirit-like wave function and things found in the real (4-space) world (like energy) is via mathematical equations like the Schrodinger equation and Born normalization.
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.
NASA Astrophysics Data System (ADS)
Geva, Eitan; Kosloff, Ronnie
1992-02-01
The finite-time operation of a quantum-mechanical heat engine with a working fluid consisting of many noninteracting spin-1/2 systems is considered. The engine is driven by an external, time-dependent and nonrotating magnetic field. The cycle of operation consists of two adiabats and two isotherms. The analysis is based on the time derivatives of the first and second laws of thermodynamics. Explicit relations linking quantum observables to thermodynamic quantities are developed. The irreversible operation of this engine is studied in three cases: (1) The sudden limit, where the performance is found to be the same as that of the spin analog of the Otto cycle. This case provides the lower bound of efficiency. (2) The step-cycle operation scheme. Here, the optimization of power is carried out in the high-temperature limit (the ``classical'' limit). The results obtained are similar to those of Andresen et al. [Phys. Rev. A 15, 2086 (1977)]. (3) The Curzon-Ahlborn operation scheme. The semigroup approach is used to model the dynamics. Then the power production is optimized. All the results obtained for Newtonian engines operating by the same scheme, such as the Curzon-Ahlborn efficiency, apply in the high-temperature limit. These results are obtained without the additional assumption of proximity to thermal equilibrium, implicitly implied by the use of Newtonian heat conduction in the original derivation. It seems that the results of the Curzon-Ahlborn analysis are always obtained in the high-temperature limit, irrespective of the details of the model. The performance beyond the classical limit is optimized numerically. The classical approximation is found to be valid for most of the spin-polarization range. The deviations from the classical limit depend heavily upon the specific nature of both the working fluid and the heat baths and exhibit great diversity and complexity.
Equivalence between Quantum Mechanics and PT Symmetric Quantum Mechanics
David Girardelli; Eduardo M. Zavanin; Marcelo M. Guzzo
2015-02-24
In this paper we develop a discussion about PT Symmetric Quantum Mechanics, working with basics elements of this theory. In a simple case of two body system, we developed the Quantum Brachistochrone problem. Comparing the results obtained through the PT Symmetric Quantum Mechanics with that ones obtained using the standard formalism, we conclude that this new approach is not able to reveal any new effect.
Quantum Leap Quantum Mechanics' Killer App
Bigelow, Stephen
Quantum Leap Quantum Mechanics' Killer App Q&A with Craig Hawker Director of the Materials Research in the nation Thomson Reuters ranked Materials research at UCSB as second in the world in terms of research. Q&A with Craig Hawker LEAP The Materials Research Laboratory is the only Wes
Emergent Quantum Mechanics and Emergent Symmetries
Hooft, Gerard 't [Institute for Theoretical Physics Utrecht University and Spinoza Institute Postbox 80.195 3508 TD Utrecht (Netherlands)
2007-11-20
Quantum mechanics is 'emergent' if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present in the underlying deterministic system. Such theories allow for a natural explanation of the existence of gauge equivalence classes (gauge orbits), including the equivalence classes generated by general coordinate transformations. Thus, local gauge symmetries and general coordinate invariance could be emergent symmetries, and this might lead to new alleys towards understanding the flatness problem of the Universe.
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
Tensorial description of quantum mechanics
J. Clemente-Gallardo; G. Marmo
2013-02-01
Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a covariant formulation of quantum mechanics under the full diffeomorphism group.
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.
Causal structure in categorical quantum mechanics
NASA Astrophysics Data System (ADS)
Lal, Raymond Ashwin
Categorical quantum mechanics is a way of formalising the structural features of quantum theory using category theory. It uses compound systems as the primitive notion, which is formalised by using symmetric monoidal categories. This leads to an elegant formalism for describing quantum protocols such as quantum teleportation. In particular, categorical quantum mechanics provides a graphical calculus that exposes the information flow of such protocols in an intuitive way. However, the graphical calculus also reveals surprising features of these protocols; for example, in the quantum teleportation protocol, information appears to flow `backwards-in-time'. This leads to question of how causal structure can be described within categorical quantum mechanics, and how this might lead to insight regarding the structural compatibility between quantum theory and relativity. This thesis is concerned with the project of formalising causal structure in categorical quantum mechanics. We begin by studying an abstract view of Bell-type experiments, as described by `no-signalling boxes', and we show that under time-reversal no-signalling boxes generically become signalling. This conflicts with the underlying symmetry of relativistic causal structure. This leads us to consider the framework of categorical quantum mechanics from the perspective of relativistic causal structure. We derive the properties that a symmetric monoidal category must satisfy in order to describe systems in such a background causal structure. We use these properties to define a new type of category, and this provides a formal framework for describing protocols in spacetime. We explore this new structure, showing how it leads to an understanding of the counter-intuitive information flow of protocols in categorical quantum mechanics. We then find that the formal properties of our new structure are naturally related to axioms for reconstructing quantum theory, and we show how a reconstruction scheme based on purification can be formalised using the structures of categorical quantum mechanics. Finally, we discuss the philosophical aspects of using category theory to describe fundamental physics. We consider a recent argument that category-theoretic formulations of physics, such as categorical quantum mechanics, can be used to support a variant of structural realism. We argue against this claim. The work of this thesis suggests instead that the philosophy of categorical quantum mechanics is subtler than either operationalism or realism.
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
Coherent states in noncommutative quantum mechanics
J Ben Geloun; F G Scholtz
2009-01-21
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.
Coherent states in noncommutative quantum mechanics
Ben Geloun, J. [National Institute for Theoretical Physics, Private Bag X1, Matieland 7602 (South Africa); International Chair of Mathematical Physics and Applications (ICMPA-UNESCO Chair) 072 B.P. 50 Cotonou (Benin); Departement de Mathematiques et Informatique, Faculte des Sciences et Techniques, Universite Cheikh Anta Diop (Senegal); Scholtz, F. G. [National Institute for Theoretical Physics, Private Bag X1, Matieland 7602 (South Africa)
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.
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.
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.
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.
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.
Symplectic Topology and Geometric Quantum Mechanics
NASA Astrophysics Data System (ADS)
Sanborn, Barbara
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
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.
Scattering Relativity in Quantum Mechanics
Richard Shurtleff
2011-08-09
Transforming from one reference frame to another yields an equivalent physical description. If quantum fields are transformed one way and quantum states transformed a different way then the physics changes. We show how to use the resulting changed physical description to obtain the equations of motion of charged, massive particles in electromagnetic and gravitational fields. The derivation is based entirely on special relativity and quantum mechanics.
Progress in Supersymmetric Quantum Mechanics
2003-01-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General dedicated to the subject of Supersymmetric Quantum Mechanics as featured in the International Conference in Supersymmetric Quantum Mechanics (PSQM03), 15--19 July 2003, University of Valladolid, Spain (http:\\/\\/metodos.fam.cie.uva.es\\/~susy_qm_03\\/). Participants at that meeting, as well as other researchers working in this area or in
No Labeling Quantum Mechanics of Indiscernible Particles
NASA Astrophysics Data System (ADS)
Domenech, G.; Holik, F.; Kniznik, L.; Krause, D.
2010-12-01
Our aim in this paper is to show an example of the formalism we have developed to avoid the label-tensor-product-vector-space-formalism of quantum mechanics when dealing with indistinguishable quanta. States in this new vector space, that we call the Q-space, refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the unobservability of permutations, a goal of quasi-set theory.
Quantum mechanics on a real Hilbert space
Jan Myrheim
1999-05-11
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics, keeping the same set of physical states, but admitting more general observables. The standard time reversal operator involves complex conjugation, in this sense it goes beyond the complex theory and may serve as an example to motivate the generalization. Another example is unconventional canonical quantization such that the harmonic oscillator of angular frequency $\\omega$ has any given finite or infinite set of discrete energy eigenvalues, limited below by $\\hbar\\omega/2$.
Quantum mechanics on a real Hilbert space
Myrheim, Jan
1999-01-01
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics, keeping the same set of physical states, but admitting more general observables. The standard time reversal operator involves complex conjugation, in this sense it goes beyond the complex theory and may serve as an example to motivate the generalization. Another example is unconventional canonical quantization such that the harmonic oscillator of angular frequency $\\omega$ has any given finite or infinite set of discrete energy eigenvalues, limited below by $\\hbar\\omega/2$.
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.
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.
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
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 ...
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
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
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
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Strings and the Strong Force Thursday, May 7, 2009 #12;Review of Quantum Mechanics In general, particles Planck's constant determines the scale where quantum mechanical effects become important Thursday, May 7
Noncommutative Poisson boundaries of unital quantum operations
Lim, Bunrith Jacques [Institut de Recherche Mathematique de Rennes (IRMAR), Universite de Rennes 1 and CNRS (UMR 6625), 35042 Rennes Cedex (France)
2010-05-15
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.
The Physical Principles of Quantum Mechanics. A critical review
F. Strocchi
2012-01-04
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more physically motivated formulation is discussed. The existence of non commuting observables, which characterizes quantum mechanics with respect to classical mechanics, is related to operationally testable complementarity relations, rather than to uncertainty relations. The drawbacks of Dirac argument for canonical quantization are avoided by a more geometrical approach.
Adding control to arbitrary unknown quantum operations
Zhou, Xiao-Qi; Ralph, Timothy C.; Kalasuwan, Pruet; Zhang, Mian; Peruzzo, Alberto; Lanyon, Benjamin P.; O'Brien, Jeremy L.
2011-01-01
Although quantum computers promise significant advantages, the complexity of quantum algorithms remains a major technological obstacle. We have developed and demonstrated an architecture-independent technique that simplifies adding control qubits to arbitrary quantum operations—a requirement in many quantum algorithms, simulations and metrology. The technique, which is independent of how the operation is done, does not require knowledge of what the operation is, and largely separates the problems of how to implement a quantum operation in the laboratory and how to add a control. Here, we demonstrate an entanglement-based version in a photonic system, realizing a range of different two-qubit gates with high fidelity. PMID:21811242
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, E-mail: cdyang@mail.ncku.edu.tw; Cheng, Lieh-Lieh, E-mail: leo8101@hotmail.com
2013-11-15
Following de Broglie’s idea of a pilot wave, this paper treats quantum mechanics as a problem of stochastic optimal guidance law design. The guidance scenario considered in the quantum world is that an electron is the flight vehicle to be guided and its accompanying pilot wave is the guidance law to be designed so as to guide the electron to a random target driven by the Wiener process, while minimizing a cost-to-go function. After solving the stochastic optimal guidance problem by differential dynamic programming, we point out that the optimal pilot wave guiding the particle’s motion is just the wavefunction ?(t,x), a solution to the Schrödinger equation; meanwhile, the closed-loop guidance system forms a complex state–space dynamics for ?(t,x), from which quantum operators emerge naturally. Quantum trajectories under the action of the optimal guidance law are solved and their statistical distribution is shown to coincide with the prediction of the probability density function ?{sup ?}?. -- Highlights: •Treating quantum mechanics as a pursuit-evasion game. •Reveal an interesting analogy between guided flight motion and guided quantum motion. •Solve optimal quantum guidance problem by dynamic programming. •Gives a formal proof of de Broglie–Bohm’s idea of a pilot wave. •The optimal pilot wave is shown to be a wavefunction solved from Schrödinger equation.
Quantum Mechanics and Determinism
Gerard't Hooft
2001-01-01
It is shown how to map the quantum states of a system of free scalar\\u000aparticles one-to-one onto the states of a completely deterministic model. It is\\u000aa classical field theory with a large (global) gauge group. The mapping is now\\u000aalso applied to free Maxwell fields. Lorentz invariance is demonstrated.
NSDL National Science Digital Library
Galvez, Enrique
This web site, authored by Enrique Galvez and Charles Holbrow of Colgate University, outlines a project to develop undergraduate physics labs that investigate quantum interference and entanglement with photons. The labs are designed for simplicity and low cost. A description of the lab set up, background information, and an article on the project are provided.
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
Quantum Mechanics (QM) Measurement Package
NSDL National Science Digital Library
Belloni, Mario
This set of tutorial worksheets, based on the OSP Quantum Mechanics Simulations, help students explore the effects of position, momentum, and energy measurements on quantum state wavepackets. The probabilistic change in the wavefunction upon measurements and the time propagation of the states are illustrated. Similar worksheets are available for measurements of single and superpositions of energy eigenstates. The worksheets can be run online or downloaded as a pdf (attached).
PT quantum mechanics - Recent results
Bender, Carl M. [Physics Department, Washington University, St. Louis, MO 63130 (United States)
2012-09-26
Most quantum physicists believe that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under matrix transposition and complex conjugation) to be sure that the energy eigenvalues are real and that time evolution is unitary. However, the non-Dirac-hermitian Hamiltonian H p{sup 2}+ix{sup 3} has a real positive discrete spectrum and generates unitary time evolution and defines a fully consistent and physical quantum theory. Evidently, Dirac Hermiticity is too restrictive. While H = p{sup 2}+ix{sup 3} is not Dirac Hermitian, it is PT symmetric (invariant under combined space reflection P and time reversal T). Another PT-symmetric Hamiltonian whose energy levels are real, positive and discrete is H = p{sup 2}-x{sup 4}, which contains an upside-down potential. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics and quantum field theory are extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past two years some of these properties have been verified in laboratory experiments. Here, we first discuss PT-symmetric Hamiltonians at a simple intuitive level and explain why the energy levels of such Hamiltonians may be real, positive, and discrete. Second, we describe a recent experiment in which the PT phase transition was observed. Third, we briefly mention that PT-symmetric theories can be useful at a fundamental level. While the double-scaling limit of an O(N)-symmetric g{phi}{sup 4} quantum field theory appears to be inconsistent because the critical value of g is negative, this limit is in fact not inconsistent because the critical theory is PT symmetric.
Quantum Mechanics: Sum Over Paths
NSDL National Science Digital Library
Taylor, Edwin F.
Created by Edwin F. Taylor a former professor at the Department of Physics at the Massachusetts Institute of Technology, this material describes methods of presenting quantum mechanics using the path-integral formulation. Included are links to a paper and presentation outlining the method, software to simulate the path integrals, and student workbook materials. This course has been used for introducing quantum physics to high school teachers.
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…
ccsd00002942, ON SUPERSYMMETRIC QUANTUM MECHANICS
ccsdÂ00002942, version 1 Â 25 Sep 2004 ON SUPERSYMMETRIC QUANTUM MECHANICS M.R. KIBLER Institut de Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl supersymmetric Quantum Mechanics corresponds to k = 2. A connection between fractional supersymmetric Quantum
Wüthrich, Christian
THE OBJECTIVE INDEFINITENESS INTERPRETATION OF QUANTUM MECHANICS: Partition logic, logical information theory, and quantum mechanics David Ellerman University of California at Riverside www ago that quantum mechanics was not compatible with Boolean logic, then the natural thing to do would
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.
Kowalevski top in quantum mechanics
Matsuyama, A., E-mail: spamatu@ipc.shizuoka.ac.jp
2013-09-15
The quantum mechanical Kowalevski top is studied by the direct diagonalization of the Hamiltonian. The spectra show different behaviors depending on the region divided by the bifurcation sets of the classical invariant tori. Some of these spectra are nearly degenerate due to the multiplicity of the invariant tori. The Kowalevski top has several symmetries and symmetry quantum numbers can be assigned to the eigenstates. We have also carried out the semiclassical quantization of the Kowalevski top by the EBK formulation. It is found that the semiclassical spectra are close to the exact values, thus the eigenstates can be also labeled by the integer quantum numbers. The symmetries of the system are shown to have close relations with the semiclassical quantum numbers and the near-degeneracy of the spectra. -- Highlights: •Quantum spectra of the Kowalevski top are calculated. •Semiclassical quantization is carried out by the EBK formulation. •Quantum states are labeled by the semiclassical integer quantum numbers. •Multiplicity of the classical torus makes the spectra nearly degenerate. •Symmetries, quantum numbers and near-degenerate spectra are closely related.
Why Do the Quantum Observables Form a Jordan Operator Algebra?
Gerd Niestegge
2010-01-21
The Jordan algebra structure of the bounded real quantum observables was recognized already in the early days of quantum mechanics. While there are plausible reasons for most parts of this structure, the existence of the distributive nonassociative multiplication operation is hard to justify from a physical or statistical point of view. Considering the non-Boolean extension of classical probabilities, presented in a recent paper, it is shown in this paper that such a multiplication operation can be derived from certain properties of the conditional probabilities and the observables, i.e., from postulates with a clear statistical interpretation. The well-known close relation between Jordan operator algebras and C*-algebras then provides the connection to the quantum-mechanical Hilbert space formalism, thus resulting in a novel axiomatic approach to general quantum mechanics that includes the types II and III von Neumann algebras.
A Rosetta Stone for Quantum Mechanics with an Introduction to Quantum Computation
Lomonaco, S J
2000-01-01
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000, and will appear in the AMS PSAPM volume entitled "Quantum Computation." Part 1 of the paper is an introduction the to the concept of the qubit. Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schrodinger's equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schrodinger picture, quantum entanglement, EPR paradox, quantum entropy. Part 3 gives a brief ...
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
Principle of Least Action in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Kobe, Donald H.
2004-10-01
We show that Hamilton's Principle of Least (or Extremum) Action for a complex scalar field to give the Schroedinger equation is equivalent to a commonly used time-dependent variational principle used in quantum mechanics with a Lagrangian density involving the wave function and the Hamiltonian operator. The method is applied to a many-boson system to derive a time-dependent Gross-Pitaevski equation.
Quantum Logical Operations on Encoded Qubits
Wojciech Hubert Zurek; Raymond Laflamme
1996-05-14
We show how to carry out quantum logical operations (controlled-not and Toffoli gates) on encoded qubits for several encodings which protect against various 1-bit errors. This improves the reliability of these operations by allowing one to correct for one bit errors which either preexisted or occurred in course of operation. The logical operations we consider allow one to cary out the vast majority of the steps in the quantum factoring algorithm. Thus, our results help bring quantum factoring and other quantum computations closer to reality
Remarks on osmosis, quantum mechanics, and gravity
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.
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.
Quantum tunneling process and Zambrini's Euclidean quantum mechanics
Mari Jibu; Kunio Yasue
1992-01-01
By adopting Zambrini's new Euclidean quantum mechanics, a theoretical procedure to describe the ill-defined problem of quantum tunneling processes studied recently in quantum cosmology is proposed. It is shown that the tunneling process from the vacuum state to a semi-classical state can be analyzed a priori in consrast with the conventional Copenhagen interpretation of quantum mechanics.
