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From Quantum Mechanics to Thermodynamics?

From Quantum Mechanics to Thermodynamics? Dresden, 22.11.2004 Jochen Gemmer UniversitÂ¨at Osnabr to thermodynamical behavior Â· Quantum approach to thermodynamical behavior Â· The route to equilibrium Â· Summary of thermodynamical behavior entirely on the basis of Hamilton models and SchrÂ¨odinger-type quantum dynamics. Â· define

Steinhoff, Heinz-JÃ¼rgen

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NONEQUILIBRIUM QUANTUM STATISTICAL MECHANICS AND THERMODYNAMICS #

NONEQUILIBRIUM QUANTUM STATISTICAL MECHANICS AND THERMODYNAMICS # Walid K. Abou Salem + Institut f recent progress in deriving the fundamental laws of thermodynamics (0 th , 1 st and 2 nd Âlaw) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and di#erent reversible

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Thermodynamic integration from classical to quantum mechanics

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

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

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The Thermodynamic Arrow-of-time and Quantum Mechanics

I give an explanation of the thermodynamic arrow-of-time (namely entropy increases with time) within a quantum mechanical framework. This entails giving a solution to the Loschmidt paradox, i.e. showing how an irreversible ...

Maccone, Lorenzo

5

Novel quantization properties related to the state vectors and the energy spectrum of a two-dimensional system of free particles are obtained in the framework of noncommutative (NC) quantum mechanics (QM) supported by the Weyl-Wigner formalism. Besides reproducing the magnetic field aspect of a Zeeman-like effect, the momentum space NC parameter introduces mutual information properties quantified by the quantum purity related to the relevant coordinates of the corresponding Hilbert space. Supported by the QM in the phase-space, the thermodynamic limit is obtained, and the results are extended to three-dimensional systems. The noncommutativity imprints on the thermodynamic variables related to free particles are identified and, after introducing some suitable constraints to fix an axial symmetry, the analysis is extended to two- and- three dimensional quantum rotor systems, for which the quantization aspects and the deviation from standard QM results are verified.

Catarina Bastos; Alex E. Bernardini; Jonas F. G. Santos

2014-11-11

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Novel quantization properties related to the state vectors and the energy spectrum of a two-dimensional system of free particles are obtained in the framework of noncommutative (NC) quantum mechanics (QM) supported by the Weyl-Wigner formalism. Besides reproducing the magnetic field aspect of the Zeeman effect, the momentum space NC parameter introduces mutual information properties quantified by the linear entropy related to the relevant Hilbert space coordinates. Supported by the QM in the phase-space, the thermodynamic limit is obtained, and the results are extended to three-dimensional systems. The noncommutativity imprints on the thermodynamic variables related to free particles are identified and, after introducing some suitable constraints to fix an axial symmetry, the analysis is extended to two- and- three dimensional quantum rotor systems, for which the quantization aspects and the deviation from standard QM results are verified.

Bastos, Catarina; Santos, Jonas F G

2014-01-01

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Nano, Quantum, and Statistical Mechanics and Thermodynamics: Data and Property Calculation Websites

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: data sites, calculation/program download sites, organizations involved with data compilation and property calculation, and bibliographies.

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Quantum thermodynamic cooling cycle

NASA Astrophysics Data System (ADS)

The quantum-mechanical and thermodynamic properties of a three-level molecular cooling cycle are derived. An inadequacy of earlier models is rectified in accounting for the spontaneous emission and absorption associated with the coupling to the coherent driving field via an environmental reservoir. This additional coupling need not be dissipative, and can provide a thermal driving force-the quantum analog of classical absorption chillers. The dependence of the maximum attainable cooling rate on temperature, at ultralow temperatures, is determined and shown to respect the recently established fundamental bound based on the second and third laws of thermodynamics.

Palao, José P.; Kosloff, Ronnie; Gordon, Jeffrey M.

2001-11-01

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An account on statistical mechanics and thermodynamics of quantum isolated horizons

This paper presents an extensive work on the study of thermodynamics of black holes in LQG framework, namely quantum isolated horizons(QIH). Having reviewed the derivation of the microcanonical entropy of a QIH, we proceed towards constructing the canonical and grand canonical partition functions for the QIH in the corresponding quantum mechanical ensembles. Some important issues regarding the conjugate parameter$(\\mu)$ corresponding to the macroscopic variable $N$(number of punctures) are discussed in details, with possible explanations of the new physical consequences which can follow from its presence in the quantum theory and absence in the classical theory. The role of $\\mu$ being dependent on the observer leads to interesting conclusions about the near horizon quantum phenomena, whereas the asymptotic physics remains unchanged. The extensive and detailed derivation of the canonical and grand canonical partition functions of the QIH lead to the effective `thermalized' forms of the partition functions which had been previously used in the literature to study the effects of thermal fluctuations of black holes. A comparative study of the present derivation with those previous approaches is made. The previous procedures were based on some heuristic models and quite expectedly plagued with some technical caveats, leaving those approaches prone to doubts of having any sort of relation to black hole thermodynamics. The novelty of this work is to eliminate those shortcomings of the earlier approaches and put the formalism of statistical mechanical approach to black hole thermodynamics on a more sound basis than ever by beginning from the very fundamental structures of the quantum theory leading to the {\\it exact} derivation of the horizon partition function, without having to make any sort of assumption or approximation regarding area spectrum, etc.

Abhishek Majhi

2014-06-28

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As assemblies of graphene sheets, carbon nanotubes, and fullerenes become components of new nanotechnologies, it is important to be able to predict the structures and properties of these systems. A problem has been that the level of quantum mechanics practical for such systems (density functional theory at the PBE level) cannot describe the London dispersion forces responsible for interaction of the graphene planes (thus graphite falls apart into graphene sheets). To provide a basis for describing these London interactions, we derive the quantum mechanics based force field for carbon (QMFF-Cx) by fitting to results from density functional theory calculations at the M06-2X level, which demonstrates accuracies for a broad class of molecules at short and medium range intermolecular distances. We carried out calculations on the dehydrogenated coronene (C24) dimer, emphasizing two geometries: parallel-displaced X (close to the observed structure in graphite crystal) and PD-Y (the lowest energy transition state for sliding graphene sheets with respect to each other). A third, eclipsed geometry is calculated to be much higher in energy. The QMFF-Cx force field leads to accurate predictions of available experimental mechanical and thermodynamics data of graphite (lattice vibrations, elastic constants, Poisson ratios, lattice modes, phonon dispersion curves, specific heat, and thermal expansion). This validates the use of M06-2X as a practical method for development of new first principles based generations of QMFF force fields. PMID:20942530

Pascal, Tod A; Karasawa, Naoki; Goddard, William A

2010-10-01

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NASA Astrophysics Data System (ADS)

As assemblies of graphene sheets, carbon nanotubes, and fullerenes become components of new nanotechnologies, it is important to be able to predict the structures and properties of these systems. A problem has been that the level of quantum mechanics practical for such systems (density functional theory at the PBE level) cannot describe the London dispersion forces responsible for interaction of the graphene planes (thus graphite falls apart into graphene sheets). To provide a basis for describing these London interactions, we derive the quantum mechanics based force field for carbon (QMFF-Cx) by fitting to results from density functional theory calculations at the M06-2X level, which demonstrates accuracies for a broad class of molecules at short and medium range intermolecular distances. We carried out calculations on the dehydrogenated coronene (C24) dimer, emphasizing two geometries: parallel-displaced X (close to the observed structure in graphite crystal) and PD-Y (the lowest energy transition state for sliding graphene sheets with respect to each other). A third, eclipsed geometry is calculated to be much higher in energy. The QMFF-Cx force field leads to accurate predictions of available experimental mechanical and thermodynamics data of graphite (lattice vibrations, elastic constants, Poisson ratios, lattice modes, phonon dispersion curves, specific heat, and thermal expansion). This validates the use of M06-2X as a practical method for development of new first principles based generations of QMFF force fields.

Pascal, Tod A.; Karasawa, Naoki; Goddard, William A.

2010-10-01

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of these concepts are still useful constructs today, and indeed can provide means for experimental testing in quantum cavity electrodynamics. However, as discussed in Sec. III, some of these early ideas by Wien

Cole, Dan C.

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NASA Astrophysics Data System (ADS)

The combination of molecular simulations and potentials obtained from quantum chemistry is shown to be able to provide reasonably accurate thermodynamic property predictions. Gibbs ensemble Monte Carlo simulations are used to understand the effects of small perturbations to various regions of the model Lennard-Jones 12-6 potential. However, when the phase behavior and second virial coefficient are scaled by the critical properties calculated for each potential, the results obey a corresponding states relation suggesting a non-uniqueness problem for interaction potentials fit to experimental phase behavior. Several variations of a procedure collectively referred to as quantum mechanical Hybrid Methods for Interaction Energies (HM-IE) are developed and used to accurately estimate interaction energies from CCSD(T) calculations with a large basis set in a computationally efficient manner for the neon-neon, acetylene-acetylene, and nitrogen-benzene systems. Using these results and methods, an ab initio, pairwise-additive, site-site potential for acetylene is determined and then improved using results from molecular simulations using this initial potential. The initial simulation results also indicate that a limited range of energies important for accurate phase behavior predictions. Second virial coefficients calculated from the improved potential indicate that one set of experimental data in the literature is likely erroneous. This prescription is then applied to methanethiol. Difficulties in modeling the effects of the lone pair electrons suggest that charges on the lone pair sites negatively impact the ability of the intermolecular potential to describe certain orientations, but that the lone pair sites may be necessary to reasonably duplicate the interaction energies for several orientations. Two possible methods for incorporating the effects of three-body interactions into simulations within the pairwise-additivity formulation are also developed. A low density approximation for the pair and three-body distribution functions is simpler to implement, but the results based on the numerical solution of the inhomogeneous Ornstein-Zernike equation using the Percus-Yevick closure are more accurate. Given the low temperatures for phase equilibria of the model system, neon, several approximations to estimate the quantum effects on the atomic nuclei are presented with reasonable success.

Garrison, Stephen L.

2005-07-01

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A Simple Quantum-Mechanical Model of Spacetime II: Thermodynamics of Spacetime

In this second part of our series of two papers, where spacetime is modelled by a graph, where Planck size quantum black holes lie on the vertices, we consider the thermodynamics of spacetime. We formulate an equation which tells in which way an accelerating, spacelike two-surface of spacetime interacts with the thermal radiation flowing through that surface. In the low temperature limit, where most quantum black holes constituting spacetime are assumed to lie in the ground state, our equation implies, among other things, the Hawking and the Unruh effects, as well as Einstein's field equation with a vanishing cosmological constant for general matter fields. We also consider the high temperature limit, where the microscopic black holes are assumed to lie in highly excited states. In this limit our model implies, among other things, that black hole entropy depends logarithmically on its area, instead of being proportional to the area.

J. Makela

2008-05-26

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NASA Astrophysics Data System (ADS)

Introduction; Part I. Basic Features of Quantum Mechanics: 1. From classical mechanics to quantum mechanics; 2. Quantum observable and states; 3. Quantum dynamics; 4. Examples of quantum dynamics; 5. Density matrix; Part II. More Advanced Topics: 6. Angular momentum and spin; 7. Identical particles; 8. Symmetries and conservation laws; 9. The measurement problem; Part III. Matter and Light: 10. Perturbations and approximation methods; 11. Hydrogen and helium atoms; 12. Hydrogen molecular ion; 13. Quantum optics; Part IV. Quantum Information: State and Correlations: 14. Quantum theory of open systems; 15. State measurement in quantum mechanics; 16. Entanglement: non-separability; 17. Entanglement: quantum information; References; Index.

Auletta, Gennaro; Fortunato, Mauro; Parisi, Giorgio

2014-01-01

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Thermodynamics and equilibrium structure of Ne38 cluster: quantum mechanics versus classical.

The equilibrium properties of classical Lennard-Jones (LJ38) versus quantum Ne38 Lennard-Jones clusters are investigated. The quantum simulations use both the path-integral Monte Carlo (PIMC) and the recently developed variational-Gaussian wave packet Monte Carlo (VGW-MC) methods. The PIMC and the classical MC simulations are implemented in the parallel tempering framework. The classical heat capacity Cv(T) curve agrees well with that of Neirotti et al. [J. Chem. Phys. 112, 10340 (2000)], although a much larger confining sphere is used in the present work. The classical Cv(T) shows a peak at about 6 K, interpreted as a solid-liquid transition, and a shoulder at approximately 4 K, attributed to a solid-solid transition involving structures from the global octahedral (Oh) minimum and the main icosahedral (C5v) minimum. The VGW method is used to locate and characterize the low energy states of Ne38, which are then further refined by PIMC calculations. Unlike the classical case, the ground state of Ne38 is a liquidlike structure. Among the several liquidlike states with energies below the two symmetric states (Oh and C5v), the lowest two exhibit strong delocalization over basins associated with at least two classical local minima. Because the symmetric structures do not play an essential role in the thermodynamics of Ne38, the quantum heat capacity is a featureless curve indicative of the absence of any structural transformations. Good agreement between the two methods, VGW and PIMC, is obtained. The present results are also consistent with the predictions by Calvo et al. [J. Chem. Phys. 114, 7312 (2001)] based on the quantum superposition method within the harmonic approximation. However, because of its approximate nature, the latter method leads to an incorrect assignment of the Ne38 ground state as well as to a significant underestimation of the heat capacity. PMID:15945633

Predescu, Cristian; Frantsuzov, Pavel A; Mandelshtam, Vladimir A

2005-04-15

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Thermodynamic anomalous Hall effect: The quantum regime

NASA Astrophysics Data System (ADS)

A quantum statistical description of the anomalous Hall effect is developed within the framework of the previously proposed thermodynamic mechanism of the anomalous Hall effect in weakly magnetic electron systems with spontaneous spin polarization. A qualitative explanation of the physical nature of the thermodynamic mechanism is followed by a general formulation of the quantum theory of the effect, based on accounting for the local-equilibrium currents. The behavior of the magnetic field dependences and quantum magnetic oscillations of the physical parameters characterizing the anomalous Hall effect is discussed.

Okulov, V. I.; Pamyatnykh, E. A.; Lonchakov, A. T.

2014-11-01

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Thermodynamics in Loop Quantum Cosmology

Loop quantum cosmology (LQC) is very powerful to deal with the behavior of early universe. And the effective loop quantum cosmology gives a successful description of the universe in the semiclassical region. We consider the apparent horizon of the Friedmann-Robertson-Walker universe as a thermodynamical system and investigate the thermodynamics of LQC in the semiclassical region. The effective density and effective pressure in the modified Friedmann equation from LQC not only determine the evolution of the universe in LQC scenario but are actually also found to be the thermodynamic quantities. This result comes from the energy definition in cosmology (the Misner-Sharp gravitational energy) and is consistent with thermodynamic laws. We prove that within the framework of loop quantum cosmology, the elementary equation of equilibrium thermodynamics is still valid.

Li-Fang Li; Jian-Yang Zhu

2008-12-18

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Effective Potentials and Quantum Fluid Models: A Thermodynamic Approach

]. As a consequence, quantum mechanical models in device simulation usually treat quantum effects with a do- main model equivalent. Second, it allows us to mix classical and quantum mechanical models in an engineeringEffective Potentials and Quantum Fluid Models: A Thermodynamic Approach C. Gardner , C. Ringhofer

Ringhofer, Christian

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Quantum-mechanical Maxwell's demon

A Maxwell's demon is a device that gets information and trades it in for thermodynamic advantage, in apparent (but not actual) contradiction to the second law of thermodynamics. Quantum-mechanical versions of Maxwell's demon exhibit features that classical versions do not: in particular, a device that gets information about a quantum system disturbs it in the process. This paper proposes experimentally

Seth Lloyd

1997-01-01

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Quantum measurement and its role in thermodynamics

A central goal of the research effort in quantum thermodynamics is the extension of standard thermodynamics to include small-scale and quantum effects. Here we lay out consequences of seeing measurement, one of the central pillars of quantum theory, not merely as a mathematical projection but as a thermodynamic process. We uncover that measurement, a component of any experimental realisation, is accompanied by work and heat contributions and that these are distinct in classical and quantum thermodynamics. Implications are far-reaching, giving a thermodynamic interpretation to quantum coherence, extending the link between thermodynamics and information theory, and providing key input for the construction of a future quantum thermodynamic framework. Repercussions for existing quantum thermodynamic relations that omitted the role of measurement are discussed, including quantum work fluctuation relations and single-shot approaches.

Philipp Kammerlander; Janet Anders

2015-02-09

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Thermodynamics of quantum photon spheres

Photon spheres, surfaces where massless particles are confined in closed orbits, are expected to be common astrophysical structures surrounding ultracompact objects. In this paper a semiclassical treatment of a photon sphere is proposed. We consider the quantum Maxwell field and derive its energy spectra. A thermodynamic approach for the quantum photon sphere is developed and explored. Within this treatment, an expression for the spectral energy density of the emitted radiation is presented. Our results suggest that photon spheres, when thermalized with their environment, have nonusual thermodynamic properties, which could lead to distinct observational signatures.

M. C. Baldiotti; Walace S. Elias; C. Molina; Thiago S. Pereira

2014-10-07

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Thermodynamics and statistical mechanics. [thermodynamic properties of gases

NASA Technical Reports Server (NTRS)

The basic thermodynamic properties of gases are reviewed and the relations between them are derived from the first and second laws. The elements of statistical mechanics are then formulated and the partition function is derived. The classical form of the partition function is used to obtain the Maxwell-Boltzmann distribution of kinetic energies in the gas phase and the equipartition of energy theorem is given in its most general form. The thermodynamic properties are all derived as functions of the partition function. Quantum statistics are reviewed briefly and the differences between the Boltzmann distribution function for classical particles and the Fermi-Dirac and Bose-Einstein distributions for quantum particles are discussed.

1976-01-01

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Quantum dynamics in the thermodynamic limit

The description of spontaneous symmetry breaking that underlies the connection between classically ordered objects in the thermodynamic limit and their individual quantum-mechanical building blocks is one of the cornerstones of modern condensed-matter theory and has found applications in many different areas of physics. The theory of spontaneous symmetry breaking, however, is inherently an equilibrium theory, which does not address the dynamics of quantum systems in the thermodynamic limit. Here, we will use the example of a particular antiferromagnetic model system to show that the presence of a so-called thin spectrum of collective excitations with vanishing energy - one of the well-known characteristic properties shared by all symmetry-breaking objects - can allow these objects to also spontaneously break time-translation symmetry in the thermodynamic limit. As a result, that limit is found to be able, not only to reduce quantum-mechanical equilibrium averages to their classical counterparts, but also to turn individual-state quantum dynamics into classical physics. In the process, we find that the dynamical description of spontaneous symmetry breaking can also be used to shed some light on the possible origins of Born's rule. We conclude by describing an experiment on a condensate of exciton polaritons which could potentially be used to experimentally test the proposed mechanism.

Wezel, Jasper van [Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE (United Kingdom)

2008-08-01

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NASA Astrophysics Data System (ADS)

Preface; 1. Introduction; 2. Mathematical preliminaries; 3. The rules of quantum mechanics; 4. The connection between the fundamental rules and wave mechanics; 5. Further illustrations of the rules of quantum mechanics; 6. Further developments in one-dimensional wave mechanics; 7. The theory of angular momentum; 8. Wave mechanics in three dimensions: hydrogenic atoms; 9. Time-independent approximations for bound state problems; 10. Applications of static perturbation theory; 11. Identical particles; 12. Atomic structure; 13. Molecules; 14. The stability of matter; 15. Photons; 16. Interaction of non-relativistic charged particles and radiation; 17. Further topics in perturbation theory; 18. Scattering; 19. Special relativity and quantum mechanics: the Klein–Gordon equation; 20. The Dirac equation; 21. Interaction of a relativistic spin 1/2 particle with an external electromagnetic field; 22. The Dirac field; 23. Interaction between relativistic electrons, positrons, and photons; 24. The quantum mechanics of weak interactions; 25. The quantum measurement problem; Appendix A: useful inequalities for quantum mechanics; Appendix B: Bell's inequality; Appendix C: spin of the photon: vector spherical waves; Works cited; Bibliography; Index.

Commins, Eugene D.

2014-10-01

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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.

De Raedt, Hans; Michielsen, Kristel

2010-03-25

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Thermodynamics of discrete quantum processes

We define thermodynamic configurations and identify two primitives of discrete quantum processes between configurations for which heat and work can be defined in a natural way. This allows us to uncover a general second law for any discrete trajectory that consists of a sequence of these primitives, linking both equilibrium and non-equilibrium configurations. Moreover, in the limit of a discrete trajectory that passes through an infinite number of configurations, i.e. in the reversible limit, we recover the saturation of the second law. Finally, we show that for a discrete Carnot cycle operating between four configurations one recovers Carnot's thermal efficiency.

Janet Anders; Vittorio Giovannetti

2012-11-01

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Quantum Collapse and the Second Law of Thermodynamics

A heat engine undergoes a cyclic operation while in equilibrium with the net result of conversion of heat into work. Quantum effects such as superposition of states can improve an engine's efficiency by breaking detailed balance, but this improvement comes at a cost due to excess entropy generated from collapse of superpositions on measurement. We quantify these competing facets for a quantum ratchet comprised of an ensemble of pairs of interacting two-level atoms. We suggest that the measurement postulate of quantum mechanics is intricately connected to the second law of thermodynamics. More precisely, if quantum collapse is not inherently random, then the second law of thermodynamics can be violated. Our results challenge the conventional approach of simply quantifying quantum correlations as a thermodynamic work deficit.

Sahand Hormoz

2012-03-02

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-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter–antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantum mechanics. PMID:23509390

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

2013-01-01

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Quantum Mechanics of Black Holes

NASA Astrophysics Data System (ADS)

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.

Witten, Edward

2012-08-01

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Information thermodynamics in a hybrid opto-mechanical system

Information thermodynamics is a recent field that investigates the links between information and energy. Its most famous "Gedankenexperiments" are Landauer erasure and Szilard engine, that describe the reversible conversion of a single bit of information into an elementary amount of work between a system and a battery. So far, direct evidences of such reversible work exchanges by measuring the battery's energy has remained elusive. In this article, we show that a hybrid optomechanical transducer is a proper platform to monitor these conversions. Such devices consist in an optically active quantum emitter, playing the role of the bit, coupled to a mechanical resonator, playing the role of the battery. Heat is exchanged with the electromagnetic reservoir. Within a mechanical oscillation, we connect the entropy variations of the quantum emitter with the mechanical energy variations, that are identi?ed with work exchanges. These results pave the road towards experimental investigation of quantum information thermodynamics.

Cyril Elouard; Maxime Richard; Alexia Auffèves

2014-09-23

32

NASA Astrophysics Data System (ADS)

A development of quantum theory that was initiated in the 1920s by Werner Heisenberg (1901-76) and Erwin Schrödinger (1887-1961). The theory drew on a proposal made in 1925 Prince Louis de Broglie (1892-1987), that particles have wavelike properties (the wave-particle duality) and that an electron, for example, could in some respects be regarded as a wave with a wavelength that depended on its mo...

Murdin, P.

2000-11-01

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A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Lévy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Lévy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and

Nikolai Laskin

2000-01-01

34

Thermodynamics of N-dimensional quantum walks

The entanglement between the position and coin state of a $N$-dimensional quantum walker is shown to lead to a thermodynamic theory. The entropy, in this thermodynamics, is associated to the reduced density operator for the evolution of chirality, taking a partial trace over positions. From the asymptotic reduced density matrix it is possible to define thermodynamic quantities, such as the asymptotic entanglement entropy, temperature, Helmholz free energy, etc. We study in detail the case of a $2$-dimensional quantum walk, in the case of two different initial conditions: a non-separable coin-position initial state, and a separable one. The resulting entanglement temperature is presented as function of the parameters of the system and those of the initial conditions.

Alejandro Romanelli; Raul Donangelo; Renato Portugal; Franklin L. Marquezino

2014-08-22

35

Quantum optical thermodynamic machines: Lasing as relaxation

NASA Astrophysics Data System (ADS)

Motivated by the growing interest in the nanophysics and the field of quantum thermodynamics we study an open quantum system consisting of two spatially separated two-level atoms (spins) coupled to a quantum oscillator (resonator field mode). There is no external driving. The spins of different energy splittings are each linked to a heat bath with different temperature. We find that the temperature gradient imposed on the system together with the oscillator operating as a kind of work reservoir makes this system act as a thermodynamic machine, in particular, as a heat engine (laser). We analyze the properties of the resulting resonator field and of the engine functionality. For the latter problem we use recently developed definitions of heat flux and power as well as a test, in which the resulting field is used as an input for a heat pump.

Youssef, M.; Mahler, G.; Obada, A.-S. F.

2009-12-01

36

Thermodynamic behavior of the quantum walk

NASA Astrophysics Data System (ADS)

A thermodynamic theory is developed to describe the behavior of the entanglement between the coin and position degrees of freedom of the quantum walk on the line. It is shown that, in spite of the unitary evolution, a steady state is established after a Markovian transient stage. This study suggests that if a quantum dynamics develops in a composite Hilbert space (i.e., the tensor product of several subspaces), then the behavior of an operator that belongs only to one of the subspaces may camouflage the unitary character of the global evolution.

