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1

Noncommutative classical and quantum mechanics for quadratic Lagrangians (Hamiltonians)  

Microsoft Academic Search

Classical and quantum mechanics based on an extended Heisenberg algebra with additional canonical commutation relations for\\u000a position and momentum coordinates are considered. In this approach additional noncommutativity is removed from the algebra\\u000a by a linear transformation of coordinates and transferred to the Hamiltonian (Lagrangian). This linear transformation does\\u000a not change the quadratic form of the Hamiltonian (Lagrangian), and Feynman’s path

Branko Dragovich; Zoran Raki?

2009-01-01

2

Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation  

NASA Astrophysics Data System (ADS)

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

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

2013-08-01

3

Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians  

NASA Astrophysics Data System (ADS)

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

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

2013-10-01

4

Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.  

PubMed

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

Chou, Chia-Chun; Kouri, Donald J

2013-04-15

5

The Interpretation of Quantum-Mechanical Models with Non-Hermitian Hamiltonians and Real Spectra  

Microsoft Academic Search

We study the quantum-mechanical interpretation of models with non-Hermitian Hamiltonians and real spectra. We set up a general framework for the analysis of such systems in terms of Hermitian Hamiltonians defined in the usual Hilbert space $L_2(-\\\\infty,\\\\infty)$. Special emphasis is put on the correct definition of the algebra of physical observables. Within this scheme we consider various examples, including the

R. Kretschmer; L. Szymanowski

2001-01-01

6

On the Semi-Classical Expansion in Quantum Mechanics for Arbitrary Hamiltonians.  

National Technical Information Service (NTIS)

The purpose of this paper is to extend to a very wide class of Hamiltonians the range of validity of a well-known and oft-used expression for the semi-classical (WKB) approximation to the quantum-mechanical propagator K((q sub b),(t sub b);(q sub a),(t su...

M. M. Mizrahi

1976-01-01

7

Revealing quantum-control mechanisms through Hamiltonian encoding in different representations  

SciTech Connect

The Hamiltonian encoding is a means for revealing the mechanism of controlled quantum dynamics. In this context, the mechanism is defined by the dominant quantum pathways starting from the initial state and proceeding through a set of intermediate states to end at the final state. The nature and interpretation of the mechanism depends on the choice of the states to represent the dynamics. Alternative representations may provide distinct insights into the system mechanism, and representations producing fewer pathways are especially interesting. In addition, a suitable choice of representation may highlight the role of certain couplings in a system that would normally be masked by other, higher magnitude couplings. A simple three-level system is chosen for illustration, where different values for the Rabi frequencies lead to mechanistic analyses that are best described in terms of particular representations. As an examlple, the role of the nonadiabatic terms in stimulated Raman adiabatic passage dynamics is analyzed through the Hamiltonian encoding.

Mitra, Abhra; Sola, Ignacio R.; Rabitz, Herschel [Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544 (United States); Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States)

2003-04-01

8

Local Hamiltonians in Quantum Computation  

Microsoft Academic Search

In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian. I show that to succeed using AQC, the Hamiltonian involved must have local structure, which leads to a result about eigenvalue gaps from information theory. I also improve results about simulating

Daniel Nagaj

2008-01-01

9

Quantum Mechanical Path Integrals with Wiener Measures for All Polynomial Hamiltonians.  

National Technical Information Service (NTIS)

We construct arbitrary matrix elements of the quantum evolution operator for a wide class of self-adjoint canonical Hamiltonians, including those which are polynomial in the Heisenberg operators, as the limit of well-defined path integrals involving Wiene...

J. R. Klauder I. Daubechies

1985-01-01

10

Salpeter equation and probability current in the relativistic Hamiltonian quantum mechanics  

SciTech Connect

The probability current for a quantum spinless relativistic particle is introduced based on the Hamiltonian dynamics approach utilizing the Salpeter equation as an alternative for the Klein-Gordon equation. The correctness of the presented formalism is illustrated by examples of exact solutions to the Salpeter equation including the new ones introduced in this work.

Kowalski, K.; Rembielinski, J. [Department of Theoretical Physics, University of Lodz, ul. Pomorska 149/153, PL-90-236 Lodz (Poland)

2011-07-15

11

Multidimensional supersymmetric quantum mechanics: a scalar Hamiltonian approach to excited states by the imaginary time propagation method.  

PubMed

Supersymmetric quantum mechanics (SUSY-QM) is shown to provide a novel approach to the construction of the initial states for the imaginary time propagation method to determine the first and second excited state energies and wave functions for a two-dimensional system. In addition, we show that all calculations are carried out in sector one and none are performed with the tensor sector two Hamiltonian. Through our tensorial approach to multidimensional supersymmetric quantum mechanics, we utilize the correspondence between the eigenstates of the sector one and two Hamiltonians to construct appropriate initial sector one states from sector two states for the imaginary time propagation method. The imaginary time version of the time-dependent Schrödinger equation is integrated to obtain the first and second excited state energies and wave functions using the split operator method for a two-dimensional anharmonic oscillator system and a two-dimensional double well potential. The computational results indicate that we can obtain the first two excited state energies and wave functions even when a quantum system does not exhibit any symmetry. Moreover, instead of dealing with the increasing computational complexity resulting from computations in the tensor sector two Hamiltonian, this study presents a new supersymmetric approach to calculations of accurate excited state energies and wave functions by directly using the scalar sector one Hamiltonian. PMID:23531036

Chou, Chia-Chun; Kouri, Donald J

2013-04-15

12

A polarizable force-field model for quantum-mechanical-molecular-mechanical Hamiltonian using expansion of point charges into orbitals  

NASA Astrophysics Data System (ADS)

We present an ab initio polarizable representation of classical molecular mechanics (MM) atoms by employing an angular momentum-based expansion scheme of the point charges into partial wave orbitals. The charge density represented by these orbitals can be fully polarized, and for hybrid quantum-mechanical-molecular-mechanical (QM/MM) calculations, mutual polarization within the QM/MM Hamiltonian can be obtained. We present the mathematical formulation and the analytical expressions for the energy and forces pertaining to the method. We further develop a variational scheme to appropriately determine the expansion coefficients and then validate the method by considering polarizations of ions by the QM system employing the hybrid GROMACS-CPMD QM/MM program. Finally, we present a simpler prescription for adding isotropic polarizability to MM atoms in a QM/MM simulation. Employing this simpler scheme, we present QM/MM energy minimization results for the classic case of a water dimer and a hydrogen sulfide dimer. Also, we present single-point QM/MM results with and without the polarization to study the change in the ionization potential of tetrahydrobiopterin (BH4) in water and the change in the interaction energy of solvated BH4 (described by MM) with the P450 heme described by QM. The model can be employed for the development of an extensive classical polarizable force-field.

Biswas, P. K.; Gogonea, Valentin

2008-10-01

13

A polarizable force-field model for quantum-mechanical-molecular-mechanical Hamiltonian using expansion of point charges into orbitals.  

PubMed

We present an ab initio polarizable representation of classical molecular mechanics (MM) atoms by employing an angular momentum-based expansion scheme of the point charges into partial wave orbitals. The charge density represented by these orbitals can be fully polarized, and for hybrid quantum-mechanical-molecular-mechanical (QM/MM) calculations, mutual polarization within the QM/MM Hamiltonian can be obtained. We present the mathematical formulation and the analytical expressions for the energy and forces pertaining to the method. We further develop a variational scheme to appropriately determine the expansion coefficients and then validate the method by considering polarizations of ions by the QM system employing the hybrid GROMACS-CPMD QM/MM program. Finally, we present a simpler prescription for adding isotropic polarizability to MM atoms in a QM/MM simulation. Employing this simpler scheme, we present QM/MM energy minimization results for the classic case of a water dimer and a hydrogen sulfide dimer. Also, we present single-point QM/MM results with and without the polarization to study the change in the ionization potential of tetrahydrobiopterin (BH(4)) in water and the change in the interaction energy of solvated BH(4) (described by MM) with the P(450) heme described by QM. The model can be employed for the development of an extensive classical polarizable force-field. PMID:19045177

Biswas, P K; Gogonea, Valentin

2008-10-21

14

Five-dimensional Hamiltonian-Jacobi approach to relativistic quantum mechanics  

SciTech Connect

A novel theory is outlined for describing the dynamics of relativistic electrons and positrons. By introducing the Lorentz-invariant universal time as a fifth independent variable, the Hamilton-Jacobi formalism of classical mechanics is extended from three to four spatial dimensions. This approach allows one to incorporate gravitation and spin interactions in the extended five-dimensional Lagrangian in a covariant form. The universal time has the function of a hidden Bell parameter. By employing the method of variation with respect to the four coordinates of the particle and the components of the electromagnetic field, the path equation and the electromagnetic field produced by the charge and the spin of the moving particle are derived. In addition the covariant equations for the dynamics of the components of the spin tensor are obtained. These equations can be transformed to the familiar BMT equation in the case of homogeneous electromagnetic fields. The quantization of the five-dimensional Hamilton-Jacobi equation yields a five-dimensional spinor wave equation, which degenerates to the Dirac equation in the stationary case if we neglect gravitation. The quantity which corresponds to the probability density of standard quantum mechanics is the four-dimensional mass density which has a real physical meaning. By means of the Green method the wave equation is transformed into an integral equation enabling a covariant relativistic path integral formulation. Using this approach a very accurate approximation for the four-dimensional propagator is derived. The proposed formalism makes Dirac's hole theory obsolete and can readily be extended to many particles.

Rose, Harald

2003-12-11

15

Quantum entangling power of adiabatically connected Hamiltonians  

SciTech Connect

The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bipartite quantum state space. When the different Hamiltonians in the family fall in the same adiabatic class, one can manipulate entanglement by moving through energy eigenstates corresponding to different values of the control parameters. We introduce an associated notion of adiabatic entangling power. This novel measure is analyzed for general dxd quantum systems, and specific two-qubit examples are studied.

Hamma, Alioscia [Institute for Scientific Interchange (ISI), Villa Gualino, Viale Settimio Severo 65, I-10133 Torino (Italy); Dipartimento di Scienze Fisiche, Universita Federico II , Via Cintia ed. G, 80126 Naples (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli, Via Cintia ed. G, 80126 Naples (Italy); Zanardi, Paolo [Institute for Scientific Interchange (ISI), Villa Gualino, Viale Settimio Severo 65, I-10133 Torino (Italy); Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

2004-06-01

16

Quantum Deformations of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Based on a deformation of the quantum mechanical phase space we study q-deformations of quantum mechanics for qk=1 and 0quantum mechanics for qk=1 is given and the dynamics for the free Hamiltonian is studied. For 0quantum mechanics and the cases of the free Hamiltonian and the one with a x2-potential are solved in terms of basic hypergeometric functions.

Ubriaco, Marcelo R.

17

Quantum Dynamics with AN Ensemble of Hamiltonians  

NASA Astrophysics Data System (ADS)

We review recent progress in the nonequilibrium dynamics of thermally isolated many-body quantum systems, evolving with an ensemble of Hamiltonians as opposed to deterministic evolution with a single time-dependent Hamiltonian. Such questions arise in (i) quantum dynamics of disordered systems, where different realizations of disorder give rise to an ensemble of real-time quantum evolutions, (ii) quantum evolution with noisy Hamiltonians (temporal disorder), which leads to stochastic Schrödinger equations, and, (iii) in the broader context of quantum optimal control, where one needs to analyze an ensemble of permissible protocols in order to find one that optimizes a given figure of merit. The theme of ensemble quantum evolution appears in several emerging new directions in noneqilibrium quantum dynamics of thermally isolated many-body systems, which include many-body localization, noise-driven systems, and shortcuts to adiabaticity.

Rahmani, Armin

2013-10-01

18

Hamiltonian quantum dynamics with separability constraints  

SciTech Connect

Schroedinger equation on a Hilbert space H, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space PH. Separable states of a bipartite quantum system form a special submanifold of PH. We analyze the Hamiltonian dynamics that corresponds to the quantum system constrained on the manifold of separable states, using as an important example the system of two interacting qubits. The constraints introduce nonlinearities which render the dynamics nontrivial. We show that the qualitative properties of the constrained dynamics clearly manifest the symmetry of the qubits system. In particular, if the quantum Hamilton's operator has not enough symmetry, the constrained dynamics is nonintegrable, and displays the typical features of a Hamiltonian dynamical system with mixed phase space. Possible physical realizations of the separability constraints are discussed.

Buric, Nikola [Institute of Physics, P.O. Box 57, 11001 Belgrade (Serbia)], E-mail: buric@phy.bg.ac.yu

2008-01-15

19

Lagrangian and Hamiltonian formalism on a quantum plane  

Microsoft Academic Search

We examine the problem of defining Lagrangian and Hamiltonian mechanics for a particle moving on a quantum plane $Q_{q,p}$. For Lagrangian mechanics, we first define a tangent quantum plane $TQ_{q,p}$ spanned by noncommuting particle coordinates and velocities. Using techniques similar to those of Wess and Zumino, we construct two different differential calculi on $TQ_{q,p}$. These two differential calculi can in

M. Lukin; A. Stern; I. Yakushin

1993-01-01

20

Hamiltonian constraint of loop quantum cosmology  

SciTech Connect

In this paper we construct the Hamiltonian constraint operator of loop quantum cosmology using holonomies defined for arbitrary irreducible SU(2) representations labeled by spin J. We show that modifications to the effective semiclassical equations of motion arise both in the gravitational part of the constraint as well as matter terms. The modifications are important for phenomenological investigations of the cosmological imprints of loop quantum cosmology. We discuss the implications for the early universe evolution.

Vandersloot, Kevin [Institute for Gravitational Physics and Geometry, Pennsylvania State University, 104 Davey Lab, University Park, Pennsylvania 16802 (United States)

2005-05-15

21

Non-Hermitian quantum Hamiltonians with PT symmetry  

SciTech Connect

We formulate quantum mechanics for non-Hermitian Hamiltonians that are invariant under PT, where P is the parity and T denotes time reversal, for the case that time-reversal symmetry is odd (T{sup 2}=-1), generalizing prior work for the even case (T{sup 2}=1). We discover an analog of Kramer's theorem for PT quantum mechanics, present a prototypical example of a PT quantum system with odd time reversal, and discuss potential applications of the formalism.

Jones-Smith, Katherine; Mathur, Harsh [Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106-7079 (United States)

2010-10-15

22

Quantum Hamiltonian reduction and WB algebra  

SciTech Connect

In this paper, the authors study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, the authors find that the coset model (B[sub n][sup (1)])k [times] (B[sub n][sup (1)])1/(B[sub n][sup (1)])[sub k = 1] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(O,n)[sup (1)]. To show this the authors also construct the Feigin-Fuchs representation of affine Lie superalgebras.

Ito, K. (Niels Bohr Inst., Copenhagen (Denmark))

1992-08-10

23

Development of a Semi-empirical Hamiltonian for Phosphorus for Quantum Mechanics Based Simulations of Phosphorous-based Nanostructures  

NASA Astrophysics Data System (ADS)

We have developed a parameterized semi-empirical Hamiltonian for phosphorous for simulation studies of phosphorous-based nanostructures including phosphorous-doped silicon nanowires.This Hamiltonian models the environment-dependent electron-ion and ion-ion interactions and electron-electron correlations, by capturing the salient features of ab initio Hamiltonians/ab initio methods, (e.g., electron screening and charge self-consistency).Such a semi-empirical Hamiltonian has been shown to be successful in predicting the properties of intermediate-sized silicon, boron, and carbon clusters and extended structures of boron and silicon [1-4]. We optimized the parameters of our Hamiltonian for phosphorous by fitting the properties of bulk (black phosphorous) and small clusters (P2 to P10) as obtained by our method to ab initio calculations. It is expected that such a Hamiltonian will have the predictive power to enable the study of larger phosphorous based nanostructures that are not possible via ab initio studies. [4pt] [1] C. Leahy, et al, Phys. Rev. B 74,155408 (2006). [2 ]P. Tandy, et al, Bulletin of the APS,2009 APS March Meeting Vol. 54, Num.1, Sess. D26, [3] Ming Yu, et al, J. Chem. Phys. 130,184708 (2009). [4] Ming Yu, S.Y. Wu, and C.S. Jayanthi, Physica E 42, 1 (2009).

Tandy, Paul; Leahy, Christopher; Yu, Ming; Jayanthi, C. S.; Wu, S. Y.

2011-03-01

24

Alternative Hamiltonian description for quantum systems  

SciTech Connect

The existence of time-invariant Kahler structures is analyzed in both Classical and Quantum Mechanics. In Quantum Mechanics, a family of such Kahler structures is found, in the finite-dimensional case it is proven that this family is complete.

Dubrovin, B.A. (Dept. Mech.Math., Moscow State Univ., Leninskiye Gory 119899, Moscow (SU)); Marno, G.; Simoni, A. (Dipartimento di Scienze Fisiche and INFN Naples Section, Mostra d'Oltremare pad.19, 80125 Napoli (IT))

1990-06-20

25

Global exploration and inversion of quantum Hamiltonian Observable relationships  

Microsoft Academic Search

High-precision, quantitative knowledge of quantum Hamiltonians is a crucial prerequisite for accurately predicting and controlling molecular behavior. Understanding the physical connection between the quantum equations of motion and the physical observables measured in the laboratory is fundamental to bridging theory and experiment. However, Hamiltonian-Observable relationships are generally complex and nonlinear, making them difficult to represent, explore, and invert. A functional

John Michael Geremia

2001-01-01

26

The Hamiltonian structure of equations for quantum averages in systems with matrix Hamiltonians  

Microsoft Academic Search

An infinite system of ordinary differential equations for¯x, ¯p, and for averages of a set of operators is derived for quantum-mechanical problems with a (K×K) matrix HamiltonianH(x,p), x \\u000aN\\u000a. The set of operators is chosen to be basis in the space Mat\\u000aK\\u000aU(W\\u000aN), whereU(W\\u000aN) is the universal enveloping algebra of the Heisenberg-Weyl algebraW\\u000aN, generated by

V. V. Belov; M. F. Kondrat'eva

1995-01-01

27

PREFACE: 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics  

Microsoft Academic Search

Attempts to understand the quantum mechanics of non-Hermitian Hamiltonian systems can be traced back to the early days, one example being Heisenberg's endeavour to formulate a consistent model involving an indefinite metric. Over the years non-Hermitian Hamiltonians whose spectra were believed to be real have appeared from time to time in the literature, for instance in the study of strong

Andreas Fring; Hugh Jones; Miloslav Znojil

2008-01-01

28

Hamiltonian models of quantum computers which evolve quantum ballistically  

SciTech Connect

Quantum computation is a subject of much recent interest. In much of the work in the literature quantum computers are described as built up from a sequence of unitary operators where each unitary operator carries out a stage of the overall quantum computation. The sequence and connection of the different unitary operators is provided presumably by some external agent which governs the overall process. However there is no description of a an overall Hamiltonian needed to give the actual quantum dynamics of the computation process. In this talk, earlier work by the author is followed in that simple, time independent Hamiltonians are used to describe quantum computation, and the Schroedinger evolution of the computation system is considered to be quantum ballistic. However, the definition of quantum ballistic evolution used here is more general than that used in the earlier work. In particular, the requirement that the step operator {ital T} associated with a process be a partial isometry, used in, is relaxed to require that {ital T} be a contraction operator. (An operator {ital T} is a partial isometry if the self-adjoint operators T{sup {dagger}}T and TT{sup {dagger}} are also projection operators.{ital T} is a contraction operator if {vert_bar}{vert_bar} {ital T} {vert_bar}{vert_bar} {<=} 1.) The main purpose of this talk is to investigate some consequences for quantum computation under this weaker requirement. It will be seen that system motion along discrete paths in a basis still occurs. However the motion occurs in ,the presence of potentials whose height and distribution along the path depends on {ital T} and the path states.

Benioff, P.

1996-12-31

29

Faster than Hermitian quantum mechanics.  

PubMed

Given an initial quantum state |psi(I)> and a final quantum state |psi(F)>, there exist Hamiltonians H under which |psi(I)> evolves into |psi(F)>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time tau? For Hermitian Hamiltonians tau has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, tau can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from |psi(I)> to |psi(F)> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing. PMID:17358747

Bender, Carl M; Brody, Dorje C; Jones, Hugh F; Meister, Bernhard K

2007-01-24

30

Estimation of many-body quantum Hamiltonians via compressive sensing  

SciTech Connect

We develop an efficient and robust approach for quantum measurement of nearly sparse many-body quantum Hamiltonians based on the method of compressive sensing. This work demonstrates that with only O(sln(d)) experimental configurations, consisting of random local preparations and measurements, one can estimate the Hamiltonian of a d-dimensional system, provided that the Hamiltonian is nearly s sparse in a known basis. The classical postprocessing is a convex optimization problem on the total Hilbert space which is generally not scalable. We numerically simulate the performance of this algorithm for three- and four-body interactions in spin-coupled quantum dots and atoms in optical lattices. Furthermore, we apply the algorithm to characterize Hamiltonian fine structure and unknown system-bath interactions.

Shabani, A.; Rabitz, H. [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States); Mohseni, M. [Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Lloyd, S. [Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Kosut, R. L. [SC Solutions, Sunnyvale, California 94085 (United States)

2011-07-15

31

Noncommutative quantum mechanics  

NASA Astrophysics Data System (ADS)

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

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

2001-09-01

32

Generation of quantum logic operations from physical Hamiltonians  

Microsoft Academic Search

We provide a systematic analysis of the physical generation of single- and two-qubit quantum operations from Hamiltonians available in various quantum systems for scalable quantum information processing. We show that generation of single-qubit operations can be transformed into a steering problem on the Bloch sphere, which represents all Rz -equivalence classes of single-qubit operations, whereas the two-qubit problem can be

Jun Zhang; K. Birgitta Whaley

2005-01-01

33

Quantum Mechanics  

NSDL National Science Digital Library

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

Michielsen, Kristel; De Raedt, Hans

2004-03-04

34

PT quantum mechanics - Recent results  

NASA Astrophysics Data System (ADS)

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 = p2+ix3 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 = p2+ix3 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 = p2-x4, 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?4 quantum field theory appears to be inconsistent because the critical value of g is negative, this limit is in fact not inconsistent because the critical theory is PT symmetric.

Bender, Carl M.

2012-09-01

35

PT quantum mechanics - Recent results  

SciTech Connect

Most quantum physicists believe that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under matrix transposition and complex conjugation) to be sure that the energy eigenvalues are real and that time evolution is unitary. However, the non-Dirac-hermitian Hamiltonian H p{sup 2}+ix{sup 3} has a real positive discrete spectrum and generates unitary time evolution and defines a fully consistent and physical quantum theory. Evidently, Dirac Hermiticity is too restrictive. While H = p{sup 2}+ix{sup 3} is not Dirac Hermitian, it is PT symmetric (invariant under combined space reflection P and time reversal T). Another PT-symmetric Hamiltonian whose energy levels are real, positive and discrete is H = p{sup 2}-x{sup 4}, which contains an upside-down potential. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics and quantum field theory are extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past two years some of these properties have been verified in laboratory experiments. Here, we first discuss PT-symmetric Hamiltonians at a simple intuitive level and explain why the energy levels of such Hamiltonians may be real, positive, and discrete. Second, we describe a recent experiment in which the PT phase transition was observed. Third, we briefly mention that PT-symmetric theories can be useful at a fundamental level. While the double-scaling limit of an O(N)-symmetric g{phi}{sup 4} quantum field theory appears to be inconsistent because the critical value of g is negative, this limit is in fact not inconsistent because the critical theory is PT symmetric.

Bender, Carl M. [Physics Department, Washington University, St. Louis, MO 63130 (United States)

2012-09-26

36

Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Quantum Mechanics aims to teach those parts of the subject which every physicist should know. The object is to display the inherent structure of quantum mechanics, concentrating on general principles and on methods of wide applicability without taking them to their full generality. This book will equip students to follow quantum-mechanical arguments in books and scientific papers, and to cope with simple cases. To bring the subject to life, the theory is applied to the all-important field of atomic physics. No prior knowledge of quantum mechanics is assumed. However, it would help most readers to have met some elementary wave mechanics before. Primarily written for students, it should also be of interest to experimental research workers who require a good grasp of quantum mechanics without the full formalism needed by the professional theorist. Quantum Mechanics features: A flow diagram allowing topics to be studied in different orders or omitted altogether. Optional "starred" and highlighted sections containing more advanced and specialized material for the more ambitious reader. Sets of problems at the end of each chapter to help student understanding. Hints and solutions to the problems are given at the end of the book.

Mandl, F.

1992-07-01

37

The detectability lemma and its applications to quantum Hamiltonian complexity  

NASA Astrophysics Data System (ADS)

Quantum Hamiltonian complexity, an emerging area at the intersection of condensed matter physics and quantum complexity theory, studies the properties of local Hamiltonians and their ground states. In this paper we focus on a seemingly specialized technical tool, the detectability lemma (DL), introduced in the context of the quantum PCP challenge (Aharonov et al 2009 arXiv:0811.3412), which is a major open question in quantum Hamiltonian complexity. We show that a reformulated version of the lemma is a versatile tool that can be used in place of the celebrated Lieb-Robinson (LR) bound to prove several important results in quantum Hamiltonian complexity. The resulting proofs are much simpler, more combinatorial and provide a plausible path toward tackling some fundamental open questions in Hamiltonian complexity. We provide an alternative simpler proof of the DL that removes a key restriction in the original statement (Aharonov et al 2009 arXiv:0811.3412), making it more suitable for the broader context of quantum Hamiltonian complexity. Specifically, we first use the DL to provide a one-page proof of Hastings' result that the correlations in the ground states of gapped Hamiltonians decay exponentially with distance (Hastings 2004 Phys. Rev. B 69 104431). We then apply the DL to derive a simpler and more intuitive proof of Hastings' seminal one-dimensional (1D) area law (Hastings 2007 J. Stat. Mech. (2007) P8024) (both these proofs are restricted to frustration-free systems). Proving the area law for two and higher dimensions is one of the most important open questions in the field of Hamiltonian complexity, and the combinatorial nature of the DL-based proof holds out hope for a possible generalization. Indeed, soon after the first publication of the methods presented here, they were applied to derive exponential improvements to Hastings' result (Arad et al 2011, Aharonov et al 2011) in the case of frustration-free 1D systems. Finally, we also provide a more general explanation of how the DL can be used to replace the LR bound.

Aharonov, Dorit; Arad, Itai; Vazirani, Umesh; Landau, Zeph

2011-11-01

38

Supersymmetry in quantum mechanics  

SciTech Connect

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

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

2004-12-23

39

Quantum tunnelling effect for the inverted Caldirola-Kanai Hamiltonian  

Microsoft Academic Search

In order to study the behaviour of the inverted Caldirola-Kanai Hamiltonian in the quantum tunnelling effect, the authors consider a wavepacket as the initial state and they calculate exactly the probability density. They also obtain the transmission and reflection probability, the expectation value of the particle's energy and the sojourn time which appears to be an increasing function of the

S. Baskoutas; A. Jannussis

1992-01-01

40

N=4 supersymmetric multidimensional quantum mechanics, partial SUSY breaking, and superconformal quantum mechanics  

Microsoft Academic Search

The multidimensional N=4 supersymmetric (SUSY) quantum mechanics (QM) is constructed using the superfield approach. As a result, the component form of the classical and quantum Lagrangian and Hamiltonian is obtained. In the SUSY QM considered, both classical and quantum N=4 algebras include central charges, and this opens various possibilities for partial supersymmetry breaking. It is shown that quantum-mechanical models with

E. E. Donets; A. Pashnev; J. Juan Rosales; M. M. Tsulaia

2000-01-01

41

Quantum and classical descriptions of position and phase-space densities of a model Hamiltonian  

Microsoft Academic Search

Excited states of a model Hamiltonian with strongly coupled modes are investigated. Comparisons are made between the classical Poincare´ surfaces of section and the Husimi function, which is a quantum mechanical phase-space density function. It is found that for the majority of states the Husimi function exhibits local maxima which resemble in shape and location the invariant tori of Poincare´

James L. Anchell; Edmonds Hamiltonian

1990-01-01

42

Phase-Space Propagators for Quantum Quadratic Hamiltonians in One and Two Dimensions  

NASA Astrophysics Data System (ADS)

After a summary of the fundamental concepts of quantum mechanics in phase space we apply the Moshinsky-Winternitz classification of the time-independent quadratic Hamiltonians in one and two dimensions to give the explicit form of the phase-space propagators, and make some comments on their spectra.

Nieto, L. M.; Noriega, J. M.

1988-09-01

43

Quantumness beyond quantum mechanics  

NASA Astrophysics Data System (ADS)

Bohmian mechanics allows us to understand quantum systems in the light of other quantum traits than the well-known ones (coherence, diffraction, interference, tunnelling, discreteness, entanglement, etc.). Here the discussion focusses precisely on two of these interesting aspects, which arise when quantum mechanics is thought within this theoretical framework: the non-crossing property, which allows for distinguishability without erasing interference patterns, and the possibility to define quantum probability tubes, along which the probability remains constant all the way. Furthermore, taking into account this hydrodynamic-like description as a link, it is also shown how this knowledge (concepts and ideas) can be straightforwardly transferred to other fields of physics (for example, the transmission of light along waveguides).

Sanz, Ángel S.

2012-05-01

44

Supersymmetric q-deformed quantum mechanics  

SciTech Connect

A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.

Traikia, M. H.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)

2012-06-27

45

Path integral and effective Hamiltonian in loop quantum cosmology  

NASA Astrophysics Data System (ADS)

We study the path integral formulation of Friedmann universe filled with a massless scalar field in loop quantum cosmology. All the isotropic models of k=0,+1,-1 are considered. To construct the path integrals in the timeless framework, a multiple group-averaging approach is proposed. Meanwhile, since the transition amplitude in the deparameterized framework can be expressed in terms of group-averaging, the path integrals can be formulated for both deparameterized and timeless frameworks. Their relation is clarified. It turns out that the effective Hamiltonian derived from the path integral in deparameterized framework is equivalent to the effective Hamiltonian constraint derived from the path integral in timeless framework, since they lead to same equations of motion. Moreover, the effective Hamiltonian constraints of above models derived in canonical theory are confirmed by the path integral formulation.

Qin, Li; Huang, Haiyun; Ma, Yongge

2013-06-01

46

Supersymmetric Quantum Mechanics  

SciTech Connect

Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulae concerning SUSY QM of first second order for one-dimensional arbitrary systems, we will illustrate the method through the trigonometric Poeschl-Teller potentials. Some intrinsically related subjects, as the algebraic structure inherited by the new Hamiltonians and the corresponding coherent states will be analyzed. The technique will be as well implemented for periodic potentials, for which the corresponding spectrum is composed of allowed bands separated by energy gaps.

David, J.; Fernandez, C. [Depto. de Fisica, Cinvestav, A.P. 14-740, 07000 Mexico D.F. (Mexico)

2010-10-11

47

Phase Transitions in Disordered Quantum Hamiltonians  

NASA Astrophysics Data System (ADS)

The problem of the interplay between disorder and interactions in quantum systems is challenging and has a long history. Disorder can, by itself, cause localization and the vanishing of the conductivity, the Anderson transition. At appropriate densities, interactions can drive insulating states, the Mott transition, as well as ordered magnetic phases. In this talk I will describe the application of Quantum Monte Carlo techniques to the fermion Hubbard model, including calculations of the conductivity and density of states at the superconductor--insulator phase transition in the attractive model, and the effect of randomness on the Mott and magnetic phase transitions in the repulsive model.(N. Trivedi, R.T. Scalettar, and M. Randeria, Phys. Rev. B54), 3756 (1996); C. Huscroft and R.T. Scalettar, Phys. Rev. B55, 1185 (1997); M. Ulmke and R.T. Scalettar, Phys. Rev. B55, 4149 (1997); M. Ulmke, P. J. H. Denteneer, R. T. Scalettar, and G. T. Zimanyi, preprint.

Scalettar, Richard T.

1998-03-01

48

Quantum finance Hamiltonian for coupon bond European and barrier options  

NASA Astrophysics Data System (ADS)

Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier option for a financial instrument is “knocked out” (terminated with zero value) if the price of the underlying instrument exceeds or falls below preset limits; the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates’ Hamiltonian. The price of the European coupon bond option and the zero coupon bond barrier option are calculated. It is shown that, is general, the constraint function for a coupon bond barrier option can—to a good approximation—be linearized. A calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option, which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function.

Baaquie, Belal E.

2008-03-01

49

Quantum integrals of motion for variable quadratic Hamiltonians  

SciTech Connect

We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

Cordero-Soto, Ricardo, E-mail: ricardojavier81@gmail.co [Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804 (United States); Suazo, Erwin, E-mail: erwin.suazo@upr.ed [Department of Mathematical Sciences, University of Puerto Rico, Mayaquez, call box 9000, PR 00681-9000 (Puerto Rico); Suslov, Sergei K., E-mail: sks@asu.ed [School of Mathematical and Statistical Sciences and Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804 (United States)

2010-09-15

50

Interest rates in quantum finance: The Wilson expansion and Hamiltonian  

NASA Astrophysics Data System (ADS)

Interest rate instruments form a major component of the capital markets. The Libor market model (LMM) is the finance industry standard interest rate model for both Libor and Euribor, which are the most important interest rates. The quantum finance formulation of the Libor market model is given in this paper and leads to a key generalization: all the Libors, for different future times, are imperfectly correlated. A key difference between a forward interest rate model and the LMM lies in the fact that the LMM is calibrated directly from the observed market interest rates. The short distance Wilson expansion [Phys. Rev. 179, 1499 (1969)] of a Gaussian quantum field is shown to provide the generalization of Ito calculus; in particular, the Wilson expansion of the Gaussian quantum field A(t,x) driving the Libors yields a derivation of the Libor drift term that incorporates imperfect correlations of the different Libors. The logarithm of Libor ?(t,x) is defined and provides an efficient and compact representation of the quantum field theory of the Libor market model. The Lagrangian and Feynman path integrals of the Libor market model of interest rates are obtained, as well as a derivation given by its Hamiltonian. The Hamiltonian formulation of the martingale condition provides an exact solution for the nonlinear drift of the Libor market model. The quantum finance formulation of the LMM is shown to reduce to the industry standard Bruce-Gatarek-Musiela-Jamshidian model when the forward interest rates are taken to be exactly correlated.

Baaquie, Belal E.

2009-10-01

51

Generation of quantum logic operations from physical Hamiltonians  

SciTech Connect

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

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

2005-05-15

52

Alternative decohering histories in quantum mechanics.  

NASA Astrophysics Data System (ADS)

The authors continue their efforts to understand, within the framework of the quantum mechanics of the universe as a whole, the quasi-classical domain of familiar experience as a feature emergent from the Hamiltonian of the elementary particles and the initial condition of the universe. Quantum mechanics assigns probabilities to exhaustive sets of alternative decoherent histories of the universe.

Gell-Mann, M.; Hartle, J. B.