Quantum tunneling process and Zambrini's Euclidean quantum mechanics
NASA Astrophysics Data System (ADS)
Jibu, Mari; Yasue, Kunio
1992-11-01
By adopting Zambrini's new Euclidean quantum mechanics, a theoretical procedure to describe the ill-defined problem of quantum tunneling processes studied recently in quantum cosmology is proposed. It is shown that the tunneling process from the vacuum state to a semi-classical state can be analyzed a priori in consrast with the conventional Copenhagen interpretation of quantum mechanics.
Quantum Mechanics and Leggett's Inequalities
NASA Astrophysics Data System (ADS)
Socolovsky, M.
2009-12-01
We show that when the proper description of the behaviour of individual photons or spin {{1}over{2}} particles in a spherically symmetric entangled pair is done through the use of the density matrix, the Leggett’s inequality is not violated by quantum mechanics.
Time, Quantum Mechanics, and Probability
Simon Saunders
2001-11-07
A "geometric" intepretation of probability is proposed, modelled on the treatment of tense in 4-dimensional spacetime. It is applied to Everett's approach to quantum mechanics, as formulated in terms of consistent histories. Standard objections to Everett's approach, based on the difficulties of interpreting probability in its terms, are considered in detail, but found to be wanting.
Probabilistic Approach to Teaching the Principles of Quantum Mechanics
ERIC Educational Resources Information Center
Santos, Emilio
1976-01-01
Approaches the representation of quantum mechanics through Hilbert space postulates. Demonstrates that if the representation is to be accurate, an evolution operator of the form of a Hamiltonian must be used. (CP)
Delay Time in Quaternionic Quantum Mechanics
Stefano De Leo; Gisele Ducati
2012-04-11
In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. The study shows in which energy region it is possible to amplify the difference between quaternionic and complex quantum mechanics.
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.
Position-dependent noncommutativity in quantum mechanics
M. Gomes; V. G. Kupriyanov
2009-06-15
The model of the position-dependent noncommutativety in quantum mechanics is proposed. We start with a given commutation relations between the operators of coordinates [x^{i},x^{j}]=\\omega^{ij}(x), and construct the complete algebra of commutation relations, including the operators of momenta. The constructed algebra is a deformation of a standard Heisenberg algebra and obey the Jacobi identity. The key point of our construction is a proposed first-order Lagrangian, which after quantization reproduces the desired commutation relations. Also we study the possibility to localize the noncommutativety.
Quantum Mechanics Revisited Jean Claude Dutailly
Boyer, Edmond
Quantum Mechanics Revisited Jean Claude Dutailly Paris (France) August 20, 2014 Abstract The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general a new theoretical foundation. ii) The quantum mechanics (QM) which is presented in all the books
Quantum Mechanics for Mathematicians: Introduction and Overview
Woit, Peter
Quantum Mechanics for Mathematicians: Introduction and Overview Peter Woit Department Richard Feynman goes "I think it is safe to say that no one understands quantum mechanics."[1 was contrasting quantum mechanics with the theory of general relativity, a supposedly equally hard to understand
On a realistic interpretation of quantum mechanics
Neumaier, Arnold
On a realistic interpretation of quantum mechanics Arnold Neumaier Institut fur Mathematik respecting the indeter- ministic nature of quantum mechanics, allows to speak of de#12;nite values for all], there are at least two levels of inter- preting quantum mechanics: the statistical interpretation in the narrower
First Day Handout Phys 430: Quantum Mechanics
Nickrent, Daniel L.
First Day Handout Phys 430: Quantum Mechanics (Dated: 18 August 2014) Meeting times: MWF 1:00-1:50 Room: Neckers 410 Text: "Introduction to Quantum Mechanics," 2nd Edition, by D. Griffiths. Instructor Interpretation (e) The Uncertainty Principle (f) Dirac Notation 4. Chapter 4: Quantum Mechanics in Three
On the interpretation of quantum mechanics
V. A. Fock
1957-01-01
After a brief discussion of the reasons for the complete failure of a deterministic interpretation of quantum mechanics (§ 1)Niels Bohr's ideas on quantum mechanics are exposed. The importance of Bohr's idea on the necessity of combining the quantum-mechanical description of atomic objects with a classical description of the instruments is stressed (§ 2).It is pointed out, however, that the
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
129 Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
129 Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We's equation of motion in mechanics. The initial condtions to solve the Newton's equation of motion
221B Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
221B Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics We the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We's equation of motion in mechanics. The initial condtions to solve the Newton's equation of motion
221B Lecture Notes Relativistic Quantum Mechanics
Murayama, Hitoshi
221B Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics We the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We, similarly to the Newton's equation of motion in mechanics. The initial condtions to solve the Newton
Quantum Mechanics: 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
A Criterion for Holism in Quantum Mechanics
Seevinck, Michiel
A Criterion for Holism in Quantum Mechanics M.P Seevinck E-mail: M.P.Seevinck@phys.uu.nl Utrecht University, The Netherlands, August 2003. 1 #12; Motivation · The question whether or not quantum mechanics is it that makes quantum mechanics a holistic theory (if so), and other physical theories not (if so). · I propose
Entanglement and Disentanglement in Relativistic Quantum Mechanics
Stanford, Kyle
Entanglement and Disentanglement in Relativistic Quantum Mechanics Jeffrey A. Barrett August 16, 2014 Abstract A satisfactory formulation of relativistic quantum mechanics re- quires that one be able in relativistic quantum mechanics must ultimately depend on the details of one's strategy for addressing
QUANTUM MECHANICS AND DUALISM JEFFREY A. BARRETT
Stanford, Kyle
QUANTUM MECHANICS AND DUALISM JEFFREY A. BARRETT Abstract. The quantum measurement problem has led mechanics, a strong variety of mind-body dualism provides a natural criterion for when collapses occur, and in a no-collapse formulation of quantum mechanics, a strong variety of dualism provides a way to account
Probability in modal interpretations of quantum mechanics
Seevinck, Michiel
Probability in modal interpretations of quantum mechanics Dennis Dieks Institute for the History interpretations have the ambition to construe quantum mechanics as an ob- jective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix
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.
Nielsen, Steven O.
The Postulates of Quantum Mechanics (from Quantum Mechanics by Claude Cohen-Tannoudji, Bernard Diu, and Franck Lalo¨e) Introduction The postulates of quantum mechanics are the theory. Their physical content to the following questions: (i) How is the state of a quantum mechanical system at a given time described
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.
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.
M. Saitoh; T. Hiramoto
2003-01-01
This paper describes the room-temperature (RT) demonstration of a newly proposed highly-functional single-electron transistor (SET) logic based on the quantum mechanical effect. We fabricate single-hole transistors (SHTs) in the form of extremely constricted channel MOSFETs and obtain large Coulomb blockade (CB) oscillations with a peak-to-valley current ratio (PVCR) of 102 at RT. In the fabricated single-dot SHTs, clear negative differential
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.
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.
Complementarity in Categorical Quantum Mechanics
NASA Astrophysics Data System (ADS)
Heunen, Chris
2012-07-01
We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a `point-free' definition of copyability we link (i) commutative von Neumann subalgebras, (ii) classical structures, and (iii) Boolean subalgebras.
Quantum theory with bold operator tensors.
Hardy, Lucien
2015-08-01
In this paper, we present a formulation of quantum theory in terms of bold operator tensors. A circuit is built up of operations where an operation corresponds to a use of an apparatus. We associate collections of operator tensors (which together comprise a bold operator) with these apparatus uses. We give rules for combining bold operator tensors such that, for a circuit, they give a probability distribution over the possible outcomes. If we impose certain physicality constraints on the bold operator tensors, then we get exactly the quantum formalism. We provide both symbolic and diagrammatic ways to represent these calculations. This approach is manifestly covariant in that it does not require us to foliate the circuit into time steps and then evolve a state. Thus, the approach forms a natural starting point for an operational approach to quantum field theory. PMID:26124254
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.
Information security and quantum mechanics: Security of quantum protocols
Patrick Oscar Boykin
2002-01-01
The problem of security of quantum key protocols is examined. In addition to the distribution of classical keys, the problem of encrypting quantum data and the structure of the operators which perform quantum encryption is studied. It is found that unitary bases are central to both encryption of quantum information, as well as the generation of states used in generalized
Information Security and Quantum Mechanics:Security of Quantum Protocols
P. Oscar Boykin
2002-01-01
The problem of security of quantum key protocols is examined. In addition to the distribution of classical keys, the problem of encrypting quantum data and the structure of the operators which perform quantum encryption is studied. It is found that unitary bases are central to both encryption of quantum information, as well as the generation of states used in generalized
Effective equations for the quantum pendulum from momentous quantum mechanics
Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)
2012-08-24
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.
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.
Exploration of similarities between classical wave mechanics and quantum mechanics
Kim Fook Lee
2002-01-01
This dissertation explores classical analogs of one particle wave mechanics and multiparticle quantum entanglement by using classical wave optics. We develop classical measurement techniques to simulate one particle wave mechanics and quantum entanglement for up to four particles. Classical simulation of multi-particle entanglement is useful for quantum information processing (QIP) because much of the QIP does not require collapse and
Quantum mechanical light harvesting mechanisms in photosynthesis
NASA Astrophysics Data System (ADS)
Scholes, Gregory
2012-02-01
More than 10 million billion photons of light strike a leaf each second. Incredibly, almost every red-coloured photon is captured by chlorophyll pigments and initiates steps to plant growth. Last year we reported that marine algae use quantum mechanics in order to optimize photosynthesis [1], a process essential to its survival. These and other insights from the natural world promise to revolutionize our ability to harness the power of the sun. In a recent review [2] we described the principles learned from studies of various natural antenna complexes and suggested how to utilize that knowledge to shape future technologies. We forecast the need to develop ways to direct and regulate excitation energy flow using molecular organizations that facilitate feedback and control--not easy given that the energy is only stored for a billionth of a second. In this presentation I will describe new results that explain the observation and meaning of quantum-coherent energy transfer. [4pt] [1] Elisabetta Collini, Cathy Y. Wong, Krystyna E. Wilk, Paul M. G. Curmi, Paul Brumer, and Gregory D. Scholes, ``Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature'' Nature 463, 644-648 (2010).[0pt] [2] Gregory D. Scholes, Graham R. Fleming, Alexandra Olaya-Castro and Rienk van Grondelle, ``Lessons from nature about solar light harvesting'' Nature Chem. 3, 763-774 (2011).
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.
Levitated Quantum Nano-Magneto-Mechanical Systems
Mauro Cirio; Jason Twamley; Gavin K. Brennen; Gerard J. Milburn
2011-01-01
Quantum nanomechanical sysems have attracted much attention as they provide new macroscopic platforms for the study of quantum mechanics but may also have applications in ultra-sensitive sensing, high precision measurements and in quantum computing. In this work we study the control and cooling of a quantum nanomechanical system which is magnetically levitated via the Meissner effect. Supercurrents in nano-sized superconducting
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.
Quantum Mechanical Observers and Time Reparametrization Symmetry
NASA Astrophysics Data System (ADS)
Konishi, Eiji
2012-07-01
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 nonunitary temporal behavior as seen in the measurement processes, we describe the concepts of the quantum mechanical observers via the time reparametrization symmetry.
Quantum Mechanics Joachim Burgdorfer and Stefan Rotter
Rotter, Stefan
1 1 Quantum Mechanics Joachim BurgdÂ¨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
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 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.
The cosmic origin of quantum mechanics
Ding-Yu Chung
2001-02-18
In this paper, the base of quantum mechanics is the spontaneous tendency for a microscopic object to fractionalize instantly into quasistates and condense instantly quasistates. This quasistate is equivalent to the eigenfunction. An object with the fractionalization-condensation is equivalent to the unitary wavefunction. Nonlocal operation is explicitly required to maintain communication among all quasistates regardless of distance during the fractionalization process. Interference effect is explicitly required for the condensation of quasistates. The collapse of the fractionalization-condensation is explicitly required when the fractionalization-condensation is disrupted. The cosmic origin of quantum mechanics is derived from the cyclic fractionalization-condensation in the cyclic universe, consisting of the unobservable cosmic vacuum and the observable universe. The cyclic fractionalization-condensation allows quasistates to appear cyclically rather than simultaneously. The cosmic vacuum involves the gradual cyclic fractionalization-condensation between the high energy eleven dimensional and low energy four dimensional spacetime. The observable universe involves the drastic cyclic fractionalization-condensation consisting of the cosmic instant fractionalization (the big bang) into various dimensional particles and the expansion-contraction by mostly cosmic radiation and gravity. The cosmic instant fractionalization leads to the microscopic instant fractionalization-condensation (the standard quantum mechanics) that allows all quasistates from an object to appear simultaneously.
The Arrow of Time in Rigged Hilbert Space Quantum Mechanics
Robert C. Bishop
2005-06-22
Arno Bohm and Ilya Prigogine's Brussels-Austin Group have been working on the quantum mechanical arrow of time and irreversibility in rigged Hilbert space quantum mechanics. A crucial notion in Bohm's approach is the so-called preparation/registration arrow. An analysis of this arrow and its role in Bohm's theory of scattering is given. Similarly, the Brussels-Austin Group uses an excitation/de-excitation arrow for ordering events, which is also analyzed. The relationship between the two approaches is initially discussed focusing on their semi-group operators and time arrows. Finally a possible realist interpretation of the rigged Hilbert space formulation of quantum mechanics is considered.
Treating time travel quantum mechanically
NASA Astrophysics Data System (ADS)
Allen, John-Mark A.
2014-10-01
The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilizing the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their nonlinearity and time-travel paradoxes. In particular, the "equivalent circuit model"—which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory—is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of alternate theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features—such as time-travel paradoxes, the ability to distinguish nonorthogonal states with certainty, and the ability to clone or delete arbitrary pure states—that are present with D-CTCs and P-CTCs. The problems with nonlinear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.
Treating Time Travel Quantum Mechanically
John-Mark A. Allen
2014-10-10
The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilising the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their non-linearity and time travel paradoxes. In particular, the "equivalent circuit model"---which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory---is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of new theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features---such as time travel paradoxes, the ability to distinguish non-orthogonal states with certainty, and the ability to clone or delete arbitrary pure states---that are present with D-CTCs and P-CTCs. The problems with non-linear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.
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.
The Linguistic Interpretation of Quantum Mechanics
Ishikawa, Shiro
2012-01-01
About twenty years ago, we proposed the mathematical formulation of Heisenberg's uncertainty principle, and further, we concluded that Heisenberg's uncertainty principle and EPR-paradox are not contradictory. This is true, however we now think that we should have argued about it under a certain firm interpretation of quantum mechanics. Recently we proposed the linguistic quantum interpretation (called quantum and classical measurement theory), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics, in other words, quantum philosophy). In fact, we can consider that traditional philosophies have progressed toward quantum philosophy. In this paper, we first review the linguistic quantum interpretation, and further, clarify the relation between EPR-paradox and Heisenberg's uncertainty...
Teaching Quantum Mechanical Commutation Relations via an Optical Experiment
Billur, A Alper; Bursal, Murat
2015-01-01
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the operator formalisms are generally given theoretically and it is documented that these abstract formalisms are usually misunderstood by the students. Based on the idea that quantum mechanical phenomena can be investigated via geometric optical tools, this study aims to introduce an experiment, where the quantum mechanical commutation relations are represented in a concrete way to provide students an easy and permanent learning. The experimental tools are chosen to be easily accessible and economic. The experiment introduced in this paper can be done with students or used as a demonstrative experiment in laboratory based or theory based courses requiring quantum physics content; particularly in physics, physics education and science education programs.
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
Fun with supersymmetric quantum mechanics
Freedman, B.; Cooper, F.
1984-04-01
One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup ..cap alpha../ for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpotentials to test various ideas about how to see if supersymmetry is broken in an arbitrary model. Recently, Witten proposed a topological invariant, the Witten index ..delta.. which counts the number of bosons minus the number of fermions having ground state energy zero. Since if supersymmetry is broken, the ground state energy cannot be zero, one expects if ..delta.. is not zero, SUSY is preserved and the theory is not a good candidate for a realistic model. In this study we evaluate ..delta.. for several examples, and show some unexpected peculiarities of the Witten index for certain choice of superpotentials W(x). We also discuss two other nonperturbative methods of studying supersymmetry breakdown. One involves relating supersymmetric quantum mechanics to a stochastic classical problem and the other involves considering a discrete (but not supersymmetric) version of the theory and studying its behavior as one removes the lattice cuttoff. In this survey we review the Hamiltonian and path integral approaches to supersymmetric quantum mechanics. We then discuss the related path integrals for the Witten Index and for stochastic processes and show how they are indications for supersymmetry breakdown. We then discuss a system where the superpotential W(x) has assymetrical values at +-infinity. We finally discuss nonperturbative strategies for studying supersymmetry breakdown based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed. 17 references.
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.
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.
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... 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...
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 mechanics as Feynman path inte- grals in imaginary time . . . . . . . . . . . . . . . . . . . 47 3.14 From classical to quantum mechanics . . . . . . . . . . . 47 3.14.1 Route I
Chaos in Bohmian quantum mechanics
NASA Astrophysics Data System (ADS)
Efthymiopoulos, C.; Contopoulos, G.
2006-02-01
This paper presents a number of numerical investigations of orbits in the de Broglie-Bohm version of quantum mechanics. We first clarify how the notion of chaos should be implemented in the case of Bohmian orbits. Then, we investigate the Bohmian orbits in three different characteristic quantum systems: (a) superposition of three stationary states in the Hamiltonian of two uncoupled harmonic oscillators with incommensurable frequencies, (b) wave packets in a Hénon-Heiles-type Hamiltonian and (c) a modified two-slit experiment. In these examples, we identify regular or chaotic orbits and also orbits exhibiting a temporarily regular and then chaotic behaviour. Then, we focus on a numerical investigation of the Bohm-Vigier (Bohm and Vigier 1954 Phys. Rev. 26 208) theory, that an arbitrary initial particle distribution P should asymptotically tend to |?|2, by considering the role of chaotic mixing in causing irregularity of Madelung's flow, a necessary condition for P to tend to |?|2. We find that the degree of chaos of a particular system correlates with the speed of convergence of P to |?|2. In the case of wave-packet dynamics, our numerical data show that the time of convergence scales exponentially with the inverse of the effective perturbation from the harmonic oscillator Hamiltonian. The latter result can be viewed as a quantum analogue of Nekhoroshev's (Nekhoroshev 1977 Russ. Math. Surveys 32 1) theorem of exponential stability in classical nonlinear Hamiltonian dynamics.
Sequential Implementation of Global Quantum Operations
NASA Astrophysics Data System (ADS)
Lamata, L.; León, J.; Pérez-García, D.; Salgado, D.; Solano, E.