Romanelli, Alejandro

2012-01-01

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Rate (k) and equilibrium (K) constants for the reaction of tetrahydrofuranol with a series of Mg(2+) complexes of methyl triphosphate analogues, CH3O-P(O2)-O-P(O2)-X-PO3(4-), X = O, CH2, CHCH3, C(CH3)2, CFCH3, CHF, CHCl, CHBr, CFCl, CF2, CCl2, and CBr2, forming phosphate diester and pyrophosphate or bisphosphonate in aqueous solution were evaluated by B3LYP/TZVP//HF/6-31G* quantum chemical calculations and Langevin dipoles and polarized continuum solvation models. The calculated log k and log K values were found to depend linearly on the experimental pKa4 of the conjugate acid of the corresponding pyrophosphate or bisphosphonate leaving group. The calculated slopes of these Brønsted linear free energy relationships were ?lg = -0.89 and ?eq = -0.93, respectively. The studied compounds also followed the linear relationship ?log k = 0.8?log K, which became less steep, ?log k = 0.6?log K, after the range of studied compounds was extended to include analogues that were doubly protonated on ?-phosphate, CH3O-P(O2)-O-P(O2)-X-PO3H2(2-). The scissile P?-Olg bond length in studied methyl triphosphate analogues slightly increases with decreasing pKa of the leaving group; concomitantly, the CH3OP?(O2) moiety becomes more positive. These structural effects indicate that substituents with low pKa can facilitate both P?-Olg bond breaking and the P?-Onuc bond forming process, thus explaining the large negative ?lg calculated for the transition state geometry that has significantly longer P?-Onuc distance than the P?-Olg distance. PMID:24901652

Zhang, Zheng; Eloge, Josh; Florián, Jan

2014-07-01

38

Statistical mechanics based on fractional classical and quantum mechanics

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

Korichi, Z.; Meftah, M. T., E-mail: mewalid@yahoo.com [Physics Department, LRPPS Laboratory, Ouargla University, Ouargla 30000 (Algeria)

2014-03-15

39

Quantum Mechanics II (Undergraduate)

, and applications of quantum mechanics to materials science/solid-state physics. Grades: Homework: 15%, Midertm: 40 other selected topics from quantum information (see the QUNET reference) and solid-state physics. All

Nickrent, Daniel L.

40

Black Hole Thermodynamics and Statistical Mechanics

We have known for more than thirty years that black holes behave as thermodynamic systems, radiating as black bodies with characteristic temperatures and entropies. This behavior is not only interesting in its own right; it could also, through a statistical mechanical description, cast light on some of the deep problems of quantizing gravity. In these lectures, I review what we currently know about black hole thermodynamics and statistical mechanics, suggest a rather speculative "universal" characterization of the underlying states, and describe some key open questions.

Steven Carlip

2008-07-28

41

Syllabus for EK424, Spring 2014 "Thermodynamics and Statistical Mechanics"

Syllabus for EK424, Spring 2014 "Thermodynamics and Statistical Mechanics" Boston University or molecules. The subject of statistical mechanics is concerned with expressing thermodynamics and statistical mechanics, therefore, are essential for explaining the forces that drive chemical and biochemical

Vajda, Sandor

42

Syllabus for EK424, Fall 2014 "Thermodynamics and Statistical Mechanics"

Syllabus for EK424, Fall 2014 "Thermodynamics and Statistical Mechanics" Boston University or molecules. The subject of statistical mechanics is concerned with expressing thermodynamics and statistical mechanics, therefore, are essential for explaining the forces that drive chemical and biochemical

43

A thermodynamical formalism describing mechanical interactions

NASA Astrophysics Data System (ADS)

The dynamical behavior of an overdamped mechanical model devoid of any usual thermal effects is analyzed by a formalism that is similar to usual thermodynamics, and completely independent of any ad hoc assumption of a probability distribution of states in phase space of the mechanical model. It leads to the definition of a new entropy function, which does not coincide with the usual thermodynamical entropy. The new step making the difference to previous studies of this system is the identification of two non-equivalent mechanical interaction mechanisms, which are defined and identified as work and pseudo-heat. Together with the introduced effective temperature ?, they make it possible to characterize the equivalent to isothermal, adiabatic, isobaric, and isochoric processes. Three statements, formally analogous to the zeroth, first, and second law of thermodynamics, are issued. The statement of the second law results from the asymmetry in the way energy can be exchanged along the two processes. A Carnot cycle is defined, for which the efficiency is expressed in terms of ? in the operating pseudo-heat reservoirs. The analogous Clausius theorem for the system operating an arbitrary reversible cycle is proved, leading to the new entropy function. Consequences of the extension of thermodynamic formalism to mechanical models with different processes of transferring energy are discussed.

Andrade, R. F. S.; Souza, A. M. C.; Curado, E. M. F.; Nobre, F. D.

2014-10-01

44

Low-temperature thermodynamics with quantum coherence

We find a new characterization of low-temperature processes, which we call "cooling processes", incorporating quantum coherence in the model of thermodynamics for the first time. We derive necessary and sufficient conditions for the feasibility of state transitions under cooling processes. We also rigorously confirm the intuitive robustness of coherence against low-temperature thermal noise. Additionally, we develop the low-temperature "Gibbs-preserving" model, and by comparing our results on the two models, we argue that the latter is a poor approximation to physical processes.

Varun Narasimhachar; Gilad Gour

2014-09-26

45

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

46

Thermodynamics of Quantum Gases for the Entire Range of Temperature

ERIC Educational Resources Information Center

We have analytically explored the thermodynamics of free Bose and Fermi gases for the entire range of temperature, and have extended the same for harmonically trapped cases. We have obtained approximate chemical potentials for the quantum gases in closed forms of temperature so that the thermodynamic properties of the quantum gases become…

Biswas, Shyamal; Jana, Debnarayan

2012-01-01

47

NASA Astrophysics Data System (ADS)

We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the BLG-model and the ABJM-model compactified on a torus are N = 16 and N = 12 superconformal gauged quantum mechanics. After integrating out the auxiliary gauge fields we find OSp (16 | 2) and SU (1 , 1 | 6) quantum mechanics from the reduced systems. The curved Riemann surface is taken as a holomorphic curve in a Calabi-Yau space to preserve supersymmetry and we present a prescription of the topological twisting. We find the N = 8 superconformal gauged quantum mechanics that may describe the motion of two wrapped M2-branes in a K3 surface.

Okazaki, Tadashi

2015-01-01

48

We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the BLG-model and the ABJM-model compactified on a torus are N = 16 and N = 12 superconformal gauged quantum mechanics. After integrating out the auxiliary gauge fields we find OSp(16|2) and SU(1,1|6) quantum mechanics from the reduced systems. The curved Riemann surface is taken as a holomorphic curve in a Calabi-Yau space to preserve supersymmetry and we present a prescription of the topological twisting. We find the N = 8 superconformal gauged quantum mechanics that may describe the motion of two wrapped M2-branes in a K3 surface.

Tadashi Okazaki

2014-11-03

49

The Lorentz covariant classical and quantum statistical mechanics and thermodynamics of an ideal relativistic gas of bradyons (particles slower than light), luxons (particles moving with the speed of light), and tachyons (hypothetical particles faster than light) is discussed. The Lorentz covariant formulation is based on the preferred frame approach which among others enables a consistent, free of paradoxes description of tachyons. The thermodynamic functions within the covariant approach are obtained both in the classical and quantum case.

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

2007-08-15

50

Syllabus Physics 531 (PHY 531) Thermodynamics and Statistical Mechanics

1 Syllabus Physics 531 (PHY 531) Thermodynamics and Statistical Mechanics Fall 2006 Professor Liviu the problems. Webpage: http://www.physics.syr.edu/~lmovilea/ThermodynamicsStatisticalMechanics2006.ht ml Course thermodynamic relations from the statistical principles. Statistical mechanics connects the properties

Movileanu, Liviu

51

PERSPECTIVE Quantum Mechanics of Black Holes

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.

Edward Witten

52

Thermodynamics of quantum-jump-conditioned feedback control

NASA Astrophysics Data System (ADS)

We consider open quantum systems weakly coupled to thermal reservoirs and subjected to quantum feedback operations triggered with or without delay by monitored quantum jumps. We establish a thermodynamic description of such systems and analyze how the first and second law of thermodynamics are modified by the feedback. We apply our formalism to study the efficiency of a qubit subjected to a quantum feedback control and operating as a heat pump between two reservoirs. We also demonstrate that quantum feedbacks can be used to stabilize coherences in nonequilibrium stationary states which in some cases may even become pure quantum states.

Strasberg, Philipp; Schaller, Gernot; Brandes, Tobias; Esposito, Massimiliano

2013-12-01

53

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

54

Thermodynamic properties of 3-dimensional quantum antiferromagnets

NASA Astrophysics Data System (ADS)

We present systematic calculations of thermal properties of 3-dimensional quantum antiferromagnets, in the thermodynamic limit, using series expansions. For this purpose, High Temperature Expansions (HTE) are supplemented by Numerical Linked Cluster (NLC) Expansions.footnotetextR. Applegate et al, Phys. Rev. Lett. 109, 097205 (2012); R. R. P. Singh and J. Oitmaa Phys. Rev. B 85, 144414 (2012); R. R. P. Singh and J. Oitmaa Phys. Rev. B 85, 104406 (2012). These expansions provide essentially exact calculations of thermodynamic properties of the system at (i) all fields at high temperatures and (ii) at all temperatures at high fields. In addition, we show that for classical exchange spin-ice model defined on the pyrochlore lattice, the first order NLC leads to the Pauling approximation, which gives even the zero-field ground state entropy to about one percent accuracy. Thus, these calculations are accurate over a wide parameter range. Results are presented and compared with a variety of experimental systems including pyrochlore materials Yb2Ti2O7 and Er2Ti2O7 and the Hyper Kagome material Na4Ir3O8

Singh, Rajiv R. P.; Oitmaa, Jaan; Gingras, Michel J. P.

2013-03-01

55

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

56

Periodic thermodynamics of isolated quantum systems.

The nature of the behavior of an isolated many-body quantum system periodically driven in time has been an open question since the beginning of quantum mechanics. After an initial transient period, such a system is known to synchronize with the driving; in contrast to the nondriven case, no fundamental principle has been proposed for constructing the resulting nonequilibrium state. Here, we analytically show that, for a class of integrable systems, the relevant ensemble is constructed by maximizing an appropriately defined entropy subject to constraints, which we explicitly identify. This result constitutes a generalization of the concepts of equilibrium statistical mechanics to a class of far-from-equilibrium systems, up to now mainly accessible using ad hoc methods. PMID:24785013

Lazarides, Achilleas; Das, Arnab; Moessner, Roderich

2014-04-18

57

Paradigms in Physics: Thermodynamics & Statistical Mechanics Activities

NSDL National Science Digital Library

This web page provides a list of learning activities for Junior level Thermodynamics and Statistical Mechanics classes. Each activity includes a description and learning goals, guides for instructors, handouts or worksheets, and reflections of instructors who have used the activity when available. Among the topics included are entropy, Maxwell equations, PV and TS diagrams, and Legendre transforms. This material is part of the Paradigms in Physics project at Oregon State University. This work promotes the use of active student learning in upper division physics courses. Both learning materials and learning strategies are provided to help both students and instructors.

2014-06-07

58

Numerical continuation in classical mechanics and thermodynamics

NASA Astrophysics Data System (ADS)

In this paper, modern numerical continuation methodologies are presented as a way of understanding and computing multiplicity of solutions in undergraduate physics problems. Mechanical and thermodynamical problems are used as a storyline to introduce the mathematical formalism required to clarify the distinction between the uniqueness and multiplicity of equilibrium solutions and the critical states of a nonlinear physical problem, as well as to illustrate how these novel numerical continuation techniques are implemented in practice. The paper provides simple numerical Matlab codes that are easily adaptable to other problems, as well as updated software and literature resources.

Gimenez, Aleix; Chausse, Victor; Meseguer, Alvaro

2015-01-01

59

Probability in Quantum Mechanics

The concept of probability played an important role in the very beginning of ? quantum theory, when Max Planck (1858–1947)\\u000a postulated the discrete emission and absorption of radiation in a ? black body radiation. The quantum statistical mechanics\\u000a developed by Planck and his successors has extraordinary consequences treated elsewhere in this Compendium. Here, however,\\u000a the emphasis will be upon the

Abner Shimony

60

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

61

TIME IN QUANTUM MECHANICS A Thesis by KIMBERLY R. CHAPIN Submitted to Texas A8M University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Approved as to style and content by: Marian O. Scully (Chair... of Committee) Edward S. Fry (Member) aan Laane (Member) Thomas W. Adair, III (Head of Department) August 1997 Major Subject: Physics TIME IN QIJANTUM MECHANICS A Thesis by KIMBERLY R. CHAPIN Submitted to the Oflice of Graduate Studies of Texas A...

Chapin, Kimberly R.

2012-06-07

62

Thermodynamics and Universality for Mean Field Quantum Spin Glasses

We study aspects of the thermodynamics of quantum versions of spin glasses. By means of the Lie-Trotter formula for exponential sums of operators, we adapt methods used to analyze classical spin glass models to answer analogous questions about quantum models.

Nick Crawford

2006-10-13

63

A Thermodynamic Sector of Quantum Gravity

The connection between gravity and thermodynamics is explored. Examining a perfect fluid in gravitational equilibrium we find that the entropy is extremal only if Einstein's equations are satisfied. Conversely, one can derive part of Einstein's equations from ordinary thermodynamical considerations. This allows the theory of this system to be recast in such a way that a sector of general relativity is purely thermodynamical and should not be quantized.

J. Oppenheim

2001-12-04

64

QUICK QUANTUM MECHANICS ---Introduction ---

to their students. Thus, it was natural that the historical evolution of quantum mechanics relied on some aspects sin 2 ` â?? OE 2 ] \\Gamma V (r) : (2) The time evolution of the system is given once we determine, replace it by q(t) + ffif (t) where ffif (t) is completely arbitrary except for the facts

Jackson, Andrew D.

65

Quantum Mechanical Models of Solids

NSDL National Science Digital Library

This web site contains the class notes for a course on Quantum Mechanical Models of Solids. Topics cover basic quantum mechanics, crystallography, exchange-correlation, metals, and semiconductors. The site also includes a list of useful books and references.

Heggie, Malcom; Martinez, Irene S.; Venables, John, 1936-

2010-08-24

66

TRANSIENT QUANTUM MECHANICAL PROCESSES

Our principal objective has centered on the development of sophisticated computational techniques to solve the time-dependent Schroedinger equation that governs the evolution of quantum mechanical systems. We have perfected two complementary methods, discrete variable representation and real space product formula, that show great promise in solving these complicated temporal problems. We have applied these methods to the interaction of laser light with molecules with the intent of not only investigating the basic mechanisms but also devising schemes for actually controlling the outcome of microscopic processes. Lasers now exist that produce pulses of such short duration as to probe a molecular process many times within its characteristic period--allowing the actual observation of an evolving quantum mechanical system. We have studied the potassium dimer as an example and found agreement with experimental changes in the intermediate state populations as a function of laser frequency--a simple control prescription. We have also employed elaborate quantum chemistry programs to improve the accuracy of basic input such as bound-bound and bound-free coupling moments. These techniques have far-ranging applicability; for example, to trapped quantum systems at very low temperatures such as Bose-Einstein condensates.

L. COLLINS; J. KRESS; R. WALKER

1999-07-01

67

"Velocities" in Quantum Mechanics

The present paper deals with some kind of quantum ``velocity'' which is introduced by the method of hydrodynamical analogy. It is found that this ``velocity'' is in general irrotational, namely, a vorticity vanishes, and then a velocity potential must exist in quantum mechanics. In some elementary examples of stable systems we will see what the ``velocities'' are. In particular, the two-dimensional flows of these examples can be expressed by complex velocity potentials whose real and imaginary parts are the velocity potentials and stream functions, respectively.

Shimbori, T; Shimbori, Toshiki; Kobayashi, Tsunehiro

2000-01-01

68

"Velocities" in Quantum Mechanics

The present paper deals with some kind of quantum ``velocity'' which is introduced by the method of hydrodynamical analogy. It is found that this ``velocity'' is in general irrotational, namely, a vorticity vanishes, and then a velocity potential must exist in quantum mechanics. In some elementary examples of stable systems we will see what the ``velocities'' are. In particular, the two-dimensional flows of these examples can be expressed by complex velocity potentials whose real and imaginary parts are the velocity potentials and stream functions, respectively.

Toshiki Shimbori; Tsunehiro Kobayashi

2000-04-21

69

The quantum field theories (QFT) constructed in [1,2] include phenomenology of interest. The constructions approximate: scattering by $1/r$ and Yukawa potentials in non-relativistic approximations; and the first contributing order of the Feynman series for Compton scattering. To have a semi-norm, photon states are constrained to transverse polarizations and for Compton scattering, the constructed cross section deviates at large momentum exchanges from the cross section prediction of the Feynman rules. Discussion includes the incompatibility of canonical quantization with the constructed interacting fields, and the role of interpretations of quantum mechanics in realizing QFT.

Glenn Eric Johnson

2014-12-21

70

Quantum thermodynamic cycles and quantum heat engines H. T. Quan,1,2

us understand the quantum-classical transition problem of thermodynamic pro- cesses 6 . The classical been clarified in many references, e.g., 21 , quantum isothermal processes and quantum isochoric pro properties of a quantum ana- logue of a Carnot engine. The difference between a QCE and its classical

Nori, Franco

71

Probabilistic Interpretation of Quantum Mechanics

The probabilistic interpretation of quantum mechanics is based on Born's 1926 papers and von Neumann's formal account of quantum\\u000a mechanics in ? Hilbert space. According to Max Born (1882–1970), the quantum mechanical ? wave function ? does not have any\\u000a direct physical meaning, whereas its square ???2 is a probability [1] ? Born rule, probability in quantum mechanics. According to

Brigitte Falkenburg; Peter Mittelstaedt

72

TORY II-A MECHANICAL AND AERO-THERMODYNAMIC DESIGN

The first nuclear reactor in the Pluto program, Tory II-A, is described ; from the standpoint of mechanical and aero-thermodynamic design. Experimental ; objectives and predicted aero-thermodynamic performance are presented. A ; discussion of mechanical design includes principal structural features, material ; selection, and a review of component design and testing. Digital computing ; machine codes used to study transient

J. W. Cox; P. M. Uthe

1962-01-01

73

Path Integrals in Quantum Mechanics

Jean Zinn-Justin's textbook Path Integrals in Quantum Mechanics aims to familiarize the reader with the path integral as a calculational tool in quantum mechanics and field theory. The emphasis is on quantum statistical mechanics, starting with the partition function Tr exp(-? H) and proceeding through the diffusion equation to barrier penetration problems and their semiclassical limit. The 'real time' path

J Louko

2005-01-01

74

EOSTA—an improved EOS quantum mechanical model in the STA opacity code

The STA model is extended to include calculations of thermodynamical quantities required for equation of state (EOS). For that purpose the plasma free electrons are now treated quantum mechanically accounting for shape resonances. The resulting gradual orbital ionization assures a regular behavior of all the thermodynamical quantities vs. density and temperature. The relativistic quantum mechanical framework that we have applied

A. Bar-Shalom; J. Oreg; M. Klapisch

2006-01-01

75

Quantum statistical mechanics of vortices in high-temperature superconductors

Starting from the vortex equation of motion, we construct an effective Euclidean action and formulate the quantum statistical mechanics of the vortex system. The formalism is applied to the calculation of various thermodynamic quantities such as the specific heat and the magnetic susceptibility of the vortex lattice. Furthermore, we investigate the effect of quantum fluctuations on the vortex-lattice melting transition.

G. Blatter; B. I. Ivlev

1994-01-01

76

Quantum statistical mechanics of vortices in high-temperature superconductors

NASA Astrophysics Data System (ADS)

Starting from the vortex equation of motion, we construct an effective Euclidean action and formulate the quantum statistical mechanics of the vortex system. The formalism is applied to the calculation of various thermodynamic quantities such as the specific heat and the magnetic susceptibility of the vortex lattice. Furthermore, we investigate the effect of quantum fluctuations on the vortex-lattice melting transition.

Blatter, G.; Ivlev, B. I.

1994-10-01

77

Time Asymmetric Quantum Mechanics

The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone--von Neumann theorem, the solutions of the dynamical equations, the Schr\\"odinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width $\\Gamma$ and exponentially decaying states of lifetime $\\tau=\\frac{\\hbar}{\\Gamma}$ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution $t_{0}\\leq tbeginning 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.

Arno R. Bohm; Manuel Gadella; Piotr Kielanowski

2011-09-03

78

On the Quantum-Corrected Black Hole Thermodynamics

Bekenstein-Hawking Black hole thermodynamics should be corrected to incorporate quantum gravitational effects. Generalized Uncertainty Principle(GUP) provides a perturbational framework to perform such modifications. In this paper we consider the most general form of GUP to find black holes thermodynamics in microcanonical ensemble. Our calculation shows that there is no logarithmic pre-factor in perturbational expansion of entropy. This feature will solve part of controversies in literatures regarding existence or vanishing of this pre-factor.

Kourosh Nozari; S. Hamid Mehdipour

2006-01-15

79

Work extraction and thermodynamics for individual quantum systems

Thermodynamics is traditionally concerned with systems comprised of a large number of particles. Here we present a framework for extending thermodynamics to individual quantum systems, including explicitly a thermal bath and work-storage device (essentially a `weight' that can be raised or lowered). We prove that the second law of thermodynamics holds in our framework, and give a simple protocol to extract the optimal amount of work from the system, equal to its change in free energy. Our results apply to any quantum system in an arbitrary initial state, in particular including non-equilibrium situations. The optimal protocol is essentially reversible, similar to classical Carnot cycles, and indeed, we show that it can be used it to construct a quantum Carnot engine.

Paul Skrzypczyk; Anthony J. Short; Sandu Popescu

2014-09-26

80

Quantum Chemical Approach to Estimating the Thermodynamics of Metabolic Reactions

NASA Astrophysics Data System (ADS)

Thermodynamics plays an increasingly important role in modeling and engineering metabolism. We present the first nonempirical computational method for estimating standard Gibbs reaction energies of metabolic reactions based on quantum chemistry, which can help fill in the gaps in the existing thermodynamic data. When applied to a test set of reactions from core metabolism, the quantum chemical approach is comparable in accuracy to group contribution methods for isomerization and group transfer reactions and for reactions not including multiply charged anions. The errors in standard Gibbs reaction energy estimates are correlated with the charges of the participating molecules. The quantum chemical approach is amenable to systematic improvements and holds potential for providing thermodynamic data for all of metabolism.

Jinich, Adrian; Rappoport, Dmitrij; Dunn, Ian; Sanchez-Lengeling, Benjamin; Olivares-Amaya, Roberto; Noor, Elad; Even, Arren Bar; Aspuru-Guzik, Alán

2014-11-01

81

Work extraction and thermodynamics for individual quantum systems.

Thermodynamics is traditionally concerned with systems comprised of a large number of particles. Here we present a framework for extending thermodynamics to individual quantum systems, including explicitly a thermal bath and work-storage device (essentially a 'weight' that can be raised or lowered). We prove that the second law of thermodynamics holds in our framework, and gives a simple protocol to extract the optimal amount of work from the system, equal to its change in free energy. Our results apply to any quantum system in an arbitrary initial state, in particular including non-equilibrium situations. The optimal protocol is essentially reversible, similar to classical Carnot cycles, and indeed, we show that it can be used to construct a quantum Carnot engine. PMID:24969511

Skrzypczyk, Paul; Short, Anthony J; Popescu, Sandu

2014-01-01

82

Quantum chemical approach to estimating the thermodynamics of metabolic reactions.

Thermodynamics plays an increasingly important role in modeling and engineering metabolism. We present the first nonempirical computational method for estimating standard Gibbs reaction energies of metabolic reactions based on quantum chemistry, which can help fill in the gaps in the existing thermodynamic data. When applied to a test set of reactions from core metabolism, the quantum chemical approach is comparable in accuracy to group contribution methods for isomerization and group transfer reactions and for reactions not including multiply charged anions. The errors in standard Gibbs reaction energy estimates are correlated with the charges of the participating molecules. The quantum chemical approach is amenable to systematic improvements and holds potential for providing thermodynamic data for all of metabolism. PMID:25387603

Jinich, Adrian; Rappoport, Dmitrij; Dunn, Ian; Sanchez-Lengeling, Benjamin; Olivares-Amaya, Roberto; Noor, Elad; Even, Arren Bar; Aspuru-Guzik, Alán

2014-01-01

83

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

84

Non-equilibrium thermodynamics approach to open quantum systems

Open quantum systems are studied from the thermodynamical point of view unifying the principle of maximum informational entropy and the hypothesis of relaxation times hierarchy. The result of the unification is a non-Markovian and local in time master equation that provides a direct connection of dynamical and thermodynamical properties of open quantum systems. The power of the approach is illustrated with the application to the damped harmonic oscillator and the damped driven two-level system resulting in analytical expressions for the non-Markovian and non-equilibrium entropy and inverse temperature.

Vitalii Semin; Francesco Petruccione

2014-10-23

85

Emergence of equilibrium thermodynamic properties in quantum pure states. I. Theory

Investigation on foundational aspects of quantum statistical mechanics recently entered a renaissance period due to novel intuitions from quantum information theory and to increasing attention on the dynamical aspects of single quantum systems. In the present contribution a simple but effective theoretical framework is introduced to clarify the connections between a purely mechanical description and the thermodynamic characterization of the equilibrium state of an isolated quantum system. A salient feature of our approach is the very transparent distinction between the statistical aspects and the dynamical aspects in the description of isolated quantum systems. Like in the classical statistical mechanics, the equilibrium distribution of any property is identified on the basis of the time evolution of the considered system. As a consequence equilibrium properties of quantum system appear to depend on the details of the initial state due to the abundance of constants of the motion in the Schroedinger dynamics. On the other hand the study of the probability distributions of some functions, such as the entropy or the equilibrium state of a subsystem, in statistical ensembles of pure states reveals the crucial role of typicality as the bridge between macroscopic thermodynamics and microscopic quantum dynamics. We shall consider two particular ensembles: the random pure state ensemble and the fixed expectation energy ensemble. The relation between the introduced ensembles, the properties of a given isolated system, and the standard quantum statistical description are discussed throughout the presentation. Finally we point out the conditions which should be satisfied by an ensemble in order to get meaningful thermodynamical characterization of an isolated quantum system.