53

Noncommutative Quantum Mechanics with Path Integral  

Microsoft Academic Search

We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment of the usual formalism. In particular, we found explicit connections between quadratic Hamiltonians and Lagrangians, in their commutative and noncommutative regimes. In the quantum case we give

Branko Dragovich; Zoran Rakic

2005-01-01

54

Path Integral Approach to Noncommutative Quantum Mechanics  

Microsoft Academic Search

We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the another one with usual commutative coordinates and momenta. We found connection between quadratic classical Hamiltonians, as well as Lagrangians, in their commutative and noncommutative

Branko Dragovich; Zoran Rakic

2004-01-01

55

Faster than Hermitian Quantum Mechanics  

SciTech Connect

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

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

2007-01-26

56

Hamiltonian models of quantum computers which evolve quantum ballistically  

Microsoft Academic Search

Quantum computation is a subject of much recent interest. In much of the work in the literature quantum computers are described as built up from a sequence of unitary operators where each unitary operator carries out a stage of the overall quantum computation. The sequence and connection of the different unitary operators is provided presumably by some external agent which

Benioff

1996-01-01

57

Emergent mechanics, quantum and un-quantum  

NASA Astrophysics Data System (ADS)

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

Ralston, John P.

2013-10-01

58

Quantum simulation via filtered Hamiltonian engineering: application to perfect quantum transport in spin networks.  

PubMed

We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a dynamical construction of a weighting function combined with a Bragg grating. As an example, we demonstrate how to generate the ideal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings starting from a large spin network, such as one naturally occurring in crystals, while decoupling all unwanted interactions. For realistic experimental parameters, our method can be used to drive almost perfect quantum information transport at room temperature. The Hamiltonian engineering method can be made more robust under decoherence and coupling disorder by a novel apodization scheme. Thus, the method is quite general and can be used to engineer the Hamiltonian of many complex spin lattices with different topologies and interactions. PMID:23767705

Ajoy, Ashok; Cappellaro, Paola

2013-05-29

59

quantum mechanics  

PubMed Central

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

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

2013-01-01

60

Quantum hamiltonian reduction and N = 2 coset models  

NASA Astrophysics Data System (ADS)

We study the quantum hamiltonian reduction of the affine Lie superalgebra A(n, n-1)(1) = sl(n + 1, n)(1) (n >=1), whose central charge is zero. After a BRST gauge fixing the model has a W algebra structure with N = 2 superconformal symmetry. We show that this model is the N = 2 coset model CPn = SU (n + 1)/SU (n) × U (1) constructed by Kazama and Suzuki. We also discuss a topological field theoretical aspect of the SL (n + 1, n) Wess-Zumino-Novikov-Witten model. Fellow of the Japan Society for the Promotion of Science.

Ito, Katsushi

1991-04-01

61

Interest rates in quantum finance: the Wilson expansion and Hamiltonian.  

PubMed

Interest rate instruments form a major component of the capital markets. The Libor market model (LMM) is the finance industry standard interest rate model for both Libor and Euribor, which are the most important interest rates. The quantum finance formulation of the Libor market model is given in this paper and leads to a key generalization: all the Libors, for different future times, are imperfectly correlated. A key difference between a forward interest rate model and the LMM lies in the fact that the LMM is calibrated directly from the observed market interest rates. The short distance Wilson expansion [Phys. Rev. 179, 1499 (1969)] of a Gaussian quantum field is shown to provide the generalization of Ito calculus; in particular, the Wilson expansion of the Gaussian quantum field A(t,x) driving the Libors yields a derivation of the Libor drift term that incorporates imperfect correlations of the different Libors. The logarithm of Libor phi(t,x) is defined and provides an efficient and compact representation of the quantum field theory of the Libor market model. The Lagrangian and Feynman path integrals of the Libor market model of interest rates are obtained, as well as a derivation given by its Hamiltonian. The Hamiltonian formulation of the martingale condition provides an exact solution for the nonlinear drift of the Libor market model. The quantum finance formulation of the LMM is shown to reduce to the industry standard Bruce-Gatarek-Musiela-Jamshidian model when the forward interest rates are taken to be exactly correlated. PMID:19905402

Baaquie, Belal E

2009-10-26

62

Hamiltonian mechanics and divergence-free fields  

SciTech Connect

The field lines, or integral curves, of a divergence-free field in three dimensions are shown to be topologically equivalent to the trajectories of a Hamiltonian with two degrees of freedom. The consideration of fields that depend on a parameter allow the construction of a canonical perturbation theory which is valid even if the perturbation is large. If the parametric dependence of the magnetic, or the vorticity field is interpreted as time dependence, evolution equations are obtained which give Kelvin's theorem or the flux conservation theorem for ideal fluids and plasmas. The Hamiltonian methods prove especially useful for study of fields in which the field lines must be known throughout a volume of space.

Boozer, A.H.

1986-08-01

63

Directed Transport of Atoms in a Hamiltonian Quantum Ratchet  

NASA Astrophysics Data System (ADS)

Classical ratchet potentials, which alternate a driving potential with periodic random dissipative motion, can account for the operation of biological motors. We demonstrate the operation of a quantum ratchet, which differs from classical ratchets in that dissipative processes are absent within the observation time of the system (Hamiltonian regime). An atomic rubidium Bose-Einstein condensate is exposed to a sawtooth-like optical lattice potential, whose amplitude is periodically modulated in time. The ratchet transport arises from broken spatiotemporal symmetries of the driven potential, resulting in a desymmetrization of transporting eigenstates (Floquet states). The full quantum character of the ratchet transport was demonstrated by the measured atomic current oscillating around a nonzero stationary value at longer observation times, resonances occurring at positions determined by the photon recoil, and dependence of the transport current on the initial phase of the driving potential.

Salger, Tobias; Kling, Sebastian; Hecking, Tim; Geckeler, Carsten; Morales-Molina, Luis; Weitz, Martin

2009-11-01

64

Directed transport of atoms in a Hamiltonian quantum ratchet.  

PubMed

Classical ratchet potentials, which alternate a driving potential with periodic random dissipative motion, can account for the operation of biological motors. We demonstrate the operation of a quantum ratchet, which differs from classical ratchets in that dissipative processes are absent within the observation time of the system (Hamiltonian regime). An atomic rubidium Bose-Einstein condensate is exposed to a sawtooth-like optical lattice potential, whose amplitude is periodically modulated in time. The ratchet transport arises from broken spatiotemporal symmetries of the driven potential, resulting in a desymmetrization of transporting eigenstates (Floquet states). The full quantum character of the ratchet transport was demonstrated by the measured atomic current oscillating around a nonzero stationary value at longer observation times, resonances occurring at positions determined by the photon recoil, and dependence of the transport current on the initial phase of the driving potential. PMID:19965469

Salger, Tobias; Kling, Sebastian; Hecking, Tim; Geckeler, Carsten; Morales-Molina, Luis; Weitz, Martin

2009-11-27

65

LETTER TO THE EDITOR: Explicit effective Hamiltonians for general linear quantum-optical networks  

Microsoft Academic Search

Linear optical networks are devices that turn classical incident modes by a linear transformation into outgoing ones. In general, the quantum version of such transformations may mix annihilation and creation operators. We derive a simple formula for the effective Hamiltonian of a general linear quantum network, if such a Hamiltonian exists. Otherwise we show how the scattering matrix of the

U. Leonhardt; A. Neumaier

2004-01-01

66

Supersymmetry in problems of quantum mechanics  

SciTech Connect

A connection is discussed between the group SU(2) and supersymmetry for a series of quantum mechanical problems. It is pointed out that the impossibility of factorizing Hamiltonians obtained based on representations of the group SU(2) indicates that the sypersymmetry of the system is broken. The authors consider a solution of the anharmonic oscillator problem, and they study properties of solutions for a series of problems for which supersymmetry is possible. They further construct a supersymmetric matrix Hamiltonian and determine supercharges.

Bagrov, V.G.; Vshivtsev, A.S.

1989-01-01

67

Kowalevski top in quantum mechanics  

NASA Astrophysics Data System (ADS)

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.

Matsuyama, A.

2013-09-01

68

Quantum-Merlin-Arthur-complete problems for stoquastic Hamiltonians and Markov matrices  

SciTech Connect

We show that finding the lowest eigenvalue of a 3-local symmetric stochastic matrix is Quantum-Merlin-Arthur-complete (QMA-complete). We also show that finding the highest energy of a stoquastic Hamiltonian is QMA-complete and that adiabatic quantum computation using certain excited states of a stoquastic Hamiltonian is universal. We also show that adiabatic evolution in the ground state of a stochastic frustration-free Hamiltonian is universal. Our results give a QMA-complete problem arising in the classical setting of Markov chains and adiabatically universal Hamiltonians that arise in many physical systems.

Jordan, Stephen P.; Gosset, David; Love, Peter J. [Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States); Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 6-304, Cambridge, Massachusetts 02139 (United States); Department of Physics, Haverford College, 370 Lancaster Avenue, Haverford, Pennsylvania 19041, USA, and Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125 (United States)

2010-03-15

69

Quantum cosmology and quantum mechanics.  

NASA Astrophysics Data System (ADS)

The interpretative framework of quantum mechanics loosely subsumed under the name "Copenhagen interpretation" contains two central assumptions which seem incompatible with a quantum cosmology built on a covariant quantum theory of spacetime. The first is a distinguished class of classical systems. The second is a distinguished time variable and its associated notion of causality. The first assumption is incompatible with the uniform application of quantum mechanics to the universe as a whole. The second is incompatible with the general covariance of gravitational theory. This paper explores the possibility that both of these distinguished features of our world arise, not as special features of the formalism of quantum mechanics, but rather as consequences of specific initial conditions for cosmology.

Hartle, J. B.

70

Adaptive Perturbation Theory: Quantum Mechanics and Field Theory.  

National Technical Information Service (NTIS)

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation theory is that it...

M. Weinstein

2005-01-01

71

Quantum mechanical Liouville model with attractive potential.  

National Technical Information Service (NTIS)

We study the quantum mechanical Liouville model with attractive potential which is obtained by Hamiltonian symmetry reduction from the system of a free particle on SL(2,R). The classical reduced system consists of a pair of Liouville subsystems which are ...

H. Kobayashi I. Tsutsui

1995-01-01

72

Quantum dynamics of methanol: Hamiltonian, representation and intensity considerations  

Microsoft Academic Search

Employing a body-fixed axis system and Jacobi coordinates, a model for the vibration–torsion–rotation Hamiltonian of the CH3OH molecule with large-amplitude internal motions has been derived. This Hamiltonian is expressed in terms of Jacobi coordinates and is partitioned in the form HA+HB+Hint, where HA and HB are the rovibrational Hamiltonians of methyl group CH3 and asymmetric rotor OH, and Hint represents

Yun-Bo Duan; Rubin Wang; Indranath Mukhopadhyay

2002-01-01

73

Quantum mechanics and symmetries  

Microsoft Academic Search

Symmetries have always played an important role in physics. With quantum mechanics, however, the interplay between physics and symmetries has reached a new dimension. The very structure of quantum mechanics invites the application of group theoretical methods to an extent that physicists would have been led to invent various concepts of group theory, such as Lie groups, by quantum mechanics

J. Wess

2000-01-01

74

Quantum Mechanical Forces in the Description of Water Silica Interactions  

Microsoft Academic Search

Using our transfer Hamiltonian approach, we have created quantum mechanical potentials to describe the interactions between water and silica under strain. The procedure for generating the transfer Hamiltonian will be discussed and illustrated by the results of MD simulations compared to those with classical potentials.

Carlos Taylor; Rodney Bartlett

2002-01-01

75

Quantum Mechanical Methods for Biomolecular Simulations  

Microsoft Academic Search

We discuss quantum mechanical methods for the description of the potential energy surface and for the treatment of nuclear\\u000a quantum effects in chemical and biological applications. Two novel electronic structure methods are described, including an\\u000a electronic structure-based explicit polarization (X-Pol) force field and an effective Hamiltonian molecular orbital and valence\\u000a bond (EH-MOVB) theory. In addition, we present two path integral

Kin-Yiu Wong; Lingchun Song; Wangshen Xie; Dan T. Major; Yen-Lin Lin; Alessandro Cembran; Jiali Gao

2009-01-01

76

Introduction to Quantum Mechanics  

Microsoft Academic Search

Discussed here is the mathematics of quantum mechanics at an introductory level. Hilbert spaces, the Bra-Ket notation, Fourier Transforms, the Schrodinger Wave Equation, and Quantum Computing are covered.

ROHIT TRIPATHI

1945-01-01

77

Introduction to Quantum Mechanics  

NSDL National Science Digital Library

This text is intended for junior/senior Quantum Mechanics courses. It covers the fundamentals of quantum theory in a concise manner, covering topics from the basic formalism through perturbation theory, the adiabatic approximation, and scattering.

Griffiths, David J.

2005-04-16

78

Symmetry of kp Hamiltonian in pyramidal InAs\\/GaAs quantum dots: Application to the calculation of electronic structure  

Microsoft Academic Search

A method for the calculation of the electronic structure of pyramidal self-assembled InAs\\/GaAs quantum dots is presented. The method is based on exploiting the C4 symmetry of the 8-band kp Hamiltonian with the strain taken into account via the continuum mechanical model. The operators representing symmetry group elements were represented in the plane wave basis and the group projectors were

Nenad Vukmirovic; Dragan Indjin; Vladimir D. Jovanovic; Zoran Ikonic; Paul Harrison

79

A classical analog of the quantum mechanical model of three Josephson junctions in a loop  

Microsoft Academic Search

It is shown that the time-dependent Schrödinger equation for a quantum mechanical system may be recast as a nonlinear flow if the Hamiltonian is a functional of the state of the system. This implies the possibility of deterministic chaos in this quantum mechanical system. If a classical Hamiltonian can be found that generates an identical flow, then a classical analog

R. H. Parmenter; L. Y. Yu

1995-01-01

80

Ph 125 Quantum Mechanics  

NSDL National Science Digital Library

This web site contains resources for a comprehensive quantum mechanics course designed for graduate and advanced undergraduate students at Cal Tech. The course has been revised to include quantum information science, and prepares students for a course in quantum computation. Lecture notes, a syllabus, homework problems with solutions, and exam solutions are available.

Mabuchi, Hideo

2011-01-21

81

Ph 125 Quantum Mechanics  

NSDL National Science Digital Library

This web site contains resources for a comprehensive quantum mechanics course designed for graduate and advanced undergraduate students at Cal Tech. The course has been revised to include quantum information science, and prepares students for a course in quantum computation. Lecture notes, a syllabus, homework problems with solutions, and exam solutions are available.

Mabuchi, Hideo

2005-12-05

82

Quantum mechanics made transparent  

NASA Astrophysics Data System (ADS)

This article is a ``sampler,'' which shows how quantum mechanics may be presented to students in a way that makes apparent how natural quantum mechanics is as a description of the world. The mathematical machinery of Hilbert space, the idea of representing observables by operators, the Schrödinger equation, and the position-momentum uncertainty relation all follow from natural assumptions that students can readily accept. The basic ideas of quantum mechanics are developed from intuitive first principles to the point where one can connect with more traditional treatments of quantum mechanics.

Henry, Richard C.

1990-11-01

83

Partial Dynamical Symmetry in Quantum Hamiltonians with Higher-Order Terms  

SciTech Connect

A generic procedure is proposed to construct many-body quantum Hamiltonians with partial dynamical symmetry. It is based on a tensor decomposition of the Hamiltonian and allows the construction of a hierarchy of interactions that have selected classes of solvable states. The method is illustrated in the SO(6) limit of the interacting boson model of atomic nuclei and applied to the nucleus {sup 196}Pt.

Garcia-Ramos, J. E. [Department of Applied Physics, University of Huelva, 21071 Huelva (Spain); Leviatan, A. [Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel); Van Isacker, P. [Grand Accelerateur National d'Ions Lourds, CEA/DSM-CNRS/IN2P3, B.P. 55027, F-14076 Caen Cedex 5 (France)

2009-03-20

84

Quantum mechanics: Entanglement goes mechanical  

Microsoft Academic Search

A neat experiment shows that the mechanical vibration of two ion pairs separated by a few hundred micrometres is entangled - their motions are intrinsically and inseparably connected in a quantum way.

Rainer Blatt

2009-01-01

85

Equation of motion for the process matrix: Hamiltonian identification and dynamical control of open quantum systems  

SciTech Connect

We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of the process matrix acting on a system. This equation is applicable to non-Markovian and/or strong-coupling regimes. We propose two distinct applications for this dynamical equation. We first demonstrate identification of quantum Hamiltonians generating dynamics of closed or open systems via performing process tomography. In particular, we argue how one can efficiently estimate certain classes of sparse Hamiltonians by performing partial tomography schemes. In addition, we introduce an optimal control theoretic setting for manipulating quantum dynamics of Hamiltonian systems, specifically for the task of decoherence suppression.

Mohseni, M. [Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 (United States); Rezakhani, A. T. [Department of Chemistry and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States)

2009-07-15

86

Advanced Visual Quantum Mechanics  

NSDL National Science Digital Library

This page provides links to a range of teaching materials for use in an upper-level undergraduate quantum mechanics course. These are developed from some of the concepts of the Visual Quantum Mechanics course for high school and introductory college classes. Materials inlcude tutorial activities in concepts of energy diagrams, probability, and wavefunctions, and some computer activities.

Axmann, Wally; Group, Kansas S.

2004-04-04

87

Hamiltonian design in atom-light interactions with rubidium ensembles: A quantum-information toolbox  

NASA Astrophysics Data System (ADS)

We study the coupling between collective variables of atomic spin and light polarization in an ensemble of cold R87b probed with polarized light. The effects of multiple hyperfine levels manifest themselves as a rank-2 tensor polarizability, whose irreducible components can be selected by means of probe detuning. The D1 and D2 lines of Rb are explored and we identify different detunings which lead to Hamiltonians with different symmetries for rotations. As possible applications of these Hamiltonians, we describe schemes for spin squeezing, quantum cloning, quantum memory, and measuring atom number.

de Echaniz, S. R.; Koschorreck, M.; Napolitano, M.; Kubasik, M.; Mitchell, M. W.

2008-03-01

88

Exact envelope-function theory versus symmetrized Hamiltonian for quantum wires: a comparison  

NASA Astrophysics Data System (ADS)

We study the influence of shape, orientation, size and material system on the band structure of quantum wires with special attention given to the differences between results obtained with the Burt Foreman and the Luttinger Kohn Hamiltonians. We also show how to derive the Hamiltonians for an arbitrary orientation. We find that the difference is independent of the shape and orientation of the quantum wire, but it does depend on the size and the material system chosen. A brief discussion of the results in terms of group theory is provided.

Lassen, B.; Lew Yan Voon, L. C.; Willatzen, M.; Melnik, R.

2004-10-01

89

Atomic physics tests of nonlinear quantum mechanics  

NASA Astrophysics Data System (ADS)

Atomic physics experiments which test a nonlinear generalization of quantum mechanics recently formulated by Weinberg are described. The experiments search for a dependence of hyperfine transition frequencies or nuclear spin precession frequencies on the relative populations of the hyperfine or nuclear spin states. The experiments set limits less than 10 ?Hz on the size of the possible nonlinear contributions to these frequencies. In some cases this can be interpreted as a limit of less than ~10-26 on the fraction of binding energy per nucleon that could be due to a nonlinear correction to a nuclear Hamiltonian. The possibility that a nonlinear addition to quantum mechanics violates causality is discussed.

Bollinger, J. J.; Heinzen, D. J.; Itano, Wayne M.; Gilbert, S. L.; Wineland, D. J.

1991-08-01

90

Quantum Mechanical Models of Turing Machines That Dissipate No Energy  

Microsoft Academic Search

Quantum mechanical Hamiltonian models of Turing machines are constructed here on a finite lattice of spin- 1\\/2 systems. The models do not dissipate any energy and they operate at the quantum limit in that the system (energy uncertainty)\\/(computation speed) is close to the limit given by the time-energy uncertainty principle.

Paul Benioff

1982-01-01

91

Mathematically rigorous quantum field theories with a nonlinear normal ordering of the Hamiltonian operator  

NASA Astrophysics Data System (ADS)

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

Maitra, Rachel Lash

92

Nonlinear Lattice Within Supersymmetric Quantum Mechanics Formalism  

NASA Astrophysics Data System (ADS)

In the last decades, the study of nonlinear one dimensional lattices has attracted much attention of the scientific community. One of these lattices is related to a simplified model for the DNA molecule, allowing to recover experimental results, such as the denaturation of DNA double helix. Inspired by this model we construct a Hamiltonian for a reflectionless potential through the Supersymmetric Quantum Mechanics formalism, SQM. Thermodynamical properties of such one dimensional lattice are evaluated aming possible biological applications.

Drigo Filho, E.; Ricotta, R. M.

2012-02-01

93

Landau problem in noncommutative quantum mechanics  

Microsoft Academic Search

The Landau problem in non-commutative quantum mechanics (NCQM) is studied. First by solving the Schrödinger equations on noncommutative (NC) space we obtain the Landau energy levels and the energy correction that is caused by space-space noncommutativity. Then we discuss the noncommutative phase space case, namely, space-space and momentum-momentum non-commutative case, and we get the explicit expression of the Hamiltonian as

Dulat Sayipjamal; Kang Li

2008-01-01

94

Quantum Mechanics Conceptual Survey  

NSDL National Science Digital Library

This web page is the home for the Quantum Mechanics Conceptual Survey (QMCS). The goal of this assessment is to provide an accurate measure of students' understanding of fundamental concepts in quantum mechanics. The QMCS is inspired by the many carefully researched and validated tests of conceptual understanding in physics. The authors developed the questions to be independent of notation unique to a specific course and avoiding jargon as much as possible. The questions in the QMCS are based on faculty interviews, textbooks and syllabi, existing assessments, research on student misconceptions in quantum mechanics, and student observations.

Mckagan, Sarah B.

2011-06-28

95

Is quantum mechanics exact?  

NASA Astrophysics Data System (ADS)

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

Kapustin, Anton

2013-06-01

96

Quantum state restoration and single-copy tomography for ground states of Hamiltonians.  

PubMed

Given a single copy of an unknown quantum state, the no-cloning theorem limits the amount of information that can be extracted from it. Given a gapped Hamiltonian, in most situations it is impractical to compute properties of its ground state, even though in principle all the information about the ground state is encoded in the Hamiltonian. We show in this Letter that if you know the Hamiltonian of a system and have a single copy of its ground state, you can use a quantum computer to efficiently compute its local properties. Specifically, in this scenario, we give efficient algorithms that copy small subsystems of the state and estimate the full statistics of any local measurement. PMID:21231156

Farhi, Edward; Gosset, David; Hassidim, Avinatan; Lutomirski, Andrew; Nagaj, Daniel; Shor, Peter

2010-11-04

97

Homogeneous binary trees as ground states of quantum critical Hamiltonians  

SciTech Connect

Many-body states whose wave functions admit a representation in terms of a uniform binary-tree tensor decomposition are shown to obey power-law two-body correlation functions. Any such state can be associated with the ground state of a translationally invariant Hamiltonian which, depending on the dimension of the systems sites, involves at most couplings between third-neighboring sites. Under general conditions it is shown that they describe unfrustrated systems which admit an exponentially large degeneracy of the ground state.

Silvi, P. [International School for Advanced Studies (SISSA), Via Bonomea 265, I-34136 Trieste (Italy); Giovannetti, V. [NEST, Scuola Normale Superiore and Istituto di Nanoscienze-CNR, I-56127 Pisa (Italy); Montangero, S. [Institut fuer Quanteninformationsverarbeitung, Universitaet Ulm, D-89069 Ulm (Germany); Rizzi, M.; Cirac, J. I. [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching (Germany); Fazio, R. [NEST, Scuola Normale Superiore and Istituto di Nanoscienze-CNR, I-56127 Pisa (Italy); Center for Quantum Technologies, National University of Singapore, 119077 (Singapore)

2010-06-15

98

Adaptive Perturbation Theory I: Quantum Mechanics  

SciTech Connect

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.

Weinstein, Marvin; /SLAC

2005-10-19

99

Visual Quantum Mechanics  

NSDL National Science Digital Library

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

Thaller, Bernd

2004-07-10

100

Graduate quantum mechanics reform  

NASA Astrophysics Data System (ADS)

We address four main areas in which graduate quantum mechanics education can be improved: course content, textbook, teaching methods, and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all these areas. In particular, we have modified the content of the course to reflect progress in the field of quantum mechanics over the last 50 years, used textbooks that include such content, incorporated a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey. We find that graduate students respond well to research-based techniques that have been tested mainly in introductory courses, and that they learn much of the new content introduced in each version of the course. We also find that students' ability to answer conceptual questions about graduate quantum mechanics is highly correlated with their ability to solve calculational problems on the same topics. In contrast, we find that students' understanding of basic undergraduate quantum mechanics concepts at the modern physics level is not improved by instruction at the graduate level.

Carr, L. D.; McKagan, S. B.

2009-04-01

101

Exploiting time-independent Hamiltonian structure as controls for manipulating quantum dynamics.  

PubMed

The opportunities offered by utilizing time-independent Hamiltonian structure as controls are explored for manipulating quantum dynamics. Two scenarios are investigated using different manifestations of Hamiltonian structure to illustrate the generality of the concept. In scenario I, optimally shaped electrostatic potentials are generated to flexibly control electron scattering in a two-dimensional subsurface plane of a semiconductor. A simulation is performed showing the utility of optimally setting the individual voltages applied to a multi-pixel surface gate array in order to produce a spatially inhomogeneous potential within the subsurface scattering plane. The coherent constructive and destructive electron wave interferences are manipulated by optimally adjusting the potential shapes to alter the scattering patterns. In scenario II, molecular vibrational wave packets are controlled by means of optimally selecting the Hamiltonian structure in cooperation with an applied field. As an illustration of the concept, a collection (i.e., a level set) of dipole functions is identified where each member serves with the same applied electric field to produce the desired final transition probability. The level set algorithm additionally found Hamiltonian structure controls exhibiting desirable physical properties. The prospects of utilizing the applied field and Hamiltonian structure simultaneously as controls is also explored. The control scenarios I and II indicate the gains offered by algorithmically guided molecular or material discovery for manipulating quantum dynamics phenomenon. PMID:22957557

Beltrani, Vincent; Rabitz, Herschel

2012-09-01

102

Complex square well - a new exactly solvable quantum mechanical model  

Microsoft Academic Search

Recently, a class of -invariant quantum mechanical models described by the non-Hermitian Hamiltonian H = p2+x2(ix) was studied. It was found that the energy levels for this theory are real for all 0. Here, the limit as is examined. It is shown that in this limit, the theory becomes exactly solvable. A generalization of this Hamiltonian, H = p2+x2M(ix) (M

Carl M. Bender; Stefan Boettcher; H. F. Jones; Van M Savage

1999-01-01

103

Hamiltonian cosmological perturbation theory with loop quantum gravity corrections  

SciTech Connect

Cosmological perturbation equations are derived systematically in a canonical scheme based on Ashtekar variables. A comparison with the covariant derivation and various subtleties in the calculation and choice of gauges are pointed out. Nevertheless, the treatment is more systematic when correction terms of canonical quantum gravity are to be included. This is done throughout the paper for one example of characteristic modifications expected from loop quantum gravity.

Bojowald, Martin; Kagan, Mikhail; Singh, Parampreet; Hernandez, Hector H.; Skirzewski, Aureliano [Institute for Gravitational Physics and Geometry, Pennsylvania State University, 104 Davey Lab, University Park, Pennsylvania 16802 (United States); Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Potsdam (Germany)

2006-12-15

104

Symplectic Topology and Geometric Quantum Mechanics  

NASA Astrophysics Data System (ADS)

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.

Sanborn, Barbara

105

Fun with supersymmetric quantum mechanics  

SciTech Connect

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.

Freedman, B.; Cooper, F.

1984-04-01

106

Optical-lattice Hamiltonians for relativistic quantum electrodynamics  

SciTech Connect

We show how interpenetrating optical lattices containing Bose-Fermi mixtures can be constructed to emulate the thermodynamics of quantum electrodynamics (QED). We present models of neutral atoms on lattices in 1+1, 2+1, and 3+1 dimensions whose low-energy effective action reduces to that of photons coupled to Dirac fermions of the corresponding dimensionality. We give special attention to (2+1)-dimensional quantum electrodynamics (QED3) and discuss how two of its most interesting features, chiral symmetry breaking and Chern-Simons physics, could be observed experimentally.

Kapit, Eliot; Mueller, Erich [Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York (United States)

2011-03-15

107

Measurement of time in nonrelativistic quantum and classical mechanics  

Microsoft Academic Search

Possible theoretical frameworks for measurement of (arrival) time in the nonrelativistic quantum mechanics are reviewed. It is argued that the ambiguity between indirect measurements by a suitably introduced time operator and direct measurements by a physical clock particle has a counterpart in the corresponding classical framework of measurement of the Newtonian time based on the Hamiltonian mechanics.

Piret Kuusk; Madis Koiv

2001-01-01

108

Physlets for Quantum Mechanics  

NSDL National Science Digital Library

This article presents the use of Physlet-based questions with proven pedagogical techniques to improve student conceptual understanding. Physlet problems are used in a Just-in-Time-Teaching approach. Most examples are from a senior level quantum mechanics class, although examples in introductory mechanics are also shown. Results of pre/post testing using the Quantum Mechanics Visualization Instrument (QMVI) show significant gain in understanding. Comparison is made with other QMVI results from undergraduate and graduate students. This article was cited as the best education article in the journal Computers in Science and Engineering for the American Institute of Physics' 75th anniversary. This citation is given below under Annotations.

Belloni, Mario; Christian, Wolfgang

2006-08-02

109

Visual Quantum Mechanics  

NSDL National Science Digital Library

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

Group, Kansas S.; Zollman, Dean A.

2003-10-10

110

Decoherence in quantum mechanics  

SciTech Connect

Research Highlights: > We study decoherence in a simple quantum mechanical model using two approaches. > Following the conventional approach to decoherence we solve the master equation. > We also consider our novel correlator approach to decoherence. > The system's total entropy increase cannot reliably be calculated in the conventional approach. > This does follow correctly from our correlator approach. - Abstract: We study decoherence in a simple quantum mechanical model using two approaches. Firstly, we follow the conventional approach to decoherence where one is interested in solving the reduced density matrix from the perturbative master equation. Secondly, we consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. We show that both methods can accurately predict decoherence time scales. However, the perturbative master equation generically suffers from instabilities which prevents us to reliably calculate the system's total entropy increase. We also discuss the relevance of the results in our quantum mechanical model for interacting field theories.

Koksma, Jurjen F., E-mail: J.F.Koksma@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); Prokopec, Tomislav, E-mail: T.Prokopec@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); Schmidt, Michael G., E-mail: M.G.Schmidt@thphys.uni-heidelberg.de [Institut fuer Theoretische Physik, Heidelberg University, Philosophenweg 16, D-69120 Heidelberg (Germany)

2011-06-15

111

Discreteness corrections to the effective Hamiltonian of isotropic loop quantum cosmology  

NASA Astrophysics Data System (ADS)

One of the qualitatively distinct and robust implications of loop quantum gravity is the underlying discrete structure. In the cosmological context elucidated by loop quantum cosmology, this is manifested by the Hamiltonian constraint equation being a (partial) difference equation. One obtains an effective Hamiltonian framework by making the continuum approximation followed by a WKB approximation. In the large volume regime, these lead to the usual classical Einstein equation which is independent of both the Barbero Immirzi parameter ? as well as planck. In this work, we present an alternative derivation of the effective Hamiltonian by-passing the continuum approximation step. As a result, the effective Hamiltonian is obtained as a closed form expression in ?. These corrections to the Einstein equation can be thought of as corrections due to the underlying discrete (spatial) geometry with ? controlling the size of these corrections. These corrections imply a bound on the rate of change of the volume of the isotropic universe. In most cases these are perturbative in nature but for a cosmological constant dominated isotropic universe, there are significant deviations.

Banerjee, Kinjal; Date, Ghanashyam

2005-06-01

112

Recursive diagonalization of quantum Hamiltonians to all orders in ({Dirac_h}/2{pi})  

SciTech Connect

We present a diagonalization method for generic matrix valued Hamiltonians based on a formal expansion in power of ({Dirac_h}/2{pi}). Considering ({Dirac_h}/2{pi}) as a running parameter, a differential equation connecting two diagonalization processes for two very close values of ({Dirac_h}/2{pi}) is derived. The integration of this differential equation allows the recursive determination of the series expansion in powers of ({Dirac_h}/2{pi}) for the diagonalized Hamiltonian. This approach results in effective Hamiltonians with Berry-phase corrections of higher order in ({Dirac_h}/2{pi}), and deepens previous works on the semiclassical diagonalization of quantum Hamiltonians, which led notably to the discovery of the intrinsic spin Hall effect. As physical applications we consider spinning massless particles in isotropic inhomogeneous media and show that both the energy and the velocity get quantum corrections of order ({Dirac_h}/2{pi}){sup 2}. We also derive formally to all orders in ({Dirac_h}/2{pi}) the energy spectrum and the equations of motion of Bloch electrons in an external electric field.

Gosselin, Pierre [Universite Grenoble I, Institut Fourier, UMR 5582 CNRS-UJF, UFR de Mathematiques, BP74, 38402 Saint Martin d'Heres, Cedex (France); Hanssen, Jocelyn; Mohrbach, Herve [Universite Paul Verlaine, Institut de Physique, ICPMB1-FR CNRS 2843, Laboratoire de Physique Moleculaire et des Collisions, 57078 Metz (France)

2008-04-15

113

Visual Quantum Mechanics  

NSDL National Science Digital Library

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

Thaller, Bernd

2009-05-14

114

Superposition and quantum mechanics  

SciTech Connect

This work is primarily concerned with finding those statements or observations from which quantum mechanics can reasonably be said to follow. Within the context of characterizing quantum mechanics as any probability field (with bounded probability density) whose associated stochastic velocity field is governed by a differential equation of first order in time, it is shown that the single statement required is the stipulation that the superposition principle is satisfied. This is demonstrated by showing that only the Schrodinger equation is an acceptable dynamic description for such probability fields if the superposition principle is to hold.

Cohn, J.

1986-08-01

115

Time Asymmetric Quantum Mechanics  

NASA Astrophysics Data System (ADS)

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

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

2011-09-01

116

Topology and mechanics with computer graphics - Linear Hamiltonian systems in four dimensions  

NASA Astrophysics Data System (ADS)

An interactive-computer-graphics approach for characterizing the constant-energy solution surfaces of classical mechanics problems formulated in four-dimensional phase space is described and demonstrated. A class of completely integrable Hamiltonians is considered, and the technique is then extended to all quadratic Hamiltonians, revealing their relatively rich topological structure. A number of typical results are presented graphically.