2008-10-01
We study the possibility for a global unitary applied on an arbitrary number of qubits to be decomposed in a sequential unitary procedure, where an ancillary system is allowed to interact only once with each qubit. We prove that sequential unitary decompositions are in general impossible for genuine entangling operations, even with an infinite-dimensional ancilla, being the controlled-NOT gate a paradigmatic example. Nevertheless, we find particular nontrivial operations in quantum information that can be performed in a sequential unitary manner, as is the case of quantum error correction and quantum cloning.
Contribution to understanding the mathematical structure of quantum mechanics
NASA Astrophysics Data System (ADS)
Skála, L.; Kapsa, V.
2007-09-01
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, the Born rule, commutation and uncertainty relations, probability density current, momentum operator, and rules for including the scalar and vector potentials and antiparticles can be obtained from the probabilistic description of results of measurement of the space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, the Schrödinger equation, and the Dirac equation are obtained from the requirement of the relativistic invariance of the space-time Fisher information. The limit case of th e ?-like probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Manyparticle systems and the postulates of quantum mechanics are also discussed.
Quantum mechanics as a complete physical theory
D. A. Slavnov
2002-11-10
We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that allow constructing a renewed mathematical scheme of quantum mechanics. This scheme involves the standard mathematical formalism of quantum mechanics. Simultaneously, it contains a mathematical object that adequately describes a single experiment. We give an example of the application of the proposed scheme.
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.
Invertible Quantum Operations and Perfect Encryption of Quantum States
Ashwin Nayak; Pranab Sen
2006-11-02
In this note, we characterize the form of an invertible quantum operation, i.e., a completely positive trace preserving linear transformation (a CPTP map) whose inverse is also a CPTP map. The precise form of such maps becomes important in contexts such as self-testing and encryption. We show that these maps correspond to applying a unitary transformation to the state along with an ancilla initialized to a fixed state, which may be mixed. The characterization of invertible quantum operations implies that one-way schemes for encrypting quantum states using a classical key may be slightly more general than the ``private quantum channels'' studied by Ambainis, Mosca, Tapp and de Wolf (FOCS 2000). Nonetheless, we show that their results, most notably a lower bound of 2n bits of key to encrypt n quantum bits, extend in a straightforward manner to the general case.
Heterogeneous THz quantum cascade lasers: Broadband operation
Joshua R. Freeman; Anthony Brewer; Julien Madeo; Pierrick Cavalie; Sukhdeep S. Dhillon; Jerome Tignon; Harvey E. Beere; David A. Ritchie
2011-01-01
We demonstrate the operation of broadband heterogeneous terahertz quantum cascade lasers by carefully designing sub-stacks to align at the same field. Time domain spectroscopy measurements confirm that a flat gain spectrum is present and when incorporated into metal-metal waveguides we find broadband operation over 380 GHz when metal-metal ridges with non-vertical side-walls are used.
Simulation of n-qubit quantum systems. III. Quantum operations
NASA Astrophysics Data System (ADS)
Radtke, T.; Fritzsche, S.
2007-05-01
During the last decade, several quantum information protocols, such as quantum key distribution, teleportation or quantum computation, have attracted a lot of interest. Despite the recent success and research efforts in quantum information processing, however, we are just at the beginning of understanding the role of entanglement and the behavior of quantum systems in noisy environments, i.e. for nonideal implementations. Therefore, in order to facilitate the investigation of entanglement and decoherence in n-qubit quantum registers, here we present a revised version of the FEYNMAN program for working with quantum operations and their associated (Jamio?kowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. Apart from the implementation of different noise models, the current program extension may help investigate the fragility of many quantum states, one of the main obstacles in realizing quantum information protocols today. Program summaryTitle of program: Feynman Catalogue identifier: ADWE_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v3_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Operating systems: Any system that supports MAPLE; tested under Microsoft Windows XP, SuSe Linux 10 Program language used:MAPLE 10 Typical time and memory requirements: Most commands that act upon quantum registers with five or less qubits take ?10 seconds of processor time (on a Pentium 4 processor with ?2 GHz or equivalent) and 5-20 MB of memory. Especially when working with symbolic expressions, however, the memory and time requirements critically depend on the number of qubits in the quantum registers, owing to the exponential dimension growth of the associated Hilbert space. For example, complex (symbolic) noise models (with several Kraus operators) for multi-qubit systems often result in very large symbolic expressions that dramatically slow down the evaluation of measures or other quantities. In these cases, MAPLE's assume facility sometimes helps to reduce the complexity of symbolic expressions, but often only numerical evaluation is possible. Since the complexity of the FEYNMAN commands is very different, no general scaling law for the CPU time and memory usage can be given. No. of bytes in distributed program including test data, etc.: 799 265 No. of lines in distributed program including test data, etc.: 18 589 Distribution format: tar.gz Reasons for new version: While the previous program versions were designed mainly to create and manipulate the state of quantum registers, the present extension aims to support quantum operations as the essential ingredient for studying the effects of noisy environments. Does this version supersede the previous version: Yes Nature of the physical problem: Today, entanglement is identified as the essential resource in virtually all aspects of quantum information theory. In most practical implementations of quantum information protocols, however, decoherence typically limits the lifetime of entanglement. It is therefore necessary and highly desirable to understand the evolution of entanglement in noisy environments. Method of solution: Using the computer algebra system MAPLE, we have developed a set of procedures that support the definition and manipulation of n-qubit quantum registers as well as (unitary) logic gates and (nonunitary) quantum operations that act on the quantum registers. The provided hierarchy of commands can be used interactively in order to simulate and analyze the evolution of n-qubit quantum systems in ideal and nonideal quantum circuits.
Characterizations of fixed points of quantum operations
Li Yuan [College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062 (China)
2011-05-15
Let {phi}{sub A} be a general quantum operation. An operator B is said to be a fixed point of {phi}{sub A}, if {phi}{sub A}(B)=B. In this note, we shall show conditions under which B, a fixed point {phi}{sub A}, implies that B is compatible with the operation element of {phi}{sub A}. In particular, we offer an extension of the generalized Lueders theorem.
Kindergarten Quantum Mechanics: Lecture Notes
NASA Astrophysics Data System (ADS)
Coecke, Bob
2006-01-01
These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in [3, 4]) which subsumes my Logic of Entanglement [11]. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes [12, 13]. In a last section we provide some pointers to the body of technical literature on the subject.
Thermodynamic integration from classical to quantum mechanics
Habershon, Scott [Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS (United Kingdom); Manolopoulos, David E. [Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ (United Kingdom)
2011-12-14
We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.
Tests of CPT and Quantum Mechanics: experiment
NASA Astrophysics Data System (ADS)
Ambrosino, F.; Antonelli, A.; Antonelli, M.; Bacci, C.; Barva, M.; Beltrame, P.; Bencivenni, G.; Bertolucci, S.; Bini, C.; Bloise, C.; Bocchetta, S.; Bocci, V.; Bossi, F.; Bowring, D.; Branchini, P.; Bulychjov, S. A.; Caloi, R.; Campana, P.; Capon, G.; Capussela, T.; Carboni, G.; Ceradini, F.; Cervelli, F.; Chi, S.; Chiefari, G.; Ciambrone, P.; Conetti, S.; De Lucia, E.; De Santis, A.; De Simone, P.; De Zorzi, G.; Dell'Agnello, S.; Denig, A.; Di Domenico, A.; Di Donato, C.; Di Falco, S.; Di Micco, B.; Doria, A.; Dreucci, M.; Farilla, A.; Felici, G.; Ferrari, A.; Ferrer, M. L.; Finocchiaro, G.; Fiore, S.; Forti, C.; Franzini, P.; Gatti, C.; Gauzzi, P.; Giovannella, S.; Gorini, E.; Graziani, E.; Incagli, M.; Kluge, W.; Kulikov, V.; Lacava, F.; Lanfranchi, G.; Lee-Franzini, J.; Leone, D.; Martemianov, M.; Martini, M.; Massarotti, P.; Matsyuk, M.; Mei, W.; Meola, S.; Messi, R.; Miscetti, S.; Moulson, M.; Müller, S.; Murtas, F.; Napolitano, M.; Nguyen, F.; Palutan, M.; Pasqualucci, E.; Passalacqua, L.; Passeri, A.; Patera, V.; Perfetto, F.; Pontecorvo, L.; Primavera, M.; Santangelo, P.; Santovetti, E.; Saracino, G.; Schamberger, R. D.; Sciascia, B.; Sciubba, A.; Scuri, F.; Sfiligoi, I.; Sibidanov, A.; Spadaro, T.; Spiriti, E.; Tabidze, M.; Testa, M.; Tortora, L.; Valente, P.; Valeriani, B.; Venanzoni, G.; Veneziano, S.; Ventura, A.; Ventura, S.; Versaci, R.; Villella, I.; Xu, G.; KLOE Collaboration
2007-05-01
Neutral kaons provide one of the systems most sensitive to quantum mechanics and CPT violation. Models predicting quantum mechanics violation, also related to CPT violation, have been tested at the CPLEAR and KLOE experiments. In this report results of CPLEAR obtained by studying the time evolution of single and two entangled kaons are reviewed. New or improved limits on decoherence and CPT violation parameters have been obtained by KLOE studying the quantum interference in the channel ??KK?????. No deviations from the expectations of quantum mechanics and CPT symmetry have been observed.
Experimental status of quaternionic quantum mechanics
S. P. Brumby; G. C. Joshi
1996-01-01
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We review the only direct search for quaternionic quantum mechanics yet carried out and outline a recent proposal by the present authors to look for quaternionic effects in
On the quantum mechanics of supermembranes
Bernard de Wit; J. Hoppe; H. Nicolai
1988-01-01
We study the quantum-mechanical properties of a supermembrane and examine the nature of its ground state. A supersymmetric gauge theory of area-preserving transformations provides a convenient framework for this study. The supermembrane can be viewed as a limiting case of a class of models in supersymmetric quantum mechanics. Its mass does not depend on the zero modes and vanishes only
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Friday, June 19, 2009 #12;String Theory Origins We introduced string theory as a possible solution to our
From Quantum Mechanics to String Theory
From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification that is naturally solved by string theory Strings vibrating in a variety of ways give rise to particles of different
Quaternionic Formulation of Supersymmetric Quantum Mechanics
Seema Rawat; O. P. S. Negi
2007-03-18
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions. Supercharges, superpartner Hamiltonians and energy eigenvalues are discussed and it has been shown that the results are consistent with the results of quantum mechanics.
Quantum mechanics in complex systems
NASA Astrophysics Data System (ADS)
Hoehn, Ross Douglas
This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown. These nodes are spaced far enough from each other to minimized the electronic repulsion of the electrons, while still providing adequate enough attraction so as to bind the excess elections into orbitals. We have found that even with relativistic considerations these species are stably bound within the field. It was also found that performing the dimensional scaling calculations for systems within the confines of laser fields to be a much simpler and more cost-effective method than the supporting D=3 SCF method. The dimensional scaling method is general and can be extended to include relativistic corrections to describe the stability of simple molecular systems in super-intense laser fields. Chapter 3, we delineate the model, and aspects therein, of inelastic electron tunneling and map this model to the protein environment. G protein-coupled receptors (GPCRs) constitute a large family of receptors that sense molecules outside of a cell and activate signal transduction pathways inside the cell. Modeling how an agonist activates such a receptor is important for understanding a wide variety of physiological processes and it is of tremendous value for pharmacology and drug design. Inelastic electron tunneling spectroscopy (IETS) has been proposed as the mechanism by which olfactory GPCRs are activated by an encapsulated agonist. In this note we apply this notion to GPCRs within the mammalian nervous system using ab initio quantum chemical modeling. We found that non-endogenous agonists of the serotonin receptor share a singular IET spectral aspect both amongst each other and with the serotonin molecule: a peak that scales in intensity with the known agonist activities. We propose an experiential validation of this model by utilizing lysergic acid dimethylamide (DAM-57), an ergot derivative, and its isotopologues in which hydrogen atoms are replaced by deuterium. If validated our theory may provide new avenues for guided drug design and better in silico prediction of efficacies. Our final chapter, explores methods which may be explored to assist in the early instructio
Imperfect cloning operations in algebraic quantum theory
Yuichiro Kitajima
2014-09-30
No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal $\\epsilon$-imperfect cloning operation which tolerates a finite loss $\\epsilon$ of fidelity in the cloned state, and show that an individual system's algebra of observables is Abelian if and only if there is a universal $\\epsilon$-imperfect cloning operation in the case where the loss of fidelity is less than 1/4. Therefore, in this case no universal $\\epsilon$-imperfect cloning operation is possible in algebraic quantum theory.
An entropic picture of emergent quantum mechanics
D. Acosta; P. Fernandez de Cordoba; J. M. Isidro; J. L. G. Santander
2011-09-20
Quantum mechanics emerges a la Verlinde from a foliation of space by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantised in units of Boltzmann's constant k. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on space. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant h from Boltzmann's constant k.
Erratum: Operational time of arrival in quantum phase space [Phys. Rev. A 60, 2689 (1999)
NASA Astrophysics Data System (ADS)
Kocha?ski, Piotr; Wódkiewicz, Krzysztof
2000-02-01
An operational time of arrival is introduced using a realistic position and momentum measurement scheme. The phase space measurement involves the dynamics of a quantum particle probed by a measuring device. For such a measurement an operational positive operator valued measure in phase space is introduced and investigated. In such an operational formalism a quantum mechanical time operator is constructed and analyzed. A phase space time and energy uncertainty relation is derived.
Quantum Mechanical Models Of The Fermi Shuttle
Sternberg, James [University of Tennessee, Department of Physics and Astronomy, Knoxville TN 37996 (United States)
2011-06-01
The Fermi shuttle is a mechanism in which high energy electrons are produced in an atomic collision by multiple collisions with a target and a projectile atom. It is normally explained purely classically in terms of the electron's orbits prescribed in the collision. Common calculations to predict the Fermi shuttle use semi-classical methods, but these methods still rely on classical orbits. In reality such collisions belong to the realm of quantum mechanics, however. In this paper we discuss several purely quantum mechanical calculations which can produce the Fermi shuttle. Being quantum mechanical in nature, these calculations produce these features by wave interference, rather than by classical orbits.
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.
Superconformal Quantum Mechanics from M2-branes
Tadashi Okazaki
2015-03-12
We discuss the superconformal quantum mechanics arising from the M2-branes. We begin with a comprehensive review on the superconformal quantum mechanics and emphasize that conformal symmetry and supersymmetry in quantum mechanics contain a number of exotic and enlightening properties which do not occur in higher dimensional field theories. We see that superfield and superspace formalism is available for $\\mathcal{N}\\le 8$ superconformal mechanical models. We then discuss the M2-branes with a focus on the world-volume descriptions of the multiple M2-branes which are superconformal three-dimensional Chern-Simons matter theories. Finally we argue that the two topics are connected in M-theoretical construction by considering the multiple M2-branes wrapped around a compact Riemann surface and study the emerging IR quantum mechanics. We establish that the resulting quantum mechanics realizes a set of novel $\\mathcal{N}\\ge 8$ superconformal quantum mechanical models which have not been reached so far. Also we discuss possible applications of the superconformal quantum mechanics to mathematical physics.
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.
Noncommutative quantum mechanics as a gauge theory
Bemfica, F. S.; Girotti, H. O. [Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 - Porto Alegre, RS (Brazil)
2009-06-15
The classical counterpart of noncommutative quantum mechanics is a constrained system containing only second-class constraints. The embedding procedure formulated by Batalin, Fradkin and Tyutin (BFT) enables one to transform this system into an Abelian gauge theory exhibiting only first class constraints. The appropriateness of the BFT embedding, as implemented in this work, is verified by showing that there exists a one to one mapping linking the second-class model with the gauge invariant sector of the gauge theory. As is known, the functional quantization of a gauge theory calls for the elimination of its gauge freedom. Then, we have at our disposal an infinite set of alternative descriptions for noncommutative quantum mechanics, one for each gauge. We study the relevant features of this infinite set of correspondences. The functional quantization of the gauge theory is explicitly performed for two gauges and the results compared with that corresponding to the second-class system. Within the operator framework the gauge theory is quantized by using Dirac's method.
The formal path integral and quantum mechanics
Johnson-Freyd, Theo [Department of Mathematics, University of California - Berkeley, 970 Evans Hall, Berkeley, California 94720 (United States)
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.
Covariant Dirac operators on quantum groups
NASA Astrophysics Data System (ADS)
Harju, Antti J.
2011-12-01
We give a construction of a Dirac operator on a quantum group based on any simple Lie algebra of classical type. The Dirac operator is an element in the vector space U_q({g}) ? cl_q({g}), where the second tensor factor is a q-deformation of the classical Clifford algebra. The tensor space U_q({g}) ? cl_q({g}) is given by a structure of the adjoint module of the quantum group and the Dirac operator is invariant under this action. The purpose of this approach is to construct equivariant Fredholm modules and K-homology cycles. This work generalizes the operator introduced by P. N. Bibikov and P. P. Kulish [J. Math. Sci. (N.Y.) 100, 2039-2050 (2000)].
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.
OPTI 570A-Quantum Mechanics Course Description
Arizona, University of
OPTI 570A- Quantum Mechanics Course Description: This is a one-semester course designed to provide students with a solid understanding of quantum mechanics formalism, techniques, and important example physics, quantum optics, relativistic quantum mechanics and other advanced quantum mechanics topics
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.
Statistical Structures Underlying Quantum Mechanics and Social Science
Ron Wright
2003-07-30
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.
Dorit Aharonov; Umesh Vazirani
2012-06-16
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity. We describe how QM can be tested in this regime by extending the usual scientific paradigm to include {\\it interactive experiments}.
Operator approach to quantum optomechanics
NASA Astrophysics Data System (ADS)
Ventura-Velázquez, C.; Rodríguez-Lara, B. M.; Moya-Cessa, H. M.
2015-06-01
We study the mirror-field interaction in several frameworks: when it is driven, when it is affected by an environment, and when a two-level atom is introduced in the cavity. By using operator techniques, we show either how these problems may be solved or how the Hamiltonians involved, via sets of unitary transformations, may be taken to known Hamiltonians for which there exist approximate solutions.
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.
Fidelity of Majorana-based quantum operations
NASA Astrophysics Data System (ADS)
Tanhayi Ahari, Mostafa; Ortiz, Gerardo; Seradjeh, Babak
2015-03-01
It is well known that one-dimensional p-wave superconductor, the so-called Kitaev model, has topologically distinct phases that are distinguished by the presence of Majorana fermions. Owing to their topological protection, these Majorana fermions have emerged as candidates for fault-tolerant quantum computation. They furnish the operation of such a computation via processes that produce, braid, and annihilate them in pairs. In this work we study some of these processes from the dynamical perspective. In particular, we determine the fidelity of the Majorana fermions when they are produced or annihilated by tuning the system through the corresponding topological phase transition. For a simple linear protocol, we derive analytical expressions for fidelity and test various perturbative schemes. For more general protocols, we present exact numerics. Our results are relevant for the operation of Majorana-based quantum gates and quantum memories.