Fresch, Barbara; Moro, Giorgio J. [Department of Chemical Science, University of Padova, Via Marzolo 1, Padova 35131 (Italy)

2010-07-21

86

Mechanical and Industrial Engineering 230 Thermodynamics Course Syllabus

Vapor power systems Evening Exam #2 (Time TBA) No class 11/24/2009 Internal combustion engine powerMechanical and Industrial Engineering 230 Fall 2009 Thermodynamics Course Syllabus Date Week 1 (9 Introductory material Concepts of energy, work and heat transfer First Law of Thermodynamics Evaluating

Rothstein, Jonathan

87

An Irreversible Thermodynamics Theory for Damage Mechanics of Solids

The entropy production is a non-negative quantity based on irreversible thermodynamics and thus serves as a basis for the systematic description of the irreversible processes occurring in a solid. In this paper, a thermodynamic framework has been presented for damage mechanics of solid materials, where entropy production is used as the sole measure of damage evolution in the system. As

Cemal Basaran; Shihua Nie

2004-01-01

88

Dynamical noncommutative quantum mechanics

NASA Astrophysics Data System (ADS)

We study some basic and interesting quantum mechanical systems in dynamical noncommutative spaces in which the space-space commutation relations are position dependent. It is observed that the fundamental objects in the dynamical noncommutative space introduced here are string-like. We show that the Stark effect can be employed to determine whether the noncommutativity of space is dynamical or non-dynamical. It appears that unlike a non-dynamical case there is a fundamental energy ??2/m in this dynamical space.

Alavi, S. A.; Abbaspour, S.

2014-01-01

89

Advanced Concepts in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction: the need for a quantum theory; 2. Experimental foundations of quantum theory; 3. Waves and particles; 4. Schrödinger picture, Heisenberg picture and probabilistic aspects; 5. Integrating the equations of motion; 6. Elementary applications: 1-dimensional problems; 7. Elementary applications: multidimensional problems; 8. Coherent states and related formalism; 9. Introduction to spin; 10. Symmetries in quantum mechanics; 11. Approximation methods; 12. Modern pictures of quantum mechanics; 13. Formulations of quantum mechanics and their physical implications; 14. Exam problems; Glossary of geometric concepts; References; Index.

Esposito, Giampiero; Marmo, Giuseppe; Miele, Gennaro; Sudarshan, George

2014-11-01

90

Sketching the History of Statistical Mechanics and Thermodynamics

NSDL National Science Digital Library

This site is a timeline of thermodynamics and statistical mechanics from approximately 150 BC to the present. Links to information about the people involved in the development of the field, and sources and references, are provided.

91

Emergent Thermodynamics in a Quenched Quantum Many-Body System

NASA Astrophysics Data System (ADS)

We study the statistics of the work done, fluctuation relations, and irreversible entropy production in a quantum many-body system subject to the sudden quench of a control parameter. By treating the quench as a thermodynamic transformation we show that the emergence of irreversibility in the nonequilibrium dynamics of closed many-body quantum systems can be accurately characterized. We demonstrate our ideas by considering a transverse quantum Ising model that is taken out of equilibrium by an instantaneous change of the transverse field.

Dorner, R.; Goold, J.; Cormick, C.; Paternostro, M.; Vedral, V.

2012-10-01

92

Quantum coherence, time-translation symmetry and thermodynamics

The first law of thermodynamics imposes not just a constraint on the energy-content of systems in extreme quantum regimes, but also symmetry-constraints related to the thermodynamic processing of quantum coherence. Harmonic analysis allows any density operator to be decomposed in terms of mode operators which quantify the coherence present in a state in a natural way. We establish upper and lower bounds for the evolution of such modes under arbitrary thermal operations, and analyse primitive coherence manipulations. Well-studied thermo-majorization relations on block-diagonal quantum states correspond to constraints only on the zero-mode of a state, governing energy transfers. A complete set of constraints for non-zero modes, governing coherence transfers, is at present unknown, but these modes are found to display similar irreversibility, which demands greater study.

Matteo Lostaglio; Kamil Korzekwa; David Jennings; Terry Rudolph

2014-10-16

93

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

94

EVENTUM MECHANICS OF QUANTUM TRAJECTORIES: CONTINUAL MEASUREMENTS, QUANTUM PREDICTIONS

EVENTUM MECHANICS OF QUANTUM TRAJECTORIES: CONTINUAL MEASUREMENTS, QUANTUM PREDICTIONS AND FEEDBACK CONTROL VIACHESLAV P BELAVKIN Abstract. Quantum mechanical systems exhibit an inherently probabilistic on the basis of an independent-increment model for quantum noise and nondemolition causal- ity principle

Belavkin, Viacheslav P.

95

Quantum mechanics probes superspace

We study quantum mechanics in one space dimension in the stochastic formalism. We show that the partition function of the theory is, in fact, equivalent to that of a model, whose action is explicitly invariant (up to surface terms) under supersymmetry transformations--but whose invariance under the stochastic identities is not obvious, due to an apparent mismatch between fermions and bosons. The resolution of the riddle is that one "fermion" is a gauge artifact and, upon fixing the local, fermionic symmetry, called $\\kappa-$symmetry, we recover the stochastic partition function. The "fermions" do not propagate in the bulk, since their kinetic term is a total derivative. Their contribution to the action is through an ultra--local bilinear term, that may be exactly integrated out, as long as the superpotential has a unique minimum and we obtain a local action for the scalar. When the superpotential does not have a unique minimum, we use a Hubbard-Stratonovich transformation of the kinetic term to obtain an action in terms of the Fourier transform of the velocity, a kind of duality transformation. The classical particle thus moves in a medium of dipoles, that parametrize the quantum fluctuations and the classical trajectory $\\phi(\\tau)$, becomes a chiral superfield, $(\\phi(\\tau),\\psi_\\alpha(\\tau),F(\\tau))$, when quantum effects are taken into account. The observable superpartner of the scalar, however, is the fermion bilinear and thus, while supersymmetry may be realized, the observable partner excitations are not degenerate in mass. We compute the stochastic identities of the auxiliary field, using a lattice regularization of the equivalent "bosonic" action, for the case of a superpotential with a single minimum. We show that the lattice action can be expressed as an ultra--local functional of the auxiliary field, up to terms that vanish with the lattice spacing.

S. Nicolis

2014-05-05

96

Zitterbewegung in Quantum Mechanics

NASA Astrophysics Data System (ADS)

The possibility that zitterbewegung opens a window to particle substructure in quantum mechanics is explored by constructing a particle model with structural features inherent in the Dirac equation. This paper develops a self-contained dynamical model of the electron as a lightlike particle with helical zitterbewegung and electromagnetic interactions. The model admits periodic solutions with quantized energy, and the correct magnetic moment is generated by charge circulation. It attributes to the electron an electric dipole moment rotating with ultrahigh frequency, and the possibility of observing this directly as a resonance in electron channeling is analyzed in detail. Correspondence with the Dirac equation is discussed. A modification of the Dirac equation is suggested to incorporate the rotating dipole moment.

Hestenes, David

2010-01-01

97

The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can be represented in a Hilbert space, that a self-adjoint operator is associated to any observable, that the result of a measure must be the eigen value of the operator and appear with the usual probability. Furthermore an equivalent of the Wigner's theorem holds, which leads to the Schr\\"{o}dinger equation. These results are based on well known mathematics, and do not involve any specific hypothesis in Physics. They validate and explain the methods currently used, which are made simpler and safer, and open new developments. In the second edition of this paper important developments have been added about interacting systems and the transitions of phases.

Jean-Paul Metailié; Jean Claude Dutailly

2014-08-20

98

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

99

Supersymmetric Quantum Mechanics of Scattering

In the quantum mechanics of collision problems we must consider scattering states of the system. For these states, the wave functions do not remain in Hilbert space, but they are expressible in terms of generalized functions of a Gel'fand triplet. Supersymmetric quantum mechanics for dealing with the scattering states is here proposed.

Shimbori, T; Shimbori, Toshiki; Kobayashi, Tsunehiro

2001-01-01

100

Supersymmetric Quantum Mechanics of Scattering

In the quantum mechanics of collision problems we must consider scattering states of the system. For these states, the wave functions do not remain in Hilbert space, but they are expressible in terms of generalized functions of a Gel'fand triplet. Supersymmetric quantum mechanics for dealing with the scattering states is here proposed.

Toshiki Shimbori; Tsunehiro Kobayashi

2000-10-27

101

Supersymmetric quantum mechanics of scattering

In the quantum mechanics of collision problems we must consider scattering states of the system. For these states, the wave functions do not remain in Hilbert space, but they are expressible in terms of generalized functions of a Gel'fand triplet. Supersymmetric quantum mechanics for dealing with the scattering states is here proposed.

Toshiki Shimbori; Tsunehiro Kobayashi

2001-01-01

102

Quantum mechanism helps agents combat \\

Quantum strategies have been successfully applied to game theory for years.\\u000aHowever, as a reverse problem of game theory, the theory of mechanism design is\\u000aignored by physicists. In this paper, the theory of mechanism design is\\u000ageneralized to a quantum domain. The main result is that by virtue of a quantum\\u000amechanism, agents who satisfy a certain condition can

Haoyang Wu

2010-01-01

103

Comment on "Thermodynamics of quantum crystalline membranes"

NASA Astrophysics Data System (ADS)

Amorim et al. [Phys. Rev. B 89, 224307 (2014), 10.1103/PhysRevB.89.224307] reported the theoretical investigation of quantum crystalline membranes. In this Comment we dismiss the validity of their calculations based on a "natural" estimation of the ultraviolet divergent contributions into correlation functions. We claim that such calculations give qualitatively the wrong results.

Kats, E. I.; Lebedev, V. V.

2014-11-01

104

On the Quantum Correction For Thermodynamic Equilibrium

The probability of a configuration is given in classical theory by the Boltzmann formula exp [-VhT] where V is the potential energy of this configuration. For high temperatures this of course also holds in quantum theory. For lower temperatures, however, a correction term has to be introduced, which can be developed into a power series of h. The formula is

E. P. Wigner

1932-01-01

105

Classical and Quantum Mechanical Waves

NSDL National Science Digital Library

This web site consists of lecture notes in classical and quantum mechanical waves. The notes include the basics of classical waves including connections to mechanical oscillators, wave packets, and acoustic and electromagnetic waves. The final section outlines the key concepts of the quantum mechanical wave equation including probability and current, free and bound states, time dependent perturbation theory, and radiation. Visual Python and Maple animations are included for download.

Riley, Lewis

2006-07-22

106

Quantum Mechanics of the Einstein-Hopf Model.

ERIC Educational Resources Information Center

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

Milonni, P. W.

1981-01-01

107

An Introduction to Thermodynamics and Statistical Mechanics

NASA Astrophysics Data System (ADS)

Preface; Part I. Introduction: 1. Introduction; Part II. Small Systems: 2. Statistics for small systems; 3. Systems with many elements; Part III. Energy and the First Law: 4. Internal energy; 5. Interactions between systems; Part IV. States and the Second Law: 6. Internal energy and the number of accessible states; 7. Entropy and the second law; 8. Entropy and thermal interactions; Part V. Constraints: 9. Natural constraints; 10. Models; 11. Choice of variables; 12. Special processes; 13. Engines; 14. Diffusive interactions; Part VI. Classical Statistics: 15. Probabilities and microscopic behaviours; 16. Kinetic theory and transport processes in gases; 17. Magnetic properties of materials; 18. The partition function; Part VII. Quantum Statistics: 19. Introduction to quantum statistics; 20. Quantum gases; 21. Blackbody radiation; 22. The thermal properties of solids; 23. The electrical properties of materials; 24. Low temperatures and degenerate systems; Appendices; Further reading; Problem solutions; Index.

Stowe, Keith

2013-10-01

108

Quantum-Mechanical Model of Spacetime

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 field equation with a vanishing cosmological constant as a sort of thermodynamical equation of state of spacetime and matter fields. In the low temperature limit, where most black holes are assumed to be in the ground state, our model implies the Unruh and the Hawking effects, whereas in the high temperature limit we find, among other things, that black hole entropy depends logarithmically on the event horizon area, instead of being proportional to the area.

Jarmo Makela

2007-06-20

109

Quantum mechanics and the psyche

In this paper we apply the last developments of the theory of measurement in quantum mechanics to the phenomenon of consciousness\\u000a and especially to the awareness of unconscious components. Various models of measurement in quantum mechanics can be distinguished\\u000a by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness

G. Galli Carminati; F. Martin

2008-01-01

110

Thermodynamic Derivation of the Equilibrium Distribution Functions of Statistical Mechanics.

ERIC Educational Resources Information Center

Presents a simplified derivation of the equilibrium distribution functions. The derivation proceeds from the change in the Helmholtz free energy when a particle is added to a system of fixed temperature, volume, and chemical potential. The derivations show the relationship between statistical mechanics and macroscopic thermodynamics. (Author/GA)

Stoeckly, Beth

1979-01-01

111

Statistical Mechanical Proof of the Second Law of Thermodynamics based on Volume Entropy

NASA Astrophysics Data System (ADS)

As pointed out in [M. Campisi. Stud. Hist. Phil. M. P. 36 (2005) 275-290] the volume entropy (that is the logarithm of the volume of phase space enclosed by the constant energy hyper-surface) provides a good mechanical analogue of thermodynamic entropy because it satisfies the heat theorem and it is an adiabatic invariant. This property explains the ``equal'' sign in Clausius principle (Sf>=Si) in a purely mechanical way and suggests that the volume entropy might explain the ``larger than'' sign (i.e. the Law of Entropy Increase) if non adiabatic transformations were considered. Based on the principles of quantum mechanics here we prove that, provided the initial equilibrium satisfy the natural condition of decreasing ordering of probabilities, the expectation value of the volume entropy cannot decrease for arbitrary transformations performed by some external sources of work on a insulated system. This can be regarded as a rigorous quantum mechanical proof of the Second Law.

Campisi, Michele

2007-10-01

112

Work Cost of Thermal Operations in Quantum and Nano Thermodynamics

Adopting a resource theory framework of thermodynamics for quantum and nano systems pioneered by Janzing et al. [Int. J. Th. Phys. 39, 2717 (2000)], we formulate the cost in useful work of transforming one resource state into another as a linear program of convex optimization. This approach is based on the characterization of thermal quasiorder given by Janzing et al. and later by Horodecki and Oppenheim [Nat. Comm. 4, 2059 (2013)]. Both characterizations are related to an extended version of majorization studied by Ruch, Schranner, and Seligman under the name mixing distance [J. Chem. Phys. 69, 386 (1978)].

Joseph M. Renes

2014-02-14

113

An Introduction to Quantum Mechanics

NSDL National Science Digital Library

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

Hanlin, Heath

114

Quantum Mechanics: Fundamentals

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

A Whitaker

2004-01-01

115

NSDL National Science Digital Library

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

Galvez, Enrique; Holbrow, Charles

2005-04-16

116

Quantum Mechanics: Sum Over Paths

NSDL National Science Digital Library

Created by Edwin F. Taylor a former professor at the Department of Physics at the Massachusetts Institute of Technology, this material describes methods of presenting quantum mechanics using the path-integral formulation. Included are links to a paper and presentation outlining the method, software to simulate the path integrals, and student workbook materials. This course has been used for introducing quantum physics to high school teachers.

Taylor, Edwin F.

2009-05-26

117

Large scale quantum mechanical enzymology

for Physics were awarded to the predominant developers of the theory of quantum mechanics (QM). These laureates were Max Planck, Niels Bohr, Louis de Broglie, Werner Heisenberg, Erwin Schro¨dinger and Paul Dirac, in chronological order. In addition, Albert... Einstein’s significant contributions cannot go unmentioned. These theoretical insights laid the foundations for the quantum chemical approach that won Walter Kohn and John Pople the prize for Chemistry in 1998. Considering earlier works, Johannes Diderik...

Lever, Greg

2014-10-07

118

PT quantum mechanics - Recent results

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

119

Locality and Nonlinear Quantum Mechanics

Nonlinear modifications of quantum mechanics generically lead to nonlocal effects which violate relativistic causality. We study these effects using the functional Schrodinger equation for quantum fields and identify a type of nonlocality which causes nearly instantaneous entanglement of spacelike separated systems. We describe a simple example involving widely separated wave-packet (coherent) states, showing that nonlinearity in the Schrodinger evolution causes spacelike entanglement, even in free field theory.

Chiu Man Ho; Stephen D. H. Hsu

2015-01-09

120

Thermodynamics and Statistical Mechanics of Macromolecular Systems

NASA Astrophysics Data System (ADS)

Preface and outline; 1. Introduction; 2. Statistical mechanics: a modern review; 3. The complexity of minimalistic lattice models for protein folding; 4. Monte Carlo and chain growth methods for molecular simulations; 5. First insights to freezing and collapse of flexible polymers; 6. Crystallization of elastic polymers; 7. Structural phases of semiflexible polymers; 8. Generic tertiary folding properties of proteins in mesoscopic scales; 9. Protein folding channels and kinetics of two-state folding; 10. Inducing generic secondary structures by constraints; 11. Statistical analyses of aggregation processes; 12. Hierarchical nature of phase transitions; 13. Adsorption of polymers at solid substrates; 14. Hybrid protein-substrate interfaces; 15. Concluding remarks and outlook; Notes; References; Index.

Bachmann, Michael

2014-04-01

121

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

122

Quantum refrigerators and the third law of thermodynamics.

The rate of temperature decrease of a cooled quantum bath is studied as its temperature is reduced to absolute zero. The third law of thermodynamics is then quantified dynamically by evaluating the characteristic exponent ? of the cooling process dT(t)/dt?-T^{?} when approaching absolute zero, T?0. A continuous model of a quantum refrigerator is employed consisting of a working medium composed either by two coupled harmonic oscillators or two coupled two-level systems. The refrigerator is a nonlinear device merging three currents from three heat baths: a cold bath to be cooled, a hot bath as an entropy sink, and a driving bath which is the source of cooling power. A heat-driven refrigerator (absorption refrigerator) is compared to a power-driven refrigerator. When optimized, both cases lead to the same exponent ?, showing a lack of dependence on the form of the working medium and the characteristics of the drivers. The characteristic exponent is therefore determined by the properties of the cold reservoir and its interaction with the system. Two generic heat bath models are considered: a bath composed of harmonic oscillators and a bath composed of ideal Bose/Fermi gas. The restrictions on the interaction Hamiltonian imposed by the third law are discussed. In the Appendices, the theory of periodically driven open systems and its implication for thermodynamics are outlined. PMID:23005070

Levy, Amikam; Alicki, Robert; Kosloff, Ronnie

2012-06-01

123

We consider the cluster of problems raised by the relation between the notion of time, gravitational theory, quantum theory and thermodynamics; in particular, we address the problem of relating the "timelessness" of the hypothetical fundamental general covariant quantum field theory with the "evidence" of the flow of time. By using the algebraic formulation of quantum theory, we propose a unifying perspective on these problems, based on the hypothesis that in a generally covariant quantum theory the physical time-flow is not a universal property of the mechanical theory, but rather it is determined by the thermodynamical state of the system ("thermal time hypothesis"). We implement this hypothesis by using a key structural property of von Neumann algebras: the Tomita-Takesaki theorem, which allows to derive a time-flow, namely a one-parameter group of automorphisms of the observable algebra, from a generic thermal physical state. We study this time-flow, its classical limit, and we relate it to various characteristic theoretical facts, as the Unruh temperature and the Hawking radiation. We also point out the existence of a state-independent notion of "time", given by the canonical one-parameter subgroup of outer automorphisms provided by the Cocycle Radon-Nikodym theorem.

A. Connes; C. Rovelli

1994-06-14

124

Non-thermal quantum channels as a thermodynamical resource

Quantum thermodynamics can be understood as a resource theory, whereby thermal states are free and the only allowed operations are unitary transformations commuting with the total Hamiltonian of the system. Previous literature on the subject has just focused on transformations between different state resources, overlooking the fact that quantum operations which do not commute with the total energy also constitute a potentially valuable resource. In this Letter, given a number of non-thermal quantum channels, we study the problem of how to integrate them in a thermal engine so as to distill a maximum amount of work. We find that the distillable work is an additive function of the considered channels, computable for both finite dimensional quantum operations and bosonic channels. We apply our results to bound the amount of distillable work due to the natural non-thermal processes postulated in the Ghirardi-Rimini-Weber (GRW) collapse model. We find that, although GRW theory predicts the possibility to extract work from the vacuum at no cost, the power which a \\emph{collapse engine} could in principle generate is extremely low.

Miguel Navascués; Luis Pedro García-Pintos

2015-01-12

125

Status of the Fundamental Laws of Thermodynamics

We describe recent progress towards deriving the Fundamental Laws of thermodynamics (the 0th, 1st and 2nd Law) from nonequilibrium quantum statistical mechanics in simple, yet physically relevant models. Along the way, we clarify some basic thermodynamic notions and discuss various reversible and irreversible thermodynamic processes from the point of view of quantum statistical mechanics.

Walid K. Abou Salem; Juerg Froehlich

2006-04-27

126

Minkowski Space and Quantum Mechanics

NASA Astrophysics Data System (ADS)

A paradigm shift distinguishes general relativity from classical mechanics. In general relativity the energy-momentum tensor is the effective cause of the ontological space-time curvature and vice-versa, while in classical physics, the structure of space-time is treated as an accidental cause, serving only as a backdrop against which the laws of physics unfold. This split in turn is inherited by quantum mechanics, which is usually developed by changing classical (including special relativity) Hamiltonians into quantum wave equations.

O'Hara, Paul

127

BOOK REVIEW: Relativistic Quantum Mechanics

NASA Astrophysics Data System (ADS)

The aim of relativistic quantum mechanics is to describe the finer details of the structure of atoms and molecules, where relativistic effects become nonnegligible. It is a sort of intermediate realm, between the familiar nonrelativistic quantum mechanics and fully relativistic quantum field theory, and thus it lacks the simplicity and elegance of both. Yet it is a necessary tool, mostly for quantum chemists. Pilkuhn's book offers to this audience an up-to-date survey of these methods, which is quite welcome since most previous textbooks are at least ten years old. The point of view of the author is to start immediately in the relativistic domain, following the lead of Maxwell's equations rather than classical mechanics, and thus to treat the nonrelativistic version as an approximation. Thus Chapter 1 takes off from Maxwell's equations (in the noncovariant Coulomb gauge) and gradually derives the basic aspects of Quantum Mechanics in a rather pedestrian way (states and observables, Hilbert space, operators, quantum measurement, scattering,. Chapter 2 starts with the Lorentz transformations, then continues with the Pauli spin equation and the Dirac equation and some of their applications (notably the hydrogen atom). Chapter 3 is entitled `Quantum fields and particles', but falls short of treating quantum field theory properly: only creation/annihilation operators are considered, for a particle in a box. The emphasis is on two-electron states (the Pauli principle, the Foldy--Wouthuysen elimination of small components of Dirac spinors, Breit projection operators. Chapter 4 is devoted to scattering theory and the description of relativistic bound states. Chapter 5, finally, covers hyperfine interactions and radiative corrections. As we said above, relativistic quantum mechanics is by nature limited in scope and rather inelegant and Pilkuhn's book is no exception. The notation is often heavy (mostly noncovariant) and the mathematical level rather low. The central topic is the description of atoms and molecules, including relativistic effects. The author fulfils this program in a reasonable way and offers a valuable tool to the targeted audience. I am not overly enthusiastic about the end result, but I might be prejudiced. Clearly, going further would require the full power of quantum field theory, but this is clearly beyond the scope of the book.

Antoine, J.-P.

2004-01-01

128

In the framework of the quantum theory of spontaneous and low-energy induced fission, the nature of quantum and thermodynamical properties of a fissioning system is analyzed taking into account adiabatic and nonadiabatic modes of motion for different fission stages. It is shown that, owing to the influence of the Coriolis interaction, the states of the fissile nucleus and of primary fission products are cold and strongly nonequilibrium. The important role of superfluid and pairing nucleon-nucleon correlations for binary and ternary fission is demonstrated. The mechanism of pumping of high values of relative orbital momenta and spins of fission fragments for binary and ternary fission and the nonevaporation mechanism of formation of third particles for ternary fission are investigated. The anisotropies and P-odd, P-even, and T-odd asymmetries for angular distributions of fission products are analyzed.

Kadmensky, S. G. [Voronezh State University (Russian Federation)], E-mail: kadmensky@phys.vsu.ru

2007-09-15

129

Remarks on osmosis, quantum mechanics, and gravity

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

2011-01-01

130

Remarks on osmosis, quantum mechanics, and gravity

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.

Robert Carroll

2011-04-03

131

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

132

Quantum mechanics and brain uncertainty.

This paper argues that molecular governing structures (such as receptors, gating molecules, or ionic channels) which operate pervasively in the brain, often with small number particle systems (as, for example, at the surfaces of membranes, synaptic clefts, or macromolecules), may plausibly be vehicles for the transmutation of quantum mechanical fluctuations to normal-level neural signaling. PMID:17125159

Macgregor, Ronald J

2006-09-01

133

Nine formulations of Quantum Mechanics

NSDL National Science Digital Library

This article provides a comprehensive review of the various formulations of quantum mechanics. The article contains a brief description of each formulation, advantages/disadvantages, application notes, and recommended references for. Recommended references include textbooks using the formulation background information and influential publications.