Kocak, Huseyin; Bisshopp, Frederic; Banchoff, Thomas; Laidlaw, David

1986-09-01

117

Ab initio no core calculations of light nuclei and preludes to Hamiltonian quantum field theory  

SciTech Connect

Recent advances in ab initio quantum many-body methods and growth in computer power now enable highly precise calculations of nuclear structure. The precision has attained a level sufficient to make clear statements on the nature of 3-body forces in nuclear physics. Total binding energies, spin-dependent structure effects, and electroweak properties of light nuclei play major roles in pinpointing properties of the underlying strong interaction. Eventually,we anticipate a theory bridge with immense predictive power from QCD through nuclear forces to nuclear structure and nuclear reactions. Light front Hamiltonian quantum field theory offers an attractive pathway and we outline key elements.

Vary, J.P.; Maris, P.; /Iowa State U.; Shirokov, A.M.; /Iowa State U. /SINP, Moscow; Honkanen, H.; li, J.; /Iowa State U.; Brodsky, S.J.; /SLAC; Harindranath, A.; /Saha Inst.; Teramond, G.F.de; /Costa Rica U.

2009-08-03

118

Ab initio no core calculations of light nuclei and preludes to Hamiltonian quantum field theory  

SciTech Connect

Recent advances in ab initio quantum many-body methods and growth in computer power now enable highly precise calculations of nuclear structure. The precision has attained a level sufficient to make clear statements on the nature of 3-body forces in nuclear physics. Total binding energies, spin-dependent structure effects, and electroweak properties of light nuclei play major roles in pinpointing properties of the underlying strong interaction. Eventually, we anticipate a theory bridge with immense predictive power from QCD through nuclear forces to nuclear structure and nuclear reactions. Light front Hamiltonian quantum field theory offers an attractive pathway and we outline key elements.

Vary, J. P.; Maris, P.; Honkanen, H.; Li, J. [Department of Physics and Astronomy, Iowa State University, Ames, Iowa, 50011 (United States); Shirokov, A. M. [Department of Physics and Astronomy, Iowa State University, Ames, Iowa, 50011 (United States); Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119991 (Russian Federation); Brodsky, S. J. [SLAC National Accelerator Laboratory, Stanford University, Menlo Park, California (United States); Harindranath, A. [Theory Group, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata, 700064 (India); Teramond, G. F. de [Universidad de Costa Rica, San Jose (Costa Rica)

2009-12-17

119

Quantum Mechanics, Locality and Realism.  

National Technical Information Service (NTIS)

We show that the concept of locality is independent of the postulates of quantum mechanics. In particular, we show that under the assumption that nature is local, the quantum-mechanical predictions concerning experiments on correlated systems satisfy Bell...

J. W. de Roever M. Streng

1993-01-01

120

Introduction to Biological Quantum Mechanics.  

National Technical Information Service (NTIS)

There are observables and eigenstates in biology as well as in physical quantum mechanics. Furthermore, the basic principle of quantum mechanics that 'measurement of an observable of a physical system will find the system in an eigenstate of the observabl...

S. Goldman

1969-01-01

121

Holistic Aspects of Quantum Mechanics.  

National Technical Information Service (NTIS)

Aspects of quantum mechanics irreconcilable with classical physics are outlined. Quantum mechanics started with a negative statement about reality, namely: it is impossible to determine momentum and position of a particle simultaneously. Meanwhile it has ...

H. Pietschmann

1987-01-01

122

A solvable quantum-mechanical model with nonlinear transformation laws  

Microsoft Academic Search

Summary  A quantum-mechanical model with three degrees of freedom and a nonlinearly realized Lorentz group is solved exactly. Moreover,\\u000a it is shown that even after breaking the symmetry by a linearly transforming term the model remains solvable. In both cases\\u000a the spectrum of the Hamiltonian is investigated and found to be positive.

G. Velo; J. Wess

1971-01-01

123

A quantum mechanical description for quasi-Landau resonances  

NASA Astrophysics Data System (ADS)

We succeed in solving quantum-mechanically the problem of a hydrogen atom in a strong magnetic field in the (r, ?, phi) coordinate system in which the main part of the Hamiltonian can be solved by separation of variables. The theoretical energy spectrum agrees to a certain extent with the experimental one.

Zhang, Yu; Zhang, Cheng-xiu; C, Chang H.

1985-07-01

124

Classification and normal forms for avoided crossings of quantum-mechanical energy levels  

Microsoft Academic Search

When using the Born-Oppenheimer approximation for molecular systems, one encounters a quantum mechanical Hamiltonian for the electrons that depends on several parameters that describe the positions of the nuclei. As these parameters are varied, the spectrum of the electron Hamiltonian may vary. In particular, discrete eigenvalues may approach very close to one another at `avoided crossings' of the electronic energy

George A. Hagedorn

1998-01-01

125

Supersymmetric quantum mechanics and its applications  

SciTech Connect

The Hamiltonian in Supersymmetric Quantum Mechanics is defined in terms of charges that obey the same algebra as that of the generators of supersymmetry in field theory. The consequences of this symmetry for the spectra of the component parts that constitute the supersymmetric system are explored. The implications of supersymmetry for the solutions of the Schroedinger equation, the Dirac equation, the inverse scattering theory and the multi-soliton solutions of the KdV equation are examined. Applications to scattering problems in Nuclear Physics with specific reference to singular potentials which arise from considerations of supersymmetry will be discussed.

Sukumar, C.V. [Wadham College, University of Oxford, Oxford OX1 3PN (United Kingdom)

2004-12-23

126

Landau Problem in Noncommutative Quantum Mechanics  

Microsoft Academic Search

The Landau problem in non-commutative quantum mechanics (NCQM) is studied.\\u000aFirst by solving the Schr$\\\\ddot{o}$dinger equations on noncommutative(NC) space\\u000awe obtain the Landau energy levels and the energy correction that is caused by\\u000aspace-space noncommutativity. Then we discuss the noncommutative phase space\\u000acase, namely, space-space and momentum-momentum non-commutative case, and we\\u000aget the explicit expression of the Hamiltonian as well

Sayipjamal Dulat; Kang Li

2008-01-01

127

Perspectives: Quantum Mechanics on Phase Space  

NASA Astrophysics Data System (ADS)

The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical particle model descriptions exhibiting either Galileian or Lorentzian symmetry. The structures of fundamental importance are the relevant (Lie) groups of symmetries and their homogeneous (and associated) spaces that, in the situations of interest, also possess Hamiltonian structures. Comments are made on the relation between the theory outlined and a recent paper by Carmeli, Cassinelli, Toigo, and Vacchini.

Brooke, J. A.; Schroeck, F. E.

2005-11-01

128

Two-component Dirac-like Hamiltonian for generating quantum walk on one-, two- and three-dimensional lattices  

PubMed Central

From the unitary operator used for implementing two-state discrete-time quantum walk on one-, two- and three- dimensional lattice we obtain a two-component Dirac-like Hamiltonian. In particular, using different pairs of Pauli basis as position translation states we obtain three different form of Hamiltonians for evolution on one-dimensional lattice. We extend this to two- and three-dimensional lattices using different Pauli basis states as position translation states for each dimension and show that the external coin operation, which is necessary for one-dimensional walk is not a necessary requirement for a walk on higher dimensions but can serve as an additional resource to control the dynamics. The two-component Hamiltonian we present here for quantum walk on different lattices can serve as a general framework to simulate, control, and study the dynamics of quantum systems governed by Dirac-like Hamiltonian.

Chandrashekar, C. M.

2013-01-01

129

(N+1)-dimensional quantum mechanical model for a closed universe  

Microsoft Academic Search

A quantum mechanical model for an (N+1)-dimensional universe arising from a quantum fluctuation is outlined. (3+1) dimensions are a closed, infinitely expanding universe, and the remaining N-3 dimensions are compact. The (3+1) noncompact dimensions are modeled by quantizing a canonical Hamiltonian description of a homogeneous isotropic universe. It is assumed that gravity and the strong-electroweak (SEW) force had equal strengths

T. R. Mongan

1999-01-01

130

Topics of Differential Geometry in Hamiltonian and Lagrangian Mechanics and Relativity.  

National Technical Information Service (NTIS)

An introduction to the tensor and exterior algebra as to the differential geometry is made. Such a geometry is used in order to study the Hamiltonian and Lagrangian mechanics stressing their geometrical aspects. Some applications are done in relativity th...

P. R. Rodrigues

1982-01-01

131

Quantum Mechanics Survey (QMS)  

NSDL National Science Digital Library

This 31-question research-based multiple-choice test is designed to evaluate studentsâ conceptual understanding of quantum mechanics in junior-level courses. The survey is based on investigations of studentsâ difficulties in quantum mechanics and should be given in a 50-minute period. Statistical results have shown the survey to be reliable and valid. A summary of the construction and analysis of the survey is available in Surveying studentsâ understanding of quantum mechanics in one spatial dimension, Am. J. Phys. 80 (3), 252-259. This assessment is free for use by instructors in their classroom. However, as it takes years of development effort to create and validate reliable assessment instruments, the file is password-protected. Furthermore, the author requests that 1. students are not given copies following examination; and 2. none of the questions are incorporated into web-based question delivery systems without adequate security to prevent printing or unauthorized access by students. To obtain the password, please send a request with your name, email, institution, and a link to a page at your institution that confirms you are an instructor.

Singh, Chandralekha; Zhu, Guangtian

2012-04-29

132

Quantum theory of atoms in molecules: results for the SR-ZORA Hamiltonian.  

PubMed

The quantum theory of atoms in molecules (QTAIM) is generalized to include relativistic effects using the popular scalar-relativistic zeroth-order regular approximation (SR-ZORA). It is usually assumed that the definition of the atom as a volume bounded by a zero-flux surface of the electron density is closely linked to the form of the kinetic energy, so it is somewhat surprising that the atoms corresponding to the relativistic kinetic-energy operator in the SR-ZORA Hamiltonian are also bounded by zero-flux surfaces. The SR-ZORA Hamiltonian should be sufficient for qualitative descriptions of molecular electronic structure across the periodic table, which suggests that QTAIM-based analysis can be useful for molecules and solids containing heavy atoms. PMID:22010759

Anderson, James S M; Ayers, Paul W

2011-10-19

133

Symmetry of k•p Hamiltonian in pyramidal InAs\\/GaAs quantum dots: Application to the calculation of electronic structure  

Microsoft Academic Search

A method for the calculation of the electronic structure of pyramidal self-assembled InAs\\/GaAs quantum dots is presented. The method is based on exploiting the Cmacr 4 symmetry of the 8-band k•p Hamiltonian with the strain taken into account via the continuum mechanical model. The operators representing symmetry group elements were represented in the plane wave basis and the group projectors

Nenad Vukmirovic; Dragan Indjin; Vladimir D. Jovanovic; Zoran Ikonic; Paul Harrison

2005-01-01

134

Logical foundation of quantum mechanics  

Microsoft Academic Search

The subject of this article is the reconstruction of quantum mechanics on the basis of a formal language of quantum mechanical propositions. During recent years, research in the foundations of the language of science has given rise to adialogic semantics that is adequate in the case of a formal language for quantum physics. The system ofsequential logic which is comprised

E. W. Stachow; Theoretische Physik

1980-01-01

135

Reality Problem in Quantum Mechanics.  

National Technical Information Service (NTIS)

A series of 12 lectures on quantum mechanics and its interpretations: The more specific part begins with chapter 8: spin and polarization measurements; the Einstein-Podolski-Rosen paradox; interpretations of quantum theory; the role of the observer and th...

D. Flamm

1988-01-01

136

Algorithms Speedup From Quantum Mechanics.  

National Technical Information Service (NTIS)

This project was concerned primarily with one central theme which is the attempt to use quantum mechanics to design algorithms that perform better than conventional (non-quantum) algorithms for solving certain problems. We looked at a variety of approache...

E. Farhi J. Goldstone

2005-01-01

137

Stochastic mechanics and quantum theory  

Microsoft Academic Search

Stochastic mechanics may be regarded as both generalizing classical mechanics to processes with intrinsic randomness, as well as providing the sort of detailed description of microscopic events declared impossible under the traditional interpretation of quantum mechanics. It avoids the many conceptual difficulties which arise from the assumption that quantum mechanics, i.e., the wave function, provides a complete description of (microscopic)

Sheldon Goldstein

1987-01-01

138

Quantum Mechanics of a Molecular System Adsorbed on a Dielectric Surface.  

National Technical Information Service (NTIS)

The study of time-dependent oscillator systems has received a great deal of attention both in classical and quantum-mechanical studies. In the usual quantum mechanical treatment of these systems, a time independent Hamiltonian is assumed, which must be ob...

H. G. Oh H. R. Lee T. F. George C. I. Um Y. M. Choi

1989-01-01

139

Gravitomagnetism in quantum mechanics  

SciTech Connect

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.

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

140

Quantum dynamics of attractive versus repulsive bosonic Josephson junctions: Bose-Hubbard and full-Hamiltonian results  

SciTech Connect

The quantum dynamics of one-dimensional bosonic Josephson junctions with attractive and repulsive interparticle interactions is studied by using the Bose-Hubbard model and by numerically exact computations of the full many-body Hamiltonian. A symmetry present in the Bose-Hubbard Hamiltonian dictates an equivalence between the evolution in time of the survival probability and the fragmentation of attractive and repulsive Josephson junctions with attractive and repulsive interactions of equal magnitude. The full many-body Hamiltonian does not possess this symmetry and, consequently, the dynamics of the attractive and repulsive junctions are different.

Sakmann, Kaspar; Streltsov, Alexej I.; Alon, Ofir E.; Cederbaum, Lorenz S. [Theoretische Chemie, Physikalisch-Chemisches Institut, Universitaet Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg (Germany)

2010-07-15

141

Structural fluctuations and quantum transport through DNA molecular wires: a combined molecular dynamics and model Hamiltonian approach  

NASA Astrophysics Data System (ADS)

Charge transport through a short DNA oligomer (Dickerson dodecamer (DD)) in the presence of structural fluctuations is investigated using a hybrid computational methodology based on a combination of quantum mechanical electronic structure calculations and classical molecular dynamics (MD) simulations with a model Hamiltonian approach. Based on a fragment orbital description, the DNA electronic structure can be coarse-grained in a very efficient way. The influence of dynamical fluctuations, arising either from the solvent fluctuations or from base-pair vibrational modes, can be taken into account in a straightforward way through the time series of the effective DNA electronic parameters, evaluated at snapshots along the MD trajectory. We show that charge transport can be promoted through the coupling to solvent fluctuations, which gate the on-site energies along the DNA wire.

Gutiérrez, R.; Caetano, R.; Woiczikowski, P. B.; Kubar, T.; Elstner, M.; Cuniberti, G.

2010-02-01

142

Quantum Mechanics as Dualism  

NASA Astrophysics Data System (ADS)

I do not agree with mind-body dualism. Today the consensus view is that thought and mind is a combination of processes like memory, generalization, comparison, deduction, organization, induction, classification, feature detection, analogy, etc. performed by computational machinery. (R. Jones, Trans. of the Kansas Acad. Sci., vol. 109, # 3/4, 2006 and www.robert-w-jones.com, philosopher, theory of thought) But I believe that quantum mechanics is a more plausible dualist theory of reality. The quantum mechanical wave function is nonphysical, it exists in a 3N space (for an N body system) not in (x,y,z,t) 4-space, and does not possess physical properties. But real physical things like energy (which do exist in our 4-space world) influence the wave function and the wave function, in its turn, influences real physical things, like where a particle can be found in 4-space. The coupling between the spirit-like wave function and things found in the real (4-space) world (like energy) is via mathematical equations like the Schrodinger equation and Born normalization.

Jones, Robert

2011-03-01

143

Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime  

Microsoft Academic Search

These are the author's lectures at the 1992 Les Houches Summer School,\\u000a``Gravitation and Quantizations''. They develop a generalized\\u000asum-over-histories quantum mechanics for quantum cosmology that does not\\u000arequire either a preferred notion of time or a definition of measurement. The\\u000a``post-Everett'' quantum mechanics of closed systems is reviewed. Generalized\\u000aquantum theories are defined by three elements (1) the set

James B. Hartle

1993-01-01

144

Contribution from the interaction Hamiltonian to the expectation value of particle number with the non-equilibrium quantum field theory  

SciTech Connect

We develop the method analyzing particle number non-conserving phenomena with non-equilibrium quantum field-theory. In this study, we consider a CP violating model with interaction Hamiltonian that breaks particle number conservation. To derive the quantum Boltzmann equation for the particle number, we solve Schwinger-Dyson equation, which are obtained from two particle irreducible closed-time-path (2PI CTP) effective action. In this calculation, we show the contribution from interaction Hamiltonian to the time evolution of expectation value of particle number.

Hotta, Ryuuichi; Morozumi, Takuya; Takata, Hiroyuki [Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526 (Japan); Tomsk state Pedagogical University Tomsk 634041 (Russian Federation)

2012-07-27

145

Strange attractors in dissipative Nambu mechanics: classical and quantum aspects  

NASA Astrophysics Data System (ADS)

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in R 3 phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and Rössler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called Nambu Hamiltonians. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian N × N matrices in R 3. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the 3 N 2 dimensional phase space.

Axenides, Minos; Floratos, Emmanuel

2010-04-01

146

Nonlocality, counterfactuals, and quantum mechanics  

NASA Astrophysics Data System (ADS)

Stapp [Am. J. Phys. 65, 300 (1997)] has recently argued from a version of the Hardy-type experiments that quantum mechanics must be nonlocal, independent of any additional assumptions such as realism or hidden variables. I argue either that his conclusions do not follow from his assumptions or that his assumptions are not true of quantum mechanics and can be interpreted as assigning an unwarranted level of reality to the value of certain quantum attributes.

Unruh, W.

1999-01-01

147

The emergence of quantum mechanics  

NASA Astrophysics Data System (ADS)

It is pointed out that a mathematical relation exists between cellular automata and quantum field theories. Although the proofs are far from perfect, they do suggest a new look at the origin of quantum mechanics: quantum mechanics may be nothing but a natural way to handle the statistical correlations of a cellular automaton. An essential role for the gravitational force in these considerations is suspected.

't Hooft, Gerard

2012-06-01

148

Symmetry of Hamiltonian and conserved quantity for a system of generalized classical mechanics  

NASA Astrophysics Data System (ADS)

This paper focuses on a new symmetry of Hamiltonian and its conserved quantity for a system of generalized classical mechanics. The differential equations of motion of the system are established. The definition and the criterion of the symmetry of Hamiltonian of the system are given. A conserved quantity directly derived from the symmetry of Hamiltonian of the generalized classical mechanical system is given. Since a Hamilton system is a special case of the generalized classical mechanics, the results above are equally applicable to the Hamilton system. The results of the paper are the generalization of a theorem known for the existing nonsingular equivalent Lagrangian. Finally, two examples are given to illustrate the application of the results. Project supported by the National Natural Science Foundation of China (Grant No. 10972151).

Zhang, Yi

2011-03-01

149

Probability Interpretation of Quantum Mechanics.  

ERIC Educational Resources Information Center

This paper draws attention to the frequency meaning of the probability concept and its implications for quantum mechanics. It emphasizes that the very meaning of probability implies the ensemble interpretation of both pure and mixed states. As a result some of the "paradoxical" aspects of quantum mechanics lose their counterintuitive character.…

Newton, Roger G.

1980-01-01

150

Quantum mechanics of cluster melting  

SciTech Connect

We present here prototype studies of the effects of quantum mechanics on the melting of clusters. Using equilibrium path integral methods, we examine the melting transition for small rare gas clusters. Argon and neon clusters are considered. We find the quantum-mechanical effects on the melting and coexistence properties of small neon clusters to be appreciable.

Beck, T.L.; Doll, J.D.; Freeman, D.L.

1989-05-15

151

Tensorial description of quantum mechanics  

NASA Astrophysics Data System (ADS)

Relevant algebraic structures for the description of quantum mechanics in the Heisenberg picture are replaced by tensor fields 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.

Clemente-Gallardo, J.; Marmo, G.

2013-03-01

152

Quantum Dynamics of Multi Harmonic Oscillators Described by Time Variant Conic Hamiltonian and their Use in Contemporary Sciences  

Microsoft Academic Search

This work focuses on the dynamics of a system of quantum multi harmonic oscillators whose Hamiltonian is conic in positions and momenta with time variant coefficients. While it is simple, this system is useful for modeling the dynamics of a number of systems in contemporary sciences where the equations governing spatial or temporal changes are described by sets of ODEs.

Metin Demiralp; Metin

2010-01-01

153

Ab-Initio Hamiltonian Approach to Light Nuclei And to Quantum Field Theory  

SciTech Connect

Nuclear structure physics is on the threshold of confronting several long-standing problems such as the origin of shell structure from basic nucleon-nucleon and three-nucleon interactions. At the same time those interactions are being developed with increasing contact to QCD, the underlying theory of the strong interactions, using effective field theory. The motivation is clear - QCD offers the promise of great predictive power spanning phenomena on multiple scales from quarks and gluons to nuclear structure. However, new tools that involve non-perturbative methods are required to build bridges from one scale to the next. We present an overview of recent theoretical and computational progress with a Hamiltonian approach to build these bridges and provide illustrative results for the nuclear structure of light nuclei and quantum field theory.

Vary, J.P.; /Iowa State U.; Honkanen, H.; /Iowa State U.; Li, Jun; /Iowa State U.; Maris, P.; /Iowa State U.; Shirokov, A.M.; /SINP, Moscow; Brodsky, S.J.; /SLAC /Stanford U., Phys. Dept.; Harindranath, A.; /Saha Inst.; de Teramond, G.F.; /Costa Rica U.; Ng, E.G.; /LBL, Berkeley; Yang, C.; /LBL, Berkeley; Sosonkina, M.; /Ames Lab

2012-06-22

154

Solvable quantum mechanical model in two-dimensional space  

Microsoft Academic Search

A one-particle non-relativistic quantum mechanical solvable model in two-dimensional space is given. The Hamiltonian is the sum of kinetic and interaction parts. Interactions are separable and can be centred at n arbitrary points of the plane. Conditions for the existence and for the number of bound states in finite linear chains are formulated in terms of the parameters of the

E de Prunelé

2006-01-01

155

N + 1 dimensional quantum mechanical model for a closed universe  

Microsoft Academic Search

A quantum mechanical model for an N + 1 dimensional universe arising from a\\u000aquantum fluctuation is outlined. (3 + 1) dimensions are a closed\\u000ainfinitely-expanding universe and the remaining N - 3 dimensions are compact.\\u000aThe (3 + 1) non-compact dimensions are modeled by quantizing a canonical\\u000aHamiltonian description of a homogeneous isotropic universe. It is assumed\\u000agravity and

T. R. Mongan

1999-01-01

156

Decoherence in Quantum Mechanics and Quantum Cosmology.  

National Technical Information Service (NTIS)

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 o...

J. B. Hartle

1992-01-01

157

Communication: Quantum mechanics without wavefunctions  

SciTech Connect

We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications--theoretical, computational, and interpretational--are discussed.

Schiff, Jeremy [Department of Mathematics, Bar-Ilan University, Ramat Gan 52900 (Israel); Poirier, Bill [Department of Chemistry and Biochemistry, Texas Tech University, Box 41061, Lubbock, Texas 79409-1061 (United States) and Department of Physics, Texas Tech University, Box 41051, Lubbock, Texas 79409-1051 (United States)

2012-01-21

158

Twist deformation of rotationally invariant quantum mechanics  

SciTech Connect

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

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

2010-11-15

159

Quantum Mechanics from Classical Logic  

NASA Astrophysics Data System (ADS)

Although quantum mechanics is generally considered to be fundamentally incompatible with classical logic, it is argued here that the gap is not as great as it seems. Any classical, discrete, time reversible system can be naturally described using a quantum Hubert space, operators, and a Schrödinger equation. The quantum states generated this way resemble the ones in the real world so much that one wonders why this could not be used to interpret all of quantum mechanics this way. Indeed, such an interpretation leads to the most natural explanation as to why a wave function appears to "collapse" when a measurement is made, and why probabilities obey the Born rule. Because it is real quantum mechanics that we generate, Bell's inequalities should not be an obstacle.

't Hooft, Gerard

2012-05-01

160

Quantum Mechanisms of Electronic Signal Propagation Along a Microtubule  

NASA Astrophysics Data System (ADS)

Evidence has been accumulating for the involvement of quantum coherence and entanglement in light harvesting photosynthetic complexes. This tests the adage that biological systems are too "warm and wet" to support quantum phenomena. Recent advancements in experiment and theory have allowed investigators to probe other warm systems for coherent phenomena including polymer chains, bacteriorhodopsin and ion channels. A debate has raged for over a decade regarding hypothetical quantum coherence/ entanglement in microtubules. Here we theoretically investigate coherent energy transfer in microtubules via dipole excitations coupled to the environment in networks of chromophoric amino acids. We present the spatial structure and Hamiltonian, containing localized site energies and couplings between aromatic amino acids, for the microtubule constituent protein tubulin. Energy transfer is discussed in terms of quantum walk formalism and energy transfer efficiency. Plausibility arguments are presented for the conditions favoring a quantum mechanism of electronic signal propagation along a microtubule.

Craddock, Travis; Friesen, Douglas; Tuszynski, Jack

2011-03-01

161

Quantum mechanics from classical statistics  

SciTech Connect

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.

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

162

Permutation interpretation of quantum mechanics  

NASA Astrophysics Data System (ADS)

We analyse quantum concepts in a constructive finite background. Introduction of continuum or other actual infinities into physics leads to non-constructivity without any need for them in description of empirical observations. We argue that quantum behavior is a natural consequence of symmetries of dynamical systems. It is a result of fundamental impossibility to trace identity of indistinguishable objects in their evolution — only information about invariant combinations of such objects is available. General mathematical arguments imply that any quantum dynamics can be reduced to a sequence of permutations. Quantum phenomena, such as interferences, arise in invariant subspaces of permutation representations of the symmetry group of a system. Observable quantities can be expressed in terms of the permutation invariants. We demonstrate that for description of quantum phenomena there is no need to use such non-constructive number system as complex numbers. It is sufficient to employ the cyclotomic numbers — a minimal extension of the natural numbers which is suitable for quantum mechanics.

Kornyak, V. V.

2012-02-01

163

Realism, operationalism, and quantum mechanics  

Microsoft Academic Search

A comprehensive formal system is developed that amalgamates the operational and the realistic approaches to quantum mechanics. In this formalism, for example, a sharp distinction is made between events, operational propositions, and the properties of physical systems.

D. Foulis; C. Piron; C. Randall

1983-01-01

164

Singular potentials in quantum mechanics.  

National Technical Information Service (NTIS)

This paper is a review of some mathematical methods as recently developed and applied to deal with singular potentials in Quantum Mechanics. Regular and singular perturbative methods as well as variational treatments are considered. (author). 25 refs. (At...

V. C. Aguilera-Navarro E. Koo

1995-01-01

165

Computing With Quantum Mechanical Oscillators.  

National Technical Information Service (NTIS)

Despite the obvious practical considerations (e.g., stability, controllability), certain quantum mechanical systems seem to naturally lend themselves in a theoretical sense to the task of performing computations. The purpose of this report is to describe ...

A. D. Parks J. L. Solka

1991-01-01

166

Yang-Mills Quantum Mechanics.  

National Technical Information Service (NTIS)

Quantum mechanical properties of the Yang-Mills space homogeneous model are considered in the Schroedinger representation. By means of compact variables the dependence of the wave function on ''rotational'' degrees of freedom is separated and effective Ha...

G. K. Savvidy

1984-01-01

167

Measurement Theory in Quantum Mechanics.  

National Technical Information Service (NTIS)

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

G. Klein

1980-01-01

168

Quantum Mechanics in Insulators  

SciTech Connect

Atomic physics is undergoing a large revival because of the possibility of trapping and cooling ions and atoms both for individual quantum control as well as collective quantum states, such as Bose-Einstein condensates. The present lectures start from the 'atomic' physics of isolated atoms in semiconductors and insulators and proceed to coupling them together to yield magnets undergoing quantum phase transitions as well as displaying novel quantum states with no classical analogs. The lectures are based on: G.-Y. Xu et al., Science 317, 1049-1052 (2007); G. Aeppli, P. Warburton, C. Renner, BT Technology Journal, 24, 163-169 (2006); H. M. Ronnow et al., Science 308, 392-395 (2005) and N. Q. Vinh et al., PNAS 105, 10649-10653 (2008).

Aeppli, G. [London Centre for Nanotechnology, 17-19 Gordon Street, London (United Kingdom); Department of Physics and Astronomy, University College of London, London (United Kingdom)

2009-08-20

169

Introduction to Quantum Mechanics: Assessment  

NSDL National Science Digital Library

This resource provides an assessment for students who have just learned the basics of quantum mechanics. The accompanying interactive lesson which may be used before this assessment is given may be found here. This five question assessment covers the concept of probability, electrons and some other basic concepts related to quantum mechanics. The other educational modules in this series can be found here. Instructors and students are encouraged to sign up with the Electron Technologies site here before starting to use these materials.

2012-03-20

170

Invariant Eigen-Operator Method of Deriving Energy-Level Gap for Noncommutative Quantum Mechanics  

Microsoft Academic Search

We propose a new method to derive energy-level gap for Hamiltonians in the context of noncommutative quantum mechanics (NCQM). This method relies on finding invariant eigen-operators whose commutators with Hamiltonian are still the operators themselves but with some eigenvalue-like coefficients, which correspond to the energy-level gaps of the systems. Based on this method, only after some simple algebra, we derive

Si-Cong Jing; Hong-Yi Fan

2005-01-01

171

Deformed Clifford algebra and supersymmetric quantum mechanics on a phase space with applications in quantum optics  

NASA Astrophysics Data System (ADS)

In order to realize supersymmetric quantum mechanics methods on a four-dimensional classical phase space, the complexified Clifford algebra of this space is extended by deforming it with the Moyal star product in composing the components of Clifford forms. Two isospectral matrix Hamiltonians having a common bosonic part but different fermionic parts depending on four real-valued phase-space functions are obtained. The Hamiltonians are doubly intertwined via matrix-valued functions which are divisors of zero in the resulting Moyal-Clifford algebra. Two illustrative examples corresponding to Jaynes-Cummings-type models of quantum optics are presented as special cases of the method. Their spectra, eigenspinors and Wigner functions as well as their constants of motion are also obtained within the autonomous framework of deformation quantization.

Bu?dayc?, ?.; Verçin, A.

2009-09-01

172

Fundamental length in quantum theories with PT-symmetric Hamiltonians. II. The case of quantum graphs  

NASA Astrophysics Data System (ADS)

PT-symmetrization of quantum graphs is proposed as an innovation where an adjustable, tunable nonlocality is admitted. The proposal generalizes the PT-symmetric square-well models of Ref. [M. Znojil, Phys. Rev. DPRVDAQ1550-7998 80, 045022 (2009).10.1103/PhysRevD.80.045022] (with real spectrum and with a variable fundamental length ?) which are reclassified as the most elementary quantum q-pointed-star graphs with minimal q=2. Their equilateral q=3,4,… generalizations are considered, with interactions attached to the vertices. Runge-Kutta discretization of coordinates simplifies the quantitative analysis by reducing our graphs to star-shaped lattices of N=qK+1 points. The resulting bound-state spectra are found real in an N-independent interval of couplings ??(-1,1). Inside this interval the set of closed-form metrics ?j(N)(?) is constructed, defining independent eligible local (at j=0) or increasingly nonlocal (at j=1,2,…) inner products in the respective physical Hilbert spaces of states Hj(N)(?). In this way each graph is assigned a menu of nonequivalent, optional probabilistic quantum interpretations.

Znojil, Miloslav

2009-11-01

173

Generalized quantum mechanics  

Microsoft Academic Search

A convex scheme of quantum theory is outlined where the states are not necessarily the density matrices in a Hilbert space. The physical interpretation of the scheme is given in terms of generalized “impossibility principles”. The geometry of the convex set of all pure and mixed states (called a statistical figure) is conditioned by the dynamics of the system. This

Bogdan Mielnik

1974-01-01

174

Quantum Mechanics Resource Packet  

NSDL National Science Digital Library

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

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

2005-07-25

175

Bohmian Mechanics and Quantum Information  

NASA Astrophysics Data System (ADS)

Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of quantum mechanics, Bohmian mechanics, is concerned, not with information but with the behavior of an objective microscopic reality given by particles and their positions. What I would like to do here is to examine whether, and to what extent, the importance of information, observation, and the like in quantum theory can be understood from a Bohmian perspective. I would like to explore the hypothesis that the idea that information plays a special role in physics naturally emerges in a Bohmian universe.

Goldstein, Sheldon

2010-04-01

176

On two-dimensional supersymmetric quantum mechanics, pseudoanalytic functions and transmutation operators  

NASA Astrophysics Data System (ADS)

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

Bilodeau, Alex; Tremblay, Sébastien

2013-10-01

177

Physicalism Versus Quantum Mechanics  

Microsoft Academic Search

The widely held philosophical position called “physicalism” has been described and defended in a recent book by Jaegwon Kim.\\u000a The physicalist position claims that the world is basically purely physical. However, “physical” is interpreted in a way predicated,\\u000a in effect, upon certain properties of classical physics that are contradicted by the precepts of orthodox quantum physics.\\u000a Kim’s arguments reveal two

Henry P. Stapp

178

Quantum Mechanics Tutorials  

NSDL National Science Digital Library

This website contains a collection of materials for use in a small group tutorial setting. The materials are a part of a model applied quantum physics course at the University of Maryland which is directed toward science and engineering students. This web page contains links to research and resources, such as pretests, tutorials, homework, and handouts. (A password must be obtained for access to resources)

Redish, Edward F.; Steinberg, Richard N.; Wittmann, Michael C.

2005-08-07

179

Supersymmetric quantum mechanics and paraquantization  

SciTech Connect

The paraquantum Hamiltonian of a free particle is shown to be supersymmetric. Depending on the space-time dimension, the corresponding N=1 and N=2 supercharges are constructed and the related Hamiltonians are derived.

Morchedi, O.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)

2012-06-27

180

New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis  

NASA Astrophysics Data System (ADS)

Loop quantum gravity (LQG) relies heavily on a connection formulation of general relativity such that (1) the connection Poisson commutes with itself and (2) the corresponding gauge group is compact. This can be achieved starting from the Palatini or Holst action when imposing the time gauge. Unfortunately, this method is restricted to D + 1 = 4 spacetime dimensions. However, interesting string theories and supergravity theories require higher dimensions and it would therefore be desirable to have higher dimensional supergravity loop quantizations at one’s disposal in order to compare these approaches. In this series of papers we take first steps toward this goal. The present first paper develops a classical canonical platform for a higher dimensional connection formulation of the purely gravitational sector. The new ingredient is a different extension of the ADM phase space than the one used in LQG which does not require the time gauge and which generalizes to any dimension D > 1. The result is a Yang-Mills theory phase space subject to Gauß, spatial diffeomorphism and Hamiltonian constraint as well as one additional constraint, called the simplicity constraint. The structure group can be chosen to be SO(1, D) or SO(D + 1) and the latter choice is preferred for purposes of quantization.