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.
An Operational Mechanism Featuring Gravity Amplification
Simon Berkovich
The least understood property of the physical Universe is non-locality. Beyond the already revealed domain of quantum correlations, non-locality must also be operational in other phenomena. In this way, the presented work tries to interpret Newton's theory of universal gravity. The distinction of the suggested approach with respect to numerous attempts of this kind is that it is not an
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. .
Extending quantum mechanics entails extending special relativity
S. Aravinda; R. Srikanth
2015-06-09
The complementarity of signaling and local randomness in the resources required to simulate singlet statistics is generalized here by relaxing the assumption of free will in the choice of measurement settings. The complementarity implies that under the assumption of full free will, simulation resources with reduced randomness will be signaling. It would appear at first sight that an ontological extension based on such a simulation protocol would contradict no-signaling and free will. We prove that this is not so, by constructing such an extension through the "oblivious embedding" of the protocol in a Newtonian spacetime. Relativistic or other intermediate spacetimes are ruled out as the locus of the embedding because they would permit the violation of no-signaling at the operational level by virtue of hidden influence inequalities. This implies that predictively superior extensions of quantum mechanics (QM) must be Lorentz non-covariant. However, the operational theory reproduced by the extensions will be compatible with no-signaling and Lorentz covariance. This clarifies why in principle there is no obstacle to the compatibility of extensions of QM such as Bohmian mechanics and GRW-type collapse theories with special relativity. Certain arguments against the extendability of QM, due to Conway and Kochen (2009) and Colbeck and Renner (2012), are attributed to their assumption that the spacetime of the extensions has Minkowskian causal structure.
Chem 7940 Quantum Mechanics II Spring 2010 Chemistry 7940
Chem 7940 Quantum Mechanics II Spring 2010 Chemistry 7940 Quantum Mechanics II Spring 2010 Mechanics in Chemistry (Dover reprint). [8] D. J. Tannor, Introduction to Quantum Mechanics: a Time. (Confucius) We shall refer to a variety of sources. You should have a standard quantum mechanics text
Chem 7940 Quantum Mechanics II Spring 2013 Chemistry 7940
Chem 7940 Quantum Mechanics II Spring 2013 Chemistry 7940 Quantum Mechanics II Spring 2013 Mechanics in Chemistry (Dover reprint). [6] P. W. Atkins and R. S. Friedman, Molecular Quantum Mechanics. (Confucius) We shall refer to a variety of sources. You should have a standard quantum mechanics text
Taming the zoo of supersymmetric quantum mechanical models
Smilga, A V
2013-01-01
We show that in many cases nontrivial and complicated supersymmetric quantum mechanical (SQM) models can be obtained from the simple model describing free dynamics in flat complex space by two operations: (i) Hamiltonian reduction and (ii) similarity transformation of the complex supercharges. We conjecture that it is true for any SQM model.
Taming the zoo of supersymmetric quantum mechanical models
A. V. Smilga
2013-05-30
We show that in many cases nontrivial and complicated supersymmetric quantum mechanical (SQM) models can be obtained from the simple model describing free dynamics in flat complex space by two operations: (i) Hamiltonian reduction and (ii) similarity transformation of the complex supercharges. We conjecture that it is true for any SQM model.
Visual Quantum Mechanics: Online Interactive Programs
NSDL National Science Digital Library
The Visual Quantum Mechanics project, from the Physics Education Group of Kansas State University's Department of Physics, develops innovative ways to "introduce quantum physics to high school and college students who do not have a background in modern physics or higher level math." Funded by the National Science Foundation, this resource for educators provides interactive computer visualizations and animations that introduce quantum mechanics. The interactive programs (which require Shockwave) include a spectroscopy lab suite, a probability illustrator, an energy band creator, quantum tunneling, a color creator (a Java version is also available), a wave function sketcher, a wave packet explorer, an energy diagram explorer, a diffraction suite, and a hydrogen spectroscopy program. These online demonstrations should prove to be excellent visual, hands-on teaching aids when introducing concepts involving quantum mechanics. Users can download Shockwave at the site.
Quantum Mechanical Search and Harmonic Perturbation
Jiang, J H R; Wu, C E; Chiou, Dah-Wei; Jiang, Jie-Hong R.; Wu, Cheng-En
2007-01-01
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some important technology advances, such as masers, lasers, nuclear magnetic resonance, etc., originated from it. Here we add quantum computation to this list with a theoretical demonstration. Based on harmonic perturbation, a quantum mechanical algorithm is devised to search the ground state of a given Hamiltonian. The intrinsic complexity of the algorithm is continuous and parametric in both time T and energy E. More precisely, the probability of locating a search target of a Hamiltonian in N-dimensional vector space is shown to be 1/(1+ c N E^{-2} T^{-2}) for some constant c. This result is optimal. As harmonic perturbation provides a different computation mechanism, the algorithm may suggest new directions in realizing quantum computers.
Quantum Mechanical Search and Harmonic Perturbation
Jie-Hong R. Jiang; Dah-Wei Chiou; Cheng-En Wu
2007-09-14
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some important technology advances, such as masers, lasers, nuclear magnetic resonance, etc., originated from it. Here we add quantum computation to this list with a theoretical demonstration. Based on harmonic perturbation, a quantum mechanical algorithm is devised to search the ground state of a given Hamiltonian. The intrinsic complexity of the algorithm is continuous and parametric in both time T and energy E. More precisely, the probability of locating a search target of a Hamiltonian in N-dimensional vector space is shown to be 1/(1+ c N E^{-2} T^{-2}) for some constant c. This result is optimal. As harmonic perturbation provides a different computation mechanism, the algorithm may suggest new directions in realizing quantum computers.
Quantum operations: technical or fundamental challenge?
NASA Astrophysics Data System (ADS)
Mielnik, Bogdan
2013-09-01
A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined. The possibility of using the ion traps as ‘operation factories’ transforming quantum states is discussed. The non-perturbative algorithms indicate that the results of abstract ?-pulses of oscillator potentials can become real. Some of them, if empirically achieved, could be essential to examine certain atypical quantum ideas. In particular, simple dynamical manipulations might contribute to the Aharonov-Bohm criticism of the time-energy uncertainty principle, while some others may verify the existence of fundamental precision limits of the position measurements or the reality of ‘non-commutative geometries’.
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.
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
The Compton effect: Transition to quantum mechanics
R. H. Stuewer
2000-01-01
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
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.
Conditional Phase Shift for Quantum CCNOT Operation
Alexander Ig. Trifanov; George P. Miroshnichenko
2011-02-11
We suggest the improvement of description methods for quantum phase gate implementation in the cavity of QED configuration. Qubits are encoded into two lowest Fock state. Three qubit phase transformation is resulted from the interaction between Rydberg atom and three modes of cavity electromagnetic field. Evolution of conditional field states appearing after atom measurement is described by Kraus transformers. One of these operators is very convenient for phase gate implementation. We show that it corresponds to conditional evolution without quantum jumps. Also we describe cavity based generating EPR pair from certain initially disentangled state.
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.
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)
A quantum mechanical investigation of silsesquioxane cages
Earley, C.W. [Univ. of Missouri, Kansas City, MO (United States)
1994-09-01
A quantum mechanical investigation of molecular silsesquioxane cages determined that molecules containing (Si-O-){sub 3} rings were more unstable than those with larger rings. 49 refs., 2 figs., 4 tabs.
Beyond Quantum Mechanics and General Relativity
Andrea Gregori
2010-02-24
In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.
Quantum 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.
Remarks on Quantum Mechanics Norbert Dragon
Dragon, Norbert
Remarks on Quantum Mechanics Norbert Dragon #12;Intended as completion, repetition and comment once: //www.itp.uni-hannover.de/~dragon. I am grateful for feedback concerning errors, including type slips
Supersymmetric q-deformed quantum mechanics
Traikia, M. H.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)
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.
Experimental status of quaternionic quantum mechanics
Brumby, S P
1996-01-01
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We review the only direct search for quaternionic quantum mechanics yet carried out and outline a recent proposal by the present authors to look for quaternionic effects in correlated multi-particle systems. We set out how such experiments might distinguish between the several quaternionic models proposed in the literature.
Experimental status of quaternionic quantum mechanics
S. P. Brumby; G. C. Joshi
1996-10-08
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We review the only direct search for quaternionic quantum mechanics yet carried out and outline a recent proposal by the present authors to look for quaternionic effects in correlated multi-particle systems. We set out how such experiments might distinguish between the several quaternionic models proposed in the literature.
Epistemic cognition: issues in learning quantum mechanics
NASA Astrophysics Data System (ADS)
Oliver, Keith; Bao, Lei
2001-10-01
Epistemology is the branch of philosophy concerned with the nature and justification of knowledge. Epistemic cognition is thinking about the general methodologies and epistemological/philosophical views about learning. Quantum mechanics is the branch of physics that involves a fundamental uncertainty and that is being continuously developed and argued both theoretically and practically. We will illustrate the potential opportunity quantum mechanics presents us in discussing epistemic issues with our students and in exploring the nature of student epistemology.
Some mutant forms of quantum mechanics
NASA Astrophysics Data System (ADS)
Takeuchi, Tatsu; Chang, Lay Nam; Lewis, Zachary; Minic, Djordje
2012-12-01
We construct a 'mutant' form of quantum mechanics on a vector space over the finite Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discretized quantum mechanics cannot be reproduced with any hidden variable theory. An alternative 'mutation' is also suggested.
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.
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.
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
Theoretical Chemistry I Quantum Mechanics 16 October 2008
Pfeifer, Holger
Theoretical Chemistry I Quantum Mechanics Axel Groß 16 October 2008 #12;#12;Preface Theoretical Chemistry 1 Quantum Mechanics Prof. Dr. Axel Groß Phone: 5022819 Room No.: O25/342 Email: axel of Quantum Mechanics 3. Quantum Dynamics 4. Angular Momentum 5. Approximation Methods 6. Symmetry in Quantum
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.
Mechanical systems in the quantum regime
Menno Poot; Herre S. J. van der Zant
2011-10-12
Mechanical systems are ideal candidates for studying quantumbehavior of macroscopic objects. To this end, a mechanical resonator has to be cooled to its ground state and its position has to be measured with great accuracy. Currently, various routes to reach these goals are being explored. In this review, we discuss different techniques for sensitive position detection and we give an overview of the cooling techniques that are being employed. The latter include sideband cooling and active feedback cooling. The basic concepts that are important when measuring on mechanical systems with high accuracy and/or at very low temperatures, such as thermal and quantum noise, linear response theory, and backaction, are explained. From this, the quantum limit on linear position detection is obtained and the sensitivities that have been achieved in recent opto and nanoelectromechanical experiments are compared to this limit. The mechanical resonators that are used in the experiments range from meter-sized gravitational wave detectors to nanomechanical systems that can only be read out using mesoscopic devices such as single-electron transistors or superconducting quantum interference devices. A special class of nanomechanical systems are bottom-up fabricated carbon-based devices, which have very high frequencies and yet a large zero-point motion, making them ideal for reaching the quantum regime. The mechanics of some of the different mechanical systems at the nanoscale is studied. We conclude this review with an outlook of how state-of-the-art mechanical resonators can be improved to study quantum {\\it mechanics}.
A Modified Lax-Phillips Scattering Theory for Quantum Mechanics
Yossi Strauss
2014-07-24
The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems) then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.
Information Security and Quantum Mechanics: Security of Quantum Protocols
P. Oscar Boykin
2002-10-28
The problem of security of quantum key protocols is examined. In addition to the distribution of classical keys, the problem of encrypting quantum data and the structure of the operators which perform quantum encryption is studied. It is found that unitary bases are central to both encryption of quantum information, as well as the generation of states used in generalized quantum key distribution (which are called mutually unbiased bases). A one-to-one correspondence between certain unitary bases and mutually unbiased bases is found. Finally, a new protocol for making anonymous classical broadcasts is given along with a security proof. An experimental procedure to implement this protocol is also given. In order to prove these new results, some new bounds for accessible information of quantum sources are obtained.
Information Security and Quantum Mechanics: Security of Quantum Protocols
NASA Astrophysics Data System (ADS)
Boykin, P. Oscar
2002-10-01
The problem of security of quantum key protocols is examined. In addition to the distribution of classical keys, the problem of encrypting quantum data and the structure of the operators which perform quantum encryption is studied. It is found that unitary bases are central to both encryption of quantum information, as well as the generation of states used in generalized quantum key distribution (which are called mutually unbiased bases). A one-to-one correspondence between certain unitary bases and mutually unbiased bases is found. Finally, a new protocol for making anonymous classical broadcasts is given along with a security proof. An experimental procedure to implement this protocol is also given. In order to prove these new results, some new bounds for accessible information of quantum sources are obtained.
Information security and quantum mechanics: Security of quantum protocols
NASA Astrophysics Data System (ADS)
Boykin, Patrick Oscar
The problem of security of quantum key protocols is examined. In addition to the distribution of classical keys, the problem of encrypting quantum data and the structure of the operators which perform quantum encryption is studied. It is found that unitary bases are central to both encryption of quantum information, as well as the generation of states used in generalized quantum key distribution (which are called mutually unbiased bases). A one-to-one correspondence between certain unitary bases and mutually unbiased bases is found. Finally, a new protocol for making anonymous classical broadcasts is given along with a security proof. An experimental procedure to implement this protocol is also given. In order to prove these new results, some new bounds for accessible information of quantum sources are obtained.
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.
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).
Testing foundations of quantum mechanics with photons
NASA Astrophysics Data System (ADS)
Shadbolt, Peter; Mathews, Jonathan C. F.; Laing, Anthony; O'Brien, Jeremy L.
2014-04-01
Quantum mechanics continues to predict effects at odds with a classical understanding of nature. Experiments with light at the single-photon level have historically been at the forefront of fundamental tests of quantum theory and the current developments in photonic technologies enable the exploration of new directions. Here we review recent photonic experiments to test two important themes in quantum mechanics: wave-particle duality, which is central to complementarity and delayed-choice experiments; and Bell nonlocality, where the latest theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different experiments.
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.
Quantum mechanics: Passage through chaos
Daniel A. Steck
2009-01-01
A quantum system can undergo tunnelling even without a barrier to tunnel through. The latest experiments visualize this process in exquisite detail, completely reconstructing the state of the evolving system.
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 2011 Chemistry 7940
Chem 7940 Quantum Mechanics II Spring 2011 Chemistry 7940 Quantum Mechanics II Spring 2011 in Chemistry (Dover reprint). [8] D. J. Tannor, Introduction to Quantum Mechanics: a Time-Dependent Perspective. (Confucius) We shall refer to a variety of sources. You should have a standard quantum mechanics text
Chem 7940 Quantum Mechanics II Spring 2012 Chemistry 7940
Chem 7940 Quantum Mechanics II Spring 2012 Chemistry 7940 Quantum Mechanics II Spring 2012 Theory (Dover reprint). [6] G.C. Schatz and M.A. Ratner, Quantum Mechanics in Chemistry (Dover reprint. (Confucius) We shall refer to a variety of sources. You should have a standard quantum mechanics text
Quantum Theory of Gravity I: Area Operators
Abhay Ashtekar; Jerzy Lewandowski
1996-01-01
A new functional calculus, developed recently for a fully non-perturbative\\u000atreatment of quantum gravity, is used to begin a systematic construction of a\\u000aquantum theory of geometry. Regulated operators corresponding to areas of\\u000a2-surfaces are introduced and shown to be self-adjoint on the underlying\\u000a(kinematical) Hilbert space of states. It is shown that their spectra are {\\\\it\\u000apurely} discrete indicating
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.
Probability in modal interpretations of quantum mechanics
Dennis Dieks
2007-03-02
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but yields probabilities. In working out these ideas an important motif is to stay close to the standard formalism of quantum mechanics and to refrain from introducing new structure by hand. In this paper we explain how this programme can be made concrete. In particular, we show that the Born probability rule, and sets of definite-valued observables to which the Born probabilities pertain, can be uniquely defined from the quantum state and Hilbert space structure. We discuss the status of probability in modal interpretations, and to this end we make a comparison with many-worlds alternatives. An overall point that we stress is that the modal ideas define a general framework and research programme rather than one definite and finished interpretation.
Statistical mechanics based on fractional classical and quantum mechanics
Korichi, Z.; Meftah, M. T., E-mail: mewalid@yahoo.com [Physics Department, LRPPS Laboratory, Ouargla University, Ouargla 30000 (Algeria)
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 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.
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
Does quantum mechanics play a non-trivial role in life?
P. C. W. Davies
2004-01-01
There have been many claims that quantum mechanics plays a key role in the origin and\\/or operation of biological organisms, beyond merely providing the basis for the shapes and sizes of biological molecules and their chemical affinities. These range from Schrödinger's suggestion that quantum fluctuations produce mutations, to Hameroff and Penrose's conjecture that quantum coherence in microtubules is linked to
Foster, Mark P.
11 1 Introduction to quantum mechanics Quantum mechanics is the basic tool needed to describe, understand and devise NMR experiments. Fortunately for NMR spectroscopists, the quantum mechanics of nuclear mathematical concepts frequently encountered in quantum mechanics and NMR. 0DWKHPDWLFDO FRQFHSWV 1.1.1 Complex
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.
Intrusion Detection with Quantum Mechanics: A Photonic Quantum Fence
Humble, Travis S [ORNL; Bennink, Ryan S [ORNL; Grice, Warren P [ORNL; Owens, Israel J [Los Alamos National Laboratory (LANL)
2008-01-01
We describe the use of quantum-mechanically entangled photons for sensing intrusions across a physical perimeter. Our approach to intrusion detection uses the no-cloning principle of quantum information science as protection against an intruder s ability to spoof a sensor receiver using a classical intercept-resend attack. We explore the bounds on detection using quantum detection and estimation theory, and we experimentally demonstrate the underlying principle of entanglement-based detection using the visibility derived from polarization-correlation measurements.
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…
Levitated Quantum Nano-Magneto-Mechanical Systems
NASA Astrophysics Data System (ADS)
Cirio, Mauro; Twamley, Jason; Brennen, Gavin K.; Milburn, Gerard J.