Styer, Dan; Balkin, Miranda; Becker, Kathryn; Wotherspoon, Tim; Forth, Scott; Kramer, Mark

2005-04-16

134

PT-symmetric quantum mechanics

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

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

1999-01-01

135

The Grammatical Universe and the Laws of Thermodynamics and Quantum Entanglement

The universal nilpotent computational rewrite system (UNCRS) is shown to formalize an irreversible process of evolution in conformity with the First, Second and Third Laws of Thermodynamics, in terms of a single algebraic creation operator (ikE+ip+jm) which delivers the whole quantum mechanical language apparatus, where k, i, j are quaternions units and E, p, m are energy, momentum and rest mass. This nilpotent evolution describes 'a dynamic zero totality universe' in terms of its fermion states (each of which, by Pauli exclusion, is unique and nonzero), where, together with their boson interactions, these define physics at the fundamental level. (The UNCRS implies that the inseparability of objects and fields in the quantum universe is based on the fact that the only valid mathematical representations are all automorphisms of the universe itself, and that this is the mathematical meaning of quantum entanglement. It thus appears that the nilpotent fermion states are in fact what is called the splitting field in Quantum Mechanics of the Galois group which leads to the roots of the corresponding algebraic equation, and concerns in this case the alternating group of even permutations which are themselves automorphisms). In the nilpotent evolutionary process: (i) the Quantum Carnot Engine (QCE) extended model of thermodynamic irreversibility, consisting of a single heat bath of an ensemble of Standard Model elementary particles, retains a small amount of quantum coherence / entanglement, so as to constitute new emergent fermion states of matter, and (ii) the metric (E{sup 2}-p{sup 2}m{sup 2}) = 0 ensures the First Law of the conservation of energy operates at each nilpotent stage, so that (iii) prior to each creation (and implied corresponding annihilation / conserve operation), E and m can be postulated to constitute dark energy and matter respectively. It says that the natural language form of the rewrite grammar of the evolution consists of the well known precepts of the Laws of Thermodynamics, formalized by the UNCRS regress, so as to become (as UNCRS rewrites already published at CASYS), firstly the Quantum Laws of Physics in the form of the generalized Dirac equation and later at higher stages of QCE ensemble complexity, the Laws of Life in the form of Nature's (DNA / RNA genetic) Code and then subsequently those of Intelligence and Consciousness (Nature's Rules).

Marcer, Peter J. [55 rue Jean Jaures, 83600 Frejus, Var (France); Rowlands, Peter [Department of Physics, University of Liverpool, Oliver Lodge Laboratory, Oxford St, Liverpool, L69 7ZE (United Kingdom)

2010-11-24

136

Quantum Mechanics Of Consciousness

A phenomenological approach using the states of spin-like observables is developed to understand the nature of consciousness and the totality of experience. The three states of consciousness are taken to form the triplet of eigenstates of a spin-one entity and are derived as the triplet resulting from the composition of two spins by treating the subject and the object as interacting two-state, spin-half systems with external and internal projections. The state of deep sleep is analysed in the light of this phenomenological approach and a novel understanding of the status of the individual consciousness in this state is obtained. The resulting fourth state i.e. the singlet state is interpreted to correspond to the superconscious state of intuitive experience and is justified by invoking the concept of the universal consciousness as the underlying source of all individual states of experience. It is proposed that the individual experiences result from the operations of four individualizing observables which project out the individual from the universal. The one-to-one correspondence between the individual and the universal states of experience is brought out and their identity in the fourth state is established by showing that all individualizing quantum numbers become zero in this state leaving no trace of any individuality.

Rajat Kumar Pradhan

2009-07-28

137

Quantum Mechanics: Structures, Axioms and Paradoxes

Quantum Mechanics: Structures, Axioms and Paradoxes Diederik Aerts Center Leo Apostel, Brussels show that two of the traditional axioms of quantum ax- iomatics are not satisfied for these `in between., 1999, "Quantum Mechanics; Structures, Axioms and Paradoxes", in Quantum Structures and the Nature

Aerts, Diederik

138

EK424 THERMODYNAMICS AND STATISTICAL MECHANICS (Spring 2013) Thermodynamics is the study in order to take place? We will study the thermodynamics of two types of processes: mechanical, or the chemical conversion of glucose into useful work), and a good understanding of thermodynamics is essential

Vajda, Sandor

139

EK424 THERMODYNAMICS AND STATISTICAL MECHANICS (Fall 2013) Thermodynamics is the study in order to take place? We will study the thermodynamics of two types of processes: mechanical, or the chemical conversion of glucose into useful work), and a good understanding of thermodynamics is essential

Vajda, Sandor

140

Irreversible work and inner friction in quantum thermodynamic processes

We discuss the thermodynamics of closed quantum systems driven out of equilibrium by a change in a control parameter and undergoing a unitary process. We compare the work actually done on the system with the one that would be performed along ideal adiabatic and isothermal transformations. The comparison with the latter leads to the introduction of irreversible work, while that with the former leads to the introduction of inner friction. We show that these two quantities can be treated on equal footing, as both can be linked with the heat exchanged in thermalization processes and both can be expressed as relative entropies. Furthermore, we show that a specific fluctuation relation for the entropy production associated with the inner friction exists, which allows the inner friction to be written in terms of its cumulants.

F. Plastina; A. Alecce; T. J. G. Apollaro; G. Falcone; G. Francica; F. Galve; N. Lo Gullo; R. Zambrini

2014-07-24

141

Thermodynamic arrow of time of quantum projective measurements

NASA Astrophysics Data System (ADS)

We investigate a thermodynamic arrow associated with quantum projective measurements in terms of the Jensen-Shannon divergence between the probability distribution of energy change caused by the measurements and its time-reversal counterpart. Two physical quantities appear to govern the asymptotic values of the time asymmetry. For an initial equilibrium ensemble prepared at a high temperature, the energy fluctuations determine the convergence of the time asymmetry approaching zero. At low temperatures, the finite survival probability of the ground state limits the time asymmetry to be less than ln?2. We illustrate our results for a concrete system and discuss the fixed point of the time asymmetry in the limit of infinitely repeated projections.

Yi, Juyeon; Kim, Beom Jun

2013-07-01

142

Irreversible Work and Inner Friction in Quantum Thermodynamic Processes

NASA Astrophysics Data System (ADS)

We discuss the thermodynamics of closed quantum systems driven out of equilibrium by a change in a control parameter and undergoing a unitary process. We compare the work actually done on the system with the one that would be performed along ideal adiabatic and isothermal transformations. The comparison with the latter leads to the introduction of irreversible work, while that with the former leads to the introduction of inner friction. We show that these two quantities can be treated on an equal footing, as both can be linked with the heat exchanged in thermalization processes and both can be expressed as relative entropies. Furthermore, we show that a specific fluctuation relation for the entropy production associated with the inner friction exists, which allows the inner friction to be written in terms of its cumulants.

Plastina, F.; Alecce, A.; Apollaro, T. J. G.; Falcone, G.; Francica, G.; Galve, F.; Lo Gullo, N.; Zambrini, R.

2014-12-01

143

Irreversible work and inner friction in quantum thermodynamic processes.

We discuss the thermodynamics of closed quantum systems driven out of equilibrium by a change in a control parameter and undergoing a unitary process. We compare the work actually done on the system with the one that would be performed along ideal adiabatic and isothermal transformations. The comparison with the latter leads to the introduction of irreversible work, while that with the former leads to the introduction of inner friction. We show that these two quantities can be treated on an equal footing, as both can be linked with the heat exchanged in thermalization processes and both can be expressed as relative entropies. Furthermore, we show that a specific fluctuation relation for the entropy production associated with the inner friction exists, which allows the inner friction to be written in terms of its cumulants. PMID:25615295

Plastina, F; Alecce, A; Apollaro, T J G; Falcone, G; Francica, G; Galve, F; Lo Gullo, N; Zambrini, R

2014-12-31

144

NASA Astrophysics Data System (ADS)

The following dissertation is an account of my research in the Mandelshtam group at UC Irvine beginning in the Fall of 2006 and ending in the Summer of 2011. My general area of study falls within the realm of equilibrium quantum statistical mechanics, a discipline which attempts to relate molecular-scale properties to time averaged, macroscopic observables. The major tools used herein are the Variational Gaussian Wavepacket (VGW) approximation for quantum calculations, and Monte-Carlo methods, particularly parallel tempering, for global optimization and the prediction of equilibrium thermodynamic properties. Much of my work used these two methods to model both small and bulk systems at equilibrium where quantum effects are significant. All the systems considered are characterized by inter-molecular van der Waals forces, which are weak but significant electrostatic attractions between atoms and molecules and posses a 1/r6 dependence. The research herein begins at the microscopic level, starting with Lennard-Jones (LJ) clusters, then later shifts to the macroscopic for a study involving bulk para-hydrogen. For the LJ clusters the structural transitions induced by a changing deBoer parameter, ?, a measure of quantum delocalization of the constituent particles, are investigated over a range of cluster sizes, N. From the data a "phase" diagram as a function of ? and N is constructed, which depicts the structural motifs favored at different size and quantum parameter. Comparisons of the "quantum induced" structural transitions depicted in the latter are also made with temperature induced transitions and those caused by varying the range of the Morse potential. Following this, the structural properties of binary para-Hydrogen/ ortho-Deuterium clusters are investigated using the VGW approximation and Monte-Carlo methods within the GMIN framework. The latter uses the "Basin-Hopping" algorithm, which simplifies the potential energy landscape, and coupled with the VGW approximation, an efficient and viable method for predicting equilibrium quantum mechanical properties is demonstrated. In the next chapter my contribution to the numerical implementation of the Thermal Gaussian Molecular Dynamics (TGMD) method is discussed. Within TGMD, a mapping of a quantum system to a classical is performed by means of an effective Hamiltonian, H eff, which is computed within the VGW framework. Using the classical dynamical equations of motion with Heff, the properties of a quantum system can be modeled within a classical framework. After this, the bulk system of fluid para-Hydrogen is investigated using the VGW in the NPT ensemble in an attempt to derive the thermodynamic properties at the phase transition and construct the equation of state. The dissertation then concludes with a discussion on the adaptation of the VGW methodology to any molecular system.

Deckman, Jason

145

A quantum mechanical model of interference

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

146

Star Products for Relativistic Quantum Mechanics

The star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. We want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in the proper time formulation.

P. Henselder

2007-05-24

147

First Day Handout Phys 430: Quantum Mechanics

First Day Handout Phys 430: Quantum Mechanics (Dated: 18 August 2014) Meeting times: MWF 1:00-1:50 Room: Neckers 410 Text: "Introduction to Quantum Mechanics," 2nd Edition, by D. Griffiths. Instructor Interpretation (e) The Uncertainty Principle (f) Dirac Notation 4. Chapter 4: Quantum Mechanics in Three

Nickrent, Daniel L.

148

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Review of Quantum Mechanics In general, particles

149

On the interpretation of quantum mechanics

After a brief discussion of the reasons for the complete failure of a deterministic interpretation of quantum mechanics (§ 1)Niels Bohr's ideas on quantum mechanics are exposed. The importance of Bohr's idea on the necessity of combining the quantum-mechanical description of atomic objects with a classical description of the instruments is stressed (§ 2).It is pointed out, however, that the

V. A. Fock

1957-01-01

150

On the interpretation of quantum mechanics

After a brief discussion of the reasons for the complete failure of a deterministic interpretation of quantum mechanics (§ 1) Niels Bohr's ideas on quantum mechanics are exposed. The importance of Bohr's idea on the necessity of combining the quantum-mechanical description of atomic objects with a classical description of the instruments is stressed (§ 2). It is pointed out, however,

V. A. Fock

1957-01-01

151

Relativistic Quantum Mechanics and Field Theory

An accessible, comprehensive reference to modern quantum mechanics and field theory. In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics. Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field. With a strong emphasis

Franz Gross

1999-01-01

152

Nonlinear Boundaries in Quantum Mechanics

Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a linear boundary condition, but not both. Further analysis shows that non-linear boundaries for the ring restore gauge invariance but lead unexpectedly to eigenfunctions with a continuous eigenvalue spectrum, a discreet subset of which forms a Hilbert space with energy bands. This Hilbert space maintains the principle of superposition of eigenfunctions despite the nonlinearity. The momentum operator remains Hermitian. If physical reality requires gauge invariance, it would appear that quantum mechanics should incorporate these nonlinear boundary conditions.

Arthur Davidson

2011-06-22

153

The Brownian motion of a quantum particle in a harmonic confining potential and coupled to harmonic quantum thermal bath is exactly solvable. Though this system presents at high temperatures a pedagogic example to explain the laws of thermodynamics, it is shown that at low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. In physical terms, this happens when the cloud of bath modes around the particle starts to play a nontrivial role, namely, when the bath temperature T is smaller than the coupling energy. Indeed, equilibrium thermodynamics of the total system, particle plus bath, does not imply standard equilibrium thermodynamics for the particle itself at low T. Various formulations of the second law are found to be invalid at low T. First, the Clausius inequality can be violated, because heat can be extracted from the zero point energy of the cloud of bath modes. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the entropy production is partly negative. In this process the energy put on the particle does not relax monotonically, but oscillates between particle and bath, even in the limit of strong damping. Third, for nonadiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobility of the second kind, having one or several work extraction cycles, enter the realm of condensed matter physics. Fourth, it follows that the equivalence between different formulations of the second law (e.g., those by Clausius and Thomson) can be violated at low temperatures. These effects are the consequence of quantum entanglement in the presence of the slightly off-equilibrium nature of the thermal bath, and become important when the characteristic quantum time scale variant Planck's over 2pi /k(B)T is larger than or comparable to other time scales of the system. They show that there is no general consensus between standard thermodynamics and quantum mechanics. The known agreements occur only due to the weak coupling limit, which does not pertain to low temperatures. Experimental setups for testing the effects are discussed. PMID:12366179

Nieuwenhuizen, Th M; Allahverdyan, A E

2002-09-01

154

Sharpening the second law of thermodynamics with the quantum Bayes theorem

NASA Astrophysics Data System (ADS)

We prove a generalization of the classic Groenewold-Lindblad entropy inequality, combining decoherence and the quantum Bayes theorem into a simple unified picture where decoherence increases entropy while observation decreases it. This provides a rigorous quantum-mechanical version of the second law of thermodynamics, governing how the entropy of a system (the entropy of its density matrix, partial-traced over the environment and conditioned on what is known) evolves under general decoherence and observation. The powerful tool of spectral majorization enables both simple alternative proofs of the classic Lindblad and Holevo inequalities without using strong subadditivity, and also novel inequalities for decoherence and observation that hold not only for von Neumann entropy, but also for arbitrary concave entropies.

Gharibyan, Hrant; Tegmark, Max

2014-09-01

155

Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology

We investigate the origin of the arrow of time in quantum mechanics in the\\u000acontext of quantum cosmology. The ``Copenhagen'' quantum mechanics of measured\\u000asubsystems incorporates a fundamental arrow of time. Extending discussions of\\u000aAharonov, Bergmann and Lebovitz, Griffiths, and others we investigate a\\u000ageneralized quantum mechanics for cosmology that utilizes both an initial and a\\u000afinal density matrix to

Murray Gell-Mann; James B. Hartle

1993-01-01

156

Two dogmas about quantum mechanics

We argue that the intractable part of the measurement problem -- the 'big' measurement problem -- is a pseudo-problem that depends for its legitimacy on the acceptance of two dogmas. The first dogma is John Bell's assertion that measurement should never be introduced as a primitive process in a fundamental mechanical theory like classical or quantum mechanics, but should always be open to a complete analysis, in principle, of how the individual outcomes come about dynamically. The second dogma is the view that the quantum state has an ontological significance analogous to the significance of the classical state as the 'truthmaker' for propositions about the occurrence and non-occurrence of events, i.e., that the quantum state is a representation of physical reality. We show how both dogmas can be rejected in a realist information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. The Everettian, too, regards the 'big' measurement problem as a pseudo-problem, because the Everettian rejects the assumption that measurements have definite outcomes, in the sense that one particular outcome, as opposed to other possible outcomes, actually occurs in a quantum measurement process. By contrast with the Everettians, we accept that measurements have definite outcomes. By contrast with the Bohmians and the GRW 'collapse' theorists who add structure to the theory and propose dynamical solutions to the 'big' measurement problem, we take the problem to arise from the failure to see the significance of Hilbert space as a new kinematic framework for the physics of an indeterministic universe, in the sense that Hilbert space imposes kinematic (i.e., pre-dynamic) objective probabilistic constraints on correlations between events.

Jeffrey Bub; Itamar Pitowsky

2007-12-27

157

Topics in Callen's Thermodynamics and an Introduction to Thermostatistics Thermodynamics of Thermodynamics (1) Equilibrium states exist as function of (U,V,N) (2) Entropy S(U,V,N). If remove constraint; second order trans. 11. Nernst postulate 12. Summary of principles of thermodynamics 13. Materials

Collins, Gary S.

158

Quantum Mechanics in symmetry language

We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better understood in this view. In particular, the abstract concept of symmetry provides a basis-independent definition for observables. Moreover, we show that the apparent projection/collapse of the state as the final step of measurement or decoherence is the result of breaking of symmetries. This phenomenon is comparable with a phase transition by spontaneous symmetry breaking, and makes the process of decoherence and classicality a natural fate of complex systems consisting of many interacting subsystems. Additionally, we demonstrate that the property of state space as a vector space representing symmetries is more fundamental than being an abstract Hilbert space, and its $L2$ integrability can be obtained from the imposed condition of being a representation of a symmetry group and general properties of probability distributions.

Houri Ziaeepour

2014-09-17

159

Quantum Mechanics Beyond Hilbert Space

NASA Astrophysics Data System (ADS)

Going Beyond Hilbert Space Why? The Different Formalisms What Does One Obtain? The Mathematical Formalism Rigged Hilbert Spaces Scales and Lattices of Hilbert Spaces Partial Inner Product Spaces Operators on PIP-Spaces Application in Quantum Mechanics: The Fock-Bargmann Representation - Revisited A RHS of Entire Functions A LHS of Entire Functions Around ? Application in Scattering Theory RHS: Resonances, Gamow Vectors, Arrow of Time LHS: Integral Equations vs. Complex Scaling Conclusion

Antoine, J.-P.

160

Modern Undergraduate Quantum Mechanics Experiments

NSDL National Science Digital Library

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

Beck, Mark

2004-07-10

161

Continuum mechanics beyond the second law of thermodynamics.

The results established in contemporary statistical physics indicating that, on very small space and time scales, the entropy production rate may be negative, motivate a generalization of continuum mechanics. On account of the fluctuation theorem, it is recognized that the evolution of entropy at a material point is stochastically (not deterministically) conditioned by the past history, with an increasing trend of average entropy production. Hence, the axiom of Clausius-Duhem inequality is replaced by a submartingale model, which, by the Doob decomposition theorem, allows classification of thermomechanical processes into four types depending on whether they are conservative or not and/or conventional continuum mechanical or not. Stochastic generalizations of thermomechanics are given in the vein of either thermodynamic orthogonality or primitive thermodynamics, with explicit models formulated for Newtonian fluids with, respectively, parabolic or hyperbolic heat conduction. Several random field models of the martingale component, possibly including spatial fractal and Hurst effects, are proposed. The violations of the second law are relevant in those situations in continuum mechanics where very small spatial and temporal scales are involved. As an example, we study an acceleration wavefront of nanoscale thickness which randomly encounters regions in the medium characterized by a negative viscosity coefficient. PMID:25383037

Ostoja-Starzewski, M; Malyarenko, A

2014-11-01

162

Game Theory in Categorical Quantum Mechanics

Categorical quantum mechanics, which examines quantum theory via dagger-compact closed categories, gives satisfying high-level explanations to the quantum information procedures such as Bell-type entanglement or complementary observables (\\cite{AC}, \\cite{Co}, \\cite{Co2}). Inspired by the fact that Quantum Game Theory can be seen as branch of quantum information, we express Quantum Game Theory procedures using the topological semantics provided by Categorical Quantum Mechanics. We also investigate Bayesian Games with correlation from this novel point of view while considering the connection between Bayesian game theory and Bell non-locality investigated recently by Brunner and Linden \\cite{BL}.

Ali Nabi Duman

2014-05-17

163

I. BASICS OF STATISTICAL MECHANICS AND QUANTUM MECHANICS Markus Holzmann

I. BASICS OF STATISTICAL MECHANICS AND QUANTUM MECHANICS Markus Holzmann LPMMC, Maison de Magist://www.lptl.jussieu.fr/users/markus/cours.html (Dated: March 1, 2010) We introduce basic concepts of classical and quantum statistical mechanics the basic concepts of statistical mechanics: partition function, free energy, density operators. As examples

164

Quantum mechanical light harvesting mechanisms in photosynthesis

NASA Astrophysics Data System (ADS)

More than 10 million billion photons of light strike a leaf each second. Incredibly, almost every red-coloured photon is captured by chlorophyll pigments and initiates steps to plant growth. Last year we reported that marine algae use quantum mechanics in order to optimize photosynthesis [1], a process essential to its survival. These and other insights from the natural world promise to revolutionize our ability to harness the power of the sun. In a recent review [2] we described the principles learned from studies of various natural antenna complexes and suggested how to utilize that knowledge to shape future technologies. We forecast the need to develop ways to direct and regulate excitation energy flow using molecular organizations that facilitate feedback and control--not easy given that the energy is only stored for a billionth of a second. In this presentation I will describe new results that explain the observation and meaning of quantum-coherent energy transfer. [4pt] [1] Elisabetta Collini, Cathy Y. Wong, Krystyna E. Wilk, Paul M. G. Curmi, Paul Brumer, and Gregory D. Scholes, ``Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature'' Nature 463, 644-648 (2010).[0pt] [2] Gregory D. Scholes, Graham R. Fleming, Alexandra Olaya-Castro and Rienk van Grondelle, ``Lessons from nature about solar light harvesting'' Nature Chem. 3, 763-774 (2011).

Scholes, Gregory

2012-02-01

165

Quantum mechanical effects from deformation theory

We consider deformations of quantum mechanical operators by using the novel construction tool of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a role. Furthermore, a quantum plane can be defined by using the deformation techniques. This in turn gives an experimentally verifiable effect.

Much, A. [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)] [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)

2014-02-15

166

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

167

Treating Time Travel Quantum Mechanically

The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilising the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their non-linearity and time travel paradoxes. In particular, the "equivalent circuit model"---which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory---is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of new theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features---such as time travel paradoxes, the ability to distinguish non-orthogonal states with certainty, and the ability to clone or delete arbitrary pure states---that are present with D-CTCs and P-CTCs. The problems with non-linear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.

John-Mark A. Allen

2014-01-20

168

Thermodynamics and Statistical Mechanics of Materials Instructor: Prof. Uday B. Pal

MS/ME 505 Thermodynamics and Statistical Mechanics of Materials Instructor: Prof. Uday B. Pal Notes and Handouts: Â· Required Text: Introduction to the Thermodynamics of Materials by David R. Gaskell, Prentice Hall Â· Reference Texts: 1. C.H.P. Lupis, Chemical Thermodynamics of Materials, Prentice

169

A quantum mechanical model of "dark matter"

The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.

V. V. Belokurov; E. T. Shavgulidze

2014-03-28

170

Propagators in polymer quantum mechanics

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

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

2013-09-15

171

Friction incorporates the close connection between classical mechanics in irreversible thermodynamics. The translation to a quantum mechanical foundation is not trivial and requires a generalization of the Lagrange function. A change to electromagnetic circuits appears to more adequate, since the electric analogue (Ohms law) is related to scatter of electrons at lattice vibrations.

Ulmer, W

2015-01-01

172

Bananaworld: Quantum Mechanics for Primates

This is intended to be a serious paper, in spite of the title. The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, since a theory of information is essentially a theory of probabilistic correlations. To make this clear, it suffices to consider measurements of two binary-valued observables, x with outcomes a = 0 or 1, performed by Alice in a region A, and y with outcomes b = 0 or 1 performed by Bob in a separated region B --or, to emphasize the banality of the phenomena, two ways of peeling a banana, resulting in one of two tastes. The imagined bananas of Bananaworld are non-standard, with operational or phenomenal probabilistic correlations for peelings and tastes that lie outside the polytope of local correlations. The 'no go' theorems tell us that we can't shoe-horn these correlations into a classical correlation polytope, which has the structure of a simplex, by supposing that something has been left out of the story, without giving up fundamental principles that define what we mean by a physical system. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are shown to be generic features of correlations that lie outside the local correlation polytope. As far as the conceptual problems are concerned, we might as well talk about bananas.

Jeffrey Bub

2013-01-08

173

Principles of a 2nd Quantum Mechanics

A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this representation as a reference-and-imbedding-structure, the foundations of an intelligible reconstruction of the Hilbert-Dirac formulation of Quantum Mechanics is developed. Inside this reconstruction the measurement problem as well as the other major problems raised by the quantum mechanical formalism, dissolve.

Mioara Mugur-Schächter

2014-10-23

174

Heisenberg and the Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.

Camilleri, Kristian

2011-09-01

175

Heisenberg and the Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.

Camilleri, Kristian

2009-02-01

176

Quantum and Thermodynamic Properties of Spontaneous and Low-Energy Induced Fission of Nuclei

It is shown that A. Bohr's concept of transition fission states can be matched with the properties of Coriolis interaction if an axisymmetric fissile nucleus near the scission point remains cold despite a nonadiabatic character of nuclear collective deformation motion. The quantum and thermodynamic properties of various stages of binary and ternary fission after the descent of a fissile nucleus from the outer saddle point are studied within quantum-mechanical fission theory. It is shown that two-particle nucleon-nucleon correlations--in particular, superfluid correlations--play an important role in the formation of fission products and in the classification of fission transitions. The distributions of thermalized primary fission fragments with respect to spins and their projections onto the symmetry axis of the fissile nucleus and fission fragments are constructed, these distributions determining the properties of prompt neutrons and gamma rays emitted by these fragments. A new nonevaporation mechanism of third-particle production in ternary fission is proposed. This mechanism involves transitions of third particles from the cluster states of the fissile-nucleus neck to high-energy states under effects of the shake-off type that are due to the nonadiabatic character of nuclear collective deformation motion.

Kadmensky, S.G. [Voronezh State University, Universitetskaya pl. 1, Voronezh, 394693 (Russian Federation)

2005-12-01

177

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

178

Quantum Monte Carlo Simulation of Nanoscale MgH2 Cluster Thermodynamics

Quantum Monte Carlo Simulation of Nanoscale MgH2 Cluster Thermodynamics Zhigang Wu,,Â§ Mark D-7 el; Nel ) number of electrons) severely limits application to larger systems. The quantum Monte Carlo simulations are performed using the fixed-node diffusion Monte Carlo7 (DMC) method with the QWalk code.8

Wu, Zhigang

179

Maxwell's Demon Assisted Thermodynamic Cycle in Superconducting Quantum Circuits H. T. Quan,1,2

Maxwell's Demon Assisted Thermodynamic Cycle in Superconducting Quantum Circuits H. T. Quan,1,2 Y; published 30 October 2006) We study a new quantum heat engine (QHE), which is assisted by a Maxwell's demon by the Maxwell demon. We derive the positive-work condition and operation efficiency of this composite QHE. Using

Nori, Franco

180

Quantum Statistical Mechanics. III. Equilibrium Probability

Given are a first principles derivation and formulation of the probabilistic concepts that underly equilibrium quantum statistical mechanics. The transition to non-equilibrium probability is traversed briefly.