Bodendorfer, N.; Thiemann, T.; Thurn, A.

2013-02-01

181

Quantum Mechanical Earth: Where Orbitals Become Orbits  

ERIC Educational Resources Information Center

|Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…

Keeports, David

2012-01-01

182

Quantum mechanical force field for water with explicit electronic polarization.  

PubMed

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

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

2013-08-01

183

Self-Referential Quantum Mechanics  

NASA Astrophysics Data System (ADS)

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

Mitchell, Mark Kenneth

1993-01-01

184

The transitions among classical mechanics, quantum mechanics, and stochastic quantum mechanics  

NASA Astrophysics Data System (ADS)

Various formalisms for recasting quantum mechanics in the framework of classical mechanics on phase space are reviewed and compared. Recent results in stochastic quantum mechanics are shown to avoid the difficulties encountered by the earlier approach of Wigner, as well as to avoid the well-known incompatibilities of relativity and ordinary quantum theory. Specific mappings among the various formalisms are given.

Schroeck, Franklin E.

1982-09-01

185

Surveying students' understanding of quantum mechanics in one spatial dimension  

NSDL National Science Digital Library

We explore the difficulties that advanced undergraduate and graduate students have with non-relativistic quantum mechanics of a single particle in one spatial dimension. To investigate these difficulties we developed a conceptual survey and administered it to more than 200 students at 10 institutions. The issues targeted in the survey include the set of possible wavefunctions, bound and scattering states, quantum measurement, expectation values, the role of the Hamiltonian, and the time-dependence of the wavefunction and expectation values. We find that undergraduate and graduate students have many common difficulties with these concepts and that research-based tutorials and peer-instruction tools can significantly reduce these difficulties. The findings also suggest that graduate quantum mechanics courses may not be effective at helping students to develop a better conceptual understanding of these topics, partly because such courses mainly focus on quantitative assessments.

Zhu, Guangtian; Singh, Chandralekha

2012-04-30

186

Quantum Dynamics of Multi Harmonic Oscillators Described by Time Variant Conic Hamiltonian and their Use in Contemporary Sciences  

SciTech Connect

This work focuses on the dynamics of a system of quantum multi harmonic oscillators whose Hamiltonian is conic in positions and momenta with time variant coefficients. While it is simple, this system is useful for modeling the dynamics of a number of systems in contemporary sciences where the equations governing spatial or temporal changes are described by sets of ODEs. The dynamical causal models used readily in neuroscience can be indirectly described by these systems. In this work, we want to show that it is possible to describe these systems using quantum wave function type entities and expectations if the dynamic of the system is related to a set of ODEs.

Demiralp, Metin [Istanbul Technical University, Informatics Institute, Group for Science and Methods of Computing, Maslak, 34469, Istanbul (Turkey)

2010-09-30

187

Time-averaged quantum dynamics and the validity of the effective Hamiltonian model  

SciTech Connect

We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the general equation to harmonic Hamiltonians, we confirm a previous formula for the effective Hamiltonian together with a additional decoherence term which should, in general, be included and whose vanishing provides the criteria for validity of the effective Hamiltonian approach. Finally, we apply the theory to examples of the ac Stark shift and three-level Raman transitions, recovering a decoherence effect in the latter.

Gamel, Omar; James, Daniel F. V. [Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7 (Canada)

2010-11-15

188

Optimal control of open quantum systems: a combined surrogate hamiltonian optimal control theory approach applied to photochemistry on surfaces.  

PubMed

In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ? = m(e) = e = a(0) = 1, have been used unless otherwise stated. PMID:22462846

Asplund, Erik; Klüner, Thorsten

2012-03-28

189

Optimal control of open quantum systems: A combined surrogate Hamiltonian optimal control theory approach applied to photochemistry on surfaces  

SciTech Connect

In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ({Dirac_h}/2{pi})=m{sub e}=e=a{sub 0}= 1, have been used unless otherwise stated.

Asplund, Erik; Kluener, Thorsten [Institut fuer Reine und Angewandte Chemie, Carl von Ossietzky Universitaet Oldenburg, Postfach 2503, D-26111 Oldenburg (Germany)

2012-03-28

190

Remarks on Osmosis, Quantum Mechanics, and Gravity  

NASA Astrophysics Data System (ADS)

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

Carroll, Robert

2012-05-01

191

A transfer Hamiltonian approach for an arbitrary quantum dot array in the self-consistent field regime  

NASA Astrophysics Data System (ADS)

A transport methodology to study electron transport between quantum dot arrays based on the transfer Hamiltonian approach is presented. The interactions between the quantum dots and between the quantum dots and the electrodes are introduced via transition rates and capacitive couplings. The effects of the local potential are computed within the self-consistent field regime. The model has been developed and expressed in a matrix form in order to make it extendable to larger systems. Transport through several quantum dot configurations has been studied in order to validate the model. Despite the simplicity of the model, well-known effects are satisfactorily reproduced and explained. The results qualitatively agree with other results obtained using more complex theoretical approaches.

Illera, S.; Garcia-Castello, N.; Prades, J. D.; Cirera, A.

2012-11-01

192

Davidson potential and SUSYQM in the Bohr Hamiltonian  

NASA Astrophysics Data System (ADS)

The Bohr Hamiltonian is modified through the Shape Invariance principle of SUper-SYmmetric Quantum Mechanics for the Davidson potential. The modification is equivalent to a conformal transformation of Bohr's metric, generating a different ?-dependence of the moments of inertia.

Georgoudis, P. E.

2013-06-01

193

OSP: Quantum-mechanical Measurement  

NSDL National Science Digital Library

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

Belloni, Mario; Christian, Wolfgang

2006-06-27

194

Effective equations for the quantum pendulum from momentous quantum mechanics  

SciTech Connect

In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.

Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)

2012-08-24

195

FAST TRACK COMMUNICATION: Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd k  

NASA Astrophysics Data System (ADS)

In a recent communication paper by Tremblay et al (2009 J. Phys. A: Math. Theor. 42 205206), it has been conjectured that for any integer value of k, some novel exactly solvable and integrable quantum Hamiltonian Hk on a plane is superintegrable and that the additional integral of motion is a 2kth-order differential operator Y2k. Here we demonstrate the conjecture for the infinite family of Hamiltonians Hk with odd k >= 3, whose first member corresponds to the three-body Calogero-Marchioro-Wolfes model after elimination of the centre-of-mass motion. Our approach is based on the construction of some D2k-extended and invariant Hamiltonian {\\cal H}_k, which can be interpreted as a modified boson oscillator Hamiltonian. The latter is then shown to possess a D2k-invariant integral of motion {\\cal Y}_{2k}, from which Y2k can be obtained by projection in the D2k identity representation space.

Quesne, C.

2010-02-01

196

Capacity and quantum mechanical tunneling  

Microsoft Academic Search

We connect the notion of capacity of sets in the theory of symmetric Markov process and Dirichlet forms with the notion of tunneling through the boundary of sets in quantum mechanics. In particular we show that for diffusion processes the notion appropriate to a boundary without tunneling is more refined than simply capacity zero. We also discuss several examples in

S. Albeverio; M. Fukushima; W. Karwowski; L. Streit

1981-01-01

197

Self-Referential Quantum Mechanics  

Microsoft Academic Search

A nonlinear quantum mechanics based upon the nonlinear logarithmic Schrodinger equation, is developed which has the property of self-reference, that is, the nonlinear term is dependent upon the square of the wavefunction. The self-referential system is examined in terms of its mathematical properties, the definition of the wavefunction, and the nonlinear system in the feedback between equation and solution. Theta

Mark Kenneth Mitchell

1993-01-01

198

Quantum Mechanics and Physical Reality  

Microsoft Academic Search

IN a recent article by A. Einstein, B. Podolsky and N. Rosen, which appeared in the Physical Review of May 15, and was reviewed in NATURE of June 22, the question of the completeness of quantum mechanical description has been discussed on the basis of a ``criterion of physical reality'', which the authors formulate as follows : ``If, without in

N. Bohr

1935-01-01

199

Negative Observations in Quantum Mechanics  

Microsoft Academic Search

In quantum mechanics, it is possible to make observations that affect\\u000aphysical entities without there being a physical interaction between the\\u000aobserver and the physical entity measured. Epstein (1945) and Renninger (1960)\\u000adiscussed this situation, and Renninger called this type of observation a\\u000a\\

Douglas M. Snyder

1999-01-01

200

Quantum mechanics, relativity and time  

Microsoft Academic Search

A discussion on quantum mechanics, general relativity and their relations is introduced. The assumption of the absolute validity of conservation laws and the extension to a 5D-space lead to reconsider several shortcomings and paradoxes of modern physics under a new light without the necessity to take into account symmetry breakings. In this picture, starting from first principles, and after a

Giuseppe Basini; Salvatore Capozziello

2005-01-01

201

Collective Motion in Quantum Mechanics  

Microsoft Academic Search

A general method of discussing quantum-mechanical problems involving collective motion is proposed, in which the emphasis is placed on consideration of sets of states rather than single states, and in which the additional collective co-ordinates are not redundant but used to describe the sets. The method is applied to a number of relatively simple examples: plasma oscillations of an electron

T. H. R. Skyrme

1957-01-01

202

Quantum Mechanical Methods for Enzyme Kinetics  

Microsoft Academic Search

This review discusses methods for the incorporation of quantum mechanical effects into enzyme kinetics simulations in which the enzyme is an explicit part of the model. We emphasize three aspects: (a) use of quantum mechanical electronic structure methods such as molecular orbital theory and density functional theory, usually in conjunction with molecular mechanics; (b) treating vibrational motions quantum mechanically, either

Jiali Gao; Donald G. Truhlar

2002-01-01

203

Probable Inference and Quantum Mechanics  

SciTech Connect

In its current very successful interpretation the quantum theory is fundamentally statistical in nature. Although commonly viewed as a probability amplitude whose (complex) square is a probability, the wavefunction or state vector continues to defy consensus as to its exact meaning, primarily because it is not a physical observable. Rather than approach this problem directly, it is suggested that it is first necessary to clarify the precise role of probability theory in quantum mechanics, either as applied to, or as an intrinsic part of the quantum theory. When all is said and done the unsurprising conclusion is that quantum mechanics does not constitute a logic and probability unto itself, but adheres to the long-established rules of classical probability theory while providing a means within itself for calculating the relevant probabilities. In addition, the wavefunction is seen to be a description of the quantum state assigned by an observer based on definite information, such that the same state must be assigned by any other observer based on the same information, in much the same way that probabilities are assigned.

Grandy, W. T. Jr. [Department of Physics and Astronomy, University of Wyoming, Laramie, WY 82070 (United States)

2009-12-08

204

Adaptive Perturbation Theory: Quantum Mechanics and Field Theory  

SciTech Connect

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable 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. In this talk I will introduce the method in the context of the pure anharmonic oscillator and then apply it to the case of tunneling between symmetric minima. After that, I will show how this method can be applied to field theory. In that discussion I will show how one can non-perturbatively extract the structure of mass, wavefunction and coupling constant renormalization.

Weinstein, Marvin; /SLAC

2005-10-19

205

Topics in quantum mechanics  

SciTech Connect

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

Moshinsky, Marcos [Instituto de Fisica-UNAM. Apartado Postal 20-364, 01000 Mexico, D.F. (Mexico)

1999-03-06

206

Student understanding of quantum mechanics  

NSDL National Science Digital Library

We investigate the difficulties of advanced undergraduate students toward the end of a full year upper-level quantum mechanics course with concepts related to quantum measurements and time development. Our analysis is based upon a test administered to 89 students from six universities and interviews with 9 students. Strikingly, most students shared the same difficulties despite variations in background, teaching styles, and textbooks. Concepts related to stationary states, eigenstates, and time dependence of expectation values were found to be particularly difficult. An analysis of written tests and interviews suggests that widespread misconceptions originate from an inability to discriminate between related concepts and a tendency to overgeneralize.

Singh, Chandralekha

2005-11-23

207

On Quantum Mechanics on Noncommutative Quantum Phase Space  

Microsoft Academic Search

In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM) is showed to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this particular transformation, we firstly find that the product of the two noncommutativity parameters possesses a lower bound in direct relation with Heisenberg incertitude relations,

A. E. F. Djemai; H. Smail

2003-01-01

208

A quantum mechanical model of interference  

Microsoft Academic Search

In this paper an ideal quantum mechanical model of interference is constructed, in particular, the role of the quantum mechanical phase difference of two harmonic modes on the interference picture is investigated.

A. Shalom; J. Zak

1973-01-01

209

The Bogoliubov-de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry  

SciTech Connect

We show that the Ginzburg-Landau expansion of the grand potential for the Bogoliubov-de Gennes Hamiltonian is determined by the integrable nonlinear equations of the AKNS hierarchy, and that this provides the natural mathematical framework for a hidden nonlinear quantum mechanical supersymmetry underlying the dynamics.

Correa, Francisco [Departamento de Fisica, Universidad de Santiago de Chile, Casilla 307, Santiago 2 (Chile); Dunne, Gerald V. [Physics Department, University of Connecticut, Storrs, CT 06269 (United States); Plyushchay, Mikhail S. [Departamento de Fisica, Universidad de Santiago de Chile, Casilla 307, Santiago 2 (Chile)], E-mail: m.plyushchay@gmail.com

2009-12-15

210

Quantum mechanics of black holes.  

PubMed

The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely. PMID:22859480

Witten, Edward

2012-08-01

211

Three-space from quantum mechanics  

SciTech Connect

We formulate a discrete quantum-mechanical precursor to spacetime geometry. The objective is to provide the foundation for a quantum mechanics that is rooted exclusively in quantum-mechanical concepts, with all classical features, including the three-dimensional spatial continuum, emerging dynamically.

Chew, G.F.; Stapp, H.P.

1988-08-01

212

Quantum mechanics and the psyche  

NASA Astrophysics Data System (ADS)

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

Galli Carminati, G.; Martin, F.

2008-07-01

213

What is an Essentially Quantum Mechanical Effect?  

Microsoft Academic Search

Abstract When asking whether consciousness is an “essentially quantum effect”, one must first lay down criteria for considering an effect ,quantum ,mechanical. After a brief survey ,of the ,interpretations of quantum theory, three such sufficient criteria are proposed and examined: wave-particle duality (or collapse), entanglement (“non-locality”), and quantum condensation (involving “identical” particles). A fourth criteria could involve the use of

Osvaldo Pessoa Jr

214

Superconformal black hole quantum mechanics  

Microsoft Academic Search

In recent work, the superconformal quantum mechanics describing D0 branes in the AdS2 × S2 × CY3 attractor geometry of a Calabi-Yau black hole with D4 brane charges pA has been constructed and found to contain a large degeneracy of chiral primary bound states. In this paper it is shown that the asymptotic growth of chiral primaries for N D0

Davide Gaiotto; Andrew Strominger; Xi Yin

2005-01-01

215

Teaching quantum mechanics on an introductory level  

NSDL National Science Digital Library

We present a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. In the context of virtual laboratories, the students discover from the very beginning how quantum phenomena deviate from our classical everyday experience. The results of the evaluation of the course show that most of the students acquired appropriate quantum mechanical conceptions, and that many of the common misconceptions encountered in traditional instruction have been avoided.

Mã¼ller, Rainer; Wiesner, Hartmut

2005-10-27

216

Facets of contextual realism in quantum mechanics  

SciTech Connect

In recent times, there is an upsurge of interest in demonstrating the quantum contextuality. In this proceedings, we explore the two different forms of arguments that have been used for showing the contextual character of quantum mechanics. First line of study concerns the violations of the noncontextual realist models by quantum mechanics, where second line of study that is qualitatively distinct from the earlier one, demonstrates the contextuality within the formalism of quantum mechanics.

Pan, Alok Kumar [LPTM (CNRS Unite 8089), Universite de Cergy-Pontoise, 95302 Cergy-Pontoise cedex (France); Home, Dipankar [CAPSS, Department of Physics, Bose Institute, Salt Lake, Calcutta 700091 (India)

2011-09-23

217

Trojan wavepackets in quantum mechanics equivalent to classical mechanics  

NASA Astrophysics Data System (ADS)

We formulate the theory of wavepackets moving on classical circular orbits in Hydrogen atom in rotating electromagnetic wave within the quantum mechanics equivalent to classical mechanics [1]. Unlike within the true quantum mechanics the wavepackets spreads during the time comparable with the time of full quantum revival within true quantum mechanics. Numerical solutions of the nonlinear Schrodingers equation are provided using non-linear split operator method for this equation. [1] D. Shay, Phys. Rev A, 13, 2261 (1976).

Kalinski, Matt

2005-05-01

218

Boundary conditions in quantum mechanics on the discretized half-line  

NASA Astrophysics Data System (ADS)

We investigate nonrelativistic quantum mechanics on the discretized half-line, constructing a one-parameter family of Hamiltonians that are analogous to the Robin family of boundary conditions in continuum half-line quantum mechanics. For classically singular Hamiltonians, the construction provides a singularity avoidance mechanism that has qualitative similarities with singularity avoidance encountered in loop quantum gravity. Applications include the free particle, the attractive Coulomb potential, the scale invariant potential and a black hole described in terms of the Einstein-Rosen wormhole throat. The spectrum is analysed by analytic and numerical techniques. In the continuum limit, the full Robin family of boundary conditions can be recovered via a suitable fine-tuning but the Dirichlet-type boundary condition emerges as generic.

Kunstatter, Gabor; Louko, Jorma

2012-08-01

219

Construction of the metric and equivalent Hermitian Hamiltonian via SUSY transformation operators  

SciTech Connect

The metric operator, which is the basic ingredient for studying a quantum system described by a pseudo-Hermitian Hamiltonian, provides the necessary means for obtaining an equivalent description of the system using a Hermitian Hamiltonian. In the framework of supersymmetric quantum mechanics, we propose a method of constructing the metric operator and to obtain the Hermitian Hamiltonian equivalent to the given pseudo-Hermitian.

Shamshutdinova, V. V., E-mail: shvv@phys.tsu.ru [Tomsk State University (Russian Federation)

2012-10-15

220

Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems  

NASA Astrophysics Data System (ADS)

We explore the role of the initial state on the onset of thermalization in isolated quantum many-body systems after a quench. The initial state is an eigenstate of an initial Hamiltonian ?I and it evolves according to a different final Hamiltonian ?F. If the initial state has a chaotic structure with respect to ?F, i.e., if it fills the energy shell ergodically, thermalization is certain to occur. This happens when ?I is a full random matrix, because its states projected onto ?F are fully delocalized. The results for the observables then agree with those obtained with thermal states at infinite temperature. However, finite real systems with few-body interactions, as the ones considered here, are deprived of fully extended eigenstates, even when described by a nonintegrable Hamiltonian. We examine how the initial state delocalizes as it gets closer to the middle of the spectrum of ?F, causing the observables to approach thermal averages, be the models integrable or chaotic. Our numerical studies are based on initial states with energies that cover the entire lower half of the spectrum of one-dimensional Heisenberg spin-1/2 systems.

Torres-Herrera, E. J.; Santos, Lea F.

2013-10-01

221

Symmetry of k•p Hamiltonian in pyramidal InAs/GaAs quantum dots: Application to the calculation of electronic structure  

NASA Astrophysics Data System (ADS)

A method for the calculation of the electronic structure of pyramidal self-assembled InAs/GaAs quantum dots is presented. The method is based on exploiting the Cmacr 4 symmetry of the 8-band k•p Hamiltonian with the strain taken into account via the continuum mechanical model. The operators representing symmetry group elements were represented in the plane wave basis and the group projectors were used to find the symmetry adapted basis in which the corresponding Hamiltonian matrix is block diagonal with four blocks of approximately equal size. The quantum number of total quasiangular momentum is introduced and the states are classified according to its value. Selection rules for interaction with electromagnetic field in the dipole approximation are derived. The method was applied to calculate electron and hole quasibound states in a periodic array of vertically stacked pyramidal self-assembled InAs/GaAs quantum dots for different values of the distance between the dots and external axial magnetic field. As the distance between the dots in an array is varied, an interesting effect of simultaneous change of ground hole state symmetry, type, and the sign of miniband effective mass is predicted. This effect is explained in terms of the change of biaxial strain. It is also found that the magnetic field splitting of Kramer’s double degenerate states is most prominent for the first and second excited state in the conduction band and that the magnetic field can both separate otherwise overlapping minibands and concatenate otherwise nonoverlapping minibands.

Vukmirovi?, Nenad; Indjin, Dragan; Jovanovi?, Vladimir D.; Ikoni?, Zoran; Harrison, Paul

2005-08-01

222

BOOK REVIEWS: Quantum Mechanics: Fundamentals  

NASA Astrophysics Data System (ADS)

This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried’s well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Quantum mechanics was already solidly established by 1966, but this second edition gives an indication of progress made and changes in perspective over the last thirty-five years, and also recognises the very substantial increase in knowledge of quantum theory obtained at the undergraduate level. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Their practical importance has now been fully recognised, and a substantial account of them is provided in the new book. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. John Bell’s work of the mid-1960s has led to genuine theoretical and experimental achievement, which has facilitated the development of quantum optics and quantum information theory. Gottfried’s 1966 book played a modest part in this development. When Bell became increasingly irritated with the standard theoretical approach to quantum measurement, Viki Weisskopf repeatedly directed him to Gottfried’s book. Gottfried had devoted a chapter of his book to these matters, titled ‘The Measurement Process and the Statistical Interpretation of Quantum Mechanics’. Gottfried considered the von Neumann or Dirac ‘collapse of state-vector’ (or ‘reduction postulate’ or ‘projection postulate’) was unsatisfactory, as he argued that it led inevitably to the requirement to include ‘consciousness’ in the theory. He replaced this by a more mathematically and conceptually sophisticated treatment in which, following measurement, the density matrix of the correlated measured and measuring systems, rho, is replaced by hat rho, in which the interference terms from rho have been removed. rho represents a pure state, and hat rho a mixture, but Gottfried argued that they are ‘indistinguishable’, and that we may make our replacement, ‘safe in the knowledge that the error will never be found’. Now our combined state is represented as a mixture, it is intuitive, Gottfried argued, to interpret it in a probabilistic way, |cm|2 being the probability of obtaining the mth measurement result. Bell liked Gottfried’s treatment little more than the cruder ‘collapse’ idea of von Neumann, and when, shortly before Bell’s death, his polemical article ‘Against measurement’ was published in the August 1990 issue of Physics World (pages 33-40), his targets included, not only Landau and Lifshitz’s classic Quantum Mechanics, pilloried for its advocacy of old-fashioned collapse, and a paper by van Kampen in Physica, but also Gottfried’s approach. Bell regarded his replacement of rho by hat rho as a ‘butchering’ of the density matrix, and considered, in any case, that even the butchered density matrix should represent co-existence of different terms, not a set of probabilities. Gottfried has replied to Bell ( Physics World, October 1991, pages 34-40; Nature 405, 533-36 (2000)). He has also become a major commentator on Bell’s work, for example editing the section on quantum foundations in the World Scientific edition of Bell’s collected works. Thus it is exceedingly interesting to disco

Whitaker, A.

2004-02-01

223

SENSIBLE QUANTUM MECHANICS: ARE ONLY PERCEPTIONS  

Microsoft Academic Search

Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so that it contains nothing probabilistic, except, in a certain frequency sense, conscious perceptions. Sets of these perceptions can be deterministi- cally realized with measures given by expectation values of positive-operator- valued awareness operators in a quantum state of the universe which never jumps or collapses. Ratios of the measures

Don N. Page

224

Teaching Quantum Mechanics on an Introductory Level.  

ERIC Educational Resources Information Center

|Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)|

Muller, Rainer; Wiesner, Hartmut

2002-01-01

225

Web-based Quantum Mechanics I Course  

NSDL National Science Digital Library

This web site is an entire web-based Quantum Mechanics I Course based at the University of Tennessee. It includes instructional materials, in-class tutorials, simulations, links to other quantum resources, homework assignments, and solutions.

Breinig, Marianne

2009-09-17

226

Multiverse interpretation of quantum mechanics  

NASA Astrophysics Data System (ADS)

We argue that the many worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics. Decoherence—the modern version of wave-function collapse—is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the environment. In fact decoherence is absent in the complete description of any region larger than the future light cone of a measurement event. However, if one restricts to the causal diamond—the largest region that can be causally probed—then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment. We argue that the global multiverse is a representation of the many worlds (all possible decoherent causal diamond histories) in a single geometry. We propose that it must be possible in principle to verify quantum-mechanical predictions exactly. This requires not only the existence of exact observables but two additional postulates: a single observer within the Universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite. In causal diamonds with a finite surface area, holographic entropy bounds imply that no exact observables exist, and both postulates fail: experiments cannot be repeated infinitely many times; and decoherence is not completely irreversible, so outcomes are not definite. We argue that our postulates can be satisfied in hats (supersymmetric multiverse regions with vanishing cosmological constant). We propose a complementarity principle that relates the approximate observables associated with finite causal diamonds to exact observables in the hat.

Bousso, Raphael; Susskind, Leonard

2012-02-01

227

Entropy Production and Equilibration in Yang-Mills Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Entropy production in relativistic heavy-ion collisions is an important physical quantity for studying the equilibration and thermalization of hot matters of quantum chromodynamics (QCD). To formulate a nontrivial definition of entropy for an isolated quantum system, a certain kind of coarse graining may be applied so that the entropy for this isolated quantum system depends on time explicitly. The Husimi distribution, which is a coarse grained distribution in the phase space, is a suitable candidate for this approach. We proposed a general and systematic method of solving the equation of motion of the Husimi distribution for an isolated quantum system. The Husimi distribution is positive (semi-)definite all over the phase space. In this method, we assume the Husimi distribution is composed of a large number of Gaussian test functions. The equation of motion of the Husimi distribution, formulated as a partial differential equation, can be transformed into a system of ordinary differential equations for the centers and the widths of these Gaussian test functions. We numerically solve the system of ordinary differential equations for the centers and the widths of these test functions to obtain the Husimi distribution as a function of time. To ensure the numerical solutions of the trajectories of the test particles preserve physical conservation laws, we obtain a constant of motion for the quantum system. We constructed a coarse grained Hamiltonian whose expectation value is exactly conserved. The conservation of the coarse grained energy confirms the validity of this method. Moreover, we calculated the time evolution of the coarse grained entropy for a model system (Yang-Mills quantum mechanics). Yang-Mills quantum mechanics is a quantum system whose classical correspondence possesses chaotic behaviors. The numerical results revealed that the coarse grained entropy for Yang-Mills quantum mechanics saturates to a value that coincides with the microcanonical entropy corresponding to the energy of the system. Our results confirmed the validity of the framework of first-principle evaluation of the coarse grained entropy growth rate. We show that, in the energy regime under study, the relaxation time for the entropy production in Yang-Mills quantum mechanics is approximately the same as the characteristic time of the system, indicating fast equilibration of the system. Fast equilibration of Yang-Mills quantum mechanics is consistent to current understanding of fast equilibration of hot QCD matter in relativistic heavy-ion collisions.

Tsai, Hung-Ming

228

Thermalization Processes in Quantum Mechanics  

NASA Astrophysics Data System (ADS)

In quantum mechanics, the emergence of thermalization processes from unitary evolution has remained one of the greatest challenges. The two outstanding theories of this issue by Srednicki and Tasaki cannot address the concepts of temperature, heat, and work. Here, we present a theory using multiple quenches to examine the thermalization processes to advance thermodynamics concepts. To perform multiple quenches, one can vary one single control parameter (?) in a series of time evolutions, which create a set of density operators. The average of these density operators results into a diagonal operator with probability distribution function that can describe the emerging ensembles. Measuring probability distribution functions of key physical observables, temperature, equal to the derivative of energy with respect to entropy, can be easily measured. Therefore, simulations via multiple quenches can mimic dynamics in open quantum systems with much cheaper computational cost. They allow (1) tuning of temperature and entropy via ?, (2) measuring work distribution functions from distributions of a reaction coordinate, and (3) computing free-energy changes via Jarzynski's Equality. We hope that this approach can provide a new foundation and open up new directions for studying control of quantum systems.

Ngo, Van; Haas, Stephan

2013-03-01

229

Introduction to Quantum Mechanics Activity  

NSDL National Science Digital Library

This resource provides an introductory activity on "the basic quantum mechanics concepts about electrons that are essential to understanding modern and future technology- especially nanotechnology that will be vitally important to the industry." Core concepts include probability distribution, electron waves, diffraction, interference, tunneling, bound states and excited states. The interactive module allows students to test their knowledge as they learn. The material would be best for high school AP classes and college level students. The other educational modules in this series can be found here. Instructors and students are encouraged to sign up with the Electron Technologies site here before starting to use these materials.

2012-02-24

230

Quantum mechanical polar surface area.  

PubMed

A correlation has been established between the absorbed fraction of training-set molecules after oral administration in humans and the Quantum Mechanical Polar Surface Area (QMPSA). This correlation holds for the QMPSA calculated with structures where carboxyl groups are deprotonated. The correlation of the absorbed fraction and the QMPSA calculated on the neutral gas phase optimized structures is much less pronounced. This suggests that the absorption process is mainly determined by polar interactions of the drug molecules in water solution. Rules are given to derive the optimal polar/apolar ranges of the electrostatic potential. PMID:22391921

Schaftenaar, Gijs; de Vlieg, Jakob

2012-03-04

231

Tunneling in fractional quantum mechanics  

NASA Astrophysics Data System (ADS)

We study tunneling through delta and double delta potentials in fractional quantum mechanics. After solving the fractional Schrödinger equation for these potentials, we calculate the corresponding reflection and transmission coefficients. These coefficients have a very interesting behavior. In particular, we can have zero energy tunneling when the order of the Riesz fractional derivative is different from 2. For both potentials, the zero energy limit of the transmission coefficient is given by {T}_0 = \\cos ^2{(\\pi /\\alpha )}, where ? is the order of the derivative (1 < ? <= 2).

Capelas de Oliveira, E.; Vaz, Jayme, Jr.

2011-05-01

232

A semiclassical correction for quantum mechanical energy levels  

SciTech Connect

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

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

2010-08-07

233

Snyder noncommutativity and pseudo-Hermitian Hamiltonians from a Jordanian twist  

SciTech Connect

Nonrelativistic quantum mechanics and conformal quantum mechanics are deformed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian Hamiltonians of the type discussed by Mostafazadeh. The quantization scheme makes use of the so-called 'unfolded formalism' discussed in previous works. A Hopf algebra structure, compatible with the physical interpretation of the coproduct, is introduced for the universal enveloping algebra of a suitably chosen dynamical Lie algebra (the Hamiltonian is contained among its generators). The multi-particle sector, uniquely determined by the deformed two-particle Hamiltonian, is composed of bosonic particles.

Castro, P. G. [DM/ICE/UFJF, Campus Universitario, cep 36036-330, Juiz de Fora (Brazil); Kullock, R.; Toppan, F. [TEO/CBPF, Rua Dr. Xavier Sigaud 150, cep 22290-180, Rio de Janeiro (Brazil)

2011-06-15

234

Propagators in polymer quantum mechanics  

NASA Astrophysics Data System (ADS)

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

Flores-González, Ernesto; Morales-Técotl, Hugo A.; Reyes, Juan D.

2013-09-01

235

Quantum mechanics on SO(3) via noncommutative dual variables  

NASA Astrophysics Data System (ADS)

We formulate quantum mechanics on the group SO(3) using a noncommutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new noncommutative variables have a clear connection to the corresponding classical variables, and our analysis confirms them as the natural phase space variables, both mathematically and physically. In particular, we derive the first order (Hamiltonian) path integral in terms of the noncommutative variables, as a formulation of the transition amplitudes alternative to that based on harmonic analysis. We find that the nontrivial phase space structure gives naturally rise to quantum corrections to the action for which we find a closed expression. We then study both the semiclassical approximation of the first order path integral and the example of a free particle on SO(3). On the basis of these results, we comment on the relevance of similar structures and methods for more complicated theories with group-based configuration spaces, such as loop quantum gravity and spin foam models.

Oriti, Daniele; Raasakka, Matti

2011-07-01

236

A Modern Approach to Quantum Mechanics  

NSDL National Science Digital Library

This textbook, unlike most others in the topic, introduces the basic quantum concepts using spin, rather than starting from wave mechanics. This grounding in quantum phenomena, rather than difficult mathematics, is then used to cover all the standard topics in quantum physics. Relationships to experimental results are stressed. An instructor's manual is available.

Townsend, John

2004-03-04

237

Gauge-invariant hydrogen-atom Hamiltonian  

Microsoft Academic Search

For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this puzzle was recently provided by us [X.-S. Chen et al., Phys. Rev. Lett. 100, 232002 (2008)]. Based on the separation of the electromagnetic potential

Wang Fan; Sun Weimin; Chen Xiangsong; Lue Xiaofu

2010-01-01

238

Unified theory of exactly and quasiexactly solvable ''discrete'' quantum mechanics. I. Formalism  

SciTech Connect

We present a simple recipe to construct exactly and quasiexactly solvable Hamiltonians in one-dimensional ''discrete'' quantum mechanics, in which the Schroedinger equation is a difference equation. It reproduces all the known ones whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. The recipe also predicts several new ones. An essential role is played by the sinusoidal coordinate, which generates the closure relation and the Askey-Wilson algebra together with the Hamiltonian. The relationship between the closure relation and the Askey-Wilson algebra is clarified.

Odake, Satoru [Department of Physics, Shinshu University, Matsumoto 390-8621 (Japan); Sasaki, Ryu [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)

2010-08-15

239

Invariant Eigen-Operator Method of Deriving Energy-Level Gap for Noncommutative Quantum Mechanics  

NASA Astrophysics Data System (ADS)

We propose a new method to derive energy-level gap for Hamiltonians in the context of noncommutative quantum mechanics (NCQM). This method relies on finding invariant eigen-operators whose commutators with Hamiltonian are still the operators themselves but with some eigenvalue-like coefficients, which correspond to the energy-level gaps of the systems. Based on this method, only after some simple algebra, we derive the energy-level gaps for several important systems in NCQM, and most of these results have not been reported in literature so far.

Jing, Si-Cong; Fan, Hong-Yi

240

Supersymmetric quantum mechanics: Engineered hierarchies of integrable potentials and related orthogonal polynomials  

NASA Astrophysics Data System (ADS)

Within the context of supersymmetric quantum mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the usual restriction of shape invariance for intertwined potentials, it is suggested to require a similar relation for Hamiltonians in the hierarchy separated by an arbitrary number of levels, N. By requiring further that these two Hamiltonians be in fact identical up to an overall shift in energy, a periodic structure is installed in the hierarchy which should allow for its resolution. Specific classes of orthogonal polynomials characteristic of such periodic hierarchies are thereby generated, while the methods of supersymmetric quantum mechanics then lead to generalised Rodrigues formulae and recursion relations for such polynomials. The approach also offers the practical prospect of quantum modelling through the engineering of quantum potentials from experimental energy spectra. In this paper, these ideas are presented and solved explicitly for the cases N = 1 and N = 2. The latter case is related to the generalised Laguerre polynomials, for which indeed new results are thereby obtained. In the context of dressing chains and deformed polynomial Heisenberg algebras, some partial results for N >= 3 also exist in the literature, which should be relevant to a complete study of the N >= 3 general periodic hierarchies.