2011-03-01
Quantum nanomechanical sysems have attracted much attention as they provide new macroscopic platforms for the study of quantum mechanics but may also have applications in ultra-sensitive sensing, high precision measurements and in quantum computing. In this work we study the control and cooling of a quantum nanomechanical system which is magnetically levitated via the Meissner effect. Supercurrents in nano-sized superconducting loops give rise to a motional restoring force (trap), when placed in an highly inhomogenous magnetic field and can yield complete trapping of all translational and rotational motions of the levitated nano-object with motional oscillation frequencies ? ~ 10 - 100 MHz. As the supercurrents experience little damping this system will possess unprecendented motional quality factors, with Qmotion ~109 -1013 , and motional superposition states may remain coherent for days. We describe how to execute sideband cooling through inductive coupling to a nearby flux qubit, cooling the mechanical motion close to the ground state.
Nonrelativistic Quantum Mechanics with Fundamental Environment
NASA Astrophysics Data System (ADS)
Gevorkyan, Ashot S.
2011-03-01
Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations ( fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantum system (QS) + FE" is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ? R { ?}, where R 3 and R { ?} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.
Creation mechanism of quantum accelerator modes
NASA Astrophysics Data System (ADS)
Ahmadi, P.; Behinaein, G.; Ramareddy, V.; Summy, G. S.
2009-11-01
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 accelerator modes can be created by exposing a Bose-Einstein condensate to a pulsed standing light wave. We show that constructive interference between momentum states populated by the pulsed light determines the stability island’s existence in the underlying pseudoclassical phase space. We generalize this interference model to incorporate higher-order accelerator modes, showing that they are generated if the rephasing occurs after multiple pulses. The model is extended to predict the momentum structure of the quantum accelerator modes close to higher-order quantum resonances. These predictions are in good agreement with our experimental observations.
Operational efficiency of decentralized Internet auction mechanisms
Roumen Vragov
2010-01-01
The recent consumer-to-consumer (C2C) Internet auction boom at eBay, Yahoo, Amazon, and other sites has added new theoretical challenges to the science of auctions. This paper uses experiments with economically-motivated human subjects to measure the operational efficiency of decentralized Internet auction mechanisms as they compare to centralized double auction mechanisms. Subjects are recruited randomly from the undergraduate population of a
Barry Simon's contributions to non-relativistic quantum mechanics: two-body and N-body
Froese, Richard
Barry Simon's contributions to non-relativistic quantum mechanics: two-body and N-body Schr Simon on the occasion of his 60th birthday. 1 Introduction Non-relativistic quantum mechanics and SchrÂ¨odinger operators occupy a central place in Barry Simon's prodigious output. This article is a review of Simon
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
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
Improving students' understanding of quantum mechanics
NASA Astrophysics Data System (ADS)
Singh, Chandralekha
2011-03-01
Learning quantum mechanics is especially challenging, in part due to the abstract nature of the subject. We have been conducting investigations of the difficulties that students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) as well as tools for peer-instruction. The goal of QuILTs and peer-instruction tools is to actively engage students in the learning process and to help them build links between the formalism and the conceptual aspects of quantum physics without compromising the technical content. They focus on helping students integrate qualitative and quantitative understanding, confront and resolve their misconceptions and difficulties, and discriminate between concepts that are often confused. In this talk, I will give examples from my research in physics education of how students' prior knowledge relevant for quantum mechanics can be assessed, and how learning tools can be designed to help students develop a robust knowledge structure and critical thinking skills. Supported by the National Science Foundation.
Multichannel framework for singular quantum mechanics
Camblong, Horacio E., E-mail: camblong@usfca.edu [Department of Physics and Astronomy, University of San Francisco, San Francisco, CA 94117-1080 (United States); Epele, Luis N., E-mail: epele@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Fanchiotti, Huner, E-mail: huner@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina)] [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); García Canal, Carlos A., E-mail: garcia@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Ordóñez, Carlos R., E-mail: ordonez@uh.edu [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States)
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.
The statistical origins of quantum mechanics
U. Klein
2011-03-08
It is shown that Schroedinger's equation may be derived from three postulates. The first is a kind of statistical metamorphosis of classical mechanics, a set of two relations which are obtained from the canonical equations of particle mechanics by replacing all observables by statistical averages. The second is a local conservation law of probability with a probability current which takes the form of a gradient. The third is a principle of maximal disorder as realized by the requirement of minimal Fisher information. The rule for calculating expectation values is obtained from a fourth postulate, the requirement of energy conservation in the mean. The fact that all these basic relations of quantum theory may be derived from premises which are statistical in character is interpreted as a strong argument in favor of the statistical interpretation of quantum mechanics. The structures of quantum theory and classical statistical theories are compared and some fundamental differences are identified.
Novel symmetries in N=2 supersymmetric quantum mechanical models
Malik, R.P., E-mail: malik@bhu.ac.in [Physics Department, BHU-Varanasi-221 005 (India); DST-CIMS, Faculty of Science, BHU-Varanasi-221 005 (India); Khare, Avinash, E-mail: khare@iiserpune.ac.in [Indian Institute of Science for Education and Research, Pune-411 021 (India)] [Indian Institute of Science for Education and Research, Pune-411 021 (India)
2013-07-15
We demonstrate the existence of a novel set of discrete symmetries in the context of the N=2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the X–Y plane under the influence of a magnetic field in the Z-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We show that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary N=2 SUSY quantum mechanical system can be shown to be a tractable model for the Hodge theory. -- Highlights: •Discrete symmetries of two completely different kinds of N=2 supersymmetric quantum mechanical models have been discussed. •The discrete symmetries provide physical realizations of Hodge duality. •The continuous symmetries provide the physical realizations of de Rham cohomological operators. •Our work sheds a new light on the meaning of the above abstract operators.
Probability in the Many-Worlds Interpretation of Quantum Mechanics
Vaidman, Lev
of standard quantum mechanics. The Quantum Sleeping Beauty controversy and "caring measure" replacing of probability. The explanation involves: (a) A "sleeping pill" gedanken experiment which makes correspondence
The Quantum Mechanics of Hyperion
Nathan Wiebe; L. E. Ballentine
2005-03-21
This paper is motivated by the suggestion [W. Zurek, Physica Scripta, T76, 186 (1998)] that the chaotic tumbling of the satellite Hyperion would become non-classical within 20 years, but for the effects of environmental decoherence. The dynamics of quantum and classical probability distributions are compared for a satellite rotating perpendicular to its orbital plane, driven by the gravitational gradient. The model is studied with and without environmental decoherence. Without decoherence, the maximum quantum-classical (QC) differences in its average angular momentum scale as hbar^{2/3} for chaotic states, and as hbar^2 for non-chaotic states, leading to negligible QC differences for a macroscopic object like Hyperion. The quantum probability distributions do not approach their classical limit smoothly, having an extremely fine oscillatory structure superimposed on the smooth classical background. For a macroscopic object, this oscillatory structure is too fine to be resolved by any realistic measurement. Either a small amount of smoothing (due to the finite resolution of the apparatus) or a very small amount of environmental decoherence is sufficient ensure the classical limit. Under decoherence, the QC differences in the probability distributions scale as (hbar^2/D)^{1/6}, where D is the momentum diffusion parameter. We conclude that decoherence is not essential to explain the classical behavior of macroscopic bodies.
A broken symmetry ontology: Quantum mechanics as a broken symmetry
Buschmann, J.E.
1988-01-01
The author proposes a new broken symmetry ontology to be used to analyze the quantum domain. This ontology is motivated and grounded in a critical epistemological analysis, and an analysis of the basic role of symmetry in physics. Concurrently, he is led to consider nonheterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows him to find a generalized principle of symmetry and a generalized symmetry-conservation formalisms. In particular, he clarifies the role of Noether's theorem in field theory. He shows how a broken symmetry ontology already operates in a description of the weak interactions. Finally, by showing how a broken symmetry ontology operates in the quantum domain, he accounts for the interpretational problem and the essential incompleteness of quantum mechanics. He proposes that the broken symmetry underlying this ontological domain is broken dilation invariance.
Fractional quantum mechanics and Lévy path integrals
NASA Astrophysics Data System (ADS)
Laskin, Nikolai
2000-04-01
A new extension of a fractality concept in quantum physics has been developed. The path integrals over the Lévy paths are defined and fractional quantum and statistical mechanics have been developed via new fractional path integrals approach. A fractional generalization of the Schrödinger equation has been found. The new relation between the energy and the momentum of non-relativistic fractional quantum-mechanical particle has been established. We have derived a free particle quantum-mechanical kernel using Fox's H-function. The equation for the fractional plane wave function has been obtained. As a physical application of the developed fQM we have proposed a new fractional approach to the QCD problem of quarkonium. A fractional generalization of the motion equation for the density matrix has been found. The density matrix of a free particle has been expressed in term of the Fox's H-function. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum and statistical mechanics.
Foundations of quantum physics: a general realistic and operational approach
Aerts, Diederik
Foundations of quantum physics: a general realistic and operational approach Diederik Aerts FUND of quantum physics: a general realistic and operational approach", International Journal of Theoretical examples in detail in the light of this formalism: a classical deterministic entity and a quantum entity
Elementary operator criterion of entanglement of quantum states
Li, Chi-Kwong
Elementary operator criterion of entanglement of quantum states Jinchuan Hou Institute information. In fact they can be used to recognize entangled states, and every quantum channel is represented with a separable complex Hilbert space H, i.e., the state space. A quantum state is described as a density operator
Quantum harmonic oscillator with position-dependent mass in the displacement operator formalism
NASA Astrophysics Data System (ADS)
Tchoffo, M.; Vubangsi, M.; Fai, L. C.
2014-10-01
The position-dependent effective mass quantum harmonic oscillator problem is considered within the displacement operator framework. Using the analytic and the algebraic approaches, exact expressions for quantum mechanical quantities of the system have been obtained. In the limit of no deformation, results of the constant mass oscillator are recovered.
Interagency mechanical operations group numerical systems group
NONE
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.
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.
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.
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 Process Algebra Approach to Quantum Mechanics
William H. Sulis
2014-09-07
The process approach to NRQM offers a fourth framework for the quantization of physical systems. Unlike the standard approaches (Schrodinger-Heisenberg, Feynman, Wigner-Gronewald-Moyal), the process approach is not merely equivalent to NRQM and is not merely a re-interpretation. The process approach provides a dynamical completion of NRQM. Standard NRQM arises as a asymptotic quotient by means of a set-valued process covering map, which links the process algebra to the usual space of wave functions and operators on Hilbert space. The process approach offers an emergentist, discrete, finite, quasi-non-local and quasi-non-contextual realist interpretation which appears to resolve many of the paradoxes and is free of divergences. Nevertheless, it retains the computational power of NRQM and possesses an emergent probability structure which agrees with NRQM in the asymptotic quotient. The paper describes the process algebra, the process covering map for single systems and the configuration process covering map for multiple systems. It demonstrates the link to NRQM through a toy model. Applications of the process algebra to various quantum mechanical situations - superpositions, two-slit experiments, entanglement, Schrodinger's cat - are presented along with an approach to the paradoxes and the issue of classicality.
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.
The ZX-calculus is complete for stabilizer quantum mechanics
NASA Astrophysics Data System (ADS)
Backens, Miriam
2014-09-01
The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics (QM), meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer QM, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations.
Generalized coherent states under deformed quantum mechanics with maximum momentum
NASA Astrophysics Data System (ADS)
Ching, Chee Leong; Ng, Wei Khim
2013-10-01
Following the Gazeau-Klauder approach, we construct generalized coherent states (GCS) as the quantum simulator to examine the deformed quantum mechanics, which exhibits an intrinsic maximum momentum. We study deformed harmonic oscillators and compute their probability distribution and entropy of states exactly. Also, a particle in an infinite potential box is studied perturbatively. In particular, unlike usual quantum mechanics, the present deformed case increases the entropy of the Planck scale quantum optical system. Furthermore, for simplicity, we obtain the modified uncertainty principle (MUP) with the perturbative treatment up to leading order. MUP turns out to increase generally. However, for certain values of ? (a parameter of GCS), it is possible that the MUP will vanish and hence will exhibit the classical characteristic. This is interpreted as the manifestation of the intrinsic high-momentum cutoff at lower momentum in a perturbative treatment. Although the GCS saturates the minimal uncertainty in a simultaneous measurement of physical position and momentum operators, thus constituting the squeezed states, complete coherency is impossible in quantum gravitational physics. The Mandel Q number is calculated, and it is shown that the statistics can be Poissonian and super-/sub-Poissonian depending on ?. The equation of motion is studied, and both Ehrenfest’s theorem and the correspondence principle are recovered. Fractional revival times are obtained through the autocorrelation, and they indicate that the superposition of a classical-like subwave packet is natural in GCS. We also contrast our results with the string-motivated (Snyder) type of deformed quantum mechanics, which incorporates a minimum position uncertainty rather than a maximum momentum. With the advances of quantum optics technology, it might be possible to realize some of these distinguishing quantum-gravitational features within the domain of future experiments.
Douglas Farenick; Michael J. Kozdron
2012-03-14
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex Hilbert space, and a quantum random variable is a measurable operator valued function. Although quantum probability measures and random variables are used extensively in quantum mechanics, some of the fundamental probabilistic features of these structures remain to be determined. In this paper we take a step toward a better mathematical understanding of quantum random variables and quantum probability measures by introducing a quantum analogue for the expected value of a quantum random variable relative to a quantum probability measure. In so doing we are led to theorems for a change of quantum measure and a change of quantum variables. We also introduce a quantum conditional expectation which results in quantum versions of some standard identities for Radon-Nikodym derivatives. This allows us to formulate and prove a quantum analogue of Bayes' rule.
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
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.
Naturalness of the space of states in quantum mechanics
NASA Astrophysics Data System (ADS)
Aguilar, M. A.; Socolovsky, M.
1997-04-01
We show how certain constructions of quantum mechanics, like monopoles, instantons, and the Schrödinger-von Neumann equation, are related to geometric functors which are representable. We study the differential geometry of the projective bundle associated with an infinite-dimensional separable Hilbert space, and we construct a universal connection which, is described as a subspace of skwe-Hermitian operators. This connection is responsible for the Berry phase.
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 ...
Perturbative expansions in quantum mechanics
Mauricio D. Garay
2007-05-21
We prove a D=1 analytic versal deformation theorem for WKB expansions. We define the spectrum of an operator in local analytic terms. We use the Morse lemma to show that the perturbation series arising in a perturbed harmonic oscillator become analytic after a formal Borel transform.
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.
Stainless steel optimization from quantum mechanical calculations
Levente Vitos; Pavel A. Korzhavyi; Börje Johansson
2003-01-01
Alloy steel design has always faced a central problem: designing for a specific property very rarely produces a simultaneous significant improvement in other properties. For instance, it is difficult to design a material that combines high values of two of the most important mechanical characteristics of metals, hardness and ductility. Here we use the most recent quantum theories of random
Euclidean formulation of relativistic quantum mechanics
W. N. Polyzou; Philip Kopp
2009-08-10
We discuss preliminary work on a formulation of relativistic quantum mechanics that uses reflection-positive Euclidean Green functions or their generating functionals as phenomenological input. We discuss the construction of a Poincare invariant S-matrix from matrix element of exp(- \\beta H).
Quantum mechanics with applications to quarkonium
C. Quigg; Jonathan L. Rosner
1979-01-01
Some methods of nonrelativistic quantum mechanics which are particularly useful for studying the variation of bound-state parameters with constituent mass and excitation energy are reviewed. These techniques rely upon elementary scaling arguments and on the semiclassical (WKB) approximation. They are of general interest, but are applied here to the study of bound systems of a heavy quark and antiquark. Properties
Physical Interpretations of Nilpotent Quantum Mechanics
Peter Rowlands
2010-01-01
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,
WEAK MEASUREMENT IN QUANTUM MECHANICS ABRAHAM NEBEN
Rosner, Jonathan L.
WEAK MEASUREMENT IN QUANTUM MECHANICS ABRAHAM NEBEN PHYS 342 Final Project March 10, 2011 Contents of Postselection 4 4. Impossible Spin Measurements 5 5. Hardy's Paradox 5 6. Controversy over Weak Measurement 8 7 of a Measurement of a Component of the Spin of a Spin-1/2 Particle Can Turn Out to be 100." [1] The topic
Dissipation in Quantum Mechanics. The Harmonic Oscillator
I. R. Senitzky
1960-01-01
The need for a quantum-mechanical formalism for systems with dissipation which is applicable to the radiation field of a cavity is discussed. Two methods that have been used in this connection are described. The first, which starts with the classical Newtonian equation of motion for a damped oscillator and applies the conventional formal quantization techniques, leads to an exact solution;
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...
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.
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.
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
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)
Toward an Information-based Interpretation of Quantum Mechanics and the Quantum-Classical Transition
Juan G. Roederer
2012-07-28
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.
Quantum Signature Scheme Using a Single Qubit Rotation Operator
NASA Astrophysics Data System (ADS)
Kang, Min-Sung; Hong, Chang-Ho; Heo, Jino; Lim, Jong-In; Yang, Hyung-Jin
2015-02-01
We present a quantum signature scheme using a single qubit rotation operator. In this protocol, the trusted center confirms the quantum signature and thus conforms with other quantum signature schemes. Utilizing the unitary properties of a single qubit rotation operator and Pauli operators, our protocol provides signature security and enhances the efficiency of communication. In addition, our protocol - using only a single qubit measurement - facilitates the ease of implementation and enhances convenience for users. The security of the protocol is analyzed.
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
Consistent interpretations of quantum mechanics
Omnes, R. (Laboratoire de Physique Theorique et Hautes Energies, Universite de Paris XI, Batiment 211, 91405 Orsay CEDEX (France))
1992-04-01
Within the last decade, significant progress has been made towards a consistent and complete reformulation of the Copenhagen interpretation (an interpretation consisting in a formulation of the experimental aspects of physics in terms of the basic formalism; it is consistent if free from internal contradiction and complete if it provides precise predictions for all experiments). The main steps involved decoherence (the transition from linear superpositions of macroscopic states to a mixing), Griffiths histories describing the evolution of quantum properties, a convenient logical structure for dealing with histories, and also some progress in semiclassical physics, which was made possible by new methods. The main outcome is a theory of phenomena, viz., the classically meaningful properties of a macroscopic system. It shows in particular how and when determinism is valid. This theory can be used to give a deductive form to measurement theory, which now covers some cases that were initially devised as counterexamples against the Copenhagen interpretation. These theories are described, together with their applications to some key experiments and some of their consequences concerning epistemology.
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.