Phil Attard

2014-04-10

181

This work has considered the intrinsic influence of bond energy on the macroscopic, thermodynamic, and mechanical properties of crystalline materials. A general criterion is proposed to evaluate the properties of nanocrystalline materials. The interrelation between the thermodynamic and mechanical properties of nanomaterials is presented and the relationship between the variation of these properties and the size of the nanomaterials is explained. The results of our work agree well with thermodynamics, molecular dynamics simulations, and experimental results. This method is of significance in investigating the size effects of nanomaterials and provides a new approach for studying their thermodynamic and mechanical properties. PMID:25288913

2014-01-01

182

Mechanical AGN feedback: controlling the thermodynamical evolution of elliptical galaxies

NASA Astrophysics Data System (ADS)

A fundamental gap in the current understanding of galaxies concerns the thermodynamical evolution of ordinary, baryonic matter. On the one hand, radiative emission drastically decreases the thermal energy content of the interstellar plasma (ISM), inducing a slow cooling flow towards the centre. On the other hand, the active galactic nucleus (AGN) struggles to prevent the runaway cooling catastrophe, injecting huge amount of energy into the ISM. The present study intends to investigate thoroughly the role of mechanical AGN feedback in (isolated or massive) elliptical galaxies, extending and completing the mass range of tested cosmic environments. Our previously successful feedback models in galaxy clusters and groups demonstrated that AGN outflows, self-regulated by cold gas accretion, are able to quench the cooling flow properly without destroying the cool core. Via three-dimensional hydrodynamic simulations (FLASH 3.3), also including stellar evolution, we show that massive mechanical AGN outflows can indeed solve the cooling-flow problem for the entire life of the galaxy, at the same time reproducing typical observational features and constraints such as buoyant underdense bubbles, elliptical shock cocoons, sonic ripples, dredge-up of metals, subsonic turbulence and extended filamentary or nuclear cold gas. In order to avoid overheating and totally emptying the isolated galaxy, the frequent mechanical AGN feedback should be less powerful and efficient (?˜ 10-4) compared with the heating required for more massive and bound ellipticals surrounded by the intragroup medium (?˜ 10-3).

Gaspari, M.; Brighenti, F.; Temi, P.

2012-07-01

183

Quantum Fluctuations and Thermodynamic Processes in the Presence of Closed Timelike Curves

NASA Astrophysics Data System (ADS)

A closed timelike curve (CTC) is a closed loop in spacetime whose tangent vector is everywhere timelike. A spacetime which contains CTC's will allow time travel. One of these spacetimes is Grant space. It can be constructed from Minkowski space by imposing periodic boundary conditions in spatial directions and making the boundaries move toward each other. If Hawking's chronology protection conjecture is correct, there must be a physical mechanism preventing the formation of CTC's. Currently the most promising candidate for the chronology protection mechanism is the back reaction of the metric to quantum vacuum fluctuations. In this thesis the quantum fluctuations for a massive scalar field, a self-interacting field, and for a field at nonzero temperature are calculated in Grant space. The stress-energy tensor is found to remain finite everywhere in Grant space for the massive scalar field with sufficiently large field mass. Otherwise it diverges on chronology horizons like the stress-energy tensor for a massless scalar field. If CTC's exist they will have profound effects on physical processes. Causality can be protected even in the presence of CTC's if the self-consistency condition is imposed on all processes. Simple classical thermodynamic processes of a box filled with ideal gas in the presence of CTC's are studied. If a system of boxes is closed, its state does not change as it travels through a region of spacetime with CTC's. But if the system is open, the final state will depend on the interaction with the environment. The second law of thermodynamics is shown to hold for both closed and open systems. A similar problem is investigated at a statistical level for a gas consisting of multiple selves of a single particle in a spacetime with CTC's.

Tanaka, Tsunefumi

1997-10-01

184

Bohmian Mechanics and the Quantum Revolution

This is a review-essay on ``Speakable and Unspeakable in Quantum Mechanics'' by John Bell and ``The Undivided Universe: An Ontological Interpretation of Quantum Mechanics'' by David Bohm and Basil Hiley. The views of these authors concerning the character of quantum theory and quantum reality---and, in particular, their approaches to the issues of nonlocality, the possibility of hidden variables, and the nature of and desiderata for a satisfactory scientific explanation of quantum phenomena---are contrasted, with each other and with the orthodox approach to these issues.

Sheldon Goldstein

1995-12-26

185

Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is “designed” by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of “classicalizing” behavior in the approach to thermal equilibrium are briefly considered.

Barnes, George L. [Department of Chemistry and Biochemistry, Siena College, Loudonville, New York 12211 (United States)] [Department of Chemistry and Biochemistry, Siena College, Loudonville, New York 12211 (United States); Kellman, Michael E. [Department of Chemistry and Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403 (United States)] [Department of Chemistry and Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403 (United States)

2013-12-07

186

Quantum mechanics: A new chapter?

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

Werner A. Hofer

2012-09-05

187

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

188

Testing quantum mechanics: a statistical approach

NASA Astrophysics Data System (ADS)

As experiments continue to push the quantum-classical boundary using increasingly complex dynamical systems, the interpretation of experimental data becomes more and more challenging: when the observations are noisy, indirect, and limited, how can we be sure that we are observing quantum behavior? This tutorial highlights some of the difficulties in such experimental tests of quantum mechanics, using optomechanics as the central example, and discusses how the issues can be resolved using techniques from statistics and insights from quantum information theory.

Tsang, Mankei

2013-12-01

189

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Relativity (Why it makes sense) Thursday, May 7

190

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Friday, May 15, 2009 #12;Quark Summary mesons and baryons

191

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Scattering Summary the best way to study

192

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics and the Strong Force Symmetry and Unification String Theory: a different kind of unification Extra Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Review of Relativity The laws of physics

193

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification that is naturally solved by string theory Strings vibrating in a variety of ways give rise to particles of different

194

From Quantum Mechanics to String Theory

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification Friday, June 19, 2009 #12;String Theory Origins We introduced string theory as a possible solution to our

195

Uncertainty and complementarity in axiomatic quantum mechanics

In this work an investigation of the uncertainty principle and the complementarity principle is carried through. A study of the physical content of these principles and their representation in the conventional Hilbert space formulation of quantum mechanics forms a natural starting point for this analysis. Thereafter is presented more general axiomatic framework for quantum mechanics, namely, a probability function formulation

Pekka J. Lahti

1980-01-01

196

PERSPECTIVE Quantum Mechanics of Black Holes

PERSPECTIVE Quantum Mechanics of Black Holes Edward Witten The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived

197

In this paper, we describe the analysis of the thermodynamic properties of cryogenic hydrogen using classical molecular dynamics (MD) and path integral MD (PIMD) method to understand the effects of the quantum nature of hydrogen molecules. We performed constant NVE MD simulations across a wide density–temperature region to establish an equation of state (EOS). Moreover, the quantum effect on the difference of molecular mechanism of pressure–volume–temperature relationship was addressed. The EOS was derived based on the classical mechanism idea only using the MD simulation results. Simulation results were compared with each MD method and experimental data. As a result, it was confirmed that although the EOS on the basis of classical MD cannot reproduce the experimental data of saturation property of hydrogen in the high-density region, the EOS on the basis of PIMD well reproduces those thermodynamic properties of hydrogen. Moreover, it was clarified that taking quantum effects into account makes the repulsion force larger and the potential well shallower. Because of this mechanism, the intermolecular interaction of hydrogen molecules diminishes and the virial pressure increases.

Nagashima, H., E-mail: nagashima@nanoint.ifs.tohoku.ac.jp [School of Engineering, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577 (Japan); Tsuda, S. [Department of Mechanical Systems Engineering, Shinshu University, Nagano 380-8553 (Japan)] [Department of Mechanical Systems Engineering, Shinshu University, Nagano 380-8553 (Japan); Tsuboi, N. [Department of Mechanical and Control Engineering, Kyushu Institute of Technology, Kitakyushu 804-8550 (Japan)] [Department of Mechanical and Control Engineering, Kyushu Institute of Technology, Kitakyushu 804-8550 (Japan); Koshi, M. [Graduate School of Environment and Information Science, Yokohama National University, Yokohama 240-8501 (Japan)] [Graduate School of Environment and Information Science, Yokohama National University, Yokohama 240-8501 (Japan); Hayashi, K. A. [Department of Mechanical Engineering, Aoyama Gakuin University, Sagamihara 229-8558 (Japan)] [Department of Mechanical Engineering, Aoyama Gakuin University, Sagamihara 229-8558 (Japan); Tokumasu, T. [Institute of Fluid Science, Tohoku University, Sendai 980-8577 (Japan)] [Institute of Fluid Science, Tohoku University, Sendai 980-8577 (Japan)

2014-04-07

198

Polymer quantum mechanics and its continuum limit

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

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

2007-08-15

199

Electronic, mechanical, and thermodynamic properties of americium dioxide

NASA Astrophysics Data System (ADS)

By performing density functional theory (DFT) +U calculations, we systematically study the electronic, mechanical, tensile, and thermodynamic properties of AmO2. It is found that the chemical bonding character in AmO2 is similar to that in PuO2, with smaller charge transfer and stronger covalent interactions between americium and oxygen atoms. The stress-strain relationship of AmO2 is examined along the three low-index directions, showing that the [1 0 0] and [1 1 1] directions are the strongest and weakest tensile directions, respectively, but the theoretical tensile strengths of AmO2 are smaller than those of PuO2. The phonon dispersion curves of AmO2 are calculated and the heat capacities as well as lattice expansion curve are subsequently determined. The lattice thermal conductivity of AmO2 is further evaluated and compared with attainable experiments. Our present work integrally reveals various physical properties of AmO2 and can be referenced for technological applications of AmO2 based materials.

Lu, Yong; Yang, Yu; Zheng, Fawei; Wang, Bao-Tian; Zhang, Ping

2013-10-01

200

Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology

We investigate the origin of the arrow of time in quantum mechanics in the context of quantum cosmology. The ``Copenhagen'' quantum mechanics of measured subsystems incorporates a fundamental arrow of time. Extending discussions of Aharonov, Bergmann and Lebovitz, Griffiths, and others we investigate a generalized quantum mechanics for cosmology that utilizes both an initial and a final density matrix to give a time-neutral formulation without a fundamental arrow of time. Time asymmetries can arise for particular universes from differences between their initial and final conditions. Theories for both would be a goal of quantum cosmology. A special initial condition and a final condition of indifference would be sufficient to explain the observed time asymmetries of the universe. In this essay we ask under what circumstances a completely time symmetric universe, with T-symmetric initial and final condition, could be consistent with the time asymmetries of the limited domain of our experience. We discuss the ap...

Gell-Mann, Murray; Gell-Mann, Murray; Hartle, James B.

1993-01-01

201

A new computational method is proposed for ab initio quantum-mechanical\\/molecular-mechanical (QM\\/MM) molecular dynamics (MD) which is limited to time-independent thermodynamic analysis. The idea is to use the mass scaling method combined with multiple-time-scale (MTS) algorithm and an approximate QM\\/MM Hamiltonian derived from the first-order Rayleigh–Schrödinger perturbation theory (PT) in which the electronic polarization is neglected as a first approximation. If

Motoyuki Shiga; Masanori Tachikawa

2007-01-01

202

Topological Strings from Quantum Mechanics

We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized theta function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P2, local P1xP1 and local F1. In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.

Alba Grassi; Yasuyuki Hatsuda; Marcos Marino

2014-11-27

203

Operational Axioms for Quantum Mechanics

The mathematical formulation of Quantum Mechanics in terms of complex Hilbert space is derived for finite dimensions, starting from a general definition of physical experiment and from five simple Postulates concerning experimental accessibility and simplicity. For the infinite dimensional case, on the other hand, a C*-algebra representation of physical transformations is derived, starting from just four of the five Postulates via a Gelfand-Naimark-Segal (GNS) construction. The present paper simplifies and sharpens the previous derivation in Ref. [1]. The main ingredient of the axiomatization is the postulated existence of faithful states that allows one to calibrate the experimental apparatus. Such notion is at the basis of the operational definitions of the scalar product and of the transposed of a physical transformation. What is new in the present paper with respect to Ref. [1], is the operational deduction of an involution corresponding to the complex-conjugation for effects, whose extension to transformations allows to define the adjoint of a transformation when the extension is composition-preserving. The existence of such composition-preserving extension among possible extensions is analyzed.

D'Ariano, Giacomo Mauro [QUIT Group, Dipartimento di Fisica 'A. Volta', via Bassi 6, I-27100 Pavia (Italy); Department of Electrical and Computer Engineering, Northwestern University, Evanston, IL 60208 (United States)

2007-02-21

204

Operational Axioms for Quantum Mechanics

The mathematical formulation of Quantum Mechanics in terms of complex Hilbert space is derived for finite dimensions, starting from a general definition of "physical experiment" and from five simple Postulates concerning "experimental accessibility and simplicity". For the infinite dimensional case, on the other hand, a C*-algebra representation of physical transformations is derived, starting from just four of the five Postulates via a Gelfand-Naimark-Segal (GNS) construction. The present paper simplifies and sharpens the previous derivation in version 1. The main ingredient of the axiomatization is the postulated existence of "faithful states" that allows one to calibrate the experimental apparatus. Such notion is at the basis of the operational definitions of the scalar product and of the "transposed" of a physical transformation. What is new in the present paper with respect to quant-ph/0603011 is the operational deduction of an involution corresponding to the "complex-conjugation" for effects, whose extension to transformations allows to define the "adjoint" of a transformation when the extension is composition-preserving.

Giacomo Mauro D'Ariano

2006-11-08

205

Kinetic potentials in quantum mechanics

NASA Astrophysics Data System (ADS)

Suppose that the Hamiltonian H=-?+vf(r) represents the energy of a particle which moves in an attractive central potential and obeys nonrelativistic quantum mechanics. The discrete eigenvalues Enl=Fnl(v) of H may be expressed as a Legendre transformation Fnl(v)=mins?0(s+vf¯nl(s)), n=1,2,3,..., l=0,1,2,..., where the ``kinetic potentials'' f¯nl(s) associated with f(r) are defined by f¯nl(s) =infDnl sup??Dnl, ???=1 ? ?(r) f ([?,-??)/s]1/2r)?(r)d3r, and Dnl is an n-dimensional subspace of L2(R3) labeled by Ylm(?,?), m=0, and contained in the domain D(H) of H. If the potential has the form f(r)=?Ni=1 g(i)( f(i)(r)) then in many interesting cases it turns out that the corresponding kinetic potentials can be closely approximated by ?Ni=1 g(i)( f¯nl(i)(s)). This nice behavior of the kinetic potentials leads to a constructive global approximation theory for Schrödinger eigenvalues. As an illustration, detailed recipes are provided for arbitrary linear combinations of power-law potentials and the log potential. For the linear plus Coulomb potential and the quartic anharmonic oscillator the approximate eigenvalues are compared to accurate values found by numerical integration.

Hall, Richard L.

1984-09-01

206

Quantum mechanical studies of lincosamides.

Lincosamides are a class of antibiotics used both in clinical and veterinary practice for a wide range of pathogens. This group of drugs inhibits the activity of the bacterial ribosome by binding to the 23S RNA of the large ribosomal subunit and blocking protein synthesis. Currently, three X-ray structures of the ribosome in complex with clindamycin are available in the Protein Data Bank, which reveal that there are two distinct conformations of the pyrrolidinyl propyl group of the bound clindamycin. In this work, we used quantum mechanical methods to investigate the probable conformations of clindamycin in order to explain the two binding modes in the ribosomal 23S RNA. We studied three lincosamide antibiotics: clindamycin, lincomycin, and pirlimycin at the B3LYP level with the 6-31G** basis set. The focus of our work was to connect the conformational landscape and electron densities of the two clindamycin conformers found experimentally with their physicochemical properties. For both functional conformers, we applied natural bond orbital (NBO) analysis and the atoms in molecules (AIM) theory, and calculated the NMR parameters. Based on the results obtained, we were able to show that the structure with the intramolecular hydrogen bond C=O…H-O is the most stable conformer of clindamycin. The charge transfer between the pyrrolidine-derivative ring and the six-atom sugar (methylthiolincosamide), which are linked via an amide bond, was found to be the dominant factor influencing the high stability of this conformer. PMID:22116607

Kulczycka-Mierzejewska, Katarzyna; Trylska, Joanna; Sadlej, Joanna

2012-06-01

207

Comment on Consistent Interpretation of Quantum Mechanics Using Quantum Trajectories

Recently, Griffiths presented a generalization of the consistent history approach to quantum mechanics. I can easily construct all possible complete families satisfying Griffiths' "noninterference conditions". Since only trivial families exist one may conclude that Griffiths' proposal has not got farther than the ordinary theory of quantum measurement.

Lajos Diosi

1993-04-27

208

Quantum mechanical wavepacket transport in quantum cascade laser structures

We present a viewpoint of the transport process in quantum cascade laser structures in which spatial transport of charge through the structure is a property of coherent quantum mechanical wave functions. In contrast, scattering processes redistribute particles in energy and momentum but do not directly cause spatial motion of charge.

S.-C. Lee; F. Banit; M. Woerner; A. Wacker

2006-01-01

209

Canonical distribution and incompleteness of quantum mechanics

The paper discusses the physical groundlessness of the models used for the derivation of canonical distribution and provides the experimental data demonstrating the incompleteness of quantum mechanics. The possibility of using statistical ensembles is presented as a consequence of the existence of probabilistic processes which are not accounted for by quantum mechanics. The paper provides a new analytical derivation of canonical distribution for macrosystems which takes into account subquantum processes. The paper discusses the possibility of the experimental study of a probability which is beyond quantum mechanics.

V. A. Skrebnev

2014-05-05

210

Playing Games with Quantum Mechanics

We present a perspective on quantum games that focuses on the physical aspects of the quantities that are used to implement a game. If a game is to be played, it has to be played with objects and actions that have some physical existence. We call such games playable. By focusing on the notion of playability for games we can more clearly see the distinction between classical and quantum games and tackle the thorny issue of what it means to quantize a game. The approach we take can more properly be thought of as gaming the quantum rather than quantizing a game and we find that in this perspective we can think of a complete quantum game, for a given set of preferences, as representing a single family of quantum games with many different playable versions. The versions of Quantum Prisoners Dilemma presented in the literature can therefore be thought of specific instances of the single family of Quantum Prisoner's Dilemma with respect to a particular measurement. The conditions for equilibrium are given for playable quantum games both in terms of expected outcomes and a geometric approach. We discuss how any quantum game can be simulated with a classical game played with classical coins as far as the strategy selections and expected outcomes are concerned.

Simon J. D. Phoenix; Faisal Shah Khan

2012-02-21

211

Visual Quantum Mechanics: Online Interactive Programs

NSDL National Science Digital Library

The Visual Quantum Mechanics project, from the Physics Education Group of Kansas State University's Department of Physics, develops innovative ways to "introduce quantum physics to high school and college students who do not have a background in modern physics or higher level math." Funded by the National Science Foundation, this resource for educators provides interactive computer visualizations and animations that introduce quantum mechanics. The interactive programs (which require Shockwave) include a spectroscopy lab suite, a probability illustrator, an energy band creator, quantum tunneling, a color creator (a Java version is also available), a wave function sketcher, a wave packet explorer, an energy diagram explorer, a diffraction suite, and a hydrogen spectroscopy program. These online demonstrations should prove to be excellent visual, hands-on teaching aids when introducing concepts involving quantum mechanics. Users can download Shockwave at the site.

212

Strange Bedfellows: Quantum Mechanics and Data Mining

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

213

Strange Bedfellows: Quantum Mechanics and Data Mining

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

Marvin Weinstein

2009-11-03

214

On the Gravitization of Quantum Mechanics 1: Quantum State Reduction

NASA Astrophysics Data System (ADS)

This paper argues that the case for "gravitizing" quantum theory is at least as strong as that for quantizing gravity. Accordingly, the principles of general relativity must influence, and actually change, the very formalism of quantum mechanics. Most particularly, an "Einsteinian", rather than a "Newtonian" treatment of the gravitational field should be adopted, in a quantum system, in order that the principle of equivalence be fully respected. This leads to an expectation that quantum superpositions of states involving a significant mass displacement should have a finite lifetime, in accordance with a proposal previously put forward by Diósi and the author.

Penrose, Roger

2014-05-01

215

Quantum-Mechanical Model of Spacetime

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

216

Quantum Mechanics and the Generalized Uncertainty Principle

The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.

Jang Young Bang; Micheal S. Berger

2006-11-30

217

Quantum mechanics and the generalized uncertainty principle

The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.

Bang, Jang Young; Berger, Micheal S. [Physics Department, Indiana University, Bloomington, Indiana 47405 (United States)

2006-12-15

218

Quantum mechanics as electrodynamics of curvilinear waves

The suggested theory is the new quantum mechanics (QM) interpretation.The\\u000aresearch proves that QM represents the electrodynamics of the curvilinear\\u000aclosed (non-linear) waves. It is entirely according to the modern\\u000ainterpretation and explains the particularities and the results of the quantum\\u000afield theory.

Alexander G. Kyriakos

2002-01-01

219

Space time symmetry in quantum mechanics

New prescription to treat position and time equally in quantum mechanics is presented. Using this prescription, we could successfully derive some interesting formulae such as time-of-arrival for a free particle and quantum tunneling formula. The physical interpretation will be discussed.

Zinkoo Yun

2014-02-26

220

The Compton effect: Transition to quantum mechanics

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

R. H. Stuewer

2000-01-01

221

Quantum Semiotics: A Sign Language for Quantum Mechanics

Semiotics is the language of signs which has been used effectively in various disciplines of human scientific endeavor. It gives a beautiful and rich structure of language to express the basic tenets of any scientific discipline. In this article we attempt to develop from first principles such an axiomatic structure of semiotics for Quantum Mechanics. This would be a further enrichment to the already existing well understood mathematical structure of Quantum Mechanics but may give new insights and understanding to the theory and may help understand more lucidly the fundamentality of Nature which Quantum Theory attempts to explain.

Prashant

2006-01-01

222

Supersymmetric q-deformed quantum mechanics

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

223

Lecture Notes in Quantum Mechanics Doron Cohen

formula Â· Fermi golden rule Â· Markovian master equations Â· Cross section / Born Â· The adiabatic equation Â· Spherical geometry, phase shifts Â· Cross section, optical theorem, resonances Quantum mechanics in practice

Cohen, Doron

224

Fundamental Quantum Mechanics--A Graphic Presentation

ERIC Educational Resources Information Center

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

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

1977-01-01

225

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

226

Stochastic Models of Quantum Mechanics - A Perspective

A subjective survey of stochastic models of quantum mechanics is given along with a discussion of some key radiative processes, the clues they offer, and the difficulties they pose for this program. An electromagnetic basis for deriving quantum mechanics is advocated, and various possibilities are considered. It is argued that only non-local or non-causal theories are likely to be a successful basis for such a derivation.

Mark P. Davidson

2006-10-06

227

Quantum correction to thermodynamical entropy of black hole

The entropy of a black hole can differ from a quarter of the area of the horizon because of quantum corrections. The correction is related to the contribution to the Euclidean functional integral from quantum fluctuations but is not simply equal to the correction to the effective action. A (2+1) dimensional rotating black hole is explicitly considered.

A. Ghosh; P. Mitra

1997-06-17

228

Explanation of the Gibbs paradox within the framework of quantum thermodynamics

NASA Astrophysics Data System (ADS)

The issue of the Gibbs paradox is that when considering mixing of two gases within classical thermodynamics, the entropy of mixing appears to be a discontinuous function of the difference between the gases: it is finite for whatever small difference, but vanishes for identical gases. The resolution offered in the literature, with help of quantum mixing entropy, was later shown to be unsatisfactory precisely where it sought to resolve the paradox. Macroscopic thermodynamics, classical or quantum, is unsuitable for explaining the paradox, since it does not deal explicitly with the difference between the gases. The proper approach employs quantum thermodynamics, which deals with finite quantum systems coupled to a large bath and a macroscopic work source. Within quantum thermodynamics, entropy generally loses its dominant place and the target of the paradox is naturally shifted to a decrease of the maximally available work before and after mixing (mixing ergotropy). In contrast to entropy this is an unambiguous quantity. For almost identical gases the mixing ergotropy continuously goes to zero, thus resolving the paradox. In this approach the concept of “difference between the gases” gets a clear operational meaning related to the possibilities of controlling the involved quantum states. Difficulties which prevent resolutions of the paradox in its entropic formulation do not arise here. The mixing ergotropy has several counterintuitive features. It can increase when less precise operations are allowed. In the quantum situation (in contrast to the classical one) the mixing ergotropy can also increase when decreasing the degree of mixing between the gases or when decreasing their distinguishability. These points go against a direct association of physical irreversibility with lack of information.

Allahverdyan, A. E.; Nieuwenhuizen, Th. M.

2006-06-01

229

Simple New Axioms for Quantum Mechanics

The space P of pure states of any physical system, classical or quantum, is identified as a Poisson space with a transition probability. The latter is a function p: PxP -> [0,1]; in addition, a Poisson bracket is defined for functions on P. These two structures are connected through unitarity. Classical and quantum mechanics are each characterized by a simple axiom on the transition probability p. Unitarity then determines the Poisson bracket of quantum mechanics up to a multiplicative constant (identified with Planck's constant). Superselection rules are naturally incorporated.