Balondo Iyela, Daddy; Govaerts, Jan; Hounkonnou, M. Norbert

2013-09-01

241

Hamiltonian Formalism  

Microsoft Academic Search

In Chapter 2, we introduced the Lagrange function (or Lagrangian) L(q, q, t), which depends on generalized coordinates q and generalized velocities q, considered as independent variables, and, possibly, on time. The Hamiltonian formalism is an alternative to the Lagrangian\\u000a formalism for the description of a mechanical system. Instead of generalized velocities employed in Lagrangian formalism,\\u000a it relies on generalized

Claude Gignoux; Bernard Silvestre-Brac

242

Interactive Learning Tutorials on Quantum Mechanics  

NSDL National Science Digital Library

We discuss the development and evaluation of quantum interactive learning tutorials (QuILTs), which are suitable for undergraduate courses in quantum mechanics. QuILTs are based on the investigation of student difficulties in learning quantum physics. They exploit computer-based visualization tools and help students build links between the formal and conceptual aspects of quantum physics without compromising the technical content. They can be used both as supplements to lectures or as self-study tools.

Singh, Chandralekha

2013-08-08

243

Bohmian mechanics and quantum field theory.  

PubMed

We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end. PMID:15447078

Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino

2004-08-23

244

Thermodynamic integration from classical to quantum mechanics  

SciTech Connect

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.

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

245

The Quantum and Classical Complexity of Translationally Invariant Tiling and Hamiltonian Problems  

Microsoft Academic Search

We study the complexity of a class of problems involving satisfying constraints which remain the same under translations in one or more spatial directions. In this pape r, we show hardness of a classical tiling problem on an N × N 2-dimensional grid and a quantum problem involving finding the ground state energy of a 1-dimensional quantum system of N

Daniel Gottesman; Sandy Irani

2009-01-01

246

Relationship between quantum walks and relativistic quantum mechanics  

SciTech Connect

Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This article revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled forms of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schroedinger form. By showing the coin to be a means to make the walk reversible and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modeled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. The Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of the quantum walk, the maximum speed of walk propagation, and earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two-state system to which the study can be extended.

Chandrashekar, C. M. [Institute for Quantum Computing, University of Waterloo, Ontario N2L 3G1 (Canada); Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada); Banerjee, Subhashish [Chennai Mathematical Institute, Padur PO, Siruseri 603 103 (India); Srikanth, R. [Poornaprajna Institute of Scientific Research, Devanahalli, Bangalore 562 110 (India); Raman Research Institute, Sadashiva Nagar, Bangalore 560 080 (India)

2010-06-15

247

Weyl Geometries, Fisher Information and Quantum Entropy in Quantum Mechanics  

NASA Astrophysics Data System (ADS)

It is known that quantum mechanics can be interpreted as a non-Euclidean deformation of the space-time geometries by means Weyl geometries. We propose here a dynamical explanation of such approach by deriving Bohm potential from minimum condition of Fisher information connected to the entropy of a quantum system.

Fiscaletti, Davide; Licata, Ignazio

2012-11-01

248

Compact versus noncompact quantum dynamics of time-dependent {ital su}(1,1)-valued Hamiltonians  

SciTech Connect

We consider the Schr{umlt o}dinger problem for time-dependent (TD) Hamiltonians represented by a linear combination of the compact generator and the hyperbolic generator of {ital su}(1,1). Several types of transitions, characterized by different time initial conditions on the generator coefficients, are analyzed by resorting to the harmonic oscillator model with a frequency vanishing for {ital t}{r_arrow}+{infinity}. We provide examples that point out how the TD states of the transitions can be constructed either by the compact eigenvector basis or by the noncompact eigenvector basis depending on the initial conditions characterizing the frequency time behavior. Copyright {copyright} 1996 Academic Press, Inc.

Penna, V. [Dipartimento di Fisica and Unita` INFM, Politecnico di Torino, Cso Duca degli Abruzzi 24, 10129 Torino (Italy)

1996-02-01

249

Variational methods in relativistic quantum mechanics  

Microsoft Academic Search

This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to the Laplacian appearing in the equations of nonrelativistic quantum mechanics, the Dirac operator has a negative continuous spectrum which is not bounded from below.

Maria J. Esteban; Mathieu Lewin; Eric séré

2007-01-01

250

Macroscopicity of Mechanical Quantum Superposition States  

NASA Astrophysics Data System (ADS)

We propose an experimentally accessible, objective measure for the macroscopicity of superposition states in mechanical quantum systems. Based on the observable consequences of a minimal, macrorealist extension of quantum mechanics, it allows one to quantify the degree of macroscopicity achieved in different experiments.

Nimmrichter, Stefan; Hornberger, Klaus

2013-04-01

251

On the quantum mechanics of supermembranes  

Microsoft Academic Search

We study the quantum-mechanical properties of a supermembrane and examine the nature of its ground state. A supersymmetric gauge theory of area-preserving transformations provides a convenient framework for this study. The supermembrane can be viewed as a limiting case of a class of models in supersymmetric quantum mechanics. Its mass does not depend on the zero modes and vanishes only

Bernard de Wit; J. Hoppe; H. Nicolai

1988-01-01

252

Quantum Mechanics in Terms of Symmetric Measurements  

NASA Astrophysics Data System (ADS)

In the neo-Bayesian view of quantum mechanics that Appleby, Caves, Pitowsky, Schack, the author, and others are developing, quantum states are taken to be compendia of partial beliefs about potential measurement outcomes, rather than objective properties of quantum systems. Different observers may validly have different quantum states for a single system, and the ultimate origin of each individual state assignment is taken to be unanalyzable within physical theory---its origin, instead, comes from prior probability assignments at stages of physical investigation or laboratory practice previous to quantum theory. The objective content of quantum mechanics thus resides somewhere else than in the quantum state, and various ideas for where that ``somewhere else'' is are presently under debate. What is overwhelmingly agreed upon in this effort is only the opening statement. Still, quantum states are not Bayesian probability assignments themselves, and different representations of the theory (in terms of state vectors or Wigner functions or C*-algebras, etc.) can take one further from or closer to a Bayesian point of view. It is thus worthwhile thinking about which representation might be the most propitious for the point of view and might quell some of the remaining debate. In this talk, I will present several results regarding a representation of quantum mechanics in terms of symmetric bases of positive-semidefinite operators. I also argue why this is probably the most natural representation for a Bayesian-style quantum mechanics.

Fuchs, Christopher

2006-03-01

253

Quantum damped oscillator II: Bateman’s Hamiltonian vs. 2D parabolic potential barrier  

NASA Astrophysics Data System (ADS)

We show that quantum Bateman's system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy plane. It is shown that this representation is more suitable than the hyperbolic one used recently by Blasone and Jizba.

Chru?ci?ski, Dariusz

2006-04-01

254

Distribution Functions in Classical and Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The correspondence between classical and quantum mechanics is an important subject for the better understandings of ``quantum chaos''. In particular, it is very important to investigate the correspondence between distribution functions in classical mechanics and in phase space representation of quantum mechanics. This is the review of our recent progresses in the study of distribution functions in classical and quantum mechanics, namely distribution functions in classical mechanics and in coarse-grained classical mechanics as well as the Wigner function and the Husimi function. Topics dealt with include formulations of the Wigner representation, the Husimi representation and coarse-grained classical mechanics, and their applications to the analyses of the eigenstates and time developments of the distribution functions.

Takahashi, K.

255

Spin-flavor oscillations of Dirac neutrinos described by relativistic quantum mechanics  

NASA Astrophysics Data System (ADS)

Spin-flavor oscillations of Dirac neutrinos in matter and a magnetic field are studied using the method of relativistic quantum mechanics. Using the exact solution of the wave equation for a massive neutrino, taking into account external fields, the effective Hamiltonian governing neutrino spin-flavor oscillations is derived. Then the The consistency of our approach with the commonly used quantum mechanical method is demonstrated. The obtained correction to the usual effective Hamiltonian results in the appearance of the new resonance in neutrino oscillations. Applications to spin-flavor neutrino oscillations in an expanding envelope of a supernova are discussed. In particular, transitions between right-polarized electron neutrinos and additional sterile neutrinos are studied for realistic background matter and magnetic field distributions. The influence of other factors such as the longitudinal magnetic field, the matter polarization, and the non-standard contributions to the neutrino effective potential, is also analyzed.

Dvornikov, M. S.

2012-02-01

256

Gauge-invariant hydrogen-atom Hamiltonian  

SciTech Connect

For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this puzzle was recently provided by us [X.-S. Chen et al., Phys. Rev. Lett. 100, 232002 (2008)]. Based on the separation of the electromagnetic potential into pure-gauge and gauge-invariant parts, we have proposed a new set of momentum and Hamiltonian operators which satisfy both the requirement of gauge invariance and the relevant commutation relations. In this paper we report a check for the case of the hydrogen-atom problem: Starting from the Hamiltonian of the coupled electron, proton, and electromagnetic field, under the infinite proton mass approximation, we derive the gauge-invariant hydrogen-atom Hamiltonian and verify explicitly that this Hamiltonian is different from the Dirac Hamiltonian, which is the time translation generator of the system. The gauge-invariant Hamiltonian is the energy operator, whose eigenvalue is the energy of the hydrogen atom. It is generally time dependent. In this case, one can solve the energy eigenvalue equation at any specific instant of time. It is shown that the energy eigenvalues are gauge independent, and by suitably choosing the phase factor of the time-dependent eigenfunction, one can ensure that the time-dependent eigenfunction satisfies the Dirac equation.

Sun Weimin; Wang Fan [Department of Physics, Nanjing University, CPNPC, Nanjing 210093 (China); Kavli Institute for Theoretical Physics China, CAS, Beijing 100190 (China); Chen Xiangsong [Department of Physics, Huazhong University of Science and Technology, Wuhan 430074 (China); Department of Physics, Nanjing University, CPNPC, Nanjing 210093 (China); Kavli Institute for Theoretical Physics China, CAS, Beijing 100190 (China); Lue Xiaofu [Department of Physics, Sichuan University, Chengdu 610064 (China)

2010-07-15

257

Realist model approach to quantum mechanics  

NASA Astrophysics Data System (ADS)

The paper proves that quantum mechanics is compatible with the constructive realism of modern philosophy of science. The proof is based on the observation that properties of quantum systems that are uniquely determined by their preparations can be assumed objective without the difficulties that are encountered by the same assumption about values of observables. The resulting realist interpretation of quantum mechanics is made rigorous by studying the space of quantum states—the convex set of state operators. Prepared states are classified according to their statistical structure into indecomposable and decomposable instead of pure and mixed. Simple objective properties are defined and showed to form a Boolean lattice.

Hájí?ek, P.

2013-06-01

258

Quantum Mechanical Models Of The Fermi Shuttle  

SciTech Connect

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.

Sternberg, James [University of Tennessee, Department of Physics and Astronomy, Knoxville TN 37996 (United States)

2011-06-01

259

Quantum-Mechanical Description of the Electromagnetic Interaction of Relativistic Particles with Electric and Magnetic Dipole Moments  

Microsoft Academic Search

The Hamiltonian of relativistic particles with electric and magnetic dipole moments that interact with an electromagnetic\\u000a field is determined in the Foldy-Wouthuysen representation. Transition to the semiclassical approximation is carried out.\\u000a The quantum-mechanical and semiclassical equations of spin motion are derived.

A. Ya. Silenko

2005-01-01

260

Quantum-mechanical models in R n associated with extensions of the energy operator in a Pontryagin space  

Microsoft Academic Search

The paper describes self-adjoint extensions of the operator Hâ = \\/minus\\/\\/triangle\\/ from the Hilbert space Lâ(R\\/sub n\\/) to a certain Pontryagin space generated by interactions represented by generalized functions. Hamiltonians of quantum-mechanical models are obtained by restricting such extensions to positive invariant subspaces.

Yu. G. Shondin; Yu. G

1988-01-01

261

Spectral and Quantum Dynamical Properties of the Weakly Coupled Fibonacci Hamiltonian  

NASA Astrophysics Data System (ADS)

We consider the spectrum of the Fibonacci Hamiltonian for small values of the coupling constant. It is known that this set is a Cantor set of zero Lebesgue measure. Here we study the limit, as the value of the coupling constant approaches zero, of its thickness and its Hausdorff dimension. We prove that the thickness tends to infinity and, consequently, the Hausdorff dimension of the spectrum tends to one. We also show that at small coupling, all gaps allowed by the gap labeling theorem are open and the length of every gap tends to zero linearly. Moreover, for a sufficiently small coupling, the sum of the spectrum with itself is an interval. This last result provides a rigorous explanation of a phenomenon for the Fibonacci square lattice discovered numerically by Even-Dar Mandel and Lifshitz. Finally, we provide explicit upper and lower bounds for the solutions to the difference equation and use them to study the spectral measures and the transport exponents.

Damanik, David; Gorodetski, Anton

2011-07-01

262

Quantum Physics Online: Wave Mechanics  

NSDL National Science Digital Library

This is a set of interactive Java applets illustrating the wave nature of quantum physics. Animations are used to illustrate propagation of wave packets, and scattering from potentials. There is also a simple illustration of a scanning tunneling microscope. These applets are part of an extensive collection of animations and simulations illustrating a large range of quantum topics, and an ongoing effort for developing a fully interactive quantum-physics class. Both French and English versions are available.

Joffre, Manuel

2004-03-28

263

Self-adjoint extensions and SUSY breaking in supersymmetric quantum mechanics  

NASA Astrophysics Data System (ADS)

We consider the self-adjoint extensions (SAE) of the symmetric supercharges and Hamiltonian for a model of SUSY quantum mechanics in {\\bb R}^+ with a singular superpotential. We show that only for two particular SAE, whose domains are scale invariant, the algebra of N = 2 SUSY is realized, one with manifest SUSY and the other with spontaneously broken SUSY. Otherwise, only the N = 1 SUSY algebra is obtained, with spontaneously broken SUSY and non-degenerate energy spectrum.

Falomir, H.; Pisani, P. A. G.

2005-05-01

264

SU ( 2 ) Dirac–Yang–Mills quantum mechanics of spatially constant quark and gluon fields  

Microsoft Academic Search

The quantum mechanics of spatially constant SU(2) Yang–Mills- and Dirac-fields minimally coupled to each other is investigated as the strong coupling limit of 2-color-QCD. Using a canonical transformation of the quark and gluon fields, which Abelianises the Gauss law constraints to be implemented, the corresponding unconstrained Hamiltonian and total angular momentum are derived. In the same way as this reduces

H.-P. Pavel

2011-01-01

265

Use of Quantum Mechanical Models in Studies of Reaction Mechanisms,  

National Technical Information Service (NTIS)

The problems involved in determining the mechanisms of reactions by quantum mechanical calculations are discussed. Various precautions must be taken if the results of any calculation are to be chemically meaningful. Ab initio studies of reactions must als...

M. J. Dewar

1988-01-01

266

Exact Parent Hamiltonian for the Quantum Hall States in a Lattice  

SciTech Connect

We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.

Kapit, Eliot; Mueller, Erich [Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York (United States)

2010-11-19

267

Strange Bedfellows: Quantum Mechanics and Data Mining  

SciTech Connect

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

Weinstein, Marvin; /SLAC

2009-12-16

268

Quantum continuum mechanics made simple  

NASA Astrophysics Data System (ADS)

In this paper we further explore and develop the quantum continuum mechanics (QCM) of Tao et al. [Phys. Rev. Lett. 103, 086401 (2009)] with the aim of making it simpler to use in practice. Our simplifications relate to the non-interacting part of the QCM equations, and primarily refer to practical implementations in which the groundstate stress tensor is approximated by its Kohn-Sham (KS) version. We use the simplified approach to directly prove the exactness of QCM for one-electron systems via an orthonormal formulation. This proof sheds light on certain physical considerations contained in the QCM theory and their implication on QCM-based approximations. The one-electron proof then motivates an approximation to the QCM (exact under certain conditions) expanded on the wavefunctions of the KS equations. Particular attention is paid to the relationships between transitions from occupied to unoccupied KS orbitals and their approximations under the QCM. We also demonstrate the simplified QCM semianalytically on an example system.

Gould, Tim; Jansen, Georg; Tokatly, I. V.; Dobson, John F.

2012-05-01

269

Functional renormalization group flow of the effective Hamiltonian action  

NASA Astrophysics Data System (ADS)

After a brief review of the definition and properties of the quantum effective Hamiltonian action, we describe its renormalization flow by a functional renormalization group equation. This equation can be used for a nonperturbative quantization and study of theories with bare Hamiltonians that are not quadratic in the momenta. As an example, the vacuum energy and gap of quantum mechanical models are computed. Extensions of this framework to quantum field theories are discussed. In particular, one possible Lorentz-covariant approach for simple scalar field theories is developed. Fermionic degrees of freedom, being naturally described by a first order formulation, can easily be accommodated in this approach.

Vacca, G. P.; Zambelli, L.

2012-10-01

270

Should PT Symmetric Quantum Mechanics Be Interpreted as Nonlinear?  

NASA Astrophysics Data System (ADS)

The Feshbach-type reduction of the Hilbert space to the physically most relevant "model" subspace is suggested as a means of a formal unification of the standard quantum mechanics with its recently proposed PT symmetric modification. The resulting "effective" Hamiltonians H(eff) are always Hermitian, and the two alternative forms of their energy-dependence are interpreted as a certain dynamical nonlinearity, responsible for the repulsion and/or attraction of the levels in the Hermitian and/or PT symmetric cases, respectively. The spontaneous PT symmetry breaking is then reflected by the loss of the Hermiticity of H(eff) while the pseudo-unitary evolution law persists in the unreduced Hilbert space.

Znojil, Miloslav

271

Conservation laws in the quantum mechanics of closed systems  

SciTech Connect

We investigate conservation laws in the quantum mechanics of closed systems and begin by reviewing an argument that exact decoherence implies the exact conservation of quantities that commute with the Hamiltonian. However, we also show that decoherence limits the alternatives that can be included in sets of histories that assess the conservation of these quantities. In the case of charge and energy, these limitations would be severe were these quantities not coupled to a gauge field. However, for the realistic cases of electric charge coupled to the electromagnetic field and mass coupled to spacetime curvature, we show that when alternative values of charge and mass decohere they always decohere exactly and are exactly conserved. Further, while decohering histories that describe possible changes in time of the total charge and mass are also subject to the limitations mentioned above, we show that these do not, in fact, restrict {ital physical} alternatives and are therefore not really limitations at all.

Hartle, J.B. [Department of Physics, University of California, Santa Barbara, California 93106 (United States)]|[Theoretical Astrophysics, T-6, MSB288, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)]|[Isaac Newton Institute for the Mathematical Sciences, University of Cambridge, 20 Clarkson Road, Cambridge, CB3 0EH (United Kingdom); Laflamme, R. [Theoretical Astrophysics, T-6, MSB288, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)]|[Isaac Newton Institute for the Mathematical Sciences, University of Cambridge, 20 Clarkson Road, Cambridge, CB3 0EH (United Kingdom); Marolf, D. [Center for Gravitational Physics and Geometry, Physics, Department, The Pennsylvania State University, University Park, Pennsylvania 16802 (United States)

1995-06-15

272

A Real Ensemble Interpretation of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ensemble have microscopic states, described by beables. The probabilities of quantum theory turn out to be just ordinary relative frequencies probabilities in these ensembles. Laws for the evolution of the beables of individual systems are given such that their ensemble relative frequencies evolve in a way that reproduces the predictions of quantum mechanics. These laws are highly non-local and involve a new kind of interaction between the members of an ensemble that define a quantum state. These include a stochastic process by which individual systems copy the beables of other systems in the ensembles of which they are a member. The probabilities for these copy processes do not depend on where the systems are in space, but do depend on the distribution of beables in the ensemble. Macroscopic systems then are distinguished by being large and complex enough that they have no copies in the universe. They then cannot evolve by the copy law, and hence do not evolve stochastically according to quantum dynamics. This implies novel departures from quantum mechanics for systems in quantum states that can be expected to have few copies in the universe. At the same time, we are able to argue that the center of masses of large macroscopic systems do satisfy Newton's laws.

Smolin, Lee

2012-10-01

273

Quantum-Mechanical Dualities on the Torus  

NASA Astrophysics Data System (ADS)

On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal, i.e. independent of the observer on classical phase space. Such is the case in all standard applications of quantum mechanics. However, recent developments suggest that the notion of a quantum may not be universal. Transformations between observers that do not agree on the notion of an elementary quantum are called dualities. Classical phase spaces admitting more than one complex-differentiable structure thus provide a natural framework to study dualities in quantum mechanics. As an example we quantise a classical mechanics whose phase space is a torus and prove explicitly that it exhibits dualities.

Isidro, José M.

274

Active Quantum Mechanics: Tutorials and Writing Assignments  

NSDL National Science Digital Library

This web site contains active-learning tutorials and writing assignments for upper-level undergraduate quantum mechanics. The tutorials focus on the mathematical formalism of quantum mechanics. The writing assignments focus on the interpretation of quantum mechanics, and particularly the role of experiments. The topics cover range from introduction to the Schrodinger equation through perturbation theory. In the course using these materials, students work in small groups to complete worksheet-based tutorials during class time, and do fairly typical homework problems and writing assignments, on their own.

Timberlake, Todd

2011-08-01

275

Quantum mechanics on Laakso spaces  

NASA Astrophysics Data System (ADS)

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

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

2012-04-01

276

Approach to Measurement to Quantum Mechanics.  

National Technical Information Service (NTIS)

An unconventional approach to the measurement problem in quantum mechanics is considered, the apparatus is treated as a classical system, belonging to the macro-world. In order to have a measurement the apparatus must interact with the quantum system. As ...

E. C. G. Sudarshan T. N. Sherry S. R. Gautam

1977-01-01

277

Web-based Quantum Mechanics II Course  

NSDL National Science Digital Library

This web site is an entire web-based Quantum Mechanics II Course based at the University of Tennessee; it has all instructional materials, in-class tutorials, simulations, links to other quantum resources, a discussion forum, homework assignments, and solutions.

Breinig, Marianne

2005-04-16

278

Quantum-Mechanical Model of Spacetime  

Microsoft Academic Search

We consider a possibility to construct a quantum-mechanical model of spacetime, where Planck size quantum black holes act as the fundamental constituents of space and time. Spacetime is assumed to be a graph, where black holes lie on the vertices. Our model implies that area has a discrete spectrum with equal spacing. At macroscopic length scales our model reproduces Einstein's

Jarmo Makela

2007-01-01

279

From Ground States to Local Hamiltonians  

Microsoft Academic Search

Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be mainly interested in local Hamiltonians with certain interaction patterns, such as nearest neighbour interactions on some type of lattices. We show that a necessary condition for a

Jianxin Chen; Zhengfeng Ji; Bei Zeng; Duanlu Zhou

2011-01-01

280

Oscillator representations for self-adjoint Calogero Hamiltonians  

Microsoft Academic Search

In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = alphax-2. We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation \\\\check{H}=-d_{x}^{2}+\\\\alpha x^{-2} for the Calogero Hamiltonian. Here, we discuss a new aspect of

D. M. Gitman; I. V. Tyutin; B. L. Voronov

2011-01-01

281

Test of quantum mechanics by neutron interferometry  

NASA Astrophysics Data System (ADS)

Interferometry with massive elementary particles combines particle and wave features in a direct way. In this respect, neutrons are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their magnetic moment, and they are subject to all basic interactions, and they are sensitive to topological effects, as well. They play a pionieering role in the development of interferometry with even heavier objects, like atoms, molecules and clusters. Deterministic and stochastic partial absorption experiments can be described by Bell-type inequalities. Recent neutron interferometry experiments based on postselection methods renewed the discussion about quantum nonlocality and the quantum measuring process. It has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast. This indicates persisting coupling in phase space even in cases of spatially separated Schrödinger cat-like situations. These states are extremely fragile and sensitive to any kind of fluctuations or other decoherence processes. More complete quantum experiments also show that a complete retrieval of quantum states behind an interaction region becomes impossible in principle. The transition from a quantum world to a classical one is still an open question and will be tackled by means of dedicated decoherence experiments. Recent measurements deal with quantum contextuality and quantum state reconstruction. The observed results agree with quantum mechanical laws and may stimulate further discussions about their interpretations.

Rauch, H.

2008-06-01

282

Relative-State Formulation of Quantum Mechanics  

NSDL National Science Digital Library

This entry in the Stanford Encyclopedia of Philosophy contains a comprehensive introduction of Everett's relative-state formulation of quantum mechanics. It explores the many attempts to reconstruct and interpret this no-collapse theory.

Barrett, Jeffrey A.

2010-04-12

283

Many-Worlds Interpretation of Quantum Mechanics  

NSDL National Science Digital Library

This entry in the Stanford Encyclopedia of Philosophy contains a comprehensive introduction to the many-worlds interpretation of quantum mechanics. It includes discussions of the probability, tests, and objections to this interpretation.

Vaidman, Lev

2010-04-09

284

Student Difficulties with Energy in Quantum Mechanics  

NSDL National Science Digital Library

This website contains the results of a study on student difficulties in understanding energy in quantum mechanics. The most common misconceptions are listed. This content was presented to the 1997 meeting of the AAPT.

Redish, Edward F.; Bao, Lei; Jolly, Pratibha

2005-07-26

285

Quantum mechanical effects on the shock Hugoniot.  

National Technical Information Service (NTIS)

Calculations of the locus of shock Hugoniot states of aluminum, using two equations of state that either omit or include a quantum mechanical treatment for the material's electronic excitations, will be presented. The difference between the loci will be a...

B. I. Bennett D. A. Liberman

1991-01-01

286

Symmetry and symmetry breaking in quantum mechanics.  

National Technical Information Service (NTIS)

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

P. Chomaz

1998-01-01

287

Quantum mechanical stabilization of Minkowski signature wormholes  

SciTech Connect

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

Visser, M.

1989-05-19

288

Advantages of quantum mechanics on phase space  

NASA Astrophysics Data System (ADS)

Quantum mechanics formulated in terms of (wave) functions over phase space is shown to have numerous advantages over the standard approach. These advantages arise in the contexts of discussion of the theoretical framework and of descriptions of laboratory experiments.

Schroeck, F. E.

1994-01-01

289

Quantum Mechanics: Rigid Rotator Applet  

NSDL National Science Digital Library

This simulation shows time-dependent quantum state wavefunctions for the rigid rotator, the spherical harmonic states projected on a sphere. Position, angular momentum, and energy of the states can all be viewed, with phase shown with color. Energy-eigenstate wavefunctions, and combinations of states, can be created through changes in the amplitude and phase of the basis states using spinors, or through the creation of Gaussian wavefunctions with the mouse. The quantum numbers of the states are shown.

Falstad, Paul

2004-05-17

290

Macroscopic quantum mechanics in a classical spacetime.  

PubMed

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

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

2013-04-22

291

SEI: Quantum Mechanics I Course Materials  

NSDL National Science Digital Library

This web site provides research-based materials for junior-level quantum mechanics I courses on quantum mechanics. Topics covered include the Schroedinger equation, bound state problems, Hilbert space and operators, the hydrogen atom, and spin. The course archives include documented student difficulties, learning goals, ConcepTests (clicker questions), class activities, homework, tutorials, and a conceptual assessment tool. All may be downloaded, although the assessment tools require permission from the authors for access.

Goldhaber, Steve; Pollock, Steven J.

2010-01-29

292

Entangled state representations in noncommutative quantum mechanics  

Microsoft Academic Search

We introduce new representations to formulate quantum mechanics on\\u000anoncommutative coordinate space, which explicitly display entanglement\\u000aproperties between degrees of freedom of different coordinate components and\\u000ahence could be called entangled state representations. Furthermore, we derive\\u000aunitary transformations between the new representations and the ordinary one\\u000aused in noncommutative quantum mechanics (NCQM) and obtain eigenfunctions of\\u000asome basic operators in

Sicong Jing; Qiu-Yu Liu; Hongyi Fan

2005-01-01

293

Local currents for a deformed algebra of quantum mechanics with a fundamental length scale  

NASA Astrophysics Data System (ADS)

We explore some explicit representations of a certain stable deformed algebra of quantum mechanics, considered by R Vilela Mendes, having a fundamental length scale. The relation of the irreducible representations of the deformed algebra to those of the (limiting) Heisenberg algebra is discussed, and we construct the generalized harmonic oscillator Hamiltonian in this framework. To obtain local currents for this algebra, we extend the usual nonrelativistic local current algebra of vector fields and the corresponding group of diffeomorphisms, modelling the quantum configuration space as a commutative spatial manifold with one additional dimension.

Goldin, Gerald A.; Sarkar, Sarben

2006-03-01

294

The Strange World of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction; 2. Classical magnetic needles; 3. The Stern-Gerlach experiment; 4. The conundrum of projections; repeated measurements; 5. Probability; 6. The Einstein-Podolsky-Rosen paradox; 7. Variations on a theme by Einstein; 8. Optical interference; 9. Quantal interference; 10. Amplitudes; 11. Working with amplitudes; 12. Two slit inventions; 13. Quantum cryptography; 14. Quantum mechanics of a bouncing ball; 15. The wavefunction; Appendix A: a brief history of quantum mechanics; Appendix B: putting weirdness to work; Appendix C: sources; Appendix D: general questions; Appendix E: bibliography; Appendix F: skeleton answers for selected problems; Index.

Styer, Daniel F.

2000-02-01

295

Comparison of quantum-mechanical and semiclassical approaches for an analysis of spin dynamics in quantum dots  

SciTech Connect

Two approaches to the description of spin dynamics of electron-nuclear system in quantum dots are compared: the quantum-mechanical one is based on direct diagonalization of the model Hamiltonian and semiclassical one is based on coupled equations for precession of mean electron spin and mean spin of nuclear spin fluctuations. The comparison was done for a model problem describing periodic excitation of electron-nuclear system by optical excitation. The computation results show that scattering of parameters related to fluctuation of the nuclear spin system leads to appearance of an ordered state in the system caused by periodic excitation and to the effect of electron-spin mode locking in an external magnetic field. It is concluded that both models can qualitatively describe the mode-locking effect, however give significantly different quantitative results. This may indicate the limited applicability of the precession model for describing the spin dynamics in quantum dots in the presence of optical pumping.

Petrov, M. Yu., E-mail: m.petrov@spbu.ru; Yakovlev, S. V. [Saint Petersburg State University (Russian Federation)

2012-08-15

296

Optimizing Matrix- and Tensor-Product Algorithms for Momentum-Space Hamiltonians using Quantum Entropy  

NASA Astrophysics Data System (ADS)

Momentum-space formulations of local models such as the Hubbard model are hard to treat using matrix- and tensor-product-based algorithms because they contain contain non-local interactions. Quantum entropy-based measures such as the single-site and block entropies and the mutual information can be used to map the entanglement structure in order to gain physical information and to optimize algorithms. In this contribution, we will discuss the optimization of density-matrix-renormalization-group and tree-tensor-network algorithms and their application to the two-dimensional Hubbard model.

Noack, Reinhard; Legeza, Örs; Sólyom, Jenö.

2012-02-01

297

Quantum theory of two-photon correlated-spontaneous-emission lasers: Exact atom-field interaction Hamiltonian approach  

SciTech Connect

A quantum theory of two-photon correlated-spontaneous-emission lasers (CEL's) is developed, starting from the exact atom-field interaction Hamiltonian for cascade three-level atoms interacting with a single-mode radiation field. We consider the situation where the active atoms are prepared initially in a coherent superposition of three atomic levels and derive a master equation for the field-density operator by using a quantum theory for coherently pumped lasers. The master equation is transformed into a Fokker-Planck equation for the antinormal-ordering {ital Q} function. The drift coefficients of the Fokker-Planck equation enable us to study the steady-state operation of the two-photon CEL's analytically. We have studied both resonant two-photon CEL for which there is no threshold, and off-resonant two-photon CEL for which there exists a threshold. In both cases the initial atomic coherences provide phase locking, and squeezing in the phase quadrature of the field is found. The off-resonant two-photon CEL can build up from a vacuum when its linear gain is larger than the cavity loss (even without population inversion). Maximum squeezing is found in the no-population-inversion region with the laser intensities far below saturation in both cases, which are more than 90% for the resonant two-photon CEL and nearly 50% for the off-resonant one. Approximate steady-state {ital Q} functions are obtained for the resonant two-photon CEL and, in certain circumstances, for the off-resonant one.

Lu, N.; Zhu, S. (Center for Advanced Studies and Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131 (US))

1989-11-15

298

On reconciling quantum mechanics and local realism  

NASA Astrophysics Data System (ADS)

Accepting nonlocal quantum correlations requires us to reject special relativity and/or probability theory. We can retain both by revising our interpretation of quantum mechanics regarding the handling of separated systems, as quantum mechanics conflicts with local realism only in its treatment of separated systems. We cannot use the joint probability formula for cases of separated measurements. We use the marginals (partial traces) together with whatever priors we have from an understanding of the system. This program can reconcile quantum mechanics with local realism. An apparent obstacle to this program is the experimental evidence, but we argue that the experiments have been misinterpreted, and that when correctly interpreted they confirm local realism. We describe a local realistic account of one important Einstein-Poldosky-Rosen-Bohm (EPRB) experiment (Weihs et al6) that claims to demonstrate nonlocal entanglement. We present a local realistic system (experiment) that can be calibrated into both quantum and classical correlation domains via adjustment of parameters (`hidden variables') of the apparatus. Weihs incorrectly dismisses these parameters as uncritical. Nonlocal entanglement is seen to be an error. The rest of quantum mechanics remains intact, and remains highly valued as a powerful probability calculus for observables. Freed from the incoherent idea of nonlocal entanglement, we can leverage powerful classical ideas, such as semiclassical radiation theory, stochastic dynamics, classical noncommutativity/contextuality, measurement effects on state, etc., to augment or complement quantum mechanics. When properly interpreted and applied, quantum mechanics lives in peaceful harmony with the local realist conception, and both perspectives offer useful paradigms for describing systems.

Graft, Donald A.

2013-10-01

299

On the Classical Limit of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results of the standard approach, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper, we shall formulate the classical limit as a scaling limit in terms of an adimensional parameter ?. We shall take the first steps toward a comprehensive understanding of the classical limit, analyzing special cases of classical behavior in the framework of a precise formulation of quantum mechanics called Bohmian mechanics which contains in its own structure the possibility of describing real objects in an observer-independent way.