BERNSTEIN PROCESSES, EUCLIDEAN QUANTUM MECHANICS AND INTEREST RATE MODELS
Lescot, Paul
works with J.-C. Zambrini, of the link between euclidean quantum mechanics, Bernstein processes = as a new parameter. In Zambrini's Euclidean Quantum Mechanics (see e.g. [1]), this equation splits into : 2
ABOUT A HUNDRED YEARS HAVE PASSED since quantum mechanics was first developed. Quantum
Bier, Martin
of Physical Law, noted: "I think I can safely say that nobody under- stands quantum mechanics."1 record in physics before he devoted himself at a later age Quantum Consciousness and Other Spooky MythsABOUT A HUNDRED YEARS HAVE PASSED since quantum mechanics was first developed. Quantum mechanics
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
Modality, Potentiality and Contradiction in Quantum Mechanics
Christian de Ronde
2015-02-17
In [11], Newton da Costa together with the author of this paper argued in favor of the possibility to consider quantum superpositions in terms of a paraconsistent approach. We claimed that, even though most interpretations of quantum mechanics (QM) attempt to escape contradictions, there are many hints that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause [1, 2, 3] have raised several arguments against this approach and claimed that, taking into account the square of opposition, quantum superpositions are better understood in terms of contrariety propositions rather than contradictory propositions. In [17] we defended the Paraconsistent Approach to Quantum Superpositions (PAQS) and provided arguments in favor of its development. In the present paper we attempt to analyze the meanings of modality, potentiality and contradiction in QM, and provide further arguments of why the PAQS is better suited, than the Contrariety Approach to Quantum Superpositions (CAQS) proposed by Arenhart and Krause, to face the interpretational questions that quantum technology is forcing us to consider.
A Signal Processing Model of Quantum Mechanics
Chris Thron; Johnny Watts
2012-05-08
This paper develops a deterministic model of quantum mechanics as an accumulation-and-threshold process. The model arises from an analogy with signal processing in wireless communications. Complex wavefunctions are interpreted as expressing the amplitude and phase information of a modulated carrier wave. Particle transmission events are modeled as the outcome of a process of signal accumulation that occurs in an extra (non-spacetime) dimension. Besides giving a natural interpretation of the wavefunction and the Born rule, the model accommodates the collapse of the wave packet and other quantum paradoxes such as EPR and the Ahanorov-Bohm effect. The model also gives a new perspective on the 'relational' nature of quantum mechanics: that is, whether the wave function of a physical system is "real" or simply reflects the observer's partial knowledge of the system. We simulate the model for a 2-slit experiment, and indicate possible deviations of the model's predictions from conventional quantum mechanics. We also indicate how the theory may be extended to a field theory.
Web-based Quantum Mechanics II Course
NSDL National Science Digital Library
Breinig, Marianne
This web site, authored by Marianne Breinig, is an entire web-based Quantum Mechanics II Course based at the University of Tennessee. It has instructional materials, in-class tutorials, simulations, links to other quantum resources, a discussion forum, homework assignments, and solutions. A schedule and syllabus are also included for easier implementation into a curriculum. Most of the tools on the website require a browser of Internet Explorer 4 or higher to function. This is a nice set of resources for students or instructors interested in physics.
Quantum mechanical coherence, resonance, and mind
Stapp, H.P.
1995-03-26
Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in natural process, the classical character of our perceptions of the quantum universe can be seen to be a consequence of evolutionary pressures for the survival of the species.
Quantum Mechanical Scattering in Nanoscale Systems
NASA Astrophysics Data System (ADS)
Gianfrancesco, A. G.; Ilyashenko, A.; Boucher, C. R.; Ram-Mohan, L. R.
2012-02-01
We investigate quantum scattering using the finite element method. Unlike textbook treatments employing asymptotic boundary conditions (BCs), we use modified BCs, which permits computation close to the near-field region and reduces the Cauchy BCs to Dirichlet BCs, greatly simplifying the analysis. Scattering from any finite quantum mechanical potential can be modeled, including scattering in a finite waveguide geometry and in the open domain. Being numerical, our analysis goes beyond the Born Approximation, and the finite element approach allows us to transcend geometric constraints. Results of the formulation will be presented with several case studies, including spin dependent scattering, demonstrating the high accuracy and flexibility attained in this approach.
Quantum-mechanical phase locking in weak-link arrays
Widom, A. (Physics Department, Northeastern University, Boston, Massachusetts 02115 (United States)); Vittoria, C. (Department of Electrical Engineering, Northeastern University, Boston, Massachusetts 02115 (United States))
1991-12-01
Quantum-mechanical descriptions of arrays of Josephson weak links often invoke electric-field-energy storage in the weak-link capacitors. However, such quantum-electrodynamic mechanism is by no means a requirement for the notion of macroscopic quantum-mechanical wave functions for the array as a whole. These statements are illustrated for the phenomena of quantum-mechanical phase locking'' in one- and two-dimensional arrays in electromagnetic fields.
Deformation Quantization: From Quantum Mechanics to Quantum Field Theory
P. Tillman
2006-10-31
The aim of this paper is to give a basic overview of Deformation Quantization (DQ) to physicists. A summary is given here of some of the key developments over the past thirty years in the context of physics, from quantum mechanics to quantum field theory. Also, we discuss some of the conceptual advantages of DQ and how DQ may be related to algebraic quantum field theory. Additionally, our previous results are summarized which includes the construction of the Fedosov star-product on dS/AdS. One of the goals of these results was to verify that DQ gave the same results as previous analyses of these spaces. Another was to verify that the formal series used in the conventional treatment converged by obtaining exact and nonperturbative results for these spaces.
Progress in Euclidean relativistic few-body quantum mechanics
Polyzou, Wayne
Progress in Euclidean relativistic few-body quantum mechanics Wayne Polyzou The University of Iowa Iowa City, IA 52242 October 9, 2012 Abstract We discuss recent progress in the Euclidean formulation of relativistic few-body quantum mechanics. 1 Introduction Euclidean relativistic quantum mechanics is a formalism
Harvard University Physics 143b: Quantum Mechanics II
Harvard University Physics 143b: Quantum Mechanics II Instructor : Subir Sachdev, Lyman 343@fas.harvard.edu This is the second half of an introductory course on quantum mechanics. The course will complete the text book: the photon 5. Relativistic quantum mechanics: the Dirac equation 6. Einstein-Podolsky-Rosen "paradox", Bell
Harvard University Physics 143b: Quantum Mechanics II
Harvard University Physics 143b: Quantum Mechanics II Instructor : Subir Sachdev, Lyman 343@physics.harvard.edu This is the second half of an introductory course on quantum mechanics. The course will complete the text book: the photon 5. Relativistic quantum mechanics: the Dirac equation 6. Scattering theory. 7. Einstein
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
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 as partition functions of physical systems Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian
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 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12;Number fields: finite
Predicting crystal structure by merging data mining with quantum mechanics
Ceder, Gerbrand
ARTICLES Predicting crystal structure by merging data mining with quantum mechanics CHRISTOPHER C@mit.edu Published online: 9 July 2006; doi:10.1038/nmat1691 Modern methods of quantum mechanics have proved with quantum mechanics if an algorithm to direct the search through the large space of possible structures
MSE 157: Quantum Mechanics of Nanoscale Materials Course Information
MSE 157: Quantum Mechanics of Nanoscale Materials Course Information Basic info Prof. Aaron there. Textbook The textbook for this course is Introduction to Quantum Mechanics by David Griffiths. We interest. Other recommended books for outside reading: Applied Quantum Mechanics by David Levi Applied
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
The Objective Inde...niteness Interpretation of Quantum Mechanics
Wüthrich, Christian
The Objective Inde...niteness Interpretation of Quantum Mechanics David Ellerman University of California at Riverside Draft (not for quotation) May 28, 2013 Abstract Quantum mechanics (QM models indef- inite elements that become more de...nite as distinctions are made. If quantum mechanics
Kink mass quantum shifts from SUSY quantum mechanics
Alonso-Izquierdo, Alberto; Plyushchay, Mikhail S
2013-01-01
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.
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.
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.
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.
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.
The preparation of states in quantum mechanics
Juerg Froehlich; Baptiste Schubnel
2014-09-28
The important problem of how to prepare a quantum mechanical system, $S$, in a specific initial state of interest - e.g., for the purposes of some experiment - is addressed. Three distinct methods of state preparation are described. One of these methods has the attractive feature that it enables one to prepare $S$ in a preassigned initial state with certainty; i.e., the probability of success in preparing $S$ in a given state is unity. This method relies on coupling $S$ to an open quantum-mechanical environment, $E$, in such a way that the dynamics of $S \\vee E$ pulls the state of $S$ towards an "attractor", which is the desired initial state of $S$. This method is analyzed in detail.
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.
Bernard S. Kay; Varqa Abyaneh
2007-01-01
We restate Kay's 1998 hypothesis which simultaneously offers an objective definition for the entropy of a closed system, a microscopic foundation for the Second Law, a resolution of the Information Loss (and other) Black-Hole Puzzle(s) and an objective mechanism for decoherence. Presupposing a conventional unitary theory of low-energy quantum gravity, it offers all this by taking the physical density operator
Applications of computational quantum mechanics
NASA Astrophysics Data System (ADS)
Temel, Burcin
This original research dissertation is composed of a new numerical technique based on Chebyshev polynomials that is applied on scattering problems, a phenomenological kinetics study for CO oxidation on RuO2 surface, and an experimental study on methanol coupling with doped metal oxide catalysts. Minimum Error Method (MEM), a least-squares minimization method, provides an efficient and accurate alternative to solve systems of ordinary differential equations. Existing methods usually utilize matrix methods which are computationally costful. MEM, which is based on the Chebyshev polynomials as a basis set, uses the recursion relationships and fast Chebyshev transforms which scale as O(N). For large basis set calculations this provides an enormous computational efficiency in the calculations. Chebyshev polynomials are also able to represent non-periodic problems very accurately. We applied MEM on elastic and inelastic scattering problems: it is more efficient and accurate than traditionally used Kohn variational principle, and it also provides the wave function in the interaction region. Phenomenological kinetics (PK) is widely used in industry to predict the optimum conditions for a chemical reaction. PK neglects the fluctuations, assumes no lateral interactions, and considers an ideal mix of reactants. The rate equations are tested by fitting the rate constants to the results of the experiments. Unfortunately, there are numerous examples where a fitted mechanism was later shown to be erroneous. We have undertaken a thorough comparison between the phenomenological equations and the results of kinetic Monte Carlo (KMC) simulations performed on the same system. The PK equations are qualitatively consistent with the KMC results but are quantitatively erroneous as a result of interplays between the adsorption and desorption events. The experimental study on methanol coupling with doped metal oxide catalysts demonstrates the doped metal oxides as a new class of catalysts with novel properties. Doping a metal oxide may alter its intrinsic properties drastically. A catalytically non-active material can be activated by doping. In this study, we showed that pure zirconia (ZrO2) has almost no activity in methanol coupling reaction, whereas when it is doped with aluminum, the doped catalyst produces dimethyl ether (DME), which is valuable as an alternative future energy source.
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
Physical Interpretations of Nilpotent Quantum Mechanics
Rowlands, Peter
2010-01-01
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.
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.
Chiral quantum mechanics (CQM) for antihydrogen systems
G. Van Hooydonk
2005-12-03
A first deception of QM on antiH already appears in one-center integrals for two-center systems (G. Van Hooydonk, physics/0511115). In reality, full QM is a theory for chiral systems but the QM establishment was wrong footed with a permutation of reference frames. With chiral quantum mechanics (CQM), the theoretical ban on natural antiH must be lifted as soon as possible.
Modern Quantum Mechanics Experiments for Undergraduates
NSDL National Science Digital Library
Beck, Mark
Authored by Mark Beck of Whitman College's Department of Physics, this site provides information about simplified quantum mechanics experiments such as the Grangier experiment and single photon interference. Included are a general description, an overview, course materials, experiments, external links and notes. Each experiment or lesson provides instructions and other need information such as images, charts or graphs. This series of resources could be used to enhance or create curricula in the field.
Collocation method for fractional quantum mechanics
Amore, Paolo; Hofmann, Christoph P.; Saenz, Ricardo A. [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico); Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Division Quimica Teorica, Diagonal 113 y 64 S/N, Sucursal 4, Casilla de correo 16, 1900 La Plata (Argentina)
2010-12-15
We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on little sinc functions, which discretizes the Schroedinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a Wentzel-Kramers-Brillouin analysis is performed.
Superconformal multi-black hole quantum mechanics
Jeremy Michelson; Andrew Strominger
1999-01-01
The quantum mechanics of N slowly-moving charged BPS black holes in five-dimensional Script N = 1 supergravity is considered. The moduli space metric of the N black holes is derived and shown to admit 4 supersymmetries. A near-horizon limit is found in which the dynamics of widely separated black holes decouples from that of strongly-interacting, near-coincident black holes. This decoupling
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.
Relativistic non-Hermitian quantum mechanics
NASA Astrophysics Data System (ADS)
Jones-Smith, Katherine; Mathur, Harsh
2014-06-01
We develop relativistic wave equations in the framework of the new non-Hermitian PT quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of PT-symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that, in particular, the mass matrix be Hermitian also allows for models that have no counterpart in conventional quantum mechanics. For example it is well known that a quartet of Weyl spinors coupled by a Hermitian mass matrix reduces to two independent Dirac fermions; here, we show that the same quartet of Weyl spinors, when coupled by a non-Hermitian but PT-symmetric mass matrix, describes a single relativistic particle that can have massless dispersion relation even though the mass matrix is nonzero. The PT-generalized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a noninteracting theory it violates P and T individually. The relativistic wave equations are reformulated as canonical fermionic field theories to facilitate the study of interactions and are shown to maintain many of the canonical structures from Hermitian field theory, but with new and interesting possibilities permitted by the non-Hermiticity parameter m2.
Quantum mechanics and low energy nucleon dynamics
Renat Kh. Gainutdinov; Aigul A. Mutygullina
2004-08-25
We discuss the problem of consistency of quantum mechanics as applied to low energy nucleon dynamics with the symmetries of QCD. It is shown that the dynamics consistent with these symmetries is not governed by the Schrodinger equation. We present a new way to formulate the effective theory of nuclear forces as an inevitable consequence of the basic principles of quantum mechanics and the symmetries of strong interactions. We show that being formulated in this way the effective theory of nuclear forces can be put on the same firm theoretical grounds as the quantum mechanics of atomic phenomena. In this case the effective theory allows one to describe with a given accuracy not only two-nucleon scattering, but also the evolution of nucleon systems, and places the constraints on the off-shell behavior of the two-nucleon interaction. In this way we predict the off-shell behavior of the S wave two-nucleon T-matrix at very low energies when the pionless theory is applicable. Further extensions and applications of this approach are discussed.
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.
Unstable trajectories and the quantum mechanical uncertainty
Moser, Hans R. [Physics Institute, University of Zuerich, Winterthurerstrasse 190, CH-8057 Zuerich (Switzerland)], E-mail: moser@physik.uzh.ch
2008-08-15
There is still an ongoing discussion about various seemingly contradictory aspects of classical particle motion and its quantum mechanical counterpart. One of the best accepted viewpoints that intend to bridge the gap is the so-called Copenhagen Interpretation. A major issue there is to regard wave functions as probability amplitudes (usually for the position of a particle). However, the literature also reports on approaches that claim a trajectory for any quantum mechanical particle, Bohmian mechanics probably being the most prominent one among these ideas. We introduce a way to calculate trajectories as well, but our crucial ingredient is their well controlled local (thus also momentaneous) degree of instability. By construction, at every moment their unpredictability, i.e., their local separation rates of neighboring trajectories, is governed by the local value of the given modulus square of a wave function. We present extensive numerical simulations of the H and He atom, and for some velocity-related quantities, namely angular momentum and total energy, we inspect their agreement with the values appearing in wave mechanics. Further, we interpret the archetypal double slit interference experiment in the spirit of our findings. We also discuss many-particle problems far beyond He, which guides us to a variety of possible applications.
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.
Quantum mechanics with coordinate dependent noncommutativity
Kupriyanov, V. G. [CMCC, Universidade Federal do ABC, Santo André, SP (Brazil)] [CMCC, Universidade Federal do ABC, Santo André, SP (Brazil)
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.
Euclidean formulation of relativistic quantum mechanics W. N. Polyzou1
Polyzou, Wayne
Euclidean formulation of relativistic quantum mechanics W. N. Polyzou1 and Philip Kopp1 1 of relativistic quantum mechanics that uses reflection-positive Euclidean Green functions or generating functionals as phenomenological input. This work is motivated by the Euclidean axioms of quantum field theory
QUANTUM MECHANICS IN SNYDER SPACE Mark K. Transtrum
Hart, Gus
QUANTUM MECHANICS IN SNYDER SPACE by Mark K. Transtrum Submitted to Brigham Young University and two dimensions. I discuss the relation between Snyder space and noncommutative quantum mechanics Huele, Advisor Date Eric Hintz, Research Coordinator Date Scott Sommerfeldt, Chair #12;ABSTRACT QUANTUM
Marinelli, Dimitri; Aquilanti, Vincenzo; Anderson, Roger W; Bitencourt, Ana Carla P; Ragni, Mirco
2014-01-01
A unified vision of the symmetric coupling of angular momenta and of the quantum mechanical volume operator is illustrated. The focus is on the quantum mechanical angular momentum theory of Wigner's 6j symbols and on the volume operator of the symmetric coupling in spin network approaches: here, crucial to our presentation are an appreciation of the role of the Racah sum rule and the simplification arising from the use of Regge symmetry. The projective geometry approach permits the introduction of a symmetric representation of a network of seven spins or angular momenta. Results of extensive computational investigations are summarized, presented and briefly discussed.
Quantum Mechanics Joachim Burgd orfer and Stefan Rotter
Rotter, Stefan
1 1 Quantum Mechanics Joachim BurgdË? orfer and Stefan Rotter 1.1 Introduction 3 1.2 Particle and Quantization 8 1.5 Angular Momentum in Quantum Mechanics 9 1.6 Formalism of Quantum Mechanics 12 1.7 Solution 29 1.8.3 Resonances 30 1.9 Semiclassical Mechanics 31 1.9.1 The WKB Approximation 31 1.9.2 The EBK
New approach to nonperturbative quantum mechanics with minimal length uncertainty
NASA Astrophysics Data System (ADS)
Pedram, Pouria
2012-01-01
The existence of a minimal measurable length is a common feature of various approaches to quantum gravity such as string theory, loop quantum gravity, and black-hole physics. In this scenario, all commutation relations are modified and the Heisenberg uncertainty principle is changed to the so-called Generalized (Gravitational) Uncertainty Principle (GUP). Here, we present a one-dimensional nonperturbative approach to quantum mechanics with minimal length uncertainty relation which implies X=x to all orders and P=p+(1)/(3)?p3 to first order of GUP parameter ?, where X and P are the generalized position and momentum operators and [x,p]=i?. We show that this formalism is an equivalent representation of the seminal proposal by Kempf, Mangano, and Mann and predicts the same physics. However, this proposal reveals many significant aspects of the generalized uncertainty principle in a simple and comprehensive form and the existence of a maximal canonical momentum is manifest through this representation. The problems of the free particle and the harmonic oscillator are exactly solved in this GUP framework and the effects of GUP on the thermodynamics of these systems are also presented. Although X, P, and the Hamiltonian of the harmonic oscillator all are formally self-adjoint, the careful study of the domains of these operators shows that only the momentum operator remains self-adjoint in the presence of the minimal length uncertainty. We finally discuss the difficulties with the definition of potentials with infinitely sharp boundaries.