N. P. Landsman

1996-04-10

230

Testing foundations of quantum mechanics with photons

The foundational ideas of quantum mechanics continue to give rise to counterintuitive theories and physical effects that are in conflict with a classical description of Nature. Experiments with light at the single photon level have historically been at the forefront of tests of fundamental quantum theory and new developments in photonics engineering continue to enable new experiments. Here we review recent photonic experiments to test two foundational themes in quantum mechanics: wave-particle duality, central to recent complementarity and delayed-choice experiments; and Bell nonlocality where recent theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different photonics experiments.

Peter Shadbolt; Jonathan C. F. Matthews; Anthony Laing; Jeremy L. O'Brien

2015-01-15

231

Projection evolution in quantum mechanics

We propose a model of time evolution of quantum objects which unites the unitary evolution and the measurement procedures. The model allows to treat the time on equal footing with other dynamical variables.

A. Gozdz; M. Pietrow; M. Debicki

2005-08-08

232

Thermodynamics of Quantum Ultra-cold Neutron Gas under Gravity of The Earth

The stored ultra-cold neutrons have been developed. A high density ultra-cold neutron gas has been recently produced by using the nuclear spallation method. We investigate the thermodynamic properties of the quantum ultra-cold neutron gas in the Earth's gravitational field. We find that the quantum effects increase temperature dependence of the chemical potential and the internal energy in the low temperature region. The density distribution of quantum ultra-cold neutron gas is modified by the Earth's gravitational field.

Hiromi Kaneko; Akihiro Tohsaki; Atsushi Hosaka

2012-05-02

233

Modal Interpretations of Quantum Mechanics and Relativity: A Reconsideration

Two of the main interpretative problems in quantum mechanics are the so-called measurement problem and the question of the compatibility of quantum mechanics with relativity theory. Modal interpretations of quantum mechanics were designed to solve both of these problems. They are no-collapse (typically) indeterministic interpretations of quantum mechanics that supplement the orthodox state description of physical systems by a set

Joseph Berkovitz; Meir Hemmo

2005-01-01

234

NASA Astrophysics Data System (ADS)

In structures made up of alternating superconducting and ferromagnet layers (S/F/S heterostructures), it is known that the macroscopic quantum wave function of the ground state changes its phase difference across the F layer from 0 to ? under certain temperature and geometrical conditions, hence the name "0-?" for this crossover. We present here a joint experimental and theoretical demonstration that 0-? is a true thermodynamic phase transition. Microwave measurements of the temperature dependence of the London penetration depth in Nb /Pd0.84Ni0.16/Nb trilayers reveal a sudden, unusual decrease of the density of the superconducting condensate (square modulus of the macroscopic quantum wave function) with decreasing temperature, which is predicted by the theory here developed as a transition from the 0 state to the ? state. Our result for the jump of the amplitude of the order parameter is a thermodynamic manifestation of such a temperature-driven quantum transition.

Pompeo, N.; Torokhtii, K.; Cirillo, C.; Samokhvalov, A. V.; Ilyina, E. A.; Attanasio, C.; Buzdin, A. I.; Silva, E.

2014-08-01

235

Symmetry and the thermodynamics of currents in open quantum systems

Symmetry is a powerful concept in physics, and its recent application to understand nonequilibrium behavior is providing deep insights and groundbreaking exact results. Here we show how to harness symmetry to control transport and statistics in open quantum systems. Such control is enabled by a first-order-type dynamic phase transition in current statistics and the associated coexistence of different transport channels (or nonequilibrium steady states) classified by symmetry. Microreversibility then ensues, via the Gallavotti-Cohen fluctuation theorem, a twin dynamic phase transition for rare current fluctuations. Interestingly, the symmetry present in the initial state is spontaneously broken at the fluctuating level, where the quantum system selects the symmetry sector that maximally facilitates a given fluctuation. We illustrate these results in a qubit network model motivated by the problem of coherent energy harvesting in photosynthetic complexes, and introduce the concept of a symmetry-controlled quantum thermal switch, suggesting symmetry-based design strategies for quantum devices with controllable transport properties.

Daniel Manzano; Pablo I. Hurtado

2014-09-25

236

Symmetry and the thermodynamics of currents in open quantum systems

NASA Astrophysics Data System (ADS)

Symmetry is a powerful concept in physics, and its recent application to understand nonequilibrium behavior is providing deep insights and groundbreaking exact results. Here we show how to harness symmetry to control transport and statistics in open quantum systems. Such control is enabled by a first-order-type dynamic phase transition in current statistics and the associated coexistence of different transport channels (or nonequilibrium steady states) classified by symmetry. Microreversibility then ensues, via the Gallavotti-Cohen fluctuation theorem, a twin dynamic phase transition for rare current fluctuations. Interestingly, the symmetry present in the initial state is spontaneously broken at the fluctuating level, where the quantum system selects the symmetry sector that maximally facilitates a given fluctuation. We illustrate these results in a qubit network model motivated by the problem of coherent energy harvesting in photosynthetic complexes, and introduce the concept of a symmetry-controlled quantum thermal switch, suggesting symmetry-based design strategies for quantum devices with controllable transport properties.

Manzano, Daniel; Hurtado, Pablo I.

2014-09-01

237

Statistical mechanics of confined quantum particles

We develop statistical mechanics and thermodynamics of Bose and Fermi systems in relativistic harmonic oscillator (RHO) confining potential, which may be applicable in quark gluon plasma (QGP), astrophysics, Bose-Einstein condensation (BEC), condensed matter physics etc. Detailed study of QGP system is carried out and compared with lattice results. Further, as an application, our equation of state (EoS) of QGP is used to study compact stars like quark star.

Vishnu M. Bannur; K. M. Udayanandan

2006-02-02

238

Quantum ballistic evolution in quantum mechanics: Application to quantum computers

Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single-step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators T is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e., motion restricted to a collection of nonintersecting or distinct

Paul Benioff

1996-01-01

239

NASA Astrophysics Data System (ADS)

We illustrate recent results concerning the validity of the work fluctuation theorem in open quantum systems (Campisi et al 2009 Phys. Rev. Lett. 102 210401), by applying them to a solvable model of an open quantum system. The central role played by the thermodynamic partition function of the open quantum system, a two-level fluctuator with a strong quantum nondemolition coupling to a harmonic oscillator, is elucidated. The corresponding quantum Hamiltonian of mean force is evaluated explicitly. We study the thermodynamic entropy and the corresponding specific heat of this open system as a function of temperature and coupling strength and show that both may assume negative values at nonzero low temperatures.

Campisi, Michele; Talkner, Peter; Hänggi, Peter

2009-10-01

240

Quantum Mechanics and the Principle of Least Radix Economy

A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this concept in a unified way. The principle reinterprets and generalizes the principle of least action yielding two classes of physical solutions: least action paths and quantum wavefunctions. A new physical foundation of the Hilbert space of quantum mechanics is then accomplished and it is used to derive the Schr\\"odinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new (pre-geometrical) foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann's principle of classical statistical thermodynamics. A new expression for a general (path-dependent) nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics.

Vladimir Garcia-Morales

2015-01-08

241

Quantum mechanics as "space-time statistical mechanics"?

In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time configurations. It is argued that this could perhaps be accomplished by giving up the assumption that the objective ``state'' of a system is independent of a future measurement performed on the system. This idea is then applied in an example of quantum state estimation on a qubit system.

Anders Månsson

2005-01-24

242

Weak measurements in quantum mechanics

The article recapitulates the concept of weak measurement in its broader sense encapsulating the trade between asymptotically weak measurement precision and asymptotically large measurement statistics. Essential applications in time-continuous measurement and in postselected measurement are presented both in classical and in quantum contexts. We discuss the anomalous quantum weak value in postselected measurement. We concentrate on the general mathematical and physical aspects of weak measurements and we do not expand on their interpretation. Particular applications, even most familiar ones, are not subject of the article which was written for Elsevier's Encyclopedia of Mathematical Physics.

Lajos Diosi

2005-05-10

243

Notes on Quantum Mechanics and Consciousness

There have lately been a variety of attempts to connect, or even explain, if not in fact, reduce human consciousness to quantum mechanical processes. Such attempts tend to draw a sharp and fundamental distinction between the role of consciousness in classical mechanics, and on the other hand, in quantum mechanics, with an insistence on the assumed exceptional character of the latter. What is strangely missed, however, is the role of human consciousness as such in the very discovery or creation of both of these physical theories. And this a priori role is far more important than all the possible a posteriori interplays between consciousness and the mentioned two theories of physics, interplays which may happen during one or another specific experiment, measurement, and so on. In this regard it is suggested that the specific features human consciousness may exhibit during interactions with quantum mechanical systems may as well have other explanations which do not appear to be less plausible, or less well founded.

Elemer E Rosinger

2005-08-13

244

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

245

We studied the energetics of the closed-ring mechanism of the acid-catalysed dehydration of D-fructose to 5-hydroxymethylfurfural (HMF) by carrying out canonical ensemble free-energy calculations using bias-sampling, hybrid Quantum Mechanics/Molecular Mechanics Molecular Dynamics simulations with explicit water solvent at 363 K. The quantum mechanical calculations are performed at the PM3 theory level. We find that the reaction proceeds via intramolecular proton and hydride transfers. Solvent dynamics effects are analysed, and we show that the activation energy for the hydride transfers is due to re-organization of the polar solvent environment. We also find that in some instances intramolecular proton transfer is facilitated by mediating water, whereas in others the presence of quantum mechanical water has no effect. From a micro-kinetic point of view, we find that the rate-determining step of the reaction involves a hydride transfer prior to the third dehydration step, requiring an activation free energy of 31.8 kcal/mol, and the respective rate is found in good agreement with reported experimental values in zeolites. Thermodynamically, the reaction is exothermic by ?F=20.5kcal/mol.

Caratzoulas, S.; Vlachos, Dion G.

2011-01-01

246

BOOK REVIEWS: Quantum Mechanics: Fundamentals

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

Kurt Gottfri; Tung-Mow Yan

2004-01-01

247

Quantum Mechanics and Algorithmic Randomness

A long sequence of tosses of a classical coin produces an apparently random bit string, but classical randomness is an illusion: the algorithmic information content of a classically-generated bit string lies almost entirely in the description of initial conditions. This letter presents a simple argument that, by contrast, a sequence of bits produced by tossing a quantum coin is, almost

Ulvi Yurtsever

1998-01-01

248

NASA Astrophysics Data System (ADS)

A fast and accurate Quantum Mechanics/Molecular Mechanics method is described for thermodynamic simulation of solutes (or active sites in flexible molecules) in polar environments. The solute is described quantum mechanically and is held fixed during averaging over solvent configurations, which are described by Molecular Mechanics. Quantum calculations during simulation are replaced by the evaluation of the response of the solute to the long range electric field of the solvent, using precalculated generalized electric moments and polarizabilities. This results in huge decrease of computational time without affecting the accuracy of the QM/MM results. Implementation in a Monte Carlo program accelerated the simulations of guanine and the phenylalanine dipeptide in TIP3P water by over four orders of magnitude. Polarizability is essential for accuracy. Its inclusion decreases the average signed energy error and its standard deviation from 5.69 to 0.003 and 1.22 to 0.013 kcal/mol, respectively, for the dipeptide. Hyperpolarizability contributions are insignificant.

Janowski, Tomasz; Wolinski, Krzysztof; Pulay, Peter

2012-03-01

249

Zeno Dynamics in Quantum Statistical Mechanics

We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time behaviour of the dynamics. Examples of quantum spin systems show that this condition can be effectively applied to quantum statistical mechanical models. Further, we derive an explicit form of the Zeno generator, and use it to construct Gibbs equilibrium states for the Zeno dynamics. As a concrete example, we consider the X-Y model, for which we show that a frequent measurement at a microscopic level, e.g. a single lattice site, can produce a macroscopic effect in changing the global equilibrium.

Andreas U. Schmidt

2002-07-11

250

Testing the limits of quantum mechanical superpositions

Quantum physics has intrigued scientists and philosophers alike, because it challenges our notions of reality and locality--concepts that we have grown to rely on in our macroscopic world. It is an intriguing open question whether the linearity of quantum mechanics extends into the macroscopic domain. Scientific progress over the last decades inspires hope that this debate may be decided by table-top experiments.

Markus Arndt; Klaus Hornberger

2014-10-01

251

. ?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

252

On Time. 6b: Quantum Mechanical Time

The existence of small amounts of advanced radiation, or a tilt in the arrow of time, makes the basic equations of physics mixed-type functional differential equations. The novel features of such equations point to a microphysical structure of time. This corresponds to a change of logic at the microphysical level. We show that the resulting logic is a quantum logic. This provides a natural and rigorous explanation of quantum interference. This structured-time interpretation of quantum mechanics is briefly compared with various other interpretations of q.m.

C. K. Raju

2008-08-09

253

Optimal guidance law in quantum mechanics

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

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

2013-11-15

254

Multichannel framework for singular quantum mechanics

A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant (“asymptotic”) observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances. -- Highlights: •A multichannel framework is proposed for singular quantum mechanics and analogues. •The framework unifies several established approaches for singular potentials. •Singular points are treated as new scattering channels. •Nonunitary asymptotic behavior is subsumed in a unitary multichannel S-matrix. •Conformal quantum mechanics and the inverse quartic potential are highlighted.

Camblong, Horacio E., E-mail: camblong@usfca.edu [Department of Physics and Astronomy, University of San Francisco, San Francisco, CA 94117-1080 (United States); Epele, Luis N., E-mail: epele@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Fanchiotti, Huner, E-mail: huner@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina)] [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); García Canal, Carlos A., E-mail: garcia@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Ordóñez, Carlos R., E-mail: ordonez@uh.edu [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States)

2014-01-15

255

Timeless path integral for relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of a timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all possible paths in the constraint surface specified by the (relativistic) Hamiltonian constraint, and each path contributes with a phase identical to the classical action divided by ?. The timeless path integral manifests the timeless feature as it is completely independent of the parametrization for paths. For the special case that the Hamiltonian constraint is a quadratic polynomial in momenta, the transition amplitude admits the timeless Feynman's path integral over the (relativistic) configuration space. Meanwhile, the difference between relativistic quantum mechanics and conventional nonrelativistic (with time) quantum mechanics is elaborated on in light of the timeless path integral.

Chiou, Dah-Wei

2013-06-01

256

Two basic Uncertainty Relations in Quantum Mechanics

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

257

First-Person Plural Quantum Mechanics

Doing justice to quantum mechanics calls for a deeper examination of the relations between our experience, its objects, and its subjects than either third-person interpretations or the first-person singular interpretation of the QBist permit. The metaphysical space opened by Bohr's employment of the "Kantian wedge" between the objective world, about which we can communicate, and the world "in itself" allows quantum mechanics to unfold its metaphysical potential. This in turn makes it possible to go a long way towards bridging the epistemological gap between the empirical and transcendental conceptions of reality.

Ulrich Mohrhoff

2014-10-22

258

Equivariant Localization for Supersymmetric Quantum Mechanics

We apply equivariant localization to supersymmetric quantum mechanics and show that the partition function localizes on the instantons of the theory. Our construction of equivariant cohomology for SUSY quantum mechanics is different than the ones that already exist in the literature. A hidden bosonic symmetry is made explicit and the supersymmetry is extended. New bosonic symmetry is the square of the new fermionic symmetry. The D term is now the parameter of the bosonic symmetry. This construction provides us with an equivariant complex together with a Cartan differential and makes the use of localization principle possible.

Levent Akant

2005-05-26

259

The local approach to quantum transport may violate the second law of thermodynamics

NASA Astrophysics Data System (ADS)

Clausius statement of the second law of thermodynamics reads: Heat will flow spontaneously from a hot to cold reservoir. This statement should hold for transport of energy through a quantum network composed of small subsystems each coupled to a heat reservoir. When the coupling between nodes is small, it seems reasonable to construct a local master equation for each node in contact with the local reservoir. The energy transport through the network is evaluated by calculating the energy flux after the individual nodes are coupled. We show by analyzing the most simple network composed of two quantum nodes coupled to a hot and cold reservoir, that the local description can result in heat flowing from cold to hot reservoirs, even in the limit of vanishing coupling between the nodes. A global derivation of the master equation which prediagonalizes the total network Hamiltonian and within this framework derives the master equation, is always consistent with the second law of thermodynamics.

Levy, Amikam; Kosloff, Ronnie

2014-07-01

260

NASA Astrophysics Data System (ADS)

We have systematically studied the thermodynamic properties of a two-dimensional half-filled SU (2 N ) Hubbard model on a square lattice by using the determinant quantum Monte Carlo method. The entropy-temperature relation, the isoentropy curve, and the probability distribution of the on-site occupation number are calculated in both SU(4) and SU(6) cases, which exhibit prominent features of the Pomeranchuk effect. We analyze these thermodynamic behaviors based on energy scales in the density and spin channels. In the density channel, the interaction strength that marks the crossover from the weak to strong interaction regimes increases with the number of fermion components. In the spin channel, increasing the number of fermion components enhances quantum spin fluctuations, which is shown in the simulations of uniform spin susceptibilities and antiferromagnetic structure factors.

Zhou, Zhichao; Cai, Zi; Wu, Congjun; Wang, Yu

2014-12-01

261

A thermodynamic framework for damage mechanics is proposed. The damage evolution function uses entropy as a damage metric. A damage-coupled viscoplastic model with kinematic and isotropic hardening is implemented in a commercial finite element code to simulate the thermo-mechanical behavior of eutectic solder interconnectsin micro electronics packaging. The damage, asan internal state variable, is coupled witha unified viscoplastic constitutive model

Cemal Basaran; Hong Tang

2002-01-01

262

Thermodynamics of quantum jump trajectories in systems driven by classical fluctuations

The large-deviation method can be used to study the measurement trajectories of open quantum systems. For optical arrangements this formalism allows to describe the long time properties of the (non-equilibrium) photon counting statistics in the context of a (equilibrium) thermodynamic approach defined in terms of dynamical phases and transitions between them in the trajectory space [J.P. Garrahan and I. Lesanovsky, Phys. Rev. Lett. 104, 160601 (2010)]. In this paper, we study the thermodynamic approach for fluorescent systems coupled to complex reservoirs that induce stochastic fluctuations in their dynamical parameters. In a fast modulation limit the thermodynamics corresponds to that of a Markovian two-level system. In a slow modulation limit, the thermodynamic properties are equivalent to those of a finite system that in an infinite-size limit is characterized by a first-order transition. The dynamical phases correspond to different intensity regimes, while the size of the system is measured by the transition rate of the bath fluctuations. As a function of a dimensionless intensive variable, the first and second derivative of the thermodynamic potential develop an abrupt change and a narrow peak respectively. Their scaling properties are consistent with a double-Gaussian probability distribution of the associated extensive variable.

Adrian A. Budini

2010-12-03

263

A new introductory quantum mechanics curriculum

NASA Astrophysics Data System (ADS)

The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum-mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of the interpretive aspects of quantum mechanics and quantum information theory. This paper gives an overview of the resources available from the IOP website. The core text includes around 80 articles which are co-authored by leading experts, arranged in themes, and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is included in the resource. Solutions to activities are available to instructors. The resources can be used in a variety of ways, from being supplemental to existing courses to forming a complete programme.

Kohnle, Antje; Bozhinova, Inna; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth

2014-01-01

264

Thermodynamic limits to the efficiency of solar energy conversion by quantum devices

NASA Technical Reports Server (NTRS)

The second law of thermodynamics imposes a strict limitation to the energy converted from direct solar radiation to useful work by a quantum device. This limitation requires that the amount of energy converted to useful work (energy in any form other than heat) can be no greater than the change in free energy of the radiation fields. Futhermore, in any real energy conversion device, not all of this available free energy in the radiation field can be converted to work because of basic limitations inherent in the device itself. A thermodynamic analysis of solar energy conversion by a completely general prototypical quantum device is presented. This device is completely described by two parameters, its operating temperature T sub R and the energy threshold of its absorption spectrum. An expression for the maximum thermodynamic efficiency of a quantum solar converter was derived in terms of these two parameters and the incident radiation spectrum. Efficiency curves for assumed solar spectral irradiance corresponding to air mass zero and air mass 1.5 are presented.

Buoncristiani, A. M.; Byvik, C. E.; Smith, B. T.

1981-01-01

265

From Cbits to Qbits: Teaching computer scientists quantum mechanics

NSDL National Science Digital Library

In this article, a strategy is suggested for teaching mathematically literate students, with no background in physics, just enough quantum mechanics for them to understand and develop algorithms in quantum computation and quantum information theory.

Mermin, N. D.

2004-04-29

266

Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics

NASA Astrophysics Data System (ADS)

A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level...

Grössing, Gerhard

2015-10-01

267

Quantum statistical mechanics, L-series, Anabelian Geometry

Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Adem Lectures, Mexico City, January 2011 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12 Mechanics, L-series and Anabelian Geometry, arXiv:1009.0736 Matilde Marcolli Quantum statistical mechanics

Marcolli, Matilde

268

Although time measurements are routinely performed in laboratories, their theoretical description is still an open problem. Correspondingly, the status of the energy-time uncertainty relation is unsettled. In the first part of this work the necessity of positive operator valued measures (POVM) as descriptions of every quantum experiment is reviewed, as well as the suggestive role played by the probability current in time measurements. Furthermore, it is shown that no POVM exists, which approximately agrees with the probability current on a very natural set of wave functions; nevertheless, the choice of the set is crucial, and on more restrictive sets the probability current does provide a good arrival time prediction. Some ideas to experimentally detect quantum effects in time measurements are discussed. In the second part of the work the energy-time uncertainty relation is considered, in particular for a model of alpha decay for which the variance of the energy can be calculated explicitly, and the variance of time can be estimated. This estimate is tight for systems with long lifetimes, in which case the uncertainty relation is shown to be satisfied. Also the linewidth-lifetime relation is shown to hold, but contrary to the common expectation, it is found that the two relations behave independently, and therefore it is not possible to interpret one as a consequence of the other. To perform the mentioned analysis quantitative scattering estimates are necessary. To this end, bounds of the form $\\|1_Re^{-iHt}\\psi\\|_2^2 \\leq C t^{-3}$ have been derived, where $\\psi$ denotes the initial state, $H$ the Hamiltonian, $R$ a positive constant, and $C$ is explicitly known. As intermediate step, bounds on the derivatives of the $S$-matrix in the form $\\|1_K S^{(n)}\\|_\\infty \\leq C_{n,K} $ have been established, with $n=1,2,3$, and the constants $C_{n,K}$ explicitly known.

Nicola Vona

2014-03-11

269

Open Source Physics: 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

2008-06-02

270

Quantum mechanics and the time travel paradox

The closed causal chains arising from backward time travel do not lead to paradoxes if they are self consistent. This raises the question as to how physics ensures that only self-consistent loops are possible. We show that, for one particular case at least, the condition of self consistency is ensured by the interference of quantum mechanical amplitudes associated with the loop. If this can be applied to all loops then we have a mechanism by which inconsistent loops eliminate themselves.

David T. Pegg

2005-06-17

271

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

272

Quantum Mechanics Studies of Cellobiose Conformations

Technology Transfer Automated Retrieval System (TEKTRAN)

Three regions of the Phi,Psi space of cellobiose were analyzed with quantum mechanics. A central region, in which most crystal structures are found, was covered by a 9 x 9 grid of 20° increments of Phi and Psi. Besides these 81 constrained minimizations, we studied two central sub-regions and two re...

273

Is Quantum Mechanics needed to explain consciousness ?

In this short comment to a recent contribution by E. Manousakis [1] it is argued that the reported agreement between the measured time evolution of conscious states during binocular rivalry and predictions derived from quantum mechanical formalisms does not require any direct effect of QM. The recursive consumption analysis process in the Ouroboros Model can yield the same behavior.

Knud Thomsen

2007-11-13

274

Vlasov hydrodynamics of a quantum mechanical model

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

275

Quantum mechanical model for Maya Blue

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

276

A Quantum Mechanical Model of Spherical Supermembranes

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

277

Comparison of Classical and Quantum Mechanical Uncertainties.

ERIC Educational Resources Information Center

Comparisons are made for the particle-in-a-box, the harmonic oscillator, and the one-electron atom. A classical uncertainty principle is derived and compared with its quantum-mechanical counterpart. The results are discussed in terms of the statistical interpretation of the uncertainty principle. (Author/BB)

Peslak, John, Jr.

1979-01-01

278

Neutron Interferometry: Lessons in Experimental Quantum Mechanics

The first successful operation of a perfect crystal neutron interferometer by Rauch, Treimer and Bonse (1974) in Vienna opened up new vistas; intricate quantum mechanical concepts that could only be dealt with in thought experiments during the Einstein-Bohr era, now became accessible to direct tests in the laboratory. In the following decade, Helmut Rauch and co-workers implemented interferometric verifications of

2001-01-01

279

Octonionic Quantum Mechanics and Complex Geometry

The use of complex geometry allows us to obtain a consistent formulation of octonionic quantum mechanics (OQM). In our octonionic formulation we solve the hermiticity problem and define an appropriate momentum operator within OQM. The nonextendability of the completeness relation and the norm conservation is also discussed in details.

Stefano De Leo; Khaled Abdel-Khalek

1996-09-03

280

Quantum mechanics with explicit time dependence

We investigate quantum mechanical Hamiltonians with explicit time dependence. We find a class of models in which an analogue of the time-independent Schrödinger equation exists. Among the models in this class is a new exactly soluble model, the harmonic oscillator with frequency inversely proportional to time.

John Rogers; Donald Spector

1992-01-01

281

The Transactional Interpretation of Quantum Mechanics

NSDL National Science Digital Library

This article introduces the interpretation of the formalism of quantum mechanics, the Transactional Interpretation (TI) which addresses some issues raised by recent tests of Bell's inequalities. TI is non-local, relativistically invariant, and fully causal. A detailed comparison is made with the Copenhagen interpretation. Also, there is a link providing articles that have cited this one.