Allori, Valia; Zanghì, Nino

2009-01-01

300

Fourier transform identities in quantum mechanics and the quantum line  

NASA Astrophysics Data System (ADS)

We give a quantum-mechanical interpretation of some modular identities (LF)3=?L2 arising in conformal field theory and the theory of quantum groups in relation to the mapping class group of a torus. The interpretation follows by evaluating the identity in the case of a non-standard group of the real line. The operation L takes the form of the Fourier transform of wave functions in L2(R) with length scale ???/m. We find that this can be factorised as ?L=exp(-i?p2/2m?) exp(-ix2/2??) P exp(-i?p2/2m?), where x, p mare the usual quantum mechanical position and momentum operators, P is the parity and ?=(1-i)/?2 is a normalization constant determined by verifying the identity on wavepackets. We understand this further in terms of the observation that the Fourier transformation is realized on the wavefunctions in quantum mechanics as the evolution by a quantum harmonic oscillator of period 2?? for 1/4 of a cycle. SERC Advanced Fellow and Drapers Fellow of Pembroke College, Cambridge.

Lyubashenko, V. V.; Majid, S.

1992-06-01

301

Quantum Transport in Crystals: Effective Mass Theorem and K·P Hamiltonians  

NASA Astrophysics Data System (ADS)

In this paper the effective mass approximation and the k·p multi-band models, describing quantum evolution of electrons in a crystal lattice, are discussed. Electrons are assumed to move in both a periodic potential and a macroscopic one. The typical period {?} of the periodic potential is assumed to be very small, while the macroscopic potential acts on a much bigger length scale. Such homogenization asymptotic is investigated by using the envelope-function decomposition of the electron wave function. If the external potential is smooth enough, the k·p and effective mass models, well known in solid-state physics, are proved to be close (in the strong sense) to the exact dynamics. Moreover, the position density of the electrons is proved to converge weakly to its effective mass approximation.

Barletti, Luigi; Ben Abdallah, Naoufel

2011-11-01

302

Mind, matter, and quantum mechanics  

SciTech Connect

A theory of psychophysical phenomena is proposed. It resolves simultaneously four basic problems of science, namely the problems of the connections between: (1) mind and matter, (2), quantum theory and reality, (3) relativity theory and ''becoming,'' and (4) relativity theory and Bell's theorem.

Stapp, H.P.

1982-04-01

303

Fuzzy quantum logic II. The logics of unsharp quantum mechanics  

NASA Astrophysics Data System (ADS)

A survey of the main results of the Italian group about the logics of unsharp quantum mechanics is presented. In particular partial ordered structures playing with respect to effect operators (linear bounded operators F on a Hilbert space ? such that ????, 0?????2) the role played by orthomodular posets with respect to orthogonal projections (corresponding to “sharp” effects) are analyzed. These structures are generally characterized by the splitting of standard orthocomplementation on projectors into two nonusual orthocomplementations (a fuzzy-like and an intuitionistic-like) giving rise to different kinds of Brouwer-Zadeh (BZ) posets: de Morgan BZ posets, BZ* posets, and BZ3 posets. Physically relevant generalizations of ortho-pair semantics (paraconsistent, regular paraconsistent, and minimal quantum logics) are introduced and their relevance with respect to the logic of unsharp quantum mechanics are discussed.

Cattaneo, Gianpiero

1993-10-01

304

Quantum Mechanics, Spacetime Locality, and Gravity  

NASA Astrophysics Data System (ADS)

Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only one of the many, bringing an apparent arbitrariness in defining probabilities, called the measure problem. In this paper, we discuss how these two problems are related with each other, developing a picture for quantum measurement and cosmological histories in the quantum mechanical universe. In order to describe the cosmological dynamics correctly within the full quantum mechanical context, we need to identify the structure of the Hilbert space for a system with gravity. We argue that in order to keep spacetime locality, the Hilbert space for dynamical spacetime must be defined only in restricted spacetime regions: in and on the (stretched) apparent horizon as viewed from a fixed reference frame. This requirement arises from eliminating all the redundancies and overcountings in a general relativistic, global spacetime description of nature. It is responsible for horizon complementarity as well as the "observer dependence" of horizons/spacetime—these phenomena arise to represent changes of the reference frame in the relevant Hilbert space. This can be viewed as an extension of the Poincaré transformation in the quantum gravitational context. Given an initial condition, the evolution of the multiverse state obeys the laws of quantum mechanics—it evolves deterministically and unitarily. The beginning of the multiverse, however, is still an open issue.

Nomura, Yasunori

2013-08-01

305

Photon Quantum Mechanics in the Undergraduate Curriculum  

NASA Astrophysics Data System (ADS)

Although it has been discussed for centuries, the true nature of light is still being debated. In fact, the quantum mechanical aspects of light have only been observed within the past 30 years. Recent advances in technology have decreased the complexity of such tests, and the Department of Physics and Astronomy at Dickinson College has worked to infuse various quantum optics experiments throughout our curriculum. We describe a set of experiments that includes the existence of photons, single-photon interference, the quantum eraser, and tests of Bell's theorem. A primary motivation is bringing undergraduate students face to face with some of the fascinating and subtle aspects of quantum mechanics in a hands-on setting.

Pearson, Brett; Carson, Zack; Jackson, David

2011-06-01

306

Levitated Quantum Nano-Magneto-Mechanical Systems  

NASA Astrophysics Data System (ADS)

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 ?˜10-100MHz. As the supercurrents experience little damping this system will possess unprecendented motional quality factors, with Qmotion˜10^9-10^13, 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.

Cirio, Mauro; Twamley, Jason; Brennen, Gavin K.; Milburn, Gerard J.

2011-03-01

307

Quantum opto-mechanics: Quantum optical control of massive mechanical resonators  

Microsoft Academic Search

The toolbox of quantum optics allows to achieve coherent quantum control over massive mechanical resonators by using radiation pressure of light inside optical cavities. Only recently, cavity-assisted ground state cooling of mechanical motion has been achieved both in the micro- and in the nanomechanical domain [1, 2]. Together with the strong coupling regime [3], this opens up a new parameter

Markus Aspelmeyer

2011-01-01

308

Quantum Mechanics Based Multiscale Modeling of Materials  

NASA Astrophysics Data System (ADS)

We present two quantum mechanics based multiscale approaches that can simulate extended defects in metals accurately and efficiently. The first approach (QCDFT) can treat multimillion atoms effectively via density functional theory (DFT). The method is an extension of the original quasicontinuum approach with DFT as its sole energetic formulation. The second method (QM/MM) has to do with quantum mechanics/molecular mechanics coupling based on the constrained density functional theory, which provides an exact framework for a self-consistent quantum mechanical embedding. Several important materials problems will be addressed using the multiscale modeling approaches, including hydrogen-assisted cracking in Al, magnetism-controlled dislocation properties in Fe and Si pipe diffusion along Al dislocation core.

Lu, Gang

2013-03-01

309

Graph reconstruction and quantum statistical mechanics  

NASA Astrophysics Data System (ADS)

We study how far it is possible to reconstruct a graph from various Banach algebras associated to its universal covering, and extensions thereof to quantum statistical mechanical systems. It turns out that most the boundary operator algebras reconstruct only topological information, but the statistical mechanical point of view allows for complete reconstruction of multigraphs with minimal degree three.

Cornelissen, Gunther; Marcolli, Matilde

2013-10-01

310

Variational methods in relativistic quantum mechanics  

Microsoft Academic Search

This review is devoted to the study of stationary solutions of linear and\\u000anonlinear equations from relativistic quantum mechanics, involving the Dirac\\u000aoperator. The solutions are found as critical points of an energy functional.\\u000aContrary to the Laplacian appearing in the equations of nonrelativistic quantum\\u000amechanics, the Dirac operator has a negative continuous spectrum which is not\\u000abounded from below.

Maria J. Esteban; Mathieu Lewin; ERIC SERE

2008-01-01

311

Statistical mechanics of disordered quantum optimization  

NASA Astrophysics Data System (ADS)

The classical statistical mechanical approach to complexity theory proceeds from the study of ensembles of computationally intractable optimization problems as a species of unusual disordered magnetic systems. Over the last thirty years, researchers have used this approach to supplement worst-case hardness results encoded by complexity theory with detailed information about thermodynamic and dynamic phase transitions in the structure of typical cases. This exchange of ideas between classical statistical mechanics and computer science enabled the development of important heuristic algorithms such as simulated annealing and survey propagation and further refined our understanding of glassiness and critical slowing in physical disordered systems. In this thesis, we map out an analogous program in the quantum context. The question is simple: what can quantum statistical mechanics reveal about the difficulty of solving hard quantum optimization problems? Or more directly, what makes those problems hard even for quantum computers? In this pursuit, we introduce the study of ensembles of optimization problems whose complexity status is intrinsically quantum mechanical (Part I) and develop techniques to study quantum spin glasses and the transverse field adiabatic algorithm applied to classically hard random optimization problems (Part II). In particular, we introduce the study of random quantum satisfiability (QSAT) and identify the coarse aspects of its phase diagram, including a new form of entanglement transition. We generalize the cavity method to the study of quantum models and use it to study the transverse field Ising glass and frustrated AKLT models on the Bethe lattice. We further apply the cavity method to extract Griffiths-McCoy singularities in a diluted (classical) ferromagnet and finally observe that there are no Goldstone bosons on the Bethe lattice.

Laumann, Christopher Richard

312

Quantum-Opto-Mechanics: Towards quantum optical control of micromechanical resonators  

NASA Astrophysics Data System (ADS)

Current experiments aim to achieve coherent quantum control over massive mechanical resonators. Quantum optics provides a rich toolbox to prepare and detect mechanical quantum states, in particular by combining nano- and micromechanical resonators with high-finesse cavities. To realize the full potential of mechanical systems for quantum experiments eventually requires the conjunction of strongly coupled mechanical resonators with the preparation of quantum ground states. I will report our latest progress in Vienna towards these goals. I will also discuss the prospect of generating optomechanical quantum entanglement, which is at the heart of Schrödinger's cat paradox, and the possibility of mechanical quantum transducers as a new technology for quantum information processing.

Cole, Garrett

2009-05-01

313

Nonstandard extension of quantum logic and Dirac's bra-ket formalism of quantum mechanics  

Microsoft Academic Search

An extension of the quantum logical approach to the axiomatization of quantum mechanics usingnonstandard analysis methods is proposed. The physical meaning of a quantum logic as a lattice of propositions is conserved by its nonstandard extension. But not only the usual Hubert space formalism of quantum mechanics can be derived from the nonstandard extended quantum logic. Also the Dirac bra-ket

Arye Friedman

1994-01-01

314

Supersymmetric quantum mechanics and solitons of the sine-Gordon and nonlinear Schroedinger equations  

SciTech Connect

We present a case demonstrating the connection between supersymmetric quantum mechanics (SUSYQM), reflectionless scattering, and soliton solutions of integrable partial differential equations. We show that the members of a class of reflectionless Hamiltonians, namely, Akulin's Hamiltonians, are connected via supersymmetric chains to a potential-free Hamiltonian, explaining their reflectionless nature. While the reflectionless property in question has been mentioned in the literature for over two decades, the enabling algebraic mechanism was previously unknown. Our results indicate that the multisoliton solutions of the sine-Gordon and nonlinear Schroedinger equations can be systematically generated via the supersymmetric chains connecting Akulin's Hamiltonians. Our findings also explain a well-known but little-understood effect in laser physics: when a two-level atom, initially in the ground state, is subjected to a laser pulse of the form V(t)=(n({h_bar}/2{pi})/{tau})/cosh(t/{tau}), with n being an integer and {tau} being the pulse duration, it remains in the ground state after the pulse has been applied, for any choice of the laser detuning.

Koller, Andrew; Olshanii, Maxim [Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125 (United States)

2011-12-15

315

Catalytic mechanism of RNA backbone cleavage by ribonuclease H from quantum mechanics/molecular mechanics simulations.  

PubMed

We use quantum mechanics/molecular mechanics simulations to study the cleavage of the ribonucleic acid (RNA) backbone catalyzed by ribonuclease H. This protein is a prototypical member of a large family of enzymes that use two-metal catalysis to process nucleic acids. By combining Hamiltonian replica exchange with a finite-temperature string method, we calculate the free energy surface underlying the RNA-cleavage reaction and characterize its mechanism. We find that the reaction proceeds in two steps. In a first step, catalyzed primarily by magnesium ion A and its ligands, a water molecule attacks the scissile phosphate. Consistent with thiol-substitution experiments, a water proton is transferred to the downstream phosphate group. The transient phosphorane formed as a result of this nucleophilic attack decays by breaking the bond between the phosphate and the ribose oxygen. In the resulting intermediate, the dissociated but unprotonated leaving group forms an alkoxide coordinated to magnesium ion B. In a second step, the reaction is completed by protonation of the leaving group, with a neutral Asp132 as a likely proton donor. The overall reaction barrier of ?15 kcal mol(-1), encountered in the first step, together with the cost of protonating Asp132, is consistent with the slow measured rate of ?1-100/min. The two-step mechanism is also consistent with the bell-shaped pH dependence of the reaction rate. The nonmonotonic relative motion of the magnesium ions along the reaction pathway agrees with X-ray crystal structures. Proton-transfer reactions and changes in the metal ion coordination emerge as central factors in the RNA-cleavage reaction. PMID:21539371

Rosta, Edina; Nowotny, Marcin; Yang, Wei; Hummer, Gerhard

2011-05-24

316

Relativistic quantum mechanics of spin-0 and spin-1 bosons  

NASA Astrophysics Data System (ADS)

It is shown that below the threshold of pair creation, a consistent quantum mechanical interpretation of relativistic spin-0 and spin-1 particles (both massive and mussless) is possible based an the Hamiltonian-Schrödinger form of the firstorder Kemmer equation together with a first-class constraint. The crucial element is the identification of a conserved four-vector current associated with the equation of motion, whose time component is proportional to the energy density which is constrained to be positive definite for all solutions. Consequently, the antiparticles must be interpreted as positive-energy states traveling backward in time. This also makes it possible to define hermitian position operators with localized eigensolutions (?-functions) as well as Bohmian trajectories for bosons. The exact theory is obtained by “second quantization” and is mathematically completely equivalent to conventional quantum field theory. The classical field emerges in the high mean number limit of coherent states of the exact theory. The formalism provides a new basis for computing tunneling times for photons and chaotic phenomena in optics.

Ghose, Partha

1996-11-01

317

Three-Hilbert-Space Formulation of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

In paper [Znojil M., Phys. Rev. D 78 (2008), 085003, 5 pages, arXiv:0809.2874] the two-Hilbert-space (2HS, a.k.a. cryptohermitian) formulation of Quantum Mechanics has been revisited. In the present continuation of this study (with the spaces in question denoted as H(auxiliary) and H(standard)) we spot a weak point of the 2HS formalism which lies in the double role played by H(auxiliary). As long as this confluence of roles may (and did!) lead to confusion in the literature, we propose an amended, three-Hilbert-space (3HS) reformulation of the same theory. As a byproduct of our analysis of the formalism we offer an amendment of the Dirac's bra-ket notation and we also show how its use clarifies the concept of covariance in time-dependent cases. Via an elementary example we finally explain why in certain quantum systems the generator H(gen) of the time-evolution of the wave functions may differ from their Hamiltonian H.

Znojil, Miloslav

2009-01-01

318

Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line  

NASA Astrophysics Data System (ADS)

A discontinuous media can be described by fractal dimensions. Fractal objects has special geometric properties, which are discrete and discontinuous structure. A fractal-time diffusion equation is a model for subdiffusive. In this work, we have generalized the Hamiltonian and Lagrangian dynamics on fractal using the fractional local derivative, so one can use as a new mathematical model for the motion in the fractal media. More, Poisson bracket on fractal subset of real line is suggested.

Golmankhaneh, Alireza Khalili; Golmankhaneh, Ali Khalili; Baleanu, Dumitru

2013-07-01

319

Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line  

NASA Astrophysics Data System (ADS)

A discontinuous media can be described by fractal dimensions. Fractal objects has special geometric properties, which are discrete and discontinuous structure. A fractal-time diffusion equation is a model for subdiffusive. In this work, we have generalized the Hamiltonian and Lagrangian dynamics on fractal using the fractional local derivative, so one can use as a new mathematical model for the motion in the fractal media. More, Poisson bracket on fractal subset of real line is suggested.

Golmankhaneh, Alireza Khalili; Golmankhaneh, Ali Khalili; Baleanu, Dumitru

2013-11-01

320

Gauge-invariant hydrogen-atom Hamiltonian  

Microsoft Academic Search

For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this puzzle was recently provided by us [X.-S. Chen , Phys. Rev. Lett.PRLTAO0031-900710.1103\\/PhysRevLett.100.232002 100, 232002 (2008)]. Based on the separation of the electromagnetic potential into

Wei-Min Sun; Xiang-Song Chen; Xiao-Fu Lü; Fan Wang

2010-01-01

321

Space and time from quantum mechanics  

SciTech Connect

Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over collapse of the quantum-mechanical state vector when measurement is performed. Additionally, pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.

Chew, G.F.

1992-09-16

322

Space and time from quantum mechanics  

NASA Astrophysics Data System (ADS)

Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over the collapse of the quantum-mechanical state vector when measurement is performed. Additionally, the pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as a coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.

Chew, G. F.

1992-09-01

323

Remarks on Dersarkissian's cosmic quantum mechanics  

NASA Astrophysics Data System (ADS)

Dersarkissian (1984) has proposed a cosmic quantum mechanics (CQM) characterized by the constant hg approximately equal to 10 to the 75th ergs approximately equal to 10 to the 102nd h, where h is Planck's constant of ordinary quantum mechanics; galaxies are the elementary particles of CQM. Uncertainty arguments in CQM give a number of constraints on the masses of galaxies and thus a concrete way to test CQM. A condition that has to be satisfied for a massive body to be subject to CQM is proposed.

Massa, C.

1985-12-01

324

Two basic Uncertainty Relations in Quantum Mechanics  

SciTech Connect

In the present article, we discuss two types of uncertainty relations in Quantum Mechanics-multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schroedinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics-Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.

Angelow, Andrey [Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko chaussee, 1784 Sofia (Bulgaria)

2011-04-07

325

Quantum mechanics and mixed quantum mechanics\\/molecular mechanics simulations of model nerve agents with acetylcholinesterase  

Microsoft Academic Search

.  ?The accurate modeling of biological processes presents major computational difficulties owing to the inherent complexity\\u000a of the macromolecular systems of interest. Simulations of biochemical reactivity tend to require highly computationally intensive\\u000a quantum mechanical methods, but localized chemical effects tend to depend significantly on properties of the extended biological\\u000a environment – a regime far more readily examined with lower-level classical empirical

M. M. Hurley; J. B. Wright; G. H. Lushington; W. E. White

2003-01-01

326

Constrained quantum mechanics and a coordinate independent theory of the collective path  

NASA Astrophysics Data System (ADS)

The settings for two formulations of quantum mechanics are, respectively, Hilbert spaces and symplectic manifolds. The former leads naturally to matrix mechanics and, for example, the shell model while the latter leads to hamiltonian mechanics, of which the time-dependent Hartree-Fock theory is a standard example. In order to obtain practical approximate theories one needs to restrict the dynamics in both cases to suitable finite-dimensional subspaces. This paper addresses the problem of constructing subspaces of the projective Hilbert space, the fundamental symplectic manifold of quantum mechanics. The collective paths of Villars, Goeke and Reinhard, the valley path and the collective path and submanifold of Rowe and Basserman are examined and phrased in a coordinate independent manner. In this way we expose the dynamical foundations and the essential geometrical structures upon which they are based.

Rowe, D. J.

1982-12-01

327

Macroscopic Quantum Mechanics in a Classical Spacetime  

NASA Astrophysics Data System (ADS)

We apply the many-particle Schr"odinger-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 find 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 it is not allowed that quantum uncertainty to be transferred from one object to another through semiclassical gravity.

Yang, Huan

2013-04-01

328

Hamiltonian complexity  

NASA Astrophysics Data System (ADS)

In recent years we have seen the birth of a new field known as Hamiltonian complexity lying at the crossroads between computer science and theoretical physics. Hamiltonian complexity is directly concerned with the question: how hard is it to simulate a physical system? Here I review the foundational results, guiding problems, and future directions of this emergent field.

Osborne, Tobias J.

2012-02-01

329

Hamiltonian complexity.  

PubMed

In recent years we have seen the birth of a new field known as Hamiltonian complexity lying at the crossroads between computer science and theoretical physics. Hamiltonian complexity is directly concerned with the question: how hard is it to simulate a physical system? Here I review the foundational results, guiding problems, and future directions of this emergent field. PMID:22790342

Osborne, Tobias J

2012-01-24

330

Pole structure of the Hamiltonian ?-function for a singular potential  

Microsoft Academic Search

We study the pole structure of the ?-function associated with the Hamiltonian H of a quantum mechanical particle living in the half-line ?+, subject to the singular potential gx?2 + x2. We show that H admits nontrivial self-adjoint extensions (SAE) in a given range of values of the parameter g. The ?-functions of these operators present poles which depend on

H Falomir; P. A. G. Pisani; A. Wipf

2002-01-01

331

Quantum mechanics is compatible with realism  

SciTech Connect

A new paradox of quantum mechanics has recently been proposed by an author claiming that any attempt to inject realism in physical theory is bound to lead to inconsistencies. In this paper the author shows that the mentioned paradox is not such a one and that at present there are no reasons to reject realism.

Burgos, M.E.

1987-08-01

332

Quantum mechanics and elements of reality  

Microsoft Academic Search

It is widely accepted that a Born probability of 1 is sufficient for the existence of a corresponding element of reality. Recently Vaidman has extended this idea to the ABL probabilities of the time-symmetrized version of quantum mechanics originated by Aharonov, Bergmann, and Lebowitz. Several authors have objected to Vaidman's time-symmetrized elements of reality without casting doubt on the widely

Ulrich Mohrhoff; Sri Aurobindo Ashram

1999-01-01

333

Student Difficulties with Quantum Mechanics Formalism  

NSDL National Science Digital Library

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

Singh, Chandralekha

2007-06-26

334

Mona Lisa - ineffable smile of quantum mechanics  

Microsoft Academic Search

The portrait of Mona Lisa is scrutinized with reference to quantum mechanics. The elements of different expressions are firstly recognized on her face. The contradictory details are then classified in two pictures that, undoubtedly representing distinct moods, confirm dichotomous character of the original. Consecutive discussion has lead to conclusion that the mysterious state Mona Lisa is in actually is coherent

Slobodan Prvanovic

2003-01-01

335

No time asymmetry from quantum mechanics  

NASA Astrophysics Data System (ADS)

With CPT-invariant initial conditions that commute with CPT-invariant final conditions, the respective probabilities (when defined) of a set of histories and its CPT reverse are equal, giving a CPT-symmetric universe. This leads me to question whether the asymmetry of the Gell-Mann-Hartle decoherence functional for ordinary quantum mechanics should be interpreted as an asymmetry of time.

Page, Don N.

1993-06-01

336

Quantum Mechanical Effects in Gravitational Collapse  

NASA Astrophysics Data System (ADS)

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 Schrödinger formalism. The Functional Schrödinger 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 Schrödinger 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.

Greenwood, Eric

2010-01-01

337

Vlasov hydrodynamics of a quantum mechanical model  

Microsoft Academic Search

We derive the Vlasov hydrodynamics from the microscopic equations of a quantum mechanical model, which simulates that of an assembly of gravitating particles. In addition we show that the local microscopic dynamics of the model corresponds, on a suitable time-scale, to that of an ideal Fermi gas.

Heide Narnhofer; Geoffrey L. Sewell

1981-01-01

338

Quantum mechanical model for Maya Blue  

Microsoft Academic Search

This work is about Maya Blue (MB), a pigment developed by Mesoamerican civilizations between the 5th and 16th centuries from an aluminosilicate mineral (palygorskite) and an organic dye (indigo). Two different supramolecular quantum-mechanical models afford explanations for the unusual stability of MB based on the oxidation of the indigo molecule during the heating process and its interaction with palygorskite. A

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

2008-01-01

339

A Quantum Mechanical Model of Spherical Supermembranes  

Microsoft Academic Search

We present a quantum mechanical model of spherical supermembranes. Using superfields to represent the Cartesian coordinates of the membrane, we are able to exactly determine its supersymmetric vacua. We find there are two classical vacua, one corresponding to an extended membrane and one corresponding to a point-like membrane. Instanton effects then lift these vacua to massive states. Similarities to spherical

John Conley; Ben Geller; Mark G. Jackson; Laura Pomerance; Sharad Shrivastava

2003-01-01

340

The Importance of Causality in Quantum Mechanics  

Microsoft Academic Search

Christian theology preferentially favors some philosophical interpretations of quantum mechanics. By using a case study of stationary states of atoms this paper examines the various interpretations. The preferred interpretation is that all localized events in space- time are part of chains of contiguous events traversing space-time at a rate limited by the speed of light. This is the process of

William R. Wharton

341

The Quantum Mechanical Basis of Conceptual Chemistry  

Microsoft Academic Search

Summary.  An experimentalist approaching theory for an understanding of conceptual chemistry that can be related to measurable properties, focuses on the electron density distribution. One finds in the topology of the electron density the definition of an atom, of the bonding between atoms, and of the boundary condition for the extension of quantum mechanics to an open system – to an

Richard F. W. Bader

2005-01-01

342

Subjective and objective probabilities in quantum mechanics  

SciTech Connect

We discuss how the apparently objective probabilities predicted by quantum mechanics can be treated in the framework of Bayesian probability theory, in which all probabilities are subjective. Our results are in accord with earlier work by Caves, Fuchs, and Schack, but our approach and emphasis are different. We also discuss the problem of choosing a noninformative prior for a density matrix.

Srednicki, Mark [Department of Physics, University of California, Santa Barbara, California 93106 (United States)

2005-05-15

343

Dissipation in Quantum Mechanics. The Harmonic Oscillator  

Microsoft Academic Search

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;

I. R. Senitzky

1960-01-01

344

Can quantum mechanics fool the cosmic censor?  

SciTech Connect

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

Matsas, G. E. A.; Silva, A. R. R. da [Instituto de Fisica Teorica, Universidade Estadual Paulista, Rua Pamplona 145, 01405-900, Sao Paulo, SP (Brazil); Richartz, M. [Instituto de Fisica Gleb Wataghin, UNICAMP, C. P. 6165, 13083-970, Campinas, SP (Brazil); Saa, A. [Departamento de Matematica Aplicada, UNICAMP, C. P. 6065, 13083-859, Campinas, SP (Brazil); Vanzella, D. A. T. [Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, Avenida Trabalhador Sao-carlense, 400, C. P. 369, 13560-970, Sao Carlos, SP (Brazil)

2009-05-15

345

The Compton effect: Transition to quantum mechanics  

NASA Astrophysics Data System (ADS)

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.

Stuewer, R. H.

2000-11-01

346

A quantum mechanics lab on a chip.  

PubMed

Chip technology has evolved from the desire to further shrink the size of semiconductor devices. The high sensitivity of the electronic properties of nanostructured semiconductors can be used to detect humidity, temperature, magnetic fields and other fundamental quantities. This in turn can be used to use electronic devices for fluidic or biophysical measurements and drastically reduce the volume of such measurements. Small semiconductor devices on the other hand, if measured at low enough temperatures and other appropriate boundary conditions, clearly display quantum effects. The quantum mechanical properties of such small charged islands, also called artificial atoms, can be measured by transport experiments and an energy spectrum similar to the one of real atoms can be detected. A variety of other quantum systems, such as tunnel barriers or phase-coherent rings can also be realized with such techniques. By coupling different quantum circuits on a chip the charge flow can be monitored in a time-resolved fashion on the level of individual electrons. The perfection of such systems has advanced to a degree where basic quantum mechanical properties can be probed on a semiconductor chip. PMID:20664881

Ensslin, Klaus; Gustavsson, Simon; Gasser, Urszula; Küng, Bruno; Ihn, Thomas

2010-07-28

347

Quantum mechanical tunneling in methylamine dehydrogenase  

Microsoft Academic Search

We report a calculation for a trideuteration kinetic isotope effect (KIE) for the proton transfer step in the oxidation of methylamine by the quinoprotein methylamine dehydrogenase (MADH). The potential field includes 11025 atoms, and the dynamics are based on a quantum mechanical\\/molecular mechanical (QM\\/MM) direct dynamics simulation and canonical variational transition state theory with small-curvature multidimensional tunneling contributions. About 1%

Cristóbal Alhambra; Maria Luz Sánchez; José Corchado; Jiali Gao; Donald G. Truhlar

2001-01-01

348

Simplified quantum mechanics of light detection for quantum cryptography  

NASA Astrophysics Data System (ADS)

Strong light signals are detected reliably on a time scale of a nanosecond; however, known detectors of weak light signals used in quantum key distribution (QKD) are much slower; they involve pulse-shaping arbiters based on flip-flops that take many nanoseconds to produce a stable output. Based on a recently shown logical independence of quantum particles from the devices that they are employed to explain, we make use of quantum mechanics fine-tuned so that particles serve not as rigid foundations but as improvised hypotheses useful in models that describe the recorded behavior of devices. On the experimental side, we augment the arbitrating flip-flop of a detector so that it fans out to a matched pair of auxiliary flip-flops, and show how this imparts to a detector a "self-awareness" of its own teetering, as announced by disagreements between the auxiliary flip-flops. We introduce a quantum model of this arrangement, invoking a pair of probe particles, and show this model corresponds well to an experiment. The matched pair of auxiliary flip-flops not only confirms the model of hesitation in a detector, but serves as an instrument, both conceptual and practical, that gives an added dimension to the characterization of signal sources.

Myers, John M.; Madjid, F. Hadi

2004-08-01

349

A 'Dysonization' scheme for identifying quasi-particles using non-Hermitian quantum mechanics.  

PubMed

Dyson analysed the low-energy excitations of a ferromagnet using a Hamiltonian that was non-Hermitian with respect to the standard inner product. This allowed for a facile rendering of these excitations (known as spin waves) as weakly interacting bosonic quasi-particles. More than 50 years later, we have the full denouement of the non-Hermitian quantum mechanics formalism at our disposal when considering Dyson's work, both technically and contextually. Here, we recast Dyson's work on ferromagnets explicitly in terms of two inner products, with respect to which the Hamiltonian is always self-adjoint, if not manifestly 'Hermitian'. Then we extend his scheme to doped anti-ferromagnets described by the t-J model, with hopes of shedding light on the physics of high-temperature superconductivity. PMID:23509382

Jones-Smith, Katherine

2013-03-18

350

The Quantum Mechanics of the Universe  

NASA Astrophysics Data System (ADS)

Classical general relativity predicts that the universe had a singular origin. The author shows that the singularity can be removed by quantum mechanics, just as in the case of the classical model of the atom. It is proposed that the quantum state of the universe is defined by a path integral over compact positive definite metrics. In a simple model this boundary condition leads to a wave function which can be regarded as a superposition of wave functions peaked around classical oscillating solutions with a long inflationary period.

Hawking, S. W.

351

The quantum mechanics of the universe  

NASA Astrophysics Data System (ADS)

Classical general relativity predicts that the universe had a singular origin. The author shows that the singularity can be removed by quantum mechanics, just as in the case of the classical model of the atom. He proposes that the quantum state of the universe is defined by a path integral over compact positive definite metrics. It is shown that in a simple model this boundary condition leads to a wave function which can be regarded as a superposition of wave functions peaked around classical oscillating solutions with a long inflationary period.

Hawking, S. W.

352

Nano, Quantum, and Statistical Mechanics and Thermodynamics: Educational Sites  

NSDL National Science Digital Library

This collection of links provides access to web sites associated with nano, quantum, and statistical mechanics and thermodynamics. The links are arranged by type: basic principles (including classical thermodynamics), nano, quantum, and statistical mechanics, mathematical techniques, applications, and references.

353

Noncommutative Chern-Simons quantum mechanics  

SciTech Connect

Chern-Simons quantum mechanics is generalized to the noncommutative plane in this paper. Compared with the commutative counterpart, we find that in addition to the mass of the charged particle, there is a dimensionless parameter which behaves interestingly when it takes zero value. We study this model from both classical and quantum aspects. We show that the classical theory has continuous limits when both the parameters tend to zero while the quantum aspect (energy spectra) does not have. We must regularize the spectra of the full theory properly when these parameters tend to zero in order to get the finite results. We resort to the Dirac theory and the Faddeev-Jackiw reduction, respectively, to show that the regularization we made is proper.

Jing Jian [Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029 (China); Department of Physics and Electronic, School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Liu Fenghua [Department of Physics and Electronic, School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Chen Jianfeng [Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029 (China)

2008-12-15

354

Neutrino oscillations: Quantum mechanics vs. quantum field theory  

SciTech Connect

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

Akhmedov, Evgeny Kh.; Kopp, Joachim

2010-01-01

355

Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations.  

PubMed

Combined ab initio quantum mechanical and molecular mechanical calculations have been widely used for modeling chemical reactions in complex systems such as enzymes, with most applications being based on the determination of a minimum energy path connecting the reactant through the transition state to the product in the enzyme environment. However, statistical mechanics sampling and reaction dynamics calculations with a combined ab initio quantum mechanical (QM) and molecular mechanical (MM) potential are still not feasible because of the computational costs associated mainly with the ab initio quantum mechanical calculations for the QM subsystem. To address this issue, a reaction path potential energy surface is developed here for statistical mechanics and dynamics simulation of chemical reactions in enzymes and other complex systems. The reaction path potential follows the ideas from the reaction path Hamiltonian of Miller, Handy and Adams for gas phase chemical reactions but is designed specifically for large systems that are described with combined ab initio quantum mechanical and molecular mechanical methods. The reaction path potential is an analytical energy expression of the combined quantum mechanical and molecular mechanical potential energy along the minimum energy path. An expansion around the minimum energy path is made in both the nuclear and the electronic degrees of freedom for the QM subsystem internal energy, while the energy of the subsystem described with MM remains unchanged from that in the combined quantum mechanical and molecular mechanical expression and the electrostatic interaction between the QM and MM subsystems is described as the interaction of the MM charges with the QM charges. The QM charges are polarizable in response to the changes in both the MM and the QM degrees of freedom through a new response kernel developed in the present work. The input data for constructing the reaction path potential are energies, vibrational frequencies, and electron density response properties of the QM subsystem along the minimum energy path, all of which can be obtained from the combined quantum mechanical and molecular mechanical calculations. Once constructed, it costs much less for its evaluation. Thus, the reaction path potential provides a potential energy surface for rigorous statistical mechanics and reaction dynamics calculations of complex systems. As an example, the method is applied to the statistical mechanical calculations for the potential of mean force of the chemical reaction in triosephosphate isomerase. PMID:15260525

Lu, Zhenyu; Yang, Weitao

2004-07-01

356

The Double Rotation as Invariant of Motion in Quantum Mechanics  

Microsoft Academic Search

Quantum mechanics may loose its weirdness if systematically geometric algebra methods would be used more. Crucial aspect is to find laws of quantum mechanics be present in macroworld in form of description of motions rather than objects. To help to reach this goal we suggest to use double rotation as one of base invariants in quantum mechanics. We suggest to

Dainis Zeps

2009-01-01

357

Attaching Theories of Consciousness to Bohmian Quantum Mechanics  

Microsoft Academic Search

The de Broglie-Bohm theory of quantum mechanics (here simply called Bohmian Mechanics or BM) [1-10] is an augmentation of ``bare'' quantum mechanics (the bare theory being given by an algebra of operators and a quantum state that sets the expectation values of these operators) that includes a definite history or Bohmian trajectory. This definite trajectory gives BM a somewhat more

Don N. Page

1995-01-01

358

Quantum Mechanics in the Exterior Region of a Schwarzschild Black Hole  

NASA Astrophysics Data System (ADS)

In this project we prove that the exterior region of a Schwarzschild Black-hole can be taken as space-time. For the case of Klein-Gordon field in the background of the Schwarzschild gravitational field we prove the existence of a self-adjoint hamiltonian operator. The problem reduces to a one-dimensional potential problem. We apply the WKB approximation to this problem. A comparison with the classical case is established. We find that in the quantum mechanical case reflection is present. We also show that probability is conserved.