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
Elio Conte
2011-06-14
We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the and Clifford algebras. This last algebra gives proof of the von Neumann basic postulates on the quantum measurement explaining thus in an algebraic manner the wave function collapse postulated in standard quantum theory. In this manner we reach the objective to expose a self-consistent version of quantum mechanics. We give proof of the quantum like Heisenberg uncertainty relations, the phenomenon of quantum Mach Zender interference as well as quantum collapse in some cases of physical interest We also discuss the problem of time evolution of quantum systems as well as the changes in space location. We also give demonstration of the Kocken-Specher theorem, and also we give an algebraic formulation and explanation of the EPR . By using the same approach we also derive Bell inequalities. Our formulation is strongly based on the use of idempotents that are contained in Clifford algebra. Their counterpart in quantum mechanics is represented by the projection operators that are interpreted as logical statements, following the basic von Neumann results. Using the Clifford algebra we are able to invert such result. According to the results previously obtained by Orlov in 1994, we are able to give proof that quantum mechanics derives from logic. We show that indeterminism and quantum interference have their origin in the logic.
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.
Statistical Quantum Mechanics of Many Universes
Gamboa-Rios, J
2003-01-01
The quantum statistical mechanics of generally covariant systems --particles, strings and membranes-- on noncommutative field spaces is studied. We discuss how to introduce non-local communication among different systems via noncommutativity. This idea is applied to cosmology where we argue that due to the breaking of relativistic invariance one can consider a privileged reference system where many universes interact as a quantum gas in a reservoir. If roughly speaking, we approximate the universes as tensionless membranes, then, the interaction among universes provided by noncommutativity is harmonic. The oscillation frequency for each universe is proportional to $B/M$, where $B$ is the noncommutativity parameter --that we identify as the primordial magnetic field, {\\it i.e.} $\\sim 10^{-16} {GeV}^2$- and $M$ is the mass of the universe ($\\sim 10^{77} {GeV}$) and, therefore each universe have the pulsation frequency $\\omega \\sim 10^{-68} s^{-1}$.
Nielsen, Steven O.
FIG. 1: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect. FIG. 2: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect. 1 #12;FIG. 3: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect
Quantum-mechanical description of Lense-Thirring effect for relativistic scalar particles
Alexander J. Silenko
2014-08-10
Exact expression for the Foldy-Wouthuysen Hamiltonian of scalar particles is used for a quantum-mechanical description of the relativistic Lense-Thirring effect. The exact evolution of the angular momentum operator in the Kerr field approximated by a spatially isotropic metric is found. The quantum-mechanical description of the full Lense-Thirring effect based on the Laplace-Runge-Lenz vector is given in the nonrelativistic and weak-field approximation. Relativistic quantum-mechanical equations for the velocity and acceleration operators are obtained. The equation for the acceleration defines the Coriolis-like and centrifugal-like accelerations and presents the quantum-mechanical description of the frame-dragging effect.
New scalar constraint operator for loop quantum gravity
Assanioussi, Mehdi; Mäkinen, Ilkka
2015-01-01
We present a concrete and explicit construction of a new scalar constraint operator for loop quantum gravity. The operator is defined on the recently introduced space of partially diffeomorphism invariant states, and this space is preserved by the action of the operator. To define the Euclidean part of the scalar constraint operator, we propose a specific regularization based on the idea of so-called "special" loops. The Lorentzian part of the quantum scalar constraint is merely the curvature operator that has been introduced in an earlier work. Due to the properties of the special loops assignment, the adjoint operator of the non-symmetric constraint operator is densely defined on the partially diffeomorphism invariant Hilbert space. This fact opens up the possibility of defining a symmetric scalar constraint operator as a suitable combination of the original operator and its adjoint. We also show that the algebra of the scalar constraint operators is anomaly free, and describe the structure of the kernel of...
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, ...
5.74 Introductory Quantum Mechanics II, Spring 2007
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 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, ...
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.
The Smith chart and quantum mechanics
Rosner, J.L. (Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637 (United States))
1993-04-01
The Schroedinger equation and the equation describing the behavior of voltage on a transmission line are both linear second-order equations, which may be solved by convenient matrix methods. By drawing analogies between these two problems, it is shown that a method used for antenna impedance matching based on the Smith chart corresponds in quantum mechanics to a simple conformal transformation of the logarithmic derivative of the wave function. One thereby can arrive at an elementary derivation of the Wentzel--Kramers--Brillouin quantization condition.
Hidden geometric character of relativistic quantum mechanics
Almeida, Jose B. [Physics Department, Universidade do Minho, 4710-057 Braga (Portugal)
2007-01-15
Geometry can be an unsuspected source of equations with physical relevance, as everybody is aware since Einstein formulated the general theory of relativity. However, efforts to extend a similar type of reasoning to other areas of physics, namely, electrodynamics, quantum mechanics, and particle physics, usually had very limited success; particularly in quantum mechanics the standard formalism is such that any possible relation to geometry is impossible to detect; other authors have previously trod the geometric path to quantum mechanics, some of that work being referred to in the text. In this presentation we will follow an alternate route to show that quantum mechanics has indeed a strong geometric character. The paper makes use of geometric algebra, also known as Clifford algebra, in five-dimensional space-time. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from such choice and their consistency with experimental results. Given a metric space of any dimension, one can define monogenic functions, the natural extension of analytic functions to higher dimensions; such functions have null vector derivative and have previously been shown by other authors to play a decisive role in lower dimensional spaces. All monogenic functions have null Laplacian by consequence; in a hyperbolic space this fact leads inevitably to a wave equation with planelike solutions. This is also true for five-dimensional space-time and we will explore those solutions, establishing a parallel with the solutions of the free particle Dirac equation. For this purpose we will invoke the isomorphism between the complex algebra of 4x4 matrices, also known as Dirac's matrices. There is one problem with this isomorphism, because the solutions to Dirac's equation are usually known as spinors (column matrices) that do not belong to the 4x4 matrix algebra and as such are excluded from the isomorphism. We will show that a solution in terms of Dirac spinors is equivalent to a plane wave solution. Just as one finds in the standard formulation, monogenic functions can be naturally split into positive/negative energy together with left/right ones. This split is provided by geometric projectors and we will show that there is a second set of projectors providing an alternate fourfold split. The possible implications of this alternate split are not yet fully understood and are presently the subject of profound research.
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.
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.
BiHermitian supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Zucchini, Roberto
2007-04-01
BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2, 2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kähler manifolds recently developed by Gualtieri in [33]. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li in [9].
The Ithaca Interpretation of Quantum Mechanics
Mermin, N David
1996-01-01
I list several strong requirements for what I would consider a sensible interpretation of quantum mechanics and I discuss two simple theorems. One, as far as I know, is new; the other was only noted a few years ago. Both have important implications for such a sensible interpretation. My talk will not clear everything up; indeed, you may conclude that it has not cleared anything up. But I hope it will provide a different perspective from which to view some old and vexing puzzles (or, if you believe nothing needs to be cleared up, some ancient verities.)
The Ithaca Interpretation of Quantum Mechanics
N. David Mermin
1996-09-17
I list several strong requirements for what I would consider a sensible interpretation of quantum mechanics and I discuss two simple theorems. One, as far as I know, is new; the other was only noted a few years ago. Both have important implications for such a sensible interpretation. My talk will not clear everything up; indeed, you may conclude that it has not cleared anything up. But I hope it will provide a different perspective from which to view some old and vexing puzzles (or, if you believe nothing needs to be cleared up, some ancient verities.)
Identifying mechanisms in the control of quantum dynamics through Hamiltonian encoding
Mitra, Abhra [Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544 (United States); Rabitz, Herschel [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States)
2003-03-01
A variety of means are now available to design control fields for manipulating the evolution of quantum systems. However, the underlying physical mechanisms often remain obscure, especially in the cases of strong fields and high quantum state congestion. This paper proposes a method to quantitatively determine the various pathways taken by a quantum system in going from the initial state to the final target. The mechanism is revealed by encoding a signal in the system Hamiltonian and decoding the resultant nonlinear distortion of the signal in the system time-evolution operator. The relevant interfering pathways determined by this analysis give insight into the physical mechanisms operative during the evolution of the quantum system. A hierarchy of mechanism identification algorithms with increasing ability to extract more detailed pathway information is presented. The mechanism identification concept is presented in the context of analyzing computer simulations of controlled dynamics. As illustrations of the concept, mechanisms are identified in the control of several simple, discrete-state quantum systems. The mechanism analysis tools reveal the roles of multiple interacting quantum pathways to maximally take advantage of constructive and destructive interference. Similar procedures may be applied directly in the laboratory to identify control mechanisms without resort to computer modeling, although this extension is not addressed in this paper.
The operator algebra approach to quantum groups
Kustermans, Johan; Vaes, Stefaan
2000-01-01
A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory. PMID:10639116
Lorentz-covariant reduced-density-operator theory for relativistic-quantum-information processing
Ahn, Doyeol [Institute of Quantum Information Processing and Systems, University of Seoul, Seoul 130-743 (Korea, Republic of); Department of Electrical and Computer Engineering, University of Seoul, Seoul 130-743 (Korea, Republic of); Lee, Hyuk-jae [Institute of Quantum Information Processing and Systems, University of Seoul, Seoul 130-743 (Korea, Republic of); Hwang, Sung Woo [Institute of Quantum Information Processing and Systems, University of Seoul, Seoul 130-743 (Korea, Republic of); Department of Electronic Engineering, Korea University, Seoul 136-701 (Korea, Republic of)
2003-03-01
In this paper, we derived a Lorentz-covariant quantum Liouville equation for the density operator which describes the relativistic-quantum-information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced density operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of the nonrelativistic case, which is valid only in some specified reference frame. To show that our formulation can be applied to practical problems, we derived the polarization of the vacuum in quantum electrodynamics up to the second order. The formulation presented in this work is general and could be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics.
Simulating Quantum Mechanics by Non-Contextual Hidden Variables
Rob Clifton; Adrian Kent
2000-05-29
No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no-go arguments against non-contextual hidden variables. All such arguments rely on choosing special sets of quantum-mechanical observables with measurement outcomes that cannot be simulated non-contextually. As a consequence, these arguments do not exclude the hypothesis that the class of physical measurements in fact corresponds to a dense subset of all theoretically possible measurements with outcomes and quantum probabilities that \\emph{can} be recovered from a non-contextual hidden variable model. We show here by explicit construction that there are indeed such non-contextual hidden variable models, both for projection valued and positive operator valued measurements.
A note on the Landauer principle in quantum statistical mechanics
Boyer, Edmond
A note on the Landauer principle in quantum statistical mechanics Vojkan Jaksi´c1 and Claude results concerning the derivation of the Landauer bound from the first principles of statistical mechanics and proof of the Landauer principle in the context of quantum statistical mechanics has led to a number
Quantum Mechanical Transport in Submicron Electronic Devices.
NASA Astrophysics Data System (ADS)
Bagwell, Philip Frederick
Electronic devices with characteristic dimensions of the order of 100 nm or less exhibit many novel quantum transport phenomena at low temperatures when the phase -breaking length becomes comparable to the device size. This thesis describes electron transport mechanisms and the resulting current-voltage relationships in quasi-one-dimensional wires, superlattices, and resonant tunneling devices. An intuitive 'convolution method' is developed to describe the energy averaging due to a finite bias voltage, finite temperature, disorder, and the influence of emitter dimensionality on these currents. We emphasize the dominant effect of evanescent or 'cutoff' electron waveguide modes in determining the shape of the electrical conductance versus Fermi energy in a confined geometry such as a quantum wire. Finally, we study experimentally the magnetoconductance of a novel Si 'grating gate' field effect transistor where the current path can be varied electrostatically in a single device from many narrow wires in parallel, to a modulated periodic potential, to a two-dimensional electron gas. Electron weak-localization, the classical Drude magnetoconductance, and the quantum Hall effect are modified by the periodic potential. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).
A quantum protective mechanism in photosynthesis
Marais, Adriana; Sinayskiy, Ilya; Petruccione, Francesco; van Grondelle, Rienk
2015-01-01
Since the emergence of oxygenic photosynthesis, living systems have developed protective mechanisms against reactive oxygen species. During charge separation in photosynthetic reaction centres, triplet states can react with molecular oxygen generating destructive singlet oxygen. The triplet product yield in bacteria is observed to be reduced by weak magnetic fields. Reaction centres from plants' photosystem II share many features with bacterial reaction centres, including a high-spin iron whose function has remained obscure. To explain observations that the magnetic field effect is reduced by the iron, we propose that its fast-relaxing spin plays a protective role in photosynthesis by generating an effective magnetic field. We consider a simple model of the system, derive an analytical expression for the effective magnetic field and analyse the resulting triplet yield reduction. The protective mechanism is robust for realistic parameter ranges, constituting a clear example of a quantum effect playing a macroscopic role vital for life. PMID:25732807
A quantum protective mechanism in photosynthesis.
Marais, Adriana; Sinayskiy, Ilya; Petruccione, Francesco; van Grondelle, Rienk
2015-01-01
Since the emergence of oxygenic photosynthesis, living systems have developed protective mechanisms against reactive oxygen species. During charge separation in photosynthetic reaction centres, triplet states can react with molecular oxygen generating destructive singlet oxygen. The triplet product yield in bacteria is observed to be reduced by weak magnetic fields. Reaction centres from plants' photosystem II share many features with bacterial reaction centres, including a high-spin iron whose function has remained obscure. To explain observations that the magnetic field effect is reduced by the iron, we propose that its fast-relaxing spin plays a protective role in photosynthesis by generating an effective magnetic field. We consider a simple model of the system, derive an analytical expression for the effective magnetic field and analyse the resulting triplet yield reduction. The protective mechanism is robust for realistic parameter ranges, constituting a clear example of a quantum effect playing a macroscopic role vital for life. PMID:25732807
Biological applications of hybrid quantum mechanics/molecular mechanics calculation.
Kang, Jiyoung; Hagiwara, Yohsuke; Tateno, Masaru
2012-01-01
Since in most cases biological macromolecular systems including solvent water molecules are remarkably large, the computational costs of performing ab initio calculations for the entire structures are prohibitive. Accordingly, QM calculations that are jointed with MM calculations are crucial to evaluate the long-range electrostatic interactions, which significantly affect the electronic structures of biological macromolecules. A UNIX-shell-based interface program connecting the quantum mechanics (QMs) and molecular mechanics (MMs) calculation engines, GAMESS and AMBER, was developed in our lab. The system was applied to a metalloenzyme, azurin, and PU.1-DNA complex; thereby, the significance of the environmental effects on the electronic structures of the site of interest was elucidated. Subsequently, hybrid QM/MM molecular dynamics (MD) simulation using the calculation system was employed for investigation of mechanisms of hydrolysis (editing reaction) in leucyl-tRNA synthetase complexed with the misaminoacylated tRNA(Leu), and a novel mechanism of the enzymatic reaction was revealed. Thus, our interface program can play a critical role as a powerful tool for state-of-the-art sophisticated hybrid ab initio QM/MM MD simulations of large systems, such as biological macromolecules. PMID:22536015
Accessing quantum secrets via local operations and classical communication
NASA Astrophysics Data System (ADS)
Gheorghiu, Vlad; Sanders, Barry C.
2013-08-01
Quantum secret-sharing and quantum error-correction schemes rely on multipartite decoding protocols, yet the nonlocal operations involved are challenging and sometimes infeasible. Here we construct a quantum secret-sharing protocol with a reduced number of quantum communication channels between the players. We introduce a scheme based on embedding a classical linear code into a quantum error-correcting code and then mapping the latter to a quantum secret-sharing protocol. In contrast to the Calderbank-Shor-Steane construction, we do not impose any restriction on the classical code; our protocol works with any arbitrary linear code. Our work paves the way towards the more general problem of simplifying the decoding of quantum error-correcting codes.
Chem 7940 Quantum Mechanics II Spring 2013 Review of Bra-Ket formalism
: ^ ^ |^| = |^ = ^| |^ | = |^ = ^ | 1 of 3 #12;Chem 7940 Quantum Mechanics II Spring 2013 · Adjoint relation ^ | |^ ^| | ^ · General · Complex linear (vector) space: | = |1 c1 + |2 c2 + · · · H, ck C. · Bra state | · Ket-bra conjugation | = | · Operators ^: ^ | | |^ · General form for operator: ket × number × bra ^ = k,k |k kk k | · Linearity ^ k |k
Topological Quantum Computation, Yang-Baxter Operators and Modular Categories
Rowell, Eric C.
-function collapse: Measuring O on | = i ai |ei gives HO-eigenstate |ei with probability |ai |2. Eric Rowell Texas A(g, ) obtained from Uqg at q = ei/ . Eric Rowell Texas A&M University Topological Quantum Computation, YangTopological Quantum Computation, Yang-Baxter Operators and Modular Categories Eric Rowell Texas A
Quantum dynamical semigroups generated by noncommutative unbounded elliptic operators
C. Bahn; C. K. Ko; Y. M. Park
2005-05-09
We study quantum dynamical semigroups generated by noncommutative unbounded elliptic operators which can be written as Lindblad type unbounded generators. Under appropriate conditions, we first construct the minimal quantum dynamical semigroups for the generators and then use Chebotarev and Fagnola's sufficient conditions for conservativity to show that the semigroups are conservative.
Quantum Mechanical Study of Nanoscale MOSFET
NASA Technical Reports Server (NTRS)
Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan
2001-01-01
The steady state characteristics of MOSFETS that are of practical Interest are the drive current, off-current, dope of drain current versus drain voltage, and threshold voltage. In this section, we show that quantum mechanical simulations yield significantly different results from drift-diffusion based methods. These differences arise because of the following quantum mechanical features: (I) polysilicon gate depletion in a manner opposite to the classical case (II) dependence of the resonant levels in the channel on the gate voltage, (III) tunneling of charge across the gate oxide and from source to drain, (IV) quasi-ballistic flow of electrons. Conclusions dI/dV versus V does not increase in a manner commensurate with the increase in number of subbands. - The increase in dI/dV with bias is much smaller then the increase in the number of subbands - a consequence of bragg reflection. Our calculations show an increase in transmission with length of contact, as seen in experiments. It is desirable for molecular electronics applications to have a small contact area, yet large coupling. In this case, the circumferential dependence of the nanotube wave function dictates: - Transmission in armchair tubes saturates around unity - Transmission in zigzag tubes saturates at two.