Cramer, John

2013-11-08

282

Introduction to Thermodynamics and Statistical Mechanics Professor Sergey Buldyrev

on two very important laws. The First Law is equivalent to the law of energy conservation. For example, a stone falls from a mountain and comes to rest at the bottom of a valley. According to the First Law not contradict the laws of Newtonian or quantum physics, however it can never happen according to the Second Law

Buldyrev, Sergey

283

Consistent interpretations of quantum mechanics

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

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

1992-04-01

284

Riemann hypothesis and quantum mechanics

NASA Astrophysics Data System (ADS)

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

Planat, Michel; Solé, Patrick; Omar, Sami

2011-04-01

285

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

286

Quantum Mechanics, Spacetime Locality, and Gravity

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 intimately related with each other, developing a complete picture for quantum measurement and cosmological histories in the quantum mechanical universe. On one hand, quantum mechanics eliminates the arbitrariness of defining probabilities in the multiverse, as discussed in arXiv:1104.2324. On the other hand, the multiverse allows for understanding why we observe an ordered world obeying consistent laws of physics, by providing an infinite-dimensional Hilbert space. This results in the irreversibility of quantum measurement, despite the fact that the evolution of the multiverse state is unitary. In order to describe the cosmological dynamics correctly, 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 Poincare transformation in the quantum gravitational context, as the Lorentz transformation is viewed as an extension of the Galilean transformation.

Yasunori Nomura

2012-05-08

287

Towards bringing Quantum Mechanics and General Relativity together

Two questions are suggested as having priority when trying to bring together Quantum Mechanics and General Relativity. Both questions have a scope which goes well beyond Physics, and in particular Quantum Mechanics and General Relativity.

Elemer E Rosinger

2005-12-16

288

A Signal Processing Model of Quantum Mechanics

This paper develops a deterministic model of quantum mechanics as an accumulation-and-threshold process. The model arises from an analogy with signal processing in wireless communications. Complex wavefunctions are interpreted as expressing the amplitude and phase information of a modulated carrier wave. Particle transmission events are modeled as the outcome of a process of signal accumulation that occurs in an extra (non-spacetime) dimension. Besides giving a natural interpretation of the wavefunction and the Born rule, the model accommodates the collapse of the wave packet and other quantum paradoxes such as EPR and the Ahanorov-Bohm effect. The model also gives a new perspective on the 'relational' nature of quantum mechanics: that is, whether the wave function of a physical system is "real" or simply reflects the observer's partial knowledge of the system. We simulate the model for a 2-slit experiment, and indicate possible deviations of the model's predictions from conventional quantum mechanics. We also indicate how the theory may be extended to a field theory.

Chris Thron; Johnny Watts

2012-05-08

289

The emergent Copenhagen interpretation of quantum mechanics

NASA Astrophysics Data System (ADS)

We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. This interpretation describes a world in which definite measurement results are obtained with probabilities that reproduce the Born rule. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint probabilities for the ergodic subsets of states of disjoint macro-systems only arise as emergent quantities. Finally we give an account of the EPR-Bohm thought experiment and show that the interpretation implies the violation of the Bell inequality characteristic of quantum mechanics but in a way that is rather novel. The final conclusion is that the Copenhagen interpretation gives a completely satisfactory phenomenology of macro-systems interacting with micro-systems.

Hollowood, Timothy J.

2014-05-01

290

Quantum mechanical coherence, resonance, and mind

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

Stapp, H.P.

1995-03-26

291

Models of Damped Oscillators in Quantum Mechanics

We consider several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schroedinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time-evolution of the expectation values of the energy related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator.

Ricardo Cordero-Soto; Erwin Suazo; Sergei K. Suslov

2009-06-04

292

NASA Astrophysics Data System (ADS)

We consider the efficiency at maximum power of a quantum Otto engine, which uses a spin or a harmonic system as its working substance and works between two heat reservoirs at constant temperatures Th and Tc (

Wu, Feilong; He, Jizhou; Ma, Yongli; Wang, Jianhui

2014-12-01

293

The discovery in the early 1970s that black holes radiate as black bodies has radically affected our understanding of general relativity, and offered us some early hints about the nature of quantum gravity. In this chapter I will review the discovery of black hole thermodynamics and summarize the many independent ways of obtaining the thermodynamic and (perhaps) statistical mechanical properties of black holes. I will then describe some of the remaining puzzles, including the nature of the quantum microstates, the problem of universality, and the information loss paradox.

S. Carlip

2014-10-06

294

NASA Astrophysics Data System (ADS)

The discovery in the early 1970s that black holes radiate as black bodies has radically affected our understanding of general relativity, and offered us some early hints about the nature of quantum gravity. In this paper, will review the discovery of black hole thermodynamics and summarize the many independent ways of obtaining the thermodynamic and (perhaps) statistical mechanical properties of black holes. I will then describe some of the remaining puzzles, including the nature of the quantum microstates, the problem of universality, and the information loss paradox.

Carlip, S.

2014-10-01

295

NASA Technical Reports Server (NTRS)

Using general thermodynamic arguments, we analyze the conversion of the energy contained in the radiation from a blackbody to useful work by a quantum system. We show that the energy available for conversion is bounded above by the change in free energy in the incident and reradiated fields and that this free energy change depends upon the temperature of the receiving device. Universal efficiency curves giving the ultimate thermodynamic conversion efficiency of the quantum system are presented in terms of the blackbody temperature and the temperature and threshold energy of the quantum system. Application of these results is made to a variety of systems including biological photosynthetic, photovoltaic, and photoelectrochemical systems.

Buoncristiani, A. M.; Smith, B. T.; Byvik, C. E.

1982-01-01

296

Operational Axioms for Quantum Mechanics Giacomo Mauro D'Ariano

Operational Axioms for Quantum Mechanics Giacomo Mauro D'Ariano QUIT Group, Dipartimento di Fisica is derived. Undeniably the axioms of Quantum Mechanics are of a highly abstract and mathematical nature of Quantum Mechanics, its "physical" axioms-- if they exist--must be of very general nature: they must even

D'Ariano, Giacomo Mauro

297

Quantum statistical mechanics, L-series, Anabelian Geometry

Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Beijing, August 2013 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12;joint work with Gunther Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12;Number fields: finite

Marcolli, Matilde

298

Quantum statistical mechanics, L-series, Anabelian Geometry

Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Colloquium, Harvard University, March 24, 2011 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12 as partition functions of physical systems Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian

Marcolli, Matilde

299

The Objective Inde...niteness Interpretation of Quantum Mechanics

The Objective Inde...niteness Interpretation of Quantum Mechanics David Ellerman University of California at Riverside Draft (not for quotation) May 28, 2013 Abstract Quantum mechanics (QM models indef- inite elements that become more de...nite as distinctions are made. If quantum mechanics

WÃ¼thrich, Christian

300

PHYS 530A: QUANTUM MECHANICS II SYLLABUS (2014 Spring)

PHYS 530A: QUANTUM MECHANICS II SYLLABUS (2014 Spring) Department of Physics, Southern Illinois be familiar with the contents of an undergraduate level course on Quantum mechanics, an equivalent of PHYS-430 Quantum Mechanics-I. Familiarity with the following topics will be assumed: complex variables, partial

Nickrent, Daniel L.

301

A Chaotic, Deterministic Model for Quantum Mechanics

With the decline of the Copenhagen interpretation of quantum mechanics and the recent experiments indicating that quantum mechanics does actually embody 'objective reality', one might ask if a 'mechanical', conceptual model for quantum mechanics could be found. We propose such a model. Vacuum energy fluctuations imply mass fluctuations and, through general relativity, curvature fluctuations. And those fluctuations are indicated by fluctuations of the metric tensor. The metric tensor fluctuations can 'explain' the uncertainty relations and non-commuting properties of conjugate variables. We argue that that the probability density is proportional to the square root of minus the determinant of the metric tensor (the differential volume element). We argue that the metric elements are not stochastic but are oscillating at a high enough frequency that measured values of same appear stochastic (i.e. crypto-stochastic). We suggest that the oscillations at the position of particles are described as torsional vibrations. A crypto-stochastic (or chaotic) oscillating metric yields, among other things, a model of super-position, photon polarization, and entanglement, and all within the confines of a 4-dimensional space-time.

Carl Frederick

2014-06-20

302

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 = ?Pk eiSk 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

303

Utilizing a combination of ab initio density-functional theory and thermodynamics formalism, we have established the microscopic mechanisms for oxidation of the binary and ternary alloy surfaces and provided a clear explanation for the experimental results of the oxidation. We construct three-dimensional surface phase diagrams (SPDs) for oxygen adsorption on three different Nb-X(110) (X = Ti, Al or Si) binary alloy surfaces. On the basis of the obtained SPDs, we conclude a general microscopic mechanism for the thermodynamic oxidation, that is, under O-rich conditions, a uniform single-phase SPD (type I) and a nonuniform double-phase SPD (type II) correspond to the sustained complete selective oxidation and the non-sustained partial selective oxidation by adding the X element, respectively. Furthermore, by revealing the framework of thermodynamics for the oxidation mechanism of ternary alloys through the comparison of the surface energies of two separated binary alloys, we provide an understanding for the selective oxidation behavior of the Nb ternary alloy surfaces. Using these general microscopic mechanisms, one could predict the oxidation behavior of any binary and multi-component alloy surfaces based on thermodynamics considerations. PMID:25681933

Liu, Shi-Yu; Liu, Shiyang; Li, De-Jun; Wang, Sanwu; Guo, Jing; Shen, Yaogen

2015-02-14

304

NASA Astrophysics Data System (ADS)

This Resource Letter draws on discipline-based education research from physics, chemistry, and biology to collect literature on the teaching of thermodynamics and statistical mechanics in the three disciplines. While the overlap among the disciplinary literatures is limited at present, we hope this Resource Letter will spark more interdisciplinary interaction.

Dreyfus, Benjamin W.; Geller, Benjamin D.; Meltzer, David E.; Sawtelle, Vashti

2015-01-01

305

Beyond relativity and quantum mechanics: space physics

NASA Astrophysics Data System (ADS)

Albert Einstein imposed an observer-based epistemology upon physics. Relativity and Quantum Mechanics limit physics to describing and modeling the observer's sensations and measurements. Their "underlying reality" consists only of ideas that serve to model the observer's experience. These positivistic models cannot be used to form physical theories of Cosmic phenomena. To do this, we must again remove the observer from the center of physics. When we relate motion to Cosmic space instead of to observers and we attempt to explain the causes of Cosmic phenomena, we are forced to admit that Cosmic space is a substance. We need a new physics of space. We can begin by replacing Relativity with a modified Lorentzian-Newtonian model of spatial flow, and Quantum Mechanics with a wave-based theory of light and electrons. Space physics will require the reinterpretation of all known phenomena, concepts, and mathematical models.

Lindner, Henry H.

2011-09-01

306

Emerging interpretations of quantum mechanics and recent progress in quantum measurement

NASA Astrophysics Data System (ADS)

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

Clarke, M. L.

2014-01-01

307

1/N expansion in noncommutative quantum mechanics

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

308

A tossed coin as quantum mechanical object

Comprehensive and physically consistent model of a tossed coin is presented in terms of geometric algebra. The model clearly shows that there is nothing elementary particle specific in the half-spin quantum mechanical formalism. It also demonstrates what really is behind this formalism, feasibly reveals the probabilistic meaning of wave function and shows that arithmetic of packed objects, namely wave functions and Pauli matrices, reduces the amount of available information.

Alexander M. Soiguine

2014-08-28

309

Non-Lipschitz approach to quantum mechanics

An attempt to reconcile quantum mechanics with Newton's laws represented by the non-Lipschitz formalism has been made. As a proof-of-concept, a line of equally spaced atoms was studied. It appeared that enforcement of atom incompressibility required relaxation of the Lipschitz condition at the points of contact. This, in turn, led to fractional powers and discreteness of values of the basic

Michail Zak

1998-01-01

310

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

311

Quantum mechanics in q-deformed calculus

Starting on the basis of q-deformed calculus and q-symmetric oscillator algebra, we introduce a generalized Schrödinger equation which admits factorized time-space solutions and the free plane wave functions can be expressed in terms of the so-called basic-hypergeometric functions. In this framework, q-deformed adjoint and q-hermitian operator properties occur i a natural way in order to satisfy the fundamental quantum mechanics

A. Lavagno; G. Gervino

2009-01-01

312

NASA Astrophysics Data System (ADS)

Based on the tensor network state representation, we develop a nonlinear dynamic theory, coined network contractor dynamics (NCD), to explore the thermodynamic properties of two-dimensional quantum lattice models. By invoking the rank-1 decomposition in the multilinear algebra, the NCD scheme makes the contraction of the tensor network of the partition function be realized through a contraction of a local tensor cluster with vectors on its boundary. An imaginary-time-sweep algorithm for implementation of the NCD method is proposed for practical numerical simulations. We benchmark the NCD scheme on the square Ising model, which shows great accuracy. Also, the results on the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice are disclosed to be in good agreement with the quantum Monte Carlo calculations. The quasientanglement entropy S, Lyapunov exponent ILya, and loop character Iloop are introduced within the dynamic scheme, which are found to display “nonlocality” near the critical point, and can be applied to determine the thermodynamic phase transitions of both classical and quantum systems.

Ran, Shi-Ju; Xi, Bin; Liu, Tao; Su, Gang

2013-08-01

313

Thermodynamics and nonlinear mechanics of materials with photoresponsive microstructure

NASA Astrophysics Data System (ADS)

The ability to directly convert visible light radiation into useful mechanical work provides many opportunities in the field of smart materials and adaptive structures ranging from biomedical applications to control of heliostat mirrors for solar harvesting. The complexities associated with coupling time-dependent Maxwell's equations with linear momentum and mechanics is discussed by introducing a set of electronic order parameters that govern the coupling between electromagnetic radiation and mechanics of a deformable solid. Numerical examples are given illustrating how this methodology is applied to a special class of liquid crystal polymer networks containing azobenzene. The dynamics associated with light absorption and its effect on deformation of the polymer are solved in three dimensions using finite difference methods and compared to experimental results. Particular emphasis is placed on the effect of polarized light on microstructure evolution and stresses that occur during photoisomerization of the optically active microstructure.

Oates, William S.; Bin, Jonghoon

2014-03-01

314

Relativistic non-Hermitian quantum mechanics

NASA Astrophysics Data System (ADS)

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

Jones-Smith, Katherine; Mathur, Harsh

2014-06-01

315

Hunting for Snarks in Quantum Mechanics

NASA Astrophysics Data System (ADS)

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

Hestenes, David

2009-12-01

316

Hunting for Snarks in Quantum Mechanics

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

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

2009-12-08

317

A quantum-mechanical relaxation model

NASA Astrophysics Data System (ADS)

The atomic origin of micromagnetic damping is investigated by developing and solving a quantum-mechanical relaxation model. A projection-operator technique is used to derive an analytical expression for the relaxation time as a function of the heat-bath and interaction parameters. The present findings are consistent with earlier research beyond the Landau-Lifshitz-Gilbert (LLG) equation and show that the underlying relaxation mechanism is very general. Zermelo's recurrence paradox means that there is no true irreversibility in non-interacting nanoparticles, but the corresponding recurrence times are very long and can be ignored in many cases.

Skomski, R.; Kashyap, A.; Sellmyer, D. J.

2012-04-01

318

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

319

A thermodynamics based damage mechanics model for particulate composites

A micro-mechanical damage model is proposed to predict the overall viscoplastic behavior and damage evolution in a particle filled polymer matrix composite. Particulate composite consists of polymer matrix, particle fillers, and an interfacial transition interphase around the filler particles. Yet the composite is treated as a two distinct phase material, namely the matrix and the equivalent particle-interface assembly. The CTE

Cemal Basaran; Shihua Nie

2007-01-01

320

Possible corrections to quantum mechanical predictions in hidden variable model

We derive possible corrections to the statistical predictions of quantum mechanics in measurement over ensemble of identically prepared system based on a hidden variable model of quantization developed in the previous work. The corrections are characterized by a dimensionless parameter $\\sigma$ and the prediction of quantum mechanics is reproduced in the formal limit $\\sigma\\rightarrow 0$. Quantum mechanics is argued to be reliable for sufficiently low quantum number.

Agung Budiyono

2012-01-22

321

Quantum mechanics, by itself, implies perception of a classical world

Several versions of reality can simultaneously exist in the states of quantum mechanics, but we perceive only one classical version. The question is whether the mathematics of quantum mechanics, by itself, implies we perceive only one classical version. Zurek has used a method involving the environment, redundancy, decoherence and quantum Darwinism to show that quantum mechanics does indeed imply this result, but the argument is quite complex. Here we give a simpler method based on linearity.

Casey Blood

2010-09-23

322

Quantum groups, coherent states, squeezing and lattice quantum mechanics

By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg algebra, $q$-WH, into the theory of entire analytic functions. The $q$--WH algebra operators are realized in terms of finite difference operators in the $z$ plane. In order to exhibit the relevance of our study, several applications to different cases of physical interest are discussed: squeezed states and the relation between coherent states and theta functions on one side, lattice quantum mechanics and Bloch functions on the other, are shown to find a deeper mathematical understanding in terms of $q$-WH. The r\\^ole played by the finite difference operators and the relevance of the lattice structure in the completeness of the coherent states system suggest that the quantization of the WH algebra is an essential tool in the physics of discretized (periodic) systems.

E. Celeghini; S. De Martino; S. De Siena; M. Rasetti; G. Vitiello

1996-04-04

323

Quantum Groups, Coherent States, Squeezing and Lattice Quantum Mechanics

By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg ($q$-WH) algebra into the theory of entire analytic functions. The main tool is the realization of the $q$--WH algebra in terms of finite difference operators. The physical relevance of our study relies on the fact that coherent states (CS) are indeed formulated in the space of entire analytic functions where they can be rigorously expressed in terms of theta functions on the von Neumann lattice. The r\\^ole played by the finite difference operators and the relevance of the lattice structure in the completeness of the CS system suggest that the $q$--deformation of the WH algebra is an essential tool in the physics of discretized (periodic) systems. In this latter context we define a quantum mechanics formalism for lattice systems.

Celeghini; S. De Martino; S. De Siena; M. Rasetti; G. Vitiello

1993-10-20

324

Neutrino oscillations: Quantum mechanics vs. quantum field theory

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

Akhmedov, Evgeny Kh.; Kopp, Joachim; ,

2010-01-01

325

Atomistic Monte Carlo simulations, coupling thermodynamic and kinetic effects, resolve a longstanding controversy regarding the origin of composition profiles in heteroepitaxial SiGe quantum dots. It is shown that profiles with cores rich in the unstrained (Si) component derive from near-equilibrium processes and intraisland diffusion. Profiles with cores rich in the strained (Ge) component are of nonequilibrium nature, i.e., they are strain driven but kinetically limited. They are shaped by the distribution of kinetic barriers of atomic diffusion in the islands. The diffusion pathways are clearly revealed for the first time. Geometrical kinetics play a minor role.

Georgiou, C. [Research Unit for Nanostructured Materials Systems, Cyprus University of Technology, P.O. Box 50329, 3603 Limassol (Cyprus); Leontiou, T. [Research Unit for Nanostructured Materials Systems, Cyprus University of Technology, P.O. Box 50329, 3603 Limassol (Cyprus); General Department, Frederich University, 1036 Nicosia (Cyprus); Kelires, P. C., E-mail: pantelis.kelires@cut.ac.cy [Research Unit for Nanostructured Materials Systems, Cyprus University of Technology, P.O. Box 50329, 3603 Limassol (Cyprus); Department of Mechanical and Materials Science Engineering, Cyprus University of Technology, P.O. Box 50329, 3603 Limassol (Cyprus)

2014-07-15

326

Bohmian mechanics in relativistic quantum mechanics, quantum field theory and string theory

I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle trajectories, the problem of particle creation and destruction, the Bohmian interpretation of fermionic fields and the intrinsically Bohmian quantization of fields and strings based on the De Donder-Weyl covariant canonical formalism.

H. Nikolic

2006-10-12

327

Electron transfer (ET) reactions are one of the most important processes in chemistry and biology. Because of the quantum nature of the processes and the complicated roles of the solvent, theoretical study of ET processes is challenging. To simulate ET processes at the electronic level, we have developed an efficient density functional theory (DFT) quantum mechanical (QM)/molecular mechanical (MM) approach that uses the fractional number of electrons as the order parameter to calculate the redox free energy of ET reactions in solution. We applied this method to study the ET reactions of the aqueous metal complexes Fe(H{sub 2}O){sub 6}{sup 2+/3+} and Ru(H{sub 2}O){sub 6}{sup 2+/3+}. The calculated oxidation potentials, 5.82 eV for Fe(II/III) and 5.14 eV for Ru(II/III), agree well with the experimental data, 5.50 and 4.96 eV, for iron and ruthenium, respectively. Furthermore, we have constructed the diabatic free energy surfaces from histogram analysis based on the molecular dynamics trajectories. The resulting reorganization energy and the diabatic activation energy also show good agreement with experimental data. Our calculations show that using the fractional number of electrons (FNE) as the order parameter in the thermodynamic integration process leads to efficient sampling and validate the ab initio QM/MM approach in the calculation of redox free energies.

Zeng Xiancheng; Hu Hao; Hu Xiangqian; Cohen, Aron J.; Yang Weitao [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States)

2008-03-28

328

Unstable trajectories and the quantum mechanical uncertainty

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

329

Quantum mechanics with coordinate dependent noncommutativity

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

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

2013-11-15

330

MSE 157: Quantum Mechanics of Nanoscale Materials Course Information

there. Textbook The textbook for this course is Introduction to Quantum Mechanics by David Griffiths. We Quantum Mechanics by Walter A. Harrison An Introduction to Quantum Physics by A.P. French and Edwin F was created to describe and explain a world of atoms and electrons far removed from everyday human experience

331

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

Natalia Kanaan; Sergio Martí; Vicent Moliner; Amnon Kohen

2007-01-01

332

Representation of natural numbers in quantum mechanics

This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural numbers or a model of arithmetic if the set and operations satisfy the axioms of number theory or arithmetic. This paper is limited to k-ary representations of length L and to the axioms for arithmetic modulo k{sup L}. A model of the axioms is described based on an abstract L-fold tensor product Hilbert space H{sup arith}. Unitary maps of this space onto a physical parameter based product space H{sup phy} are then described. Each of these maps makes states in H{sup phy}, and the induced operators, a model of the axioms. Consequences of the existence of many of these maps are discussed along with the dependence of Grover's and Shor's algorithms on these maps. The importance of the main physical requirement, that the basic arithmetic operations are efficiently implementable, is discussed. This condition states that there exist physically realizable Hamiltonians that can implement the basic arithmetic operations and that the space-time and thermodynamic resources required are polynomial in L.

Benioff, Paul

2001-03-01

333

As a point of departure it is suggested that Quantum Cosmology is a topological concept independent from metrical constraints. Methods of continuous topological evolution and topological thermodynamics are used to construct a cosmological model of the present universe, using the techniques based upon Cartan's theory of exterior differential systems. Thermodynamic domains, which are either Open, Closed, Isolated, or in Equilibrium, can be put into correspondence with topological systems of Pfaff topological dimension 4, 3, 2 and 1. If the environment of the universe is assumed to be a physical vacuum of Pfaff topological dimension 4, then continuous but irreversible topological evolution can cause the emergence of topologically coherent defect structures of Pfaff topological dimension less than 4. As galaxies and stars exchange radiation but not matter with the environment, they are emergent topological defects of Pfaff topological dimension 3 which are far from equilibrium. DeRham topological theory of period integrals over closed but not exact exterior differential systems leads to the emergence of quantized, deformable, but topologically coherent, singular macrostates at all scales. The method leads to the conjecture that dark matter and energy is represented by those thermodynamic topological defect structures of Pfaff dimension 2 or less.

R. M. Kiehn

2006-03-17

334

Adaptive Perturbation Theory I: Quantum Mechanics

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

335

Background Gram-negative bacteria use periplasmic-binding proteins (bPBP) to transport nutrients through the periplasm. Despite immense diversity within the recognized substrates, all members of the family share a common fold that includes two domains that are separated by a conserved hinge. The hinge allows the protein to cycle between open (apo) and closed (ligated) conformations. Conformational changes within the proteins depend on a complex interplay of mechanical and thermodynamic response, which is manifested as an increase in thermal stability and decrease of flexibility upon ligand binding. Results We use a distance constraint model (DCM) to quantify the give and take between thermodynamic stability and mechanical flexibility across the bPBP family. Quantitative stability/flexibility relationships (QSFR) are readily evaluated because the DCM links mechanical and thermodynamic properties. We have previously demonstrated that QSFR is moderately conserved across a mesophilic/thermophilic RNase H pair, whereas the observed variance indicated that different enthalpy-entropy mechanisms allow similar mechanical response at their respective melting temperatures. Our predictions of heat capacity and free energy show marked diversity across the bPBP family. While backbone flexibility metrics are mostly conserved, cooperativity correlation (long-range couplings) also demonstrate considerable amount of variation. Upon ligand removal, heat capacity, melting point, and mechanical rigidity are, as expected, lowered. Nevertheless, significant differences are found in molecular cooperativity correlations that can be explained by the detailed nature of the hydrogen bond network. Conclusion Non-trivial mechanical and thermodynamic variation across the family is explained by differences within the underlying H-bond networks. The mechanism is simple; variation within the H-bond networks result in altered mechanical linkage properties that directly affect intrinsic flexibility. Moreover, varying numbers of H-bonds and their strengths control the likelihood for energetic fluctuations as H-bonds break and reform, thus directly affecting thermodynamic properties. Consequently, these results demonstrate how unexpected large differences, especially within cooperativity correlation, emerge from subtle differences within the underlying H-bond network. This inference is consistent with well-known results that show allosteric response within a family generally varies significantly. Identifying the hydrogen bond network as a critical determining factor for these large variances may lead to new methods that can predict such effects. PMID:18700034

Livesay, Dennis R; Huynh, Dang H; Dallakyan, Sargis; Jacobs, Donald J

2008-01-01

336

5.74 Introductory Quantum Mechanics II, Spring 2005

Time-dependent quantum mechanics and spectroscopy. Topics covered include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, ...

Tokmakoff, Andrei

337

Probability Representation of Quantum Mechanics: Comments and Bibliography

The probability representation of states in standard quantum mechanics where the quantum states are associated with fair probability distributions (instead of wave function or density matrix) is shortly commented and bibliography related to the probability representation is given.