Caroprese, Blas

1988-12-01

359

Quantum-mechanical description of spin-1 particles with electric dipole moments  

NASA Astrophysics Data System (ADS)

The Proca-Corben-Schwinger equations for a spin-1 particle with an anomalous magnetic moment are added by a term describing an electric dipole moment, then they are reduced to a Hamiltonian form, and finally they are brought to the Foldy-Wouthuysen representation. Relativistic equations of motion are derived. The needed agreement between quantum-mechanical and classical relativistic equations of motion is proved. The scalar and tensor electric and magnetic polarizabilities of pointlike spin-1 particles (W bosons) are calculated for the first time.

Silenko, Alexander J.

2013-04-01

360

Hermiticity of the Dirac Hamiltonian in curved spacetime  

SciTech Connect

In previous work on the quantum mechanics of an atom freely falling in a general curved background spacetime, the metric was taken to be sufficiently slowly varying on time scales relevant to atomic transitions that time derivatives of the metric in the vicinity of the atom could be neglected. However, when the time dependence of the metric cannot be neglected, it was shown that the Hamiltonian used there was not Hermitian with respect to the conserved scalar product. This Hamiltonian was obtained directly from the Dirac equation in curved spacetime. This raises the paradox of how it is possible for this Hamiltonian to be non-Hermitian. Here, we show that this non-Hermiticity results from a time dependence of the position eigenstates that enter into the Schroedinger wave function, and we write the expression for the Hamiltonian that is Hermitian for a general metric when the time dependence of the metric is not neglected.

Huang Xing; Parker, Leonard [Physics Department, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201 (United States)

2009-01-15

361

Script PScript T Symmetric Hamiltonian Model and Exactly Solvable Potentials  

NASA Astrophysics Data System (ADS)

Searching for non-Hermitian, Script PScript T-symmetric Hamiltonians [1] with real spectra has been acquiring much interest for fourteen years. In this article, we have introduced a Script PScript T symmetric non-Hermitian Hamiltonian model which is given as where ? and ? are real constants, and are first order differential operators. Because the Hamiltonian Script H is pseudo-Hermitian, we have obtained the Hermitian equivalent of Script H which is in Sturm- Liouville form leads to exactly solvable potential models which are effective screened and hyperbolic Rosen-Morse II potentials. Using convenient sinilarity transformations, we have obtained a physical Hamiltonian h for each case. Then, the Schrödinger equation is solved exactly using Shape Invariance method of Supersymmetric Quantum Mechanics [2].

Ye?ilta?, Özlem

2013-02-01

362

Information geometry, dynamics and discrete quantum mechanics  

NASA Astrophysics Data System (ADS)

We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the picture. We do this in three steps. Our starting point is information geometry, the natural geometry of the space of probability distributions. Dynamics requires additional structure. To evolve the Pk, we introduce coordinates Sk canonically conjugate to the Pk and a symplectic structure. We then seek to extend the metric structure of information geometry, to define a geometry over the full space of the Pk and Sk. Consistency between the metric tensor and the symplectic form forces us to introduce a Kähler geometry. The construction has notable features. A complex structure is obtained in a natural way. The canonical coordinates of the ?k = PkeiSk Kähler space are precisely the wave functions of quantum mechanics. The full group of unitary transformations is obtained. Finally, one may associate a Hilbert space with the Kähler space, which leads to the standard version of quantum theory. We also show that the metric that we derive here using purely geometrical arguments is precisely the one that leads to Wootters' expression for the statistical distance for quantum systems.

Reginatto, Marcel; Hall, Michael J. W.

2013-08-01

363

Reversible logic and quantum computers  

Microsoft Academic Search

This article is concerned with the construction of a quantum-mechanical Hamiltonian describing a computer. This Hamiltonian generates a dynamical evolution which mimics a sequence of elementary logical steps. This can be achieved if each logical step is locally reversible (global reversibility is insufficient). Computational errors due to noise can be corrected by means of redundancy. In particular, reversible error-correcting codes

Asher Peres

1985-01-01

364

Quantum KAM technique and Yang{endash}Mills quantum mechanics  

SciTech Connect

We study a quantum analogue of the iterative perturbation theory by Kolmogorov used in the proof of the Kolmogorov{endash}Arnold{endash}Moser (KAM) theorem. The method is based on sequent canonical transformations with a {open_quote}{open_quote}running{close_quote}{close_quote} coupling constant {lambda}, {lambda}{sup 2}, {lambda}{sup 4}, etc. The proposed scheme, as its classical predecessor, is {open_quote}{open_quote}superconvergent{close_quote}{close_quote} in the sense that after the {ital n}th step, a theory is solved to the accuracy of order {lambda}{sup 2{ital n}{minus}1}. It is shown that the Kolmogorov technique corresponds to an infinite resummation of the usual perturbative series. The corresponding expansion is convergent for the quantum anharmonic oscillator due to the fact that it turns out to be identical to the Pade series. The method is easily generalizable to many-dimensional cases. The Kolmogorov technique is further applied to a non-perturbative treatment of Yang{endash}Mills quantum mechanics. A controllable expansion for the wave function near the origin is constructed. For large fields, we build an asymptotic adiabatic expansion in inverse powers of the field. This asymptotic solution contains arbitrary constants which are not fixed by the boundary conditions at infinity. To find them, we approximately match the two expansions in an intermediate region. We also discuss some analogies between this problem and the method of QCD sum rules. Copyright {copyright} 1995 Academic Press, Inc.

Halperin, I. [Department of Physics, Technion-Israel Institute of Technology, Haifa 32000 (Israel)

1995-12-01

365

Quantum Mechanics, Gravity, and the Multiverse  

NASA Astrophysics Data System (ADS)

The discovery of accelerating expansion of the universe has led us to take the dramatic view that our universe may be one of the many universes in which low energy physical laws take different forms: the multiverse. I explain why/how this view is supported both observationally and theoretically, especially by string theory and eternal inflation. I then describe how quantum mechanics plays a crucial role in understanding the multiverse, even at the largest distance scales. The resulting picture leads to a revolutionary change of our view of spacetime and gravity, and completely unifies the paradigm of the eternally inflating multiverse with the many worlds interpretation of quantum mechanics. The picture also provides a solution to a long-standing problem in eternal inflation, called the measure problem, which I briefly describe.

Nomura, Yasunori

2012-04-01

366

Suppression of the quantum-mechanical collapse by repulsive interactions in a quantum gas  

NASA Astrophysics Data System (ADS)

The quantum-mechanical collapse (alias fall onto the center of particles attracted by potential -r-2) is a well-known issue in quantum theory. It is closely related to the quantum anomaly, i.e., breaking of the scaling invariance of the respective Hamiltonian by quantization. We demonstrate that the mean-field repulsive nonlinearity prevents the collapse and thus puts forward a solution to the quantum-anomaly problem that differs from that previously developed in the framework of the linear quantum-field theory. This solution may be realized in the 3D or 2D gas of dipolar bosons attracted by a central charge and in the 2D gas of magnetic dipoles attracted by a current filament. In the 3D setting, the dipole-dipole interactions are also taken into regard, in the mean-field approximation, resulting in a redefinition of the scattering length which accounts for the contact repulsion between the bosons. In lieu of the collapse, the cubic nonlinearity creates a 3D ground state (GS), which does not exist in the respective linear Schrödinger equation. The addition of the harmonic trap gives rise to a tristability, in the case when the Schrödinger equation still does not lead to the collapse. In the 2D setting, the cubic nonlinearity is not strong enough to prevent the collapse; however, the quintic term does it, creating the GS, as well as its counterparts carrying the angular momentum (vorticity). Counterintuitively, such self-trapped 2D modes exist even in the case of a weakly repulsive potential r-2. The 2D vortical modes avoid the phase singularity at the pivot (r=0) by having the amplitude diverging at r?0 instead of the usual situation with the amplitude of the vortical mode vanishing at r?0 (the norm of the mode converges despite of the singularity of the amplitude at r?0). In the presence of the harmonic trap, the 2D quintic model with a weakly repulsive central potential r-2 gives rise to three confined modes, the middle one being unstable, spontaneously developing into a breather. In both the 3D and 2D cases, the GS wave functions are found in a numerical form and in the form of an analytical approximation, which is asymptotically exact in the limit of the large norm.

Sakaguchi, Hidetsugu; Malomed, Boris A.

2011-01-01

367

Suppression of the quantum-mechanical collapse by repulsive interactions in a quantum gas  

SciTech Connect

The quantum-mechanical collapse (alias fall onto the center of particles attracted by potential -r{sup -2}) is a well-known issue in quantum theory. It is closely related to the quantum anomaly, i.e., breaking of the scaling invariance of the respective Hamiltonian by quantization. We demonstrate that the mean-field repulsive nonlinearity prevents the collapse and thus puts forward a solution to the quantum-anomaly problem that differs from that previously developed in the framework of the linear quantum-field theory. This solution may be realized in the 3D or 2D gas of dipolar bosons attracted by a central charge and in the 2D gas of magnetic dipoles attracted by a current filament. In the 3D setting, the dipole-dipole interactions are also taken into regard, in the mean-field approximation, resulting in a redefinition of the scattering length which accounts for the contact repulsion between the bosons. In lieu of the collapse, the cubic nonlinearity creates a 3D ground state (GS), which does not exist in the respective linear Schroedinger equation. The addition of the harmonic trap gives rise to a tristability, in the case when the Schroedinger equation still does not lead to the collapse. In the 2D setting, the cubic nonlinearity is not strong enough to prevent the collapse; however, the quintic term does it, creating the GS, as well as its counterparts carrying the angular momentum (vorticity). Counterintuitively, such self-trapped 2D modes exist even in the case of a weakly repulsive potential r{sup -2}. The 2D vortical modes avoid the phase singularity at the pivot (r=0) by having the amplitude diverging at r{yields}0 instead of the usual situation with the amplitude of the vortical mode vanishing at r{yields}0 (the norm of the mode converges despite of the singularity of the amplitude at r{yields}0). In the presence of the harmonic trap, the 2D quintic model with a weakly repulsive central potential r{sup -2} gives rise to three confined modes, the middle one being unstable, spontaneously developing into a breather. In both the 3D and 2D cases, the GS wave functions are found in a numerical form and in the form of an analytical approximation, which is asymptotically exact in the limit of the large norm.

Sakaguchi, Hidetsugu [Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580 (Japan); Malomed, Boris A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

2011-01-15

368

Singular potentials in nonrelativistic quantum mechanics  

Microsoft Academic Search

Summary  The mathematical aspects of singular potentials in nonrelativistic quantum mechanics are studied in terms of the self-adjoint\\u000a transformations related to singular differential operators in the space L2(0, ?). The physical content is expressed by the spectral decompositions and for attractive potentials found to be determined\\u000a only up to a parameter denning a particular extension. In general it is not possible

K. Meetz

1964-01-01

369

Auxiliary nRules of Quantum Mechanics  

Microsoft Academic Search

Standard quantum mechanics makes use of four auxiliary rules that allow the\\u000aSchrodinger solutions to be related to laboratory experience, such as the Born\\u000arule that connects square modulus to probability. These rules (here called the\\u000asRules) lead to some unacceptable results. They do not allow the primary\\u000aobserver to be part of the system. They do not allow individual

Richard A Mould

2005-01-01

370

Grounding quantum probability in psychological mechanism.  

PubMed

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

Love, Bradley C

2013-06-01

371

Quantum-mechanical noise in an interferometer  

Microsoft Academic Search

The interferometers now being developed to detect gravitational waves work by measuring the relative positions of widely separated masses. Two fundamental sources of quantum-mechanical noise determine the sensitivity of such an interferometer: (i) fluctuations in number of output photons (photon-counting error) and (ii) fluctuations in radiation pressure on the masses (radiation-pressure error). Because of the low power of available continuous-wave

Carlton Caves

1981-01-01

372

Collocation method for fractional quantum mechanics  

SciTech Connect

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

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

2010-12-15

373

Nine Formulations of Quantum Mechanics: Lecture  

NSDL National Science Digital Library

In this lecture, Dr. Daniel Styer, a physics professor at Oberlin College, guides the listener through nine formulations of quantum mechanics. Styer discusses each formulation's unique abilities and challenges, then offers his perspective on the application to undergraduate education. This lecture was delivered at the Kavli Institute for Physics, as a part of the Theorists at Undergraduate Institutions mini-program. Audio, video and slides are included.

Styer, Dan

2005-08-07

374

Commutator Anomaly in Noncommutative Quantum Mechanics  

NASA Astrophysics Data System (ADS)

In this paper, the Schrödinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space-space and space-momentum as well as momentum-momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.

Dulat, Sayipjamal; Li, Kang

375

Deformation quantization of noncommutative quantum mechanics  

Microsoft Academic Search

The Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantization. In this paper, we investigate the basic aspects of deformation quantization for noncommutative quantum mechanics (NCQM). We first prove some general relations of the Weyl correspondence in non-commuting phase-space. Then we derive explicit form of the Wigner

Sicong Jing; Fen Zuo; Taihua Heng

2004-01-01

376

Commutator Anomaly in Noncommutative Quantum Mechanics  

Microsoft Academic Search

In this paper, the Schrödinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space-space and space-momentum as well as momentum-momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical

Sayipjamal Dulat; Kang Li

2006-01-01

377

1/N expansion in noncommutative quantum mechanics  

SciTech Connect

We study the 1/N expansion in noncommutative quantum mechanics for the anharmonic and Coulombian potentials. The expansion for the anharmonic oscillator presented good convergence properties, but for the Coulombian potential, we found a divergent large N expansion when using the usual noncommutative generalization of the potential. We proposed a modified version of the noncommutative Coulombian potential which provides a well-behaved 1/N expansion.

Ferrari, A. F. [Universidade Federal do ABC, Centro de Ciencias Naturais e Humanas, Rua Santa Adelia, 166, 09210-170, Santo Andre, SP (Brazil); Gomes, M.; Stechhahn, C. A. [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo - SP (Brazil)

2010-08-15

378

Theory of spontaneous emission of quantum dots in the linear regime  

Microsoft Academic Search

We develop a fully quantum-mechanical theory for the interaction of light and electron-hole excitations in semiconductor quantum dots. Our theoretical analysis results in an expression for the photoluminescence intensity of quantum dots in the linear regime. Taking into account the single-particle Hamiltonian, the free-photon Hamiltonian, the electron-hole interaction Hamiltonian, and the interaction of carriers with light, and applying the Heisenberg

A. Zora; C. Simserides; G. P. Triberis

2007-01-01

379

The 1925 Born and Jordan paper ``On quantum mechanics''  

NASA Astrophysics Data System (ADS)

The 1925 paper ``On quantum mechanics'' by M. Born and P. Jordan, and the sequel ``On quantum mechanics II'' by M. Born, W. Heisenberg, and P. Jordan, developed Heisenberg's pioneering theory into the first complete formulation of quantum mechanics. The Born and Jordan paper is the subject of the present article. This paper introduced matrices to physicists. We discuss the original postulates of quantum mechanics, present the two-part discovery of the law of commutation, and clarify the origin of Heisenberg's equation. We show how the 1925 proof of energy conservation and Bohr's frequency condition served as the gold standard with which to measure the validity of the new quantum mechanics.

Fedak, William A.; Prentis, Jeffrey J.

2009-02-01

380

TOPICAL REVIEW: Quantum systems with finite Hilbert space: Galois fields in quantum mechanics  

Microsoft Academic Search

A 'Galois quantum system' in which the position and momentum take values in the Galois field GF(pell) is considered. It is comprised of ell-component systems which are coupled in a particular way and is described by a certain class of Hamiltonians. Displacements in the GF(pell) × GF(pell) phase space and the corresponding Heisenberg Weyl group are studied. Symplectic transformations are

A. Vourdas

2007-01-01

381

Crypto-Unitary Forms of Quantum Evolution Operators  

NASA Astrophysics Data System (ADS)

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

Znojil, Miloslav

2013-06-01

382

Connecting Spin and Statistics in Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor (-1)2 s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required.

Jabs, Arthur

2010-07-01

383

Bohmian Mechanics In A Macroscopic Quantum System  

NASA Astrophysics Data System (ADS)

In the so called `causal' interpretation of quantum mechanics, an electron is considered as a particle and such particle is influenced not only by a classical but also by a so called quantum potential. This idea was developed by Professor Bohm in an important paper. In this paper we use some of the basics of this interpretation in a financial option pricing environment. The causal interpretation allows for trajectories. Path breaking work by Professors Bohm and Hiley and Khrennikov and Choustova have made that the causal interpretation is a step closer to potential applications in social science. In this paper we consider the wave function as a wave of information. We consider the gradient of the phase of this wave function and show how the option price could be influenced by this gradient.

Haven, Emmanuel

2006-01-01

384

From quantum mechanics to universal structures of conceptualization and feedback on quantum mechanics  

SciTech Connect

In previous works we have established that the spacetime probabilistic organization of the quantum theory is determined by the spacetime characteristics of the operations by which the observer produces the objects to be studied (states of microsystems) and obtains qualifications of these. Guided by this first conclusion, we have then built a general syntax of relativized conceptualization where any description is explicity and systematically referred to the two basic epistemic operations by which the conceptor introduces the object to be qualified and then obtains qualifications of it. Inside this syntax there emerges a general typology of the relativized descriptions. Here we show that with respect to this typology the type of the predictive quantum mechanical descriptions acquires a precise definition. It appears that the quantum mechanical formalism has captured and has expressed directly in a mathematical language the most complex form in which can occur a first descriptional phase that lies universally at the bottom of any chain of conceptualization. The main features of the Hilbert-Dirac algorithms are decoded in terms of the general syntax of relativized conceptualiztion. This renders explicit the semantical contents of the quantum mechanical representations relating each one of these to its mathematical quantum mechanical expression. Basic insufficiencies are thus identified and, correlatively, false problems as well as answers to these, or guides towards the answers. Globally the results obtained provide a basis for the future attempts at a general mathematical representation of the processes of conceptualization.

Mugur-Schaechter, M. (Univ. of Reims (France))

1993-01-01

385

Unstable trajectories and the quantum mechanical uncertainty  

SciTech Connect

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.

Moser, Hans R. [Physics Institute, University of Zuerich, Winterthurerstrasse 190, CH-8057 Zuerich (Switzerland)], E-mail: moser@physik.uzh.ch

2008-08-15

386

Unstable trajectories and the quantum mechanical uncertainty  

NASA Astrophysics Data System (ADS)

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.

Moser, Hans R.

2008-08-01

387

Reciprocal relativity of noninertial frames: quantum mechanics  

NASA Astrophysics Data System (ADS)

Noninertial transformations on time-position-momentum-energy space {t, q, p, e} with invariant Born-Green metric ds^{2}=-d t^{2}+\\frac{1}{c^{2}}\\,d q^{2}+\\frac{1}{b^{2}} \\big(d p^{2}-\\frac{1}{c^{2}}\\,d e^{2}\\big) and the symplectic metric -de ? dt + dp ? dq are studied. This {\\cal U}1,3) group of transformations contains the Lorentz group as the inertial special case and, in the limit of small forces and velocities, reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds2 = -dt2. The {\\cal U}( 1,3) transformations bound relative velocities by c and relative forces by b. Spacetime is no longer an invariant subspace but is relative to noninertial observer frames. In the limit of b ? ?, spacetime is invariant. Born was lead to the metric by a concept of reciprocity between position and momentum degrees of freedom and for this reason we call this reciprocal relativity. For large b, such effects will almost certainly only manifest in a quantum regime. Wigner showed that special relativistic quantum mechanics follows from the projective representations of the inhomogeneous Lorentz group. Projective representations of a Lie group are equivalent to the unitary representations of its central extension. The same method of projective representations for the inhomogeneous {\\cal U}( 1,3) group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous {\\cal U}( 1,3) group is the cover of the quaplectic group {\\cal Q}( 1,3) ={\\cal U}( 1,3) \\otimes _{s}{\\cal H}(4) . {\\cal H}( 4) is the Weyl-Heisenberg group. The {\\cal H}( 4) group, and the associated Heisenberg commutation relations central to quantum mechanics, results directly from requiring projective representations. A set of second-order wave equations result from the representations of the Casimir operators.

Low, Stephen G.

2007-04-01

388

Direct Quantum Mechanical Simulations of Shocked Energetic Materials.  

National Technical Information Service (NTIS)

Quantum mechanical calculations based on density functional theory (DFT) are used to study dynamic behavior of shocked energetic materials (EM). In this work, we present results of quantum molecular dynamics (QMD) simulations of shocked pentaerythritol te...

B. M. Rice R. Balu W. D. Mattson

2008-01-01

389

On the Ehrenfest theorem of quantum mechanics  

SciTech Connect

We give a mathematically rigorous derivation of Ehrenfest's equations for the evolution of position and momentum expectation values under general and natural assumptions which include atomic and molecular Hamiltonians with Coulomb interactions.

Friesecke, Gero; Koppen, Mario [Center for Mathematics, TU Munich, Boltzmannstr. 3, Garching D-85748 (Germany)

2009-08-15

390

Uniform description of polar optical phonon states and their Fröhlich electron-phonon interaction Hamiltonians in multi-layer wurtzite nitride low-dimensional quantum structures  

NASA Astrophysics Data System (ADS)

The general features of four types of polar optical phonon modes [including the quasi-confined (QC) modes, the propagating (PR) modes, the half-space (HS) modes and the interface optical (IO) modes] and their electron-phonon coupling properties in wurtzite nitride low-dimensional quantum structures are discussed and concluded. Based on the transfer matrix method and the dielectric continuum (DC) and Loudon's uniaxial crystal models, the analytical and uniform phonon states of the QC, PR, HS and IO phonon modes in wurtzite quasi-2-dimensional (Q2D) quantum wells (QWs), quasi-1-dimensional (Q1D) quantum wires (QWRs) and quasi-0-dimensional (Q0D) quantum dots (QDs) are given. The Fröhlich electron-phonon interaction Hamiltonian for the four types of dispersive phonon modes in these wurtzite quantum systems is deduced. It is found that the QC, HS and PR phonon modes always appear in GaN/AlGaN or InGaN/GaN low-dimensional quantum systems. But the PR phonon modes only exist in the low-doped x GaN/AlxGa1-xN (x < 0.34) and InxGa1-xN/GaN quantum structures (x < 0.35). The general features of dispersive phonon spectra in wurtzite QWs, QWRs and QDs including the frequency subranges of phonon modes, the continuous and discrete spectra, the limited frequencies and the "reducing" behaviors are discussed and concluded in detailed. The electron-phonon coupling functions are analyzed. The total tendency of the electron-phonon coupling function decreases with the increase of the free wave-numbers, the orbital and azimuthal quantum numbers. But the electron-phonon coupling functions sometimes take maximum values at some certain wave-(quantum) numbers, which is attributed to the "modulating" effect of dielectric functions ratio (&z.epsi;t/&z.epsi;z) of wurtzite nitride materials in different directions to the electron-phonon coupling functions. The electron-phonon coupling strength of the high-frequency phonon modes is stronger than that of the low-frequency ones. Moreover, the higher the orders of QC, PR and HS modes are, the weaker the electron-phonon coupling strengths become. The results and conclusions are meaningful and helpful for understanding and analyzing phonon spectra and polaronic effect in wurtzite low-dimensional quantum systems.

Zhang, Li

2013-01-01

391

QUANTUM MECHANICS: Enhanced: Schrodinger's Cat Is Out of the Hat.  

PubMed

In 1935, Erwin Schrödinger suggested his famous gedanken experiment of the cat that is simultaneously "dead" and "alive" inside its box until the box is opened. But as Tesche explains in her Perspective, such a macroscopic manifestation of quantum mechanics has remained elusive until recently. The experiments by van der Wal et al. are an important step toward demonstrating that quantum mechanics can describe macroscopic phenomena. The approach may be exploited in quantum computing and quantum cryptography. PMID:17780511

Tesche, C

2000-10-27

392

Combined quantum mechanical\\/molecular mechanics modeling for large organometallic and metallobiochemical systems  

Microsoft Academic Search

A method of combined quantum mechanics\\/molecular mechanics has been developed to model larger organometallic and metallobiochemical systems where neither quantum mechanics nor molecular mechanics, applied separately, can solve the problem. An electronically transparent interface, which allows charge transfers between the quantum and classical fragments, is devised and realized by employing a special iterative procedure of double (intrafragment and interfragment) self-consistent

Max Kangchien Leong

1997-01-01

393

Quantum optimal control for the full ensemble of randomly oriented molecules having different field-free Hamiltonians  

Microsoft Academic Search

We have presented the optimal control theory formulation to calculate optimal fields that can control the full ensemble of randomly oriented molecules having different field-free Hamiltonians. The theory is applied to the fifty-fifty mixture of randomly oriented 133CsI and 135CsI isotopomers and an optimal field is sought to achieve isotope-selective vibrational excitations with high efficiency. Rotational motion is frozen and

Yuzuru Kurosaki; Akira Ichihara; Keiichi Yokoyama

2011-01-01

394

Simulation Of Wave Function And Probability Density Of Modified Poschl Teller Potential Derived Using Supersymmetric Quantum Mechanics  

SciTech Connect

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

Angraini, Lily Maysari [STKIP Hamzanwadi Selong East Lombok, NTB, PostGraduate student at Physics Department UNS, Jl. Ir. Sutami 36 A, Surakarta (Indonesia); Suparmi,; Variani, Viska Inda [Physics Department UNS, Jl. Ir. Sutami 36 A, Surakarta (Indonesia)

2010-12-23

395

A fully 3D atomistic quantum mechanical study on random dopant induced effects in 25nm MOSFETs  

SciTech Connect

We present a fully 3D atomistic quantum mechanical simulation for nanometered MOSFET using a coupled Schroedinger equation and Poisson equation approach. Empirical pseudopotential is used to represent the single particle Hamiltonian and linear combination of bulk band (LCBB) method is used to solve the million atom Schroedinger's equation. We studied gate threshold fluctuations and threshold lowering due to the discrete dopant configurations. We compared our results with semiclassical simulation results. We found quantum mechanical effects increase the threshold fluctuation while decreases the threshold lowering. The increase of threshold fluctuation is in agreement with previous study based on approximated density gradient approach to represent the quantum mechanical effect. However, the decrease in threshold lowering is in contrast with the previous density gradient calculations.

Wang, Lin-Wang; Jiang, Xiang-Wei; Deng, Hui-Xiong; Luo, Jun-Wei; Li, Shu-Shen; Wang, Lin-Wang; Xia, Jian-Bai

2008-07-11

396

A new generalization of supersymmetric quantum mechanics to arbitrary dimensionality or number of distinguishable particles  

NASA Astrophysics Data System (ADS)

We present here a new approach to generalize supersymmetric quantum mechanics to treat multiparticle and multi-dimensional systems. We do this by introducing a vector superpotential in an orthogonal hyperspace. In the case of N distinguishable particles in three dimensions this results in a vector superpotential with 3N orthogonal components. The original scalar Schrödinger operator can be factored into vector ``charge'' operators: Q1 and Q1^. Using these operators, we can write the original (scalar) Hamiltonian as H1= Q1^.Q1+ E0^(1). The second sector Hamiltonian is a tensor given by H2= Q1Q1^ + E0^(1) and is isospectral with H1. The vector ground state of sector two, ?0^(2), can be used with the charge operator Q1^ to obtain the excited state wave functions of the first sector. This can be used with the sector Hamiltonians alternating between scalar and tensor forms accommodating both variational and Monte Carlo methods to obtain approximate solutions to both scalar and tensor sectors. We demonstrate the approach with examples of a pair of separable 1D harmonic oscillators and the example of a non-separable 2D anharmonic oscillator (or equivalently a pair of coupled 1D oscillators).

Markovich, Thomas

2010-10-01

397

Statistical Mechanics of Quantum Integrable Systems  

NASA Astrophysics Data System (ADS)

Recent developments in statistical mechanics of quantum integrable systems are reviewed. Those studies are fundamental and have a renewed interest related to newly developing fields such as atomic Bose-Einstein condensations, photonic crystals and quantum computations. After a brief summary of the basic concepts and methods, the following three topics are discussed. First, by the thermal Bethe ansatz (TBA), a hard-core Bose gas is exactly solved. The model includes fully the effect of excluded volume and is identified to be a c=1 conformal field theory. Second, the cluster expansion method based on the periodic boundary condition for the Bethe wave function, which we call the Bethe ansatz cluster expansion (BACE) method, is developed for a ?-function gas and the XXX Heisenberg chain. This directly proves the TBA and reveals intrinsic properties of quantum integrable systems. Third, for a ?-function gas, the integral equations for the distribution functions of the quasi-momentum and the quasi-particle energy are solved in the form of power series. In the weak coupling case, the results reproduce those of Bogoliubov theory.

Wadati, Miki; Kato, Go; Iida, Toshiaki

398

BiHermitian supersymmetric quantum mechanics  

NASA Astrophysics Data System (ADS)

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].

Zucchini, Roberto

2007-04-01

399

Hidden geometric character of relativistic quantum mechanics  

NASA Astrophysics Data System (ADS)

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 4×4 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 4×4 matrix algebra and as such are excluded from the isomorphism. We will show that a solution in terms of Dirac spinors is equivalent to a plane wave solution. Just as one finds in the standard formulation, monogenic functions can be naturally split into positive/negative energy together with left/right ones. This split is provided by geometric projectors and we will show that there is a second set of projectors providing an alternate fourfold split. The possible implications of this alternate split are not yet fully understood and are presently the subject of profound research.

Almeida, José B.

2007-01-01

400

Position-dependent noncommutativity in quantum mechanics  

SciTech Connect

The model of the position-dependent noncommutativity in quantum mechanics is proposed. We start with given commutation relations between the operators of coordinates [x-circumflex{sup i},x-circumflex{sup j}]={omega}{sup ij}(x-circumflex), 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 obeys 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 noncommutativity.

Gomes, M.; Kupriyanov, V. G. [Instituto de Fisica, Universidade de Sao Paulo (Brazil)

2009-06-15

401

Topological Solution of Bohmian Quantum Mechanics  

NASA Astrophysics Data System (ADS)

The topological solutions of the De Broglie-Bohm quantum mechanics are presented. Starting from the Schrödinger equation for one particle system and ?-mapping topological current theory, the trajectory of the particle is derived explicitly, and can be used as the world line of the particle. The world line is just at the zero point of the wave function and it is shown that the vorticity of the world line can be expressed by Hopf index and Brouwer degree. The evolution of the world line at the bifurcation point is given.

Shi, Xuguang; Yu, Ming; Duan, Yishi

402

Formulation, interpretation and application of non-commutative quantum mechanics  

NASA Astrophysics Data System (ADS)

In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the standard quantum mechanical interpretation based on positive operator valued measures, provides a sufficient framework for the consistent interpretation of this quantum system. The implications of this formalism for rotational and time reversal symmetry are discussed. The formalism is applied to the free particle and harmonic oscillator in two dimensions and the physical signatures of non-commutativity are identified.

Scholtz, F. G.; Gouba, L.; Hafver, A.; Rohwer, C. M.

2009-05-01

403

Second order average Hamiltonian theory of symmetry-based pulse schemes in the nuclear magnetic resonance of rotating solids: Application to triple-quantum dipolar recoupling  

NASA Astrophysics Data System (ADS)

The average Hamiltonian theory (AHT) of several classes of symmetry-based radio-frequency pulse sequences is developed to second order, allowing quantitative analyses of a wide range of recoupling and decoupling applications in magic-angle-spinning solid state nuclear magnetic resonance. General closed analytical expressions are presented for a cross term between any two interactions recoupled to second order AHT. We classify them into different categories and show that some properties of the recoupling pulse sequence may be predicted directly from this classification. These results are applied to examine a novel homonuclear recoupling strategy, effecting a second order average dipolar Hamiltonian comprising trilinear triple quantum (3Q) spin operators. We discuss general features and design principles of such 3Q recoupling sequences and demonstrate by numerical simulations and experiments that they provide more efficient excitation of 13C 3Q coherences compared to previous techniques. We passed up to 15% of the signal through a state of 3Q coherence in rotating powders of uniformly 13C-labeled alanine and tyrosine. Second order recoupling-based 13C homonuclear 3Q correlation spectroscopy is introduced and demonstrated on tyrosine.

Brinkmann, Andreas; Edén, Mattias

2004-06-01

404

Super classical quantum mechanics: The best interpretation of nonrelativistic quantum mechanics  

NASA Astrophysics Data System (ADS)

It has been shown that Newtonian classical mechanics (NCM) suffers from several kinds of chaotic indeterminacies. That means, a large set of problems treated with NCM gives results which are in wild disagreement with observation. In the present paper, these shortcomings are repaired in a simple, obvious, and essentially unique manner. The NCM theory is thereby transformed into a new theory which is fully equivalent to the Heisenberg, Schrödinger, and Dirac nonrelativistic quantum mechanics, with the vital addition of Born's probabilistic interpretation of the wave function built in from the start. I call this new theory ``super classical quantum mechanics'' (SCQM). Using Ehrenfest's theorem of 1927, the classical limit of the new theory, SCQM, is seen to give exactly the results expected of the repaired Newtonian theory of classical mechanics.

Lamb, Willis E.

2001-04-01

405

Loop transfer matrix and loop quantum mechanics  

NASA Astrophysics Data System (ADS)

The gonihedric model of random surfaces on a 3d euclidean lattice has equivalent representation in terms of transfer matrix K(Qi,Qf) which describes the propagation of loops Q. We extend the previous construction of loop transfer matrix to the case of non-zero self-intersection coupling constant kappa. We introduce loop generalization of Fourier transformation which allows to diagonalize transfer matrices depending on symmetric difference of loops and express all eigenvalues of 3d loop transfer matrix through the correlation functions of the corresponding 2d statistical system. The loop Fourier transformation allows to carry out analogy with quantum mechanics of point particles, to introduce conjugate momentum loop P and to define loop quantum mechanics. We also consider transfer matrix on 4d lattice which describes propagation of memebranes. This transfer matrix can also be diagonalized by using generalized Fourier transformation, and all its eigenvalues are equal to the correlation functions of the corresponding 3d statistical system. Particularly the free energy of the 4d membrane system is equal to the free energy of 3d gonihedric system of loops.