A Foundation Theory of Quantum Mechanics
Richard A Mould
2006-07-10
The nRules are empirical regularities that were discovered in macroscopic situations where the outcome is known. When they are projected theoretically into the microscopic domain they predict a novel ontology including the frequent collapse of an atomic wave function, thereby defining an nRule based foundation theory. Future experiments can potentially discriminate between this and other foundation theories of (non-relativistic) quantum mechanics. Important features of the nRules are: (1) they introduce probability through probability current rather than the Born rule, (2) they are valid independent of size (micro or macroscopic), (3) they apply to individual trials, not just to ensembles of trials. (4) they allow all observers to be continuously included in the system without ambiguity, (5) they account for the collapse of the wave function without introducing new or using old physical constants, and (6) in dense environments they provide a high frequency of stochastic localizations of quantum mechanical objects. Key words: measurement, stochastic choice, state reduction.
Continuous quantum error correction through local operations
Mascarenhas, Eduardo; Franca Santos, Marcelo [Departamento de Fisica, Universidade Federal de Minas Gerais, 31270-901, Belo Horizonte (Brazil); Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, 117542 Singapore (Singapore); Marques, Breno [Departamento de Fisica, Universidade Federal de Minas Gerais, 31270-901, Belo Horizonte (Brazil); Terra Cunha, Marcelo [Departamento de Matematica, Universidade Federal de Minas Gerais, 30123-970, Belo Horizonte (Brazil)
2010-09-15
We propose local strategies to protect global quantum information. The protocols, which are quantum error-correcting codes for dissipative systems, are based on environment measurements, direct feedback control, and simple encoding of the logical qubits into physical qutrits whose decaying transitions are indistinguishable and equally probable. The simple addition of one extra level in the description of the subsystems allows for local actions to fully and deterministically protect global resources such as entanglement. We present codes for both quantum jump and quantum state diffusion measurement strategies and test them against several sources of inefficiency. The use of qutrits in information protocols suggests further characterization of qutrit-qutrit disentanglement dynamics, which we also give together with simple local environment measurement schemes able to prevent distillability sudden death and even enhance entanglement in situations in which our feedback error correction is not possible.
Bodek, K.; Rozp?dzik, D.; Zejma, J. [Jagiellonian University, Faculty of Physics, Astronomy and Applied Informatics, Reymonta 4, 30059 Kraków (Poland); Caban, P.; Rembieli?ski, J.; W?odarczyk, M. [University of ?ód?, Faculty of Physics and Applied Informatics, Pomorska 149/153, 90236 ?ód? (Poland); Ciborowski, J. [University of Warsaw, Faculty of Physics, Hoza 69, 00681 Warsaw (Poland); Enders, J.; Köhler, A. [Technische Universität Darmstadt, Institut für Kernphysik, Schlossgartenstraße 9, 64289 Darmstadt (Germany); Kozela, A. [Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31342 Kraków (Poland)
2013-11-07
The Polish-German project QUEST aims at studying relativistic quantum spin correlations of the Einstein-Rosen-Podolsky-Bohm type, through measurement of the correlation function and the corresponding probabilities for relativistic electron pairs. The results will be compared to theoretical predictions obtained by us within the framework of relativistic quantum mechanics, based on assumptions regarding the form of the relativistic spin operator. Agreement or divergence will be interpreted in the context of non-uniqueness of the relativistic spin operator in quantum mechanics as well as dependence of the correlation function on the choice of observables representing the spin. Pairs of correlated electrons will originate from the Mo/ller scattering of polarized 15 MeV electrons provided by the superconducting Darmstadt electron linear accelerator S-DALINAC, TU Darmstadt, incident on a Be target. Spin projections will be determined using the Mott polarimetry technique. Measurements (starting 2013) are planned for longitudinal and transverse beam polarizations and different orientations of the beam polarization vector w.r.t. the Mo/ller scattering plane. This is the first project to study relativistic spin correlations for particles with mass.
A ROSETTA STONE FOR QUANTUM MECHANICS WITH AN INTRODUCTION TO QUANTUM COMPUTATION VERSION 1.5
SAMUEL J. LOMONACO
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American
A Rosetta Stone for Quantum Mechanics with an Introduction to Quantum Computation
Samuel J. Lomonaco; jr
2000-01-01
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American
Tulsi Dass
2006-12-29
Supmech, an algebraic scheme of mechanics integrating noncommutative symplectic geometry and noncommutative probability, subsumes quantum and classical mechanics and permits consistent treatment of interaction of quantum and classical systems. Quantum measurements are treated in this framework; the von Neumann reduction rule (generally postulated) is derived and interpreted in physical terms.
Minnesota, University of
A Combined Quantum Mechanical and Molecular Mechanical Study of the Reaction Mechanism and r-Amino Acidity in Alanine Racemase Dan Thomas Major and Jiali Gao* Contribution from the Department of Chemistry Received August 31, 2006; E-mail: gao@chem.umn.edu Abstract: Combined quantum mechanical
From fractional Fourier transformation to quantum mechanical fractional squeezing transformation
NASA Astrophysics Data System (ADS)
Lv, Cui-Hong; Fan, Hong-Yi; Li, Dong-Wei
2015-02-01
By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function, i.e., tan ? ? tanh ?, sin ? ? sinh ?, we find the quantum mechanical fractional squeezing transformation (FrST) which satisfies additivity. By virtue of the integration technique within the ordered product of operators (IWOP) we derive the unitary operator responsible for the FrST, which is composite and is made of ei?a†a/2 and exp . The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches. Project supported by the National Natural Science Foundation of China (Grant No. 11304126), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130532), the Natural Science Fund for Colleges and Universities in Jiangsu Province, China (Grant No. 13KJB140003), the Postdoctoral Science Foundation of China (Grant No. 2013M541608), and the Postdoctoral Science Foundation of Jiangsu Province, China (Grant No. 1202012B).
Fundamental phenomena of quantum mechanics explored with neutron interferometers
J. Klepp; S. Sponar; Y. Hasegawa
2014-07-11
Ongoing fascination with quantum mechanics keeps driving the development of the wide field of quantum-optics, including its neutron-optics branch. Application of neutron-optical methods and, especially, neutron interferometry and polarimetry has a long-standing tradition for experimental investigations of fundamental quantum phenomena. We give an overview of related experimental efforts made in recent years.
Multiple-time states and multiple-time measurements in quantum mechanics
Y. Aharonov; S. Popescu; J. Tollaksen; L. Vaidman
2007-12-03
We discuss experimental situations that consist of multiple preparation and measurement stages. This leads us to a new approach to quantum mechanics. In particular, we introduce the idea of multi-time quantum states which are the appropriate tools for describing these experimental situations. We also describe multi-time measurements and discuss their relation to multi-time states. A consequence of our new formalism is to put states and operators on an equal footing. Finally we discuss the implications of our new approach to quantum mechanics for the problem of the flow of time.
Symmetry as a foundational concept in Quantum Mechanics
Ziaeepour, Houri
2015-01-01
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a fundamental concept in the construction of physical systems. Based on this idea, we propose a series of postulates for describing quantum systems, and establish their relation and correspondence with axioms of standard quantum mechanics. Through some examples we show that this reformulation helps better understand some of ambiguities of standard description. Nonetheless its application is not limited to explaining confusing concept and it may be a necessary step toward a consistent model of quantum cosmology and gravity.
Hilbert space for quantum mechanics on superspace
Coulembier, K.; De Bie, H. [Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Krijgslaan 281, 9000 Gent (Belgium)
2011-06-15
In superspace a realization of sl{sub 2} is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie, and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, Proc. London Math. Soc. (accepted) arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl{sub 2}-representation is proven. Finally, the Heisenberg uncertainty principle for the super Fourier transform is constructed.
Bopp operators and phase-space spin dynamics: Application to rotational quantum brownian motion
D. Zueco; Ivan Calvo
2007-04-20
As already known for nonrelativistic spinless particles, Bopp operators give an elegant and simple way to compute the dynamics of quasiprobability distributions in the phase space formulation of Quantum Mechanics. In this work, we present a generalization of Bopp operators for spins and apply our results to the case of open spin systems. This approach allows to take the classical limit in a transparent way, recovering the corresponding Fokker-Planck equation.
Supersymmetric quantum mechanics and Painlevé equations
Bermudez, David; Fernández C, David J. [Departamento de Física, Cinvestav, A.P. 14-740, 07000 México D.F. (Mexico)
2014-01-08
In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order the potential is determined by solutions to Painlevé IV (PIV) and Painlevé V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.
Quantum mechanics without an equation of motion
Alhaidari, A. D. [Saudi Center for Theoretical Physics, Jeddah 21438 (Saudi Arabia)
2011-06-15
We propose a formulation of quantum mechanics for a finite level system whose potential function is not realizable and/or analytic solution of the wave equation is not feasible. The system's wavefunction is written as an infinite sum in a complete set of square integrable functions. Interaction in the theory is introduced in function space by a real finite tridiagonal symmetric matrix. The expansion coefficients of the wavefunction satisfy a three-term recursion relation incorporating the parameters of the interaction. Information about the structure and dynamics of the system is contained in the scattering matrix, which is defined in the usual way. The bound state energy spectrum (system's structure) is finite. Apart from the 2M- 1 dimensionless parameters of the interaction matrix, whose rank is M, the theory has one additional scale parameter. In the development, we utilize the kinematic tools of the J-matrix method.
Quantum mechanical calculations to chemical accuracy
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Langhoff, Stephen R.
1991-01-01
The accuracy of current molecular-structure calculations is illustrated with examples of quantum mechanical solutions for chemical problems. Two approaches are considered: (1) the coupled-cluster singles and doubles (CCSD) with a perturbational estimate of the contribution of connected triple excitations, or CCDS(T); and (2) the multireference configuration-interaction (MRCI) approach to the correlation problem. The MRCI approach gains greater applicability by means of size-extensive modifications such as the averaged-coupled pair functional approach. The examples of solutions to chemical problems include those for C-H bond energies, the vibrational frequencies of O3, identifying the ground state of Al2 and Si2, and the Lewis-Rayleigh afterglow and the Hermann IR system of N2. Accurate molecular-wave functions can be derived from a combination of basis-set saturation studies and full configuration-interaction calculations.
Supersymmetric quantum mechanics and Painlevé equations
NASA Astrophysics Data System (ADS)
Bermudez, David; Fernández C., David J.
2014-01-01
In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order the potential is determined by solutions to Painlevé IV (PIV) and Painlevé V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.
Driving quantum-walk spreading with the coin operator
Romanelli, A. [Instituto de Fisica, Facultad de Ingenieria, Universidad de la Republica, CC 30, CP 11000 Montevideo (Uruguay)
2009-10-15
We generalize the discrete quantum walk on the line using a time-dependent unitary coin operator. We find an analytical relation between the long-time behaviors of the standard deviation and the coin operator. Selecting the coin time sequence allows to obtain a variety of predetermined asymptotic wave-function spreadings: ballistic, sub-ballistic, diffusive, subdiffusive, and localized.
A Causal Net Approach to Relativistic Quantum Mechanics
R. D. Bateson
2012-05-13
In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on Reichenbach-like conjunctive forks in proper time we can exactly derive the 1+1 dimension Dirac equation for a relativistic fermion and correctly model quantum mechanical statistics. Symmetries of the net provide various quantum mechanical effects such as quantum uncertainty and wavefunction, phase, spin, negative energy states and the effect of a potential. The causal net can be embedded in 3+1 dimensions and is consistent with the conventional Dirac equation. In the low velocity limit the causal net approximates to the Schrodinger equation and Pauli equation for an electromagnetic field. Extending to different momentum states the net is compatible with the Feynman path integral approach to quantum mechanics that allows calculation of well known quantum phenomena such as diffraction.
Equivalence relations between deterministic and quantum mechanical systems
Gerard't Hooft
1988-01-01
Several quantum mechanical models are shown to be equivalent to certain deterministic systems because a basis can be found in terms of which the wave function does not “spread.” This suggests that apparently indeterministic behavior typical for a quantum mechanical world can be the result of locally deterministic laws of physics. We show how certain deterministic systems allow the construction
Euclidean Relativistic Quantum Mechanics W. N. Polyzou, 1
Polyzou, Wayne
Euclidean Relativistic Quantum Mechanics W. N. Polyzou, 1 Philip Kopp 1 1 Department of Physics of exactly Poincarâ??e invariant quantum mechanics where the input is model Euclidean Green functions not have a simple connection with the Lagrangian formulation of the field theory. The Euclidean Green
Euclidean Relativistic Quantum Mechanics W. N. Polyzou,1
Polyzou, Wayne
Euclidean Relativistic Quantum Mechanics W. N. Polyzou,1 Philip Kopp1 1 Department of Physics of exactly PoincarÂ´e invariant quantum mechanics where the input is model Euclidean Green functions not have a simple connection with the Lagrangian formulation of the field theory. The Euclidean Green
Predicting crystal structure by merging data mining with quantum mechanics
Christopher C. Fischer; Kevin J. Tibbetts; Dane Morgan; Gerbrand Ceder
2006-01-01
Modern methods of quantum mechanics have proved to be effective tools to understand and even predict materials properties. An essential element of the materials design process, relevant to both new materials and the optimization of existing ones, is knowing which crystal structures will form in an alloy system. Crystal structure can only be predicted effectively with quantum mechanics if an
Quaternionic quantum mechanics allows non-local boxes
Matthew McKague
2009-11-09
We consider non-local properties of quanternionic quantum mechanics, in which the complex numbers are replaced by the quaternions as the underlying algebra. Specifically, we show that it is possible to construct a non-local box. This allows one to rule out quaternionic quantum mechanics using assumptions about communication complexity or information causality.
Design and Validation of the Quantum Mechanics Conceptual Survey
ERIC Educational Resources Information Center
McKagan, S. B.; Perkins, K. K.; Wieman, C. E.
2010-01-01
The Quantum Mechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantum mechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper, we describe the design and validation of the survey, a process that included…
Unraveling quantum mechanical effects in water using isotopic fractionation
Berne, Bruce J.
Unraveling quantum mechanical effects in water using isotopic fractionation Thomas E. Marklanda that equilibrium fractionation ratios, an entirely quantum mechan- ical property, also provide a sensitive probe- predict the magnitude of isotope fractionation. Models that account for anharmonicity in this coordinate
Quantum Mechanics from Periodic Dynamics: the bosonic case
Dolce, Donatello [Johannes-Gutenberg Universitaet, D-55099 Mainz (Germany)
2010-05-04
Enforcing the periodicity hypothesis of the 'old' formulation of Quantum Mechanics we show the possibility for a new scenario where Special Relativity and Quantum Mechanics are unified in a deterministic field theory. A novel interpretation of the AdS/CFT conjecture is discussed.
In Defense of a Heuristic Interpretation of Quantum Mechanics
ERIC Educational Resources Information Center
Healy, Eamonn F.
2010-01-01
Although the presentation of quantum mechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantum mechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift…
Categorization of Quantum Mechanics Problems by Professors and Students
ERIC Educational Resources Information Center
Lin, Shih-Yin; Singh, Chandralekha
2010-01-01
We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…
Developing and Evaluating Animations for Teaching Quantum Mechanics Concepts
ERIC Educational Resources Information Center
Kohnle, Antje; Douglass, Margaret; Edwards, Tom J.; Gillies, Alastair D.; Hooley, Christopher A.; Sinclair, Bruce D.
2010-01-01
In this paper, we describe animations and animated visualizations for introductory and intermediate-level quantum mechanics instruction developed at the University of St Andrews. The animations aim to help students build mental representations of quantum mechanics concepts. They focus on known areas of student difficulty and misconceptions by…
Environment-Induced Decoherence in Noncommutative Quantum Mechanics
Joao Nuno Prata; Nuno Costa Dias
2006-12-02
We address the question of the appearence of ordinary quantum mechanics in the context of noncommutative quantum mechanics. We obtain the noncommutative extension of the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators. We consider the particular case of an Ohmic regime.
Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems
ERIC Educational Resources Information Center
Ozcan, Ozgur; Didis, Nilufer; Tasar, Mehmet Fatih
2009-01-01
In this study, students' conceptual difficulties about some basic concepts in quantum mechanics like one-dimensional potential well problems and probability density of tunneling particles were identified. For this aim, a multiple choice instrument named Quantum Mechanics Conceptual Test has been developed by one of the researchers of this study…
Quantum mechanical retrocausation? Call for nonlocal causal models!
Antoine Suarez
1998-02-12
A new possible version of multisimultaneous causality is proposed, and real experiments allowing us to decide between this view and quantum mechanical retrocausation are further discussed. The interest of testing quantum mechanics against as many nonlocal causal models as possible is stressed.
Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation
NASA Astrophysics Data System (ADS)
Polyak, Iakov; Benighaus, Tobias; Boulanger, Eliot; Thiel, Walter
2013-08-01
The dual Hamiltonian free energy perturbation (DH-FEP) method is designed for accurate and efficient evaluation of the free energy profile of chemical reactions in quantum mechanical/molecular mechanical (QM/MM) calculations. In contrast to existing QM/MM FEP variants, the QM region is not kept frozen during sampling, but all degrees of freedom except for the reaction coordinate are sampled. In the DH-FEP scheme, the sampling is done by semiempirical QM/MM molecular dynamics (MD), while the perturbation energy differences are evaluated from high-level QM/MM single-point calculations at regular intervals, skipping a pre-defined number of MD sampling steps. After validating our method using an analytic model potential with an exactly known solution, we report a QM/MM DH-FEP study of the enzymatic reaction catalyzed by chorismate mutase. We suggest guidelines for QM/MM DH-FEP calculations and default values for the required computational parameters. In the case of chorismate mutase, we apply the DH-FEP approach in combination with a single one-dimensional reaction coordinate and with a two-dimensional collective coordinate (two individual distances), with superior results for the latter choice.
Sheaf Logic, Quantum Set Theory and the Interpretation of Quantum Mechanics
J. Benavides
2012-02-07
Based on the Sheaf Logic approach to set theoretic forcing, a hierarchy of Quantum Variable Sets is constructed which generalizes and simplifies the analogous construction developed by Takeuti on boolean valued models of set theory. Over this model two alternative proofs of Takeuti's correspondence, between self adjoint operators and the real numbers of the model, are given. This approach results to be more constructive showing a direct relation with the Gelfand representation theorem, revealing also the importance of these results with respect to the interpretation of Quantum Mechanics in close connection with the Deutsch-Everett multiversal interpretation. Finally, it is shown how in this context the notion of genericity and the corresponding generic model theorem can help to explain the emergence of classicality also in connection with the Deutsch- Everett perspective.