Savvidy, George K.

2000-09-01

406

Molecular model with quantum mechanical bonding information.  

PubMed

The molecular structure can be defined quantum mechanically thanks to the theory of atoms in molecules. Here, we report a new molecular model that reflects quantum mechanical properties of the chemical bonds. This graphical representation of molecules is based on the topology of the electron density at the critical points. The eigenvalues of the Hessian are used for depicting the critical points three-dimensionally. The bond path linking two atoms has a thickness that is proportional to the electron density at the bond critical point. The nuclei are represented according to the experimentally determined atomic radii. The resulting molecular structures are similar to the traditional ball and stick ones, with the difference that in this model each object included in the plot provides topological information about the atoms and bonding interactions. As a result, the character and intensity of any given interatomic interaction can be identified by visual inspection, including the noncovalent ones. Because similar bonding interactions have similar plots, this tool permits the visualization of chemical bond transferability, revealing the presence of functional groups in large molecules. PMID:21894893

Bohórquez, Hugo J; Boyd, Russell J; Matta, Chérif F

2011-09-06

407

Attaching Theories of Consciousness to Bohmian Quantum Mechanics  

Microsoft Academic Search

The de Broglie-Bohm theory of quantum mechanics (here simply called Bohmian\\u000aMechanics or BM) [1-10] is an augmentation of ``bare'' quantum mechanics (the\\u000abare theory being given by an algebra of operators and a quantum state that\\u000asets the expectation values of these operators) that includes a definite\\u000ahistory or Bohmian trajectory. This definite trajectory gives BM a somewhat\\u000amore

Don N. Page

1995-01-01

408

Probability in the formalism of quantum mechanics on phase space  

NASA Astrophysics Data System (ADS)

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

Schroeck, Franklin E., Jr.

2012-02-01

409

Mind, Matter and Quantum Mechanics (2nd edition)  

Microsoft Academic Search

Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried

G Mahler

2004-01-01

410

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

Microsoft Academic Search

Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried

H. P. Stapp

2004-01-01

411

INTRODUCTION TO RELATIVISTIC QUANTUM MECHANICS AND THE DIRAC EQUATION  

Microsoft Academic Search

The development of quantum mechanics is presented from a his- torical perspective. The principles of special relativity are reviewed. Relativis- tic quantum mechanics is developed, including the Klein-Gordon equation and up to the Dirac equation. Near the end of the 19th century, physicists were confident in their view of the world. Newton's mechanics had explained the dynamics of everything from

JACOB E. SONE

412

Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics  

NASA Astrophysics Data System (ADS)

We extend the mathematical theory of quantum hypothesis testing to the general W*-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.

Jakši?, V.; Ogata, Y.; Pillet, C.-A.; Seiringer, R.

2012-07-01

413

Algorithm for quantum-mechanical finite-nuclear-mass variational calculations of atoms with two p electrons using all-electron explicitly correlated Gaussian basis functions  

SciTech Connect

A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with two p electrons or a single d electron have been derived and implemented. The Hamiltonian used in the approach was obtained by rigorously separating the center-of-mass motion and it explicitly depends on the finite mass of the nucleus. The approach was employed to perform test calculations on the isotopes of the carbon atom in their ground electronic states and to determine the finite-nuclear-mass corrections for these states.

Sharkey, Keeper L.; Pavanello, Michele [Department of Chemistry, University of Arizona, Tucson, Arizona 85721 (United States); Bubin, Sergiy [Quantum Chemistry Research Institute, Kyodai Katsura Venture Plaza 106, Goryo Oohara 1-36, Nishikyo-ku, Kyoto 615-8245 (Japan); Department of Chemistry, University of Arizona, Tucson, Arizona 85721 (United States); Adamowicz, Ludwik [Department of Chemistry, University of Arizona, Tucson, Arizona 85721 (United States); Department of Physics, University of Arizona, Tucson, Arizona 85721 (United States)

2009-12-15

414

On phase-space representations of quantum mechanics  

NASA Astrophysics Data System (ADS)

We discuss a class of representations of quantum mechanics which uses functions defined on a parameter space to represent observable quantities. We show that infinitesimal canonical transformations could be used to introduce a phase-space-like structure consistent with the requirements of quantum mechanics. The resulting family of phase-space representations of quantum mechanics contains many well-known representations as special cases, e.g., the Weyl-Wigner-Moyal, normal and antinormal one. It is also flexible enough to represent, e.g., /PT-symmetric theories, introduced recently within the context of non-Hermitian quantum mechanics.

Wlodarz, J. J.

2001-07-01

415

Lyapunov exponent in quantum mechanics. A phase-space approach  

NASA Astrophysics Data System (ADS)

Using the symplectic tomography map, both for the probability distributions in classical phase-space and for the Wigner functions of its quantum counterpart, we discuss a notion of Lyapunov exponent for quantum dynamics. Because the marginal distributions, obtained by the tomography map, are always well-defined probabilities, the correspondence between classical and quantum notions is very clear. Then we also obtain the corresponding expressions in Hilbert space. Some examples are worked out. Classical and quantum exponents are seen to coincide for local and non-local time-dependent quadratic potentials. For non-quadratic potentials classical and quantum exponents are different and some insight is obtained on the taming effect of quantum mechanics on classical chaos. A detailed analysis is made for the standard map. Providing an unambiguous extension of the notion of Lyapunov exponent to quantum mechanics, the method that is developed is also computationally efficient in obtaining analytical results for the Lyapunov exponent, both classical and quantum.

Man'ko, V. I.; Vilela Mendes, R.

2000-11-01

416

Oscillator representations for self-adjoint Calogero Hamiltonians  

NASA Astrophysics Data System (ADS)

In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = ?x-2. We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation \\check{H}=-d_{x}^{2}+\\alpha x^{-2} for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form \\hat{N}=\\hat{a}^{+}\\hat{a} and \\hat{A}=\\hat{a}\\hat{a}^{+} are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators \\hat{a } are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators \\hat{a} and \\hat{a} ^{+}. An oscillator-type representation for a given Hamiltonian is generally not unique.

Gitman, D. M.; Tyutin, I. V.; Voronov, B. L.

2011-10-01

417

Exponential complexity and ontological theories of quantum mechanics  

SciTech Connect

Ontological theories of quantum mechanics describe a single system by means of well-defined classical variables and attribute the quantum uncertainties to our ignorance about the underlying reality represented by these variables. We consider the general class of ontological theories describing a quantum system by a set of variables with Markovian (either deterministic or stochastic) evolution. We provide proof that the number of continuous variables cannot be smaller than 2N-2, N being the Hilbert-space dimension. Thus, any ontological Markovian theory of quantum mechanics requires a number of variables which grows exponentially with the physical size. This result is relevant also in the framework of quantum Monte Carlo methods.

Montina, A. [Dipartimento di Fisica, Universita di Firenze, Via Sansone 1, 50019 Sesto Fiorentino (Italy)

2008-02-15

418

Paul A.M. Dirac's The Principles of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Paul A.M. Dirac’s book, The Principles of Quantum Mechanics, summarized the foundations of a new science, much of which was his own creation. It expressed the spirit of the new quantum mechanics, creating a descriptive language that we still use. I discuss the successive editions of Dirac’s book and their critical reception, noting changes, especially in the formulation of the general theory and in its treatment of relativistic quantum theory and quantum electrodynamics. In the case of the later editions, I discuss Dirac’s negative attitude toward renormalized quantum electrodynamics.

Brown, Laurie M.

2006-12-01

419

Relativistic quantum mechanics and the S matrix  

NASA Astrophysics Data System (ADS)

In the standard development of scattering theory the Hamiltonian of the system plays a central role; however when the Bakamjian-Thomas method is used to construct a relativistic model of a few-particle system, the mass operator plays the essential role. Here a simple procedure for translating the Hamiltonian formulation of scattering theory to a mass-operator formulation is given. A simple proof of the Poincaré invariance of the S operator that is obtained from a Bakamjian-Thomas model is also given.

Fuda, Michael G.

2001-08-01

420

Measurement theory and stochastic differential equations in quantum mechanics  

NASA Astrophysics Data System (ADS)

Continuous (in time) measurements can be introduced in quantum mechanics by using operation-valued measures and quantum stochastic calculus. In this paper quantum stochastic calculus is used for showing the connections between measurement theory and open-system theory. In particular, it is shown how continuous measurements are strictly related to the concept of output channels, introduced in the framework of quantum stochastic differential equations by Gardiner and Collet.

Barchielli, Alberto

1986-09-01

421

Causal Quantum Mechanics Treating Position and Momentum Symmetrically  

NASA Astrophysics Data System (ADS)

De Broglie and Bohm formulated a causal quantum mechanics with a phase space density whose integral over momentum reproduces the position probability density of the usual statistical quantum theory. We propose a causal quantum theory with a joint probability distribution such that the separate probability distributions for position and momentum agree with the usual quantum theory. Unlike the Wigner distribution the suggested distribution is positive-definite and obeys the Liouville condition.

Roy, S. M.; Singh, Virendra

422

Moyal quantum mechanics: The semiclassical Heisenberg dynamics  

SciTech Connect

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

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

1995-07-01

423

Momentum diffusion of the quantum kicked rotor: Comparison of Bohmian and standard quantum mechanics  

Microsoft Academic Search

Momentum diffusion of the quantum kicked rotor is studied with both de Broglie–Bohm and standard approach to quantum mechanics. The Schrödinger equation is solved exactly for the case of quantum resonance and an analytical expression is given for the momentum diffusion. Numerical solutions for both resonance and nonresonance are obtained. We obtain agreement between the two approaches only when the

Yindong Zheng; Donald H. Kobe

2007-01-01

424

Sedeonic Generalization of Relativistic Quantum Mechanics  

NASA Astrophysics Data System (ADS)

We represent sixteen-component values "sedeons," generating associative noncommutative space-time algebra. We demonstrate a generalization of relativistic quantum mechanics using sedeonic wave functions and sedeonic space-time operators. It is shown that the sedeonic second-order equation for the sedeonic wave function, obtained from the Einstein relation for energy and momentum, describes particles with spin 1/2. We showed that the sedeonic second-order wave equation can be reformulated in the form of the system of the first-order Maxwell-like equations for the massive fields. We proposed the sedeonic first-order equations analogous to the Dirac equation, which differ in space-time properties and describe several types of massive and massless particles. In particular we proposed four different equations, which could describe four types of neutrinos.

Mironov, Victor L.; Mironov, Sergey V.

425

Auxiliary nRules of Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Standard quantum mechanics makes use of four auxiliary rules that allow the Schrödinger solutions to be related to laboratory experience - such as the Born rule that connects square modulus to probability. These rules (here called the sRules) lead to some unacceptable results. They do not allow the primary observer to be part of the system. They do not allow individual observations (as opposed to ensembles) to be part of the system. They make a fundamental distinction between microscopic and macroscopic things, and they are ambiguous in their description of secondary observers such as Schrödinger's cat. The nRules are an alternative set of auxiliary rules that avoid the above difficulties. In this paper we look at a wide range of representative experiments showing that the nRules adequately relate the Schrödinger solutions to empirical experience.

Mould, Richard A.

2006-01-01

426

Quantum mechanics without an equation of motion  

SciTech Connect

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

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

2011-06-15

427

Supersymmetric quantum mechanics for string-bits  

SciTech Connect

The authors develop possible versions of supersymmetric single particle quantum mechanics, with application to superstring-bit models in view. The authors focus principally on space dimensions d = 1,2,4,8, the transverse dimensionalities of superstring in 3, 4, 7, 10 space-time dimensions. These are the cases for which classical superstring makes sense, and also the values of d for which Hooke`s force law is compatible with the simplest superparticle dynamics. The basic question they address is: when is it possible to replace such harmonic force laws with more general ones, including forces which vanish at large distances? This is an important question because forces between string-bits that do not fall off with distance will almost certainly destroy cluster decomposition. They show that the answer is affirmative for d = 1,2, negative for d = 8, and so far inconclusive for d = 4.

Thorn, C.B. [Univ. of Florida, Gainesville, FL (United States). Dept. of Physics

1997-08-01

428

Deformation quantization of noncommutative quantum mechanics  

NASA Astrophysics Data System (ADS)

The Wigner phase-space distribution function provides the basis for Moyal's deformation quantization alternative to the more conventional Hilbert space and path integral quantization. In this paper, we investigate the basic aspects of deformation quantization for noncommutative quantum mechanics (NCQM). We first prove some general relations of the Weyl correspondence in non-commuting phase-space. Then we derive explicit form of the Wigner Function (WF) for NCQM starting from fundamental principle of the Weyl correspondence, and show that it satisfies a generalized lowast-genvalue equation. We also demonstrate that the new WFs possess orthonormality and completeness, so they can be used as a basis to expand all phase-space functions. Some example is discussed to support our results.

Jing, Sicong; Zuo, Fen; Heng, Taihua

2004-10-01

429

New methods for quantum mechanical reaction dynamics  

SciTech Connect

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

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

1996-12-01

430

Calculation of Host-Guest Binding Affinities Using a Quantum-Mechanical Energy Model  

PubMed Central

The prediction of protein-ligand binding affinities is of central interest in computer-aided drug discovery, but it is still difficult to achieve a high degree of accuracy. Recent studies suggesting that available force fields may be a key source of error motivate the present study, which reports the first mining minima (M2) binding affinity calculations based on a quantum mechanical energy model, rather than an empirical force field. We apply a semi-empirical quantum-mechanical energy function, PM6-DH+, coupled with the COSMO solvation model, to 29 host-guest systems with a wide range of measured binding affinities. After correction for a systematic error, which appears to derive from the treatment of polar solvation, the computed absolute binding affinities agree well with experimental measurements, with a mean error 1.6 kcal/mol and a correlation coefficient of 0.91. These calculations also delineate the contributions of various energy components, including solute energy, configurational entropy, and solvation free energy, to the binding free energies of these host-guest complexes. Comparison with our previous calculations, which used empirical force fields, point to significant differences in both the energetic and entropic components of the binding free energy. The present study demonstrates successful combination of a quantum mechanical Hamiltonian with the M2 affinity method.

Muddana, Hari S.; Gilson, Michael K.

2012-01-01

431

Two-dimensional quantum mechanical modeling of nanotransistors  

Microsoft Academic Search

Quantization in the inversion layer and phase coherent transport are anticipated to have significant impact on device performance in ``ballistic'' nanoscale transistors. While the role of some quantum effects have been analyzed qualitatively using simple one-dimensional ballistic models, two-dimensional (2D) quantum mechanical simulation is important for quantitative results. In this paper, we present a framework for 2D quantum mechanical simulation

A. Svizhenko; M. P. Anantram; T. R. Govindan; B. Biegel; R. Venugopal

2002-01-01

432

Property Definiteness in Quantum Mechanics: Modal Interpretations.  

NASA Astrophysics Data System (ADS)

Recently, several writers have independently proposed similar solutions to the quantum-mechanical measurement problem. This dissertation examines the conception of physical properties implicit in these proposals, which are known as modal interpretations of quantum mechanics. The dissertation focuses on Richard Healey's interpretation, which I regard as the most promising of the proposals. Chapter One reviews the measurement problem and the way in which modal interpretations address the problem. Chapter Two discusses certain mathematical theorems that impose strict limits on the number of properties that a system can possess at any instant. I examine a number of inferences that interpreters have drawn from these theorems, and argue that some of these inferences are misguided. This discussion leads to the recognition that, despite overarching similarities between Healey's interpretations and several of the other modal interpretations, the interpretations differ in fundamental respects. Chapter Three presents several desiderata on the set of properties possessed by a quantum system at an instant. One of these desiderata concerns the relation between a system's properties and the properties of that system's subsystems. To borrow Frank Arntzenius's illustration, the desideratum demands, for instance, that the left-hand leaf of a table be green if and only if the table has a green left-hand leaf. Unfortunately, most modal interpretations fail to satisfy this demand. Using mathematical arguments, I show that Healey's interpretation satisfies the demand. Chapter Four turns to a problematic feature of Healey's interpretation, namely its violation of a desideratum called Property Intersection. Property Intersection demands that if a variable's value is restricted to a set Delta and is also restricted to a set Gamma, then the value is restricted to the intersection of Delta and Gamma. I propose two strategies for amending Healey's interpretation so that it respects Property Intersection, but I find both of these strategies unsatisfactory, since each creates new problems. I then consider several possible reasons for imposing Property Intersection as a requirement, and I argue that none of these reasons is compelling; thus, I claim, Healey's violation of Property Intersection is defensible.

Reeder, Nicholas Lee

433

Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems  

ERIC Educational Resources Information Center

|In this study, students' conceptual difficulties about some basic concepts in quantum mechanics like one-dimensional potential well problems and probability density of tunneling particles were identified. For this aim, a multiple choice instrument named Quantum Mechanics Conceptual Test has been developed by one of the researchers of this study…

Ozcan, Ozgur; Didis, Nilufer; Tasar, Mehmet Fatih

2009-01-01

434

In Defense of a Heuristic Interpretation of Quantum Mechanics  

ERIC Educational Resources Information Center

Although the presentation of quantum mechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantum mechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift…

Healy, Eamonn F.

2010-01-01

435

On the End of a Quantum Mechanical Romance  

Microsoft Academic Search

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

Gregory R. Mulhauser

1995-01-01

436

Quantum mechanics needs no consciousness (and the other way around)  

Microsoft Academic Search

It has been suggested that consciousness plays an important role in quantum mechanics as it is necessary for the collapse of wave function during the measurement. Furthermore, this idea has spawned a symmetrical proposal: a possibility that quantum mechanics explains the emergence of consciousness in the brain. Here we formulated several predictions that follow from this hypothetical relationship and that

Shan Yu; Danko Nikolic

2010-01-01

437

Quantum Mechanics and Consciousness: A Causal Correspondence Theory  

Microsoft Academic Search

We may suspect that quantum mechanics and consciousness are re- lated, but the details are not at all clear. In this paper, I suggest how the mind and brain might fit together intimately while still maintaining dis- tinct identities. The connection is based on the correspondence of similar functions in both the mind and the quantum-mechanical brain.

I. J. Thompson

438

On a generalization of quantum mechanics of biquaternions  

SciTech Connect

A generalization of the quantum mechanical formalism by biquaternions is proposed. By a direct example, it is evidenced that such a generalization explains in an algebraic manner the {open_quotes}wave packet reduction{close_quotes} of quantum mechanics. 8 refs.

Conte, E. [Inst. of Cybernetics, San Marino (Italy)

1993-06-01

439

Using a Computer-Rich Curriculum to Teach Quantum Mechanics  

NSDL National Science Digital Library

This site is the notes for a seminar on the use of java applets in quantum mechanics pedagogy. Applets are included that cover basic quantum mechanics, hydrogenic and two-particle systems, and some simulation techniques. Time dependent results are stressed.

Belloni, Mario; Carroll, Meghan

2004-03-10

440

New Potentials for Old: The Darboux Transformation in Quantum Mechanics  

ERIC Educational Resources Information Center

|The Darboux transformation in quantum mechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics

Williams, Brian Wesley; Celius, Tevye C.

2008-01-01

441

Categorization of Quantum Mechanics Problems by Professors and Students  

ERIC Educational Resources Information Center

|We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…

Lin, Shih-Yin; Singh, Chandralekha

2010-01-01

442

Design and Validation of the Quantum Mechanics Conceptual Survey  

ERIC Educational Resources Information Center

|The Quantum Mechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantum mechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper, we describe the design and validation of the survey, a process that included…

McKagan, S. B.; Perkins, K. K.; Wieman, C. E.

2010-01-01

443

Developing and Evaluating Animations for Teaching Quantum Mechanics Concepts  

ERIC Educational Resources Information Center

|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…

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

2010-01-01

444

In Defense of a Heuristic Interpretation of Quantum Mechanics  

ERIC Educational Resources Information Center

|Although the presentation of quantum mechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantum mechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift…

Healy, Eamonn F.

2010-01-01

445

Phase Space Correspondence between Classical Optics and Quantum Mechanics  

Microsoft Academic Search

The paper scrutinizes both the similarities and the differences between the classical optics and quantum mechanical theories in phase space, especially between the Wigner distribution functions defined in the respective phase spaces. Classical optics is able to provide an understanding of either the corpuscular or wave aspects of quantum mechanics, reflected in phase space through the classical limit of the

Daniela Dragoman

2004-01-01

446

Predicting crystal structure by merging data mining with quantum mechanics  

Microsoft Academic Search

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

Christopher C. Fischer; Kevin J. Tibbetts; Dane Morgan; Gerbrand Ceder

2006-01-01

447

On the representation of quantum mechanics on phase space  

NASA Astrophysics Data System (ADS)

It is shown that Hilbert-space quantum mechanics can be represented on phase space in the sense that the density operators can be identified with phase-space densities and the observables can be described by functions on phase space. In particular, we consider phase-space representations of quantum mechanics which are related to certain joint position-momentum observables.

Stulpe, Werner

1992-09-01

448

Quantum Mechanics from Periodic Dynamics: the bosonic case  

SciTech Connect

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.

Dolce, Donatello [Johannes-Gutenberg Universitaet, D-55099 Mainz (Germany)

2010-05-04

449

Linear Logic for Generalized Quantum Mechanics  

Microsoft Academic Search

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

Vaughan Pratt

1993-01-01

450

Amplitude Phase-Space Model for Quantum Mechanics  

NASA Astrophysics Data System (ADS)

We show that there is a close relationship between quantum mechanics and ordinary probability theory. The main difference is that in quantum mechanics the probability is computed in terms of an amplitude function, while in probability theory a probability distribution is used. Applying this idea, we then construct an amplitude model for quantum mechanics on phase space. In this model, states are represented by amplitude functions and observables are represented by functions on phase space. If we now postulate a conjugation condition, the model provides the same predictions as conventional quantum mechanics. In particular, we obtain the usual quantum marginal probabilities, conditional probabilities and expectations. The commutation relations and uncertainty principle also follow. Moreover Schrödinger's equation is shown to be an averaged version of Hamilton's equation in classical mechanics.

Gudder, Stanley P.

1985-04-01

451

Biological Applications of Hybrid Quantum Mechanics/Molecular Mechanics Calculation  

PubMed Central

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 tRNALeu, 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.

Kang, Jiyoung; Hagiwara, Yohsuke; Tateno, Masaru

2012-01-01

452

Quantum Mechanics as Quantum Information (and only a little more)  

Microsoft Academic Search

In this paper, I try once again to cause some good-natured trouble. The issue\\u000aremains, when will we ever stop burdening the taxpayer with conferences devoted\\u000ato the quantum foundations? The suspicion is expressed that no end will be in\\u000asight until a means is found to reduce quantum theory to two or three\\u000astatements of crisp physical (rather than

Christopher A. Fuchs

2002-01-01

453

Quantum mechanics in rotating-radio-frequency traps and Penning traps with a quadrupole rotating field  

SciTech Connect

Quantum-mechanical analysis of ion motion in a rotating-radio-frequency (rrf) trap or in a Penning trap with a quadrupole rotating field is carried out. Rrf traps were introduced by Hasegawa and Bollinger [Phys. Rev. A 72, 043404 (2005)]. The classical motion of a single ion in this trap is described by only trigonometric functions, whereas in the conventional linear radio-frequency (rf) traps it is by the Mathieu functions. Because of the simple classical motion in the rrf trap, it is expected that the quantum-mechanical analysis of the rrf traps is also simple compared to that of the linear rf traps. The analysis of Penning traps with a quadrupole rotating field is also possible in a way similar to the rrf traps. As a result, the Hamiltonian in these traps is the same as the two-dimensional harmonic oscillator, and energy levels and wave functions are derived as exact results. In these traps, it is found that one of the vibrational modes in the rotating frame can have negative energy levels, which means that the zero-quantum-number state (''ground'' state) is the highest energy state.

Abe, K.; Hasegawa, T. [Department of Physics, Keio University, Kanagawa 223-8522 (Japan)

2010-03-15

454

Calendar effects in quantum mechanics in view of interactive holography  

NASA Astrophysics Data System (ADS)

Quantum mechanics in terms of interactive holography appears as `normal' science [1]. With the holography quantum behavior is determined by the interplay of material formations and their conjugate images. To begin with, this effortlessly elucidates the nonlocality in quantum entanglements. Then, it has been shown that Schr"odinger's dynamics for a single particle arises from Bi-Fragmental random walks of the particle itself and its holographic image. For many particles this picture blurs with fragments merging as bosons or fermions. In biomolecules, swapping of particles and their holographic placeholders leads to self-replication of the living matter. Because of broad interpretations of quantum formalism direct experiments attributing it to holography may not be very compelling. The holographic mechanism better reveals as an absolute frame of reference. A number of physical and biological events exhibit annual variations when Earth orbital position changes with respect to the universal holographic mechanism. The well established calendar variations of heart attacks can be regarded as a positive outcome of a generalization of the Michelson experiment, where holography is interferometry and ailing hearts are detectors of pathologically replicated proteins. Also, there have been already observed calendar changes in radioactive decay rates. The same could be expected for various fine quantum experiences, like, e.g., Josephson tunneling. In other words, Quantum Mechanics (February) Quantum Mechanics (August). [1] S. Berkovich, ``A comprehensive explanation of quantum mechanics,'' www.cs.gwu.edu/research/technical-report/170 .

Berkovich, Simon

2013-04-01

455

Quantum optimal control for the full ensemble of randomly oriented molecules having different field-free Hamiltonians  

NASA Astrophysics Data System (ADS)

We have presented the optimal control theory formulation to calculate optimal fields that can control the full ensemble of randomly oriented molecules having different field-free Hamiltonians. The theory is applied to the fifty-fifty mixture of randomly oriented 133CsI and 135CsI isotopomers and an optimal field is sought to achieve isotope-selective vibrational excitations with high efficiency. Rotational motion is frozen and two total times (T's) of electric field duration, 460 000 and 920 000 a.u. (11.1 and 22.2 ps), are chosen in the present calculation. As a result, the final yields for T = 460 000 and 920 000 a.u. are calculated to be 0.706 and 0.815, respectively. The relatively high final yield obtained for T = 920 000 a.u. strongly suggests that a single laser pulse can control the full ensemble of randomly oriented non-identical molecules. The result is quite encouraging in terms of the application to isotope-separation processes.

Kurosaki, Yuzuru; Ichihara, Akira; Yokoyama, Keiichi

2011-08-01

456

The Discovery of Quantum Structure and Quantum Mechanic Reinterpretation  

NASA Astrophysics Data System (ADS)

My recent interdisciplinary researches lead me to re-visit the quantum wave-particle duality property. By comparing many of the quantum physics results in scientific literatures I concluded the structure of quantum particle and formulated a new explanation of the wave effect. This discovery is further confirmed by many of the results in other fields. Evident also suggested inside quantum has a not-continuous multi-dimensional space. With this light I formed a hypostasis of space as a not-continuous infinite dimensional space. To proof or disproof this hypostasis I found strong evidences in literature supporting my hypostasis. By evaluating space properties it lead me to the same conclusion of Special Relativity and Uncertainty Principle. Evidence also support quantum is part of space itself and space carries electrical charges on both sides of its dimensional boundaries therefore we can detect the electromagnetic energy in vacuum. These discoveries also give good answers to many of the big questions in science such as gravity, dark energy and space travel.

Zhang, Meggie

2012-10-01

457

New generalization of supersymmetric quantum mechanics to arbitrary dimensionality or number of distinguishable particles.  

PubMed

We present here a new approach to generalize supersymmetric quantum mechanics to treat multiparticle and multidimensional systems. We do this by introducing a vector superpotential in an orthogonal hyperspace. In the case of N distinguishable particles in three dimensions this results in a vector superpotential with 3N orthogonal components. The original scalar Schrödinger operator can be factored using a 3N-component gradient operator and introducing vector "charge" operators: Q(1) and Q(1)(dagger). Using these operators, we can write the original (scalar) Hamiltonian as H(1) = Q(1)(dagger) x Q(1) + E(0)((1)), where E(0)((1)) is the ground-state energy. The second sector Hamiltonian is a tensor given by H(2) = Q(1)Q(1)(dagger) + E(0)((1)) and is isospectral with H(1). The vector ground state of sector 2, psi(0)((2)), canbe used with the charge operator Q(1)(dagger) to obtain the excited-state wave function of the first sector. In addition, we show that H(2) can also be factored in terms of a sector 2 vector superpotential with components W(2j) = -(partial partial differential ln psi(0j)((2)))/partial partial differentialx(j). Here psi(0j)((2)) is the jth component of psi(0)((2)). Then one obtains charge operators Q(2) and Q(2)(dagger) so that the second sector Hamiltonian can be written as H(2) = Q(2)(dagger)Q(2) + E(0)((2)). This allows us to define a third sector Hamiltonian which is a scalar, H(3) = Q(2) x Q(2)(dagger) + E(0)((2)). This prescription continues with the sector Hamiltonians alternating between scalar and tensor forms, both of which can be treated by the variational method to obtain approximate solutions to both scalar and tensor sectors. We demonstrate the approach with examples of a pair of separable 1D harmonic oscillators and the example of a nonseparable 2D anharmonic oscillator (or equivalently a pair of coupled 1D oscillators). We consider both degenerate and nondegenerate cases. We also present a generalization to arbitrary curvilinear coordinate systems in the Appendix. PMID:20701330

Kouri, Donald J; Maji, Kaushik; Markovich, Thomas; Bittner, Eric R

2010-08-19

458

Quantum mechanics and the principle of equivalence  

NASA Astrophysics Data System (ADS)

Einstein's principle of equivalence is based on the notion of classical trajectories in spacetime, and the question arises of how this principle applies to quantum particles, especially those in delocalized, highly-non-classical states. I shall describe a quantum version of Galileo's classic experiment, using a model quantum clock to measure the time of flight of a quantum particle in a background gravitational field. Because the particle's mass does not scale out of Schrodinger's equation, unlike in the Newtonian case, conformity with the principle of equivalence is far from obvious and involves some interesting subtleties. It also suggests some new experiments.

Davies, Paul

2007-10-01

459

Computing the wavefunction from trajectories: particle and wave pictures in quantum mechanics and their relation  

NASA Astrophysics Data System (ADS)

We describe the particle method in quantum mechanics which provides an exact scheme to calculate the time-dependent wavefunction from a single-valued continuum of determinstic trajectories where two spacetime points are linked by at most a single orbit. A natural language for the theory is offered by the hydrodynamic analogy, in which wave mechanics corresponds to the Eulerian picture and the particle theory to the Lagrangian picture. The Lagrangian model for the quantum fluid may be developed from a variational principle. The Euler Lagrange equations imply a fourth-order nonlinear partial differential equation to calculate the trajectories of the fluid particles as functions of their initial coordinates using as input the initial wavefunction. The admissible solutions are those consistent with quasi-potential flow. The effect of the superposition principle is represented via a nonclassical force on each particle. The wavefunction is computed via the standard map between the Lagrangian coordinates and the Eulerian fields, which provides the analogue in this model of Huygens’ principle in wave mechanics. The method is illustrated by calculating the time-dependence of a free Gaussian wavefunction. The Eulerian and Lagrangian pictures are complementary descriptions of a quantum process in that they have associated Hamiltonian formulations that are connected by a canonical transformation. The de Broglie Bohm interpretation, which employs the same set of trajectories, should not be conflated with the Lagrangian version of the hydrodynamic interpretation. The theory implies that the mathematical results of the de Broglie Bohm model may be regarded as statements about quantum mechanics itself rather than about its interpretation.

Holland, Peter

2005-02-01

460

Testing Quantum Mechanics in High-Energy Physics  

Microsoft Academic Search

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

Beatrix C. Hiesmayr

461

Can you do quantum mechanics without Einstein?  

SciTech Connect

The present form of quantum mechanics is based on the Copenhagen school of interpretation. Einstein did not belong to the Copenhagen school, because he did not believe in probabilistic interpretation of fundamental physical laws. This is the reason why we are still debating whether there is a more deterministic theory. One cause of this separation between Einstein and the Copenhagen school could have been that the Copenhagen physicists thoroughly ignored Einstein's main concern: the principle of relativity. Paul A. M. Dirac was the first one to realize this problem. Indeed, from 1927 to 1963, Paul A. M. Dirac published at least four papers to study the problem of making the uncertainty relation consistent with Einstein's Lorentz covariance. It is interesting to combine those papers by Dirac to make the uncertainty relation consistent with relativity. It is shown that the mathematics of two coupled oscillators enables us to carry out this job. We are then led to the question of whether the concept of localized probability distribution is consistent with Lorentz covariance.

Kim, Y. S. [Department of Physics, University of Maryland, College Park, Maryland 20742 (United States); Noz, Marilyn E. [Department of Radiology, New York University, New York, New York 10016 (United States)

2007-02-21

462

Quantum mechanical studies on model ?-pleated sheets  

PubMed Central

Pauling and Corey proposed a pleated-sheet configuration, now called ?-sheet, as one of the protein secondary structures in addition to ?-helix and ?-sheet. Recently, it has been suggested that ?-sheet is a common feature of amyloidogenic intermediates. We have investigated the stability of anti-parallel ?-sheet and two conformations of ?-sheet in solution phase using the density functional theoretical method. The peptides are modeled as two-strand Acetyl-(Ala)2-N-methylamine. Using stages of geometry optimization and single point energy calculation at B3LYP/cc-pVTZ//B3LYP/6-31G* level and including zero-point energies, thermal, and entropic contribution, we have found that ?-sheet is the most stable conformation, while the ?-sheet proposed by Pauling and Corey has 13.6 kcal/mol higher free energy than the ?-sheet. The ?-sheet that resembles the structure observed in molecular dynamics simulations of amyloidogenic proteins at low pH becomes distorted after stages of geometry optimization in solution. Whether the ?-sheets with longer chains would be increasingly favorable in water relative to the increase in internal energy of the chain needs further investigation. Different from the quantum mechanics results, AMBER parm94 force field gives small difference in solution phase energy between ?-sheet and ?-sheet. The predicted amide I IR spectra of ?-sheet shows the main band at higher frequency than ?-sheet.

Wu, Hao; Canfield, Alana; Adhikari, Jhashanath; Huo, Shuanghong

2009-01-01

463

Quantum mechanical model for Maya Blue  

NASA Astrophysics Data System (ADS)

This work is about Maya Blue (MB), a pigment developed by Mesoamerican civilizations between the 5th and 16th centuries from an aluminosilicate mineral (palygorskite) and an organic dye (indigo). Two different supramolecular quantum-mechanical models affor