V. I. Man'ko; O. V. Pilyavets; V. G. Zborovskii

2006-10-17

338

EOS, thermodynamic, and structural-mechanical properties of intermetallic compounds

This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). Several classes of binary intermetallic compounds have important potential application as high temperature structural materials because of their high melting temperature, low density, and high strength, but their use is limited by their poor low temperature ductility and fracture toughness. The goal of this project was to further the development of techniques for performing ab-initio calculations of the electronic, structural, and elastic properties of these materials in an investigation of the relation between structure, composition, and mechanical properties of intermetallics. Materials properties to be addressed in these calculations included the equation of state (EOS), defect structure energetics, and elastic constants and phonons. Major accomplishments included calculations of stacking fault and twin energies in layered TiAl, structural stability in binary and ternary Ti-Al-Nb compounds, and point defect energies and elastic moduli of Laves phase intermetallics.

Wills, J.M.; Straub, G.; Albers, R.C.

1998-12-31

339

Comparison of Differing Credit Hour Allotments for Thermodynamics and Fluid Mechanics Courses

NSDL National Science Digital Library

Each institution determines how many credit hours will be allotted for each course. Thermodynamics and fluid mechanics in an undergraduate Bachelor of Science Mechanical Engineering curriculum in the United States typically are allotted three or four credit hours. For a semester system, this allows for 42-45 or 56-60 fifty-minute class sessions in three and four credit hour courses, respectively. Opinions vary whether thermodynamics and fluid mechanics should each be three credit hours, each be four credit hours, or one should be three and the other four. Two universities have conducted a study to determine the advantages, disadvantages, and consequences of three vs. four credit hours. One university has a four credit hour thermodynamics and a three credit hour fluid mechanics, while the other university has exactly the opposite. Through student surveys, course objectives/outcomes, course syllabi, instructors experiences, and average grades, conclusions are drawn on the effects of course length. Other issues are examined such as challenges facing instructors who have previously taught a four credit hour course that now must cover the same material within a three credit hour allotment. Finally recommendations are given for instructors that are allotted less than desirable credit hours.

Fletcher, Robert

340

Lecture Script: Introduction to Computational Quantum Mechanics

This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding analytical as well as numerical solutions and their visualization. Most of these calculations are too complicated to be done by hand. Even relatively simple problems, such as two interacting particles in a one-dimensional trap, do not have analytic solutions and require the use of computers for their solution and visualization. More complex problems scale exponentially with the number of degrees of freedom, and make the use of large computer simulations unavoidable. The course is taught using the Mathematica programming language; however, the concepts presented are readily translated to any other programming language.

Roman Schmied

2014-03-27

341

Euclidean Quantum Mechanics and Universal Nonlinear Filtering

An important problem in applied science is the continuous nonlinear filtering problem, i.e., the estimation of a Langevin state that is observed indirectly. In this paper, it is shown that Euclidean quantum mechanics is closely related to the continuous nonlinear filtering problem. The key is the configuration space Feynman path integral representation of the fundamental solution of a Fokker-Planck type of equation termed the Yau Equation of continuous-continuous filtering. A corollary is the equivalence between nonlinear filtering problem and a time-varying Schr\\"odinger equation.

Bhashyam Balaji

2008-09-25

342

Scattering in PT-symmetric quantum mechanics

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

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

2007-02-15

343

Hidden geometric character of relativistic quantum mechanics

Geometry can be an unsuspected source of equations with physical relevance, as everybody is aware since Einstein formulated the general theory of relativity. However, efforts to extend a similar type of reasoning to other areas of physics, namely, electrodynamics, quantum mechanics, and particle physics, usually had very limited success; particularly in quantum mechanics the standard formalism is such that any possible relation to geometry is impossible to detect; other authors have previously trod the geometric path to quantum mechanics, some of that work being referred to in the text. In this presentation we will follow an alternate route to show that quantum mechanics has indeed a strong geometric character. The paper makes use of geometric algebra, also known as Clifford algebra, in five-dimensional space-time. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from such choice and their consistency with experimental results. Given a metric space of any dimension, one can define monogenic functions, the natural extension of analytic functions to higher dimensions; such functions have null vector derivative and have previously been shown by other authors to play a decisive role in lower dimensional spaces. All monogenic functions have null Laplacian by consequence; in a hyperbolic space this fact leads inevitably to a wave equation with planelike solutions. This is also true for five-dimensional space-time and we will explore those solutions, establishing a parallel with the solutions of the free particle Dirac equation. For this purpose we will invoke the isomorphism between the complex algebra of 4x4 matrices, also known as Dirac's matrices. There is one problem with this isomorphism, because the solutions to Dirac's equation are usually known as spinors (column matrices) that do not belong to the 4x4 matrix algebra and as such are excluded from the isomorphism. We will show that a solution in terms of Dirac spinors is equivalent to a plane wave solution. Just as one finds in the standard formulation, monogenic functions can be naturally split into positive/negative energy together with left/right ones. This split is provided by geometric projectors and we will show that there is a second set of projectors providing an alternate fourfold split. The possible implications of this alternate split are not yet fully understood and are presently the subject of profound research.

Almeida, Jose B. [Physics Department, Universidade do Minho, 4710-057 Braga (Portugal)

2007-01-15

344

A toy model for quantum mechanics

The toy model used by Spekkens [R. Spekkens, Phys. Rev. A 75, 032110 (2007)] to argue in favor of an epistemic view of quantum mechanics is extended by generalizing his definition of pure states (i.e. states of maximal knowledge) and by associating measurements with all pure states. The new toy model does not allow signaling but, in contrast to the Spekkens model, does violate Bell-CHSH inequalities. Negative probabilities are found to arise naturally within the model, and can be used to explain the Bell-CHSH inequality violations.

S. J. van Enk

2007-05-18

345

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

346

A Quantum Mechanical Model of Spherical Supermembranes

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. For the ${\\mathcal N} = 2$ case, instanton effects then lift these vacua to massive states. For the ${\\mathcal N} = 4$ case, there is no instanton tunneling, and the vacua remain massless. Similarities to spherical supermembranes as giant gravitons and in Matrix theory on pp-waves is discussed.

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

2003-02-07

347

Supersymmetric quantum mechanics and its applications

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

348

From PT-symmetric quantum mechanics to conformal field theory

One of the simplest examples of a PT-symmetric quantum system is the scaling Yang-Lee model, a quantum field theory with cubic interaction and purely imaginary coupling. We give a historical review of some facts about this model in d PT-symmetric quantum mechanics. We also discuss some more general results on PT-symmetric quantum mechanics and the ODE/IM correspondence, and mention applications to magnetic systems and cold atom physics.

Patrick Dorey; Clare Dunning; Roberto Tateo

2009-06-05

349

The metaphysics of quantum mechanics: Modal interpretations

NASA Astrophysics Data System (ADS)

This dissertation begins with the argument that a preferred way of doing metaphysics is through philosophy of physics. An understanding of quantum physics is vital to answering questions such as: What counts as an individual object in physical ontology? Is the universe fundamentally indeterministic? Are indiscernibles identical? This study explores how the various modal interpretations of quantum mechanics answer these sorts of questions; modal accounts are one of the two classes of interpretations along with so-called collapse accounts. This study suggests a new alternative within the class of modal views that yields a more plausible ontology, one in which the Principle of the Identity of Indisceribles is necessarily true. Next, it shows that modal interpretations can consistently deny that the universe must be fundamentally indeterministic so long as they accept certain other metaphysical commitments: either a perfect initial distribution of states in the universe or some form of primitive dispositional properties. Finally, the study sketches out a future research project for modal interpretations based on developing quantified quantum logic.

Gluck, Stuart Murray

2004-11-01

350

Smallest Relational Mechanics Model of Quantum Cosmology

Relational particle mechanics are models in which there is, overall, no time, position, orientation (nor, sometimes, scale). They are useful for whole-universe modelling - the setting for quantum cosmology. This note concerns 3 particles in 1d in shape-scale split variables. The scale part parallels certain Friedmann equations, while in this note the shape part involves functions on the circle. The scale part is taken to be `heavy' and `slow' so the semiclassical approach applies and scale provides an approximate timestandard with repect to which the light physics runs. Relational particle mechanics moreover provide conceptual models of inhomogeneity, structure formation and nontrivial linear constraints (minisuperspace models do not and midisuperspace models only do at the cost of substantial complications).

Edward Anderson

2009-08-13

351

Ewald mesh method for quantum mechanical calculations

The Fourier transform Coulomb (FTC) method has been shown to be effective for the fast and accurate calculation of long-range Coulomb interactions between diffuse (low-energy cutoff) densities in quantum mechanical (QM) systems. In this work, we split the potential of a compact (high-energy cutoff) density into short-range and long-range components, similarly to how point charges are handled in the Ewald mesh methods in molecular mechanics simulations. With this linear scaling QM Ewald mesh method, the long-range potential of compact densities can be represented on the same grid as the diffuse densities that are treated by the FTC method. The new method is accurate and significantly reduces the amount of computational time on short-range interactions, especially when it is compared to the continuous fast multipole method. PMID:22443753

Chang, Chun-Min; Shao, Yihan; Kong, Jing

2012-01-01

352

INTRODUCTION TO RELATIVISTIC QUANTUM MECHANICS AND THE DIRAC EQUATION

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

353

A note on the Landauer principle in quantum statistical mechanics

A note on the Landauer principle in quantum statistical mechanics Vojkan JaksiÂ´c1 and Claude results concerning the derivation of the Landauer bound from the first principles of statistical mechanics and proof of the Landauer principle in the context of quantum statistical mechanics has led to a number

Boyer, Edmond

354

Quantum Mechanical Study of Nanoscale MOSFET

NASA Technical Reports Server (NTRS)

The steady state characteristics of MOSFETS that are of practical Interest are the drive current, off-current, dope of drain current versus drain voltage, and threshold voltage. In this section, we show that quantum mechanical simulations yield significantly different results from drift-diffusion based methods. These differences arise because of the following quantum mechanical features: (I) polysilicon gate depletion in a manner opposite to the classical case (II) dependence of the resonant levels in the channel on the gate voltage, (III) tunneling of charge across the gate oxide and from source to drain, (IV) quasi-ballistic flow of electrons. Conclusions dI/dV versus V does not increase in a manner commensurate with the increase in number of subbands. - The increase in dI/dV with bias is much smaller then the increase in the number of subbands - a consequence of bragg reflection. Our calculations show an increase in transmission with length of contact, as seen in experiments. It is desirable for molecular electronics applications to have a small contact area, yet large coupling. In this case, the circumferential dependence of the nanotube wave function dictates: - Transmission in armchair tubes saturates around unity - Transmission in zigzag tubes saturates at two.

Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan

2001-01-01

355

Supersymmetric quantum mechanics and the Korteweg--de Vries hierarchy

The connection between supersymmetric quantum mechanics and the Korteweg--de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the [tau] function by means of supersymmetric quantum mechanics is discussed.

Grant, A.K.; Rosner, J.L. (Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637 (United States))

1994-05-01

356

Biological applications of hybrid quantum mechanics/molecular mechanics calculation.

Since in most cases biological macromolecular systems including solvent water molecules are remarkably large, the computational costs of performing ab initio calculations for the entire structures are prohibitive. Accordingly, QM calculations that are jointed with MM calculations are crucial to evaluate the long-range electrostatic interactions, which significantly affect the electronic structures of biological macromolecules. A UNIX-shell-based interface program connecting the quantum mechanics (QMs) and molecular mechanics (MMs) calculation engines, GAMESS and AMBER, was developed in our lab. The system was applied to a metalloenzyme, azurin, and PU.1-DNA complex; thereby, the significance of the environmental effects on the electronic structures of the site of interest was elucidated. Subsequently, hybrid QM/MM molecular dynamics (MD) simulation using the calculation system was employed for investigation of mechanisms of hydrolysis (editing reaction) in leucyl-tRNA synthetase complexed with the misaminoacylated tRNA(Leu), and a novel mechanism of the enzymatic reaction was revealed. Thus, our interface program can play a critical role as a powerful tool for state-of-the-art sophisticated hybrid ab initio QM/MM MD simulations of large systems, such as biological macromolecules. PMID:22536015

Kang, Jiyoung; Hagiwara, Yohsuke; Tateno, Masaru

2012-01-01

357

Quantum mechanical model for the study of pressure ionization in the superconfiguration approach

NASA Astrophysics Data System (ADS)

The knowledge of plasma equation of state and photoabsorption requires suitable and realistic models for the description of ions. The number of relevant electronic configurations of ions in hot dense plasmas can be immense (increasing with atomic number Z). In such cases, calculations relying on the superconfiguration approximation appear to be among the best statistical approaches to photoabsorption in plasmas. The superconfiguration approximation enables one to perform rapid calculation of averages over all possible configurations representing excited states of bound electrons. We present a thermodynamically consistent model involving detailed screened ions (described by superconfigurations) in plasmas. The density effects are introduced via the ion-sphere model. In the usual approaches, bound electrons are treated quantum mechanically while free electrons are described within the framework of semi-classical Thomas-Fermi theory. Such a hybrid treatment can lead to discontinuities in the thermodynamic quantities when pressure ionization occurs. We propose a model in which all electrons (bound and free) are treated quantum mechanically. Furthermore, resonances are carefully taken into account in the self-consistent calculation of the electronic structure of each superconfiguration. The model provides the contribution of electrons to the main thermodynamic quantities, together with a treatment of pressure ionization, and gives a better insight into the electronic properties of hot dense plasmas.

Pain, J. C.; Dejonghe, G.; Blenski, T.

2006-04-01

358

The Many-Worlds Interpretation of Quantum Mechanics

NSDL National Science Digital Library

This encyclopedia entry 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

2005-04-16

359

It is shown that thermal energy from a heat source can be converted to useful work in the form of maser-laser light by using a combination of a Stern-Gerlach device and stimulated emissions of excited particles in a maser-laser cavity. We analyze the populations of atoms or quantum dots exiting the cavity, the photon statistics, and the internal entropy as a function of atomic transit time, using the quantum theory of masers and lasers. The power of the laser light is estimated to be sufficiently high for device applications. The thermodynamics of the heat converter is analyzed as a heat engine operating between two reservoirs of different temperature but is generalized to include the change of internal quantum states. The von Neumann entropies for the internal degree are obtained. The sum of the internal and external entropies increases after each cycle and the second law is not violated, even if the photon entropy due to finite photon number distribution is not included. An expression for efficiency relating to the Carnot efficiency is obtained. We resolve the subtle paradox on the reduction of the internal entropy with regards to the path separation after the Stern-Gerlach device.

Ooi, C. H. Raymond [Department of Physics, University of Malaya, 50603 Kuala Lumpur (Malaysia)

2011-04-15

360

Three attempts at two axioms for quantum mechanics

The axioms of nonrelativistic quantum mechanics lack clear physical meaning. In particular, they say nothing about nonlocality. Yet quantum mechanics is not only nonlocal, it is twice nonlocal: there are nonlocal quantum correlations, and there is the Aharonov-Bohm effect, which implies that an electric or magnetic field h e r e may act on an electron t h e r e. Can we invert the logical hierarchy? That is, can we adopt nonlocality as an axiom for quantum mechanics and derive quantum mechanics from this axiom and an additional axiom of causality? Three versions of these two axioms lead to three different theories, characterized by "maximal nonlocal correlations", "jamming" and "modular energy". Where is quantum mechanics in these theories?

Daniel Rohrlich

2010-11-24

361

We report the results of our first-principles calculations of structural stability, mechanical, magnetic, and thermodynamic properties for ?-M(23)C(6) (M = Fe, Cr) compounds with each of the four metal Wyckoff sites being occupied in turn by Fe. The thermodynamic properties and the temperature dependence of the mechanical behavior of ?-M(23)C(6) compounds are investigated based on the quasi-harmonic Debye model. The results show that the thermodynamic properties of ?-M(23)C(6) (M = Fe, Cr) compounds are more dependent on the position of Fe atoms than the amount of Fe. PMID:23172712

Han, J J; Wang, C P; Liu, X J; Wang, Y; Liu, Zi-Kui

2012-12-19

362

NASA Astrophysics Data System (ADS)

We report the results of our first-principles calculations of structural stability, mechanical, magnetic, and thermodynamic properties for ?-M23C6 (M = Fe, Cr) compounds with each of the four metal Wyckoff sites being occupied in turn by Fe. The thermodynamic properties and the temperature dependence of the mechanical behavior of ?-M23C6 compounds are investigated based on the quasi-harmonic Debye model. The results show that the thermodynamic properties of ?-M23C6 (M = Fe, Cr) compounds are more dependent on the position of Fe atoms than the amount of Fe.

Han, J. J.; Wang, C. P.; Liu, X. J.; Wang, Y.; Liu, Zi-Kui

2012-12-01

363

Reciprocal relativity of noninertial frames: quantum mechanics

Noninertial transformations on time-position-momentum-energy space {t,q,p,e} with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and the symplectic metric -de/\\dt+dp/\\dq are studied. This U(1,3) group of transformations contains the Lorentz group as the inertial special case. In the limit of small forces and velocities, it reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds^2=dt^2. The 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. 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 reprentations of its central extension. The same method of projective representations of the inhomogeneous U(1,3) group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous U(1,3) group is the cover of the quaplectic group Q(1,3)=U(1,3)*s H(4). H(4) is the Weyl-Heisenberg group. A set of second order wave equations results from the representations of the Casimir operators.

Stephen G. Low

2007-03-23

364

Quantum phase transition and thermodynamic properties of a fourfold magnetic periodic system

NASA Astrophysics Data System (ADS)

Based on the experimental synthesis of organic compound verdazyl radical ?-3-(2,6-dichlorophenyl)-1,5-diphenylverdazyl, consisting of four antiferromagnetic couplings, we study the magnetic properties and thermodynamic behaviors for different antiferromagnetic interactions using Green’s function theory. Under different fields, there are five regimes containing two gapless phases and three magnetization plateaus (M=0, 1/2 and saturated magnetization) distinguished by four critical lines, which are evidenced by the two-site entanglement entropy and closely related to the energy spectra. In addition, we calculate the susceptibility and specific heat, to demonstrate the low-lying excitations at low temperatures. It will provide guidance for us to synthesize varieties of unconventional magnetic materials, and stimulate future studies on quantum spin systems.

Wang, Shuling; Li, Ruixue; Ding, Linjie; Fu, Hua-Hua; Zhu, Si-cong; Ni, Yun; Meng, Yan; Yao, Kailun

2014-12-01

365

Quantum topological method studies on the thermodynamic properties of polychlorinated phenoxazines

NASA Astrophysics Data System (ADS)

The novel quantum topological indices PY1,2 were derived from molecular structure combined with the effect of atom space, the character of bonding atoms (such as equilibrium electro-negativity) and the branching effect between the atoms. The quantitative structure-property relationships (QSPRs) were proposed between PY1,2 and the thermodynamic properties (?fH?, ?fG? and ?fGR?) of phenoxazine (Phx) and 135 kinds of polychlorinated phenoxazines (PCPXs), by Multiple linear regression (MLR) analysis method. The high-quality prediction models were evidenced by the correlation coefficient R, the standard error of estimate S, the Fisher statistic value and the cross-validated correlation coefficient RCV. With the new QSPR model, we are able to predict a wide range of thermodynamic properties of an extensive number of molecules. And the model is statistically significant and shows good stability for data variation as tested by the leave-one-out cross-validation (LOO-CV).

Xiao, Fangzhu; Peng, Guowen; Nie, Changming; Wu, Yaxin; Dai, Yimin

2014-09-01

366

Thermodynamic study of non-linear electrodynamics in loop quantum cosmology

NASA Astrophysics Data System (ADS)

In this work, we have discussed the Maxwell's electrodynamics in non-linear forms in FRW universe. The energy density and pressure for non-linear electrodynamics have been written in the electro-magnetic universe. The Einstein's field equations for flat FRW model in loop quantum cosmology have been considered if the universe is filled with the matter and electro-magnetic field. We separately assumed the magnetic universe and electric universe. The interaction between matter and magnetic field have been considered in one section and for some particular form of interaction term, we have found the solutions of magnetic field and the energy density of matter. We have also considered the interaction between the matter and electric field and another form of interaction term has been chosen to solve the field equations. The validity of generalized second law of thermodynamics has been investigated on apparent and event horizons using Gibb's law and the first law of thermodynamics for magnetic and electric universe separately.

Bandyopadhyay, Tanwi; Debnath, Ujjal

2014-04-01

367

Exponential complexity and ontological theories of quantum mechanics

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

368

Supersymmetric quantum mechanics and Painlevé equations

NASA Astrophysics Data System (ADS)

In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order the potential is determined by solutions to Painlevé IV (PIV) and Painlevé V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.

Bermudez, David; Fernández C., David J.

2014-01-01

369

Quantum-mechanical suppression of bremsstrahlung

We have studied quantum-mechanical suppression of bremsstrahlung of low-energy 1-500 MeV photons from high-energy 25 GeV electrons. We measured the LPM effect, where multiple scattering of the radiating electron destroys coherence required for the emission of low-energy photons, and the dielectric effect, where the emitted photon traveling in the radiator medium interferes with itself. For the experiment, the collaboration developed a novel method of extracting a parasitic low-intensity high-energy electron beam into the fixed target area during normal SLC operation of the accelerator. The results agree quantitatively with Migdal`s calculation of the LPM effect. Surface effects, for which there is no satisfactory theoretical prediction, are visible at low photon energies. For very thin targets, the suppression disappears, as expected. Preliminary results on dielectric suppression of bremsstrahlung are in qualitative agreement with the expectation.

Becker-Szendy, R. [Stanford Linear Accelerator Center, Menlo Park, CA (United States); Anthony, P. [Stanford Linear Accelerator Center, Menlo Park, CA (United States)]|[Lawrence Livermore National Lab., CA (United States); Bosted, P. [American Univ., Washington, DC (United States)] [and others

1993-12-01

370

Twist deformation of rotationally invariant quantum mechanics

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

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

2010-11-15

371

Supersymmetric quantum mechanics and Painlevé equations

In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order the potential is determined by solutions to Painlevé IV (PIV) and Painlevé V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.

Bermudez, David; Fernández C, David J. [Departamento de Física, Cinvestav, A.P. 14-740, 07000 México D.F. (Mexico)

2014-01-08

372

Is Quantum Mechanics the Whole Truth?

Quantum mechanics has been enormously successful in describing nature at the atomic level and most physicists believe it is, in principle, the 'whole truth' about the world even at the everyday level. However, such a view, at first glance, leads to a severe problem. In certain circumstances, the most natural interpretation of the theory implies that no definite outcome of an experiment occurs until the act of observation. For many decades this problem was regarded as merely philosophical-it was thought it had no consequences that could be tested in experiment. However, in the last dozen years or so, the situation has changed dramatically in this respect. The problem, some popular resolutions of it, the current experimental situation and prospects for the future are discussed.

Leggett, Anthony J. [University of Illinois at Urbana-Champaign (United States)

2008-05-29

373

Quantum mechanical systems exhibit an inherently probabilistic nature upon\\u000ameasurement which excludes in principle the singular direct observability\\u000acontinual case. Quantum theory of time continuous measurements and quantum\\u000aprediction theory, developed by the author on the basis of an\\u000aindependent-increment model for quantum noise and nondemolition causality\\u000aprinciple in the 80's, solves this problem allowing continual quantum\\u000apredictions and reducing

VIACHESLAV P BELAVKIN

2007-01-01

374

New methods for quantum mechanical reaction dynamics

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

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

1996-12-01

375

Tampering detection system using quantum-mechanical systems

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

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

2011-12-13

376

Quantum Information Theory Quantum mechanics makes probabilistic predictions about experiments lead to the development of a theory of quantum information that generalises previous notions allow us to build unbreakable cryptosystems based on quantum communication, and how our intuitive

Burton, Geoffrey R.

377

NASA Astrophysics Data System (ADS)

We propose mutant versions of quantum mechanics constructed on vector spaces over the finite Galois fields GF(3) and GF(9). The mutation we consider here is distinct from what we proposed in previous papers on Galois field quantum mechanics. In this new mutation, the canonical expression for expectation values is retained instead of that for probabilities. In fact, probabilities are indeterminate. Furthermore, it is shown that the mutant quantum mechanics over the finite field GF(9) exhibits super-quantum correlations (i.e. the Bell-Clauser-Horne-Shimony-Holt bound is 4). We comment on the fundamental physical importance of these results in the context of quantum gravity.

Chang, Lay Nam; Lewis, Zachary; Minic, Djordje; Takeuchi, Tatsu

2013-12-01

378

Vortex Line Fluctuations in Superconductors from Elementary Quantum Mechanics

Concepts from elementary quantum mechanics can be used to understand vortex line fluctuations in high-temperature superconductors. Flux lines are essentially classical objects, described by a string tension, their mutual repulsion, and interactions with pinning centers. The classical partition function, however, is isomorphic to the imaginary time path integral description of quantum mechanics. This observation is used to determine the thermal

David R. Nelson

1993-01-01

379

Quantum mechanical retrocausation? Call for nonlocal causal models!

A new possible version of multisimultaneous causality is proposed, and real experiments allowing us to decide between this view and quantum mechanical retrocausation are further discussed. The interest of testing quantum mechanics against as many nonlocal causal models as possible is stressed.

Antoine Suarez

1998-02-12

380

Quantum mechanical features of optically pumped CW FIR lasers

NASA Technical Reports Server (NTRS)

Quantum mechanical predictions for the gain of an optically pumped CW FIR laser are presented for cases in which one or both of the pump and FIR transitions are pressure or Doppler broadened. The results are compared to those based on the rate equation model. Some of the quantum mechanical predictions are verified in CH3OH.

Seligson, D.; Leite, J. R. R.; Sanchez, A.; Feld, M. S.; Ducloy, M.

1977-01-01

381

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

382

An overview of the transactional interpretation of quantum mechanics

We summarize the transactional interpretation of quantum mechanics (TI) and consider various points concerning the TI and its relation to the Copenhagen interpretation (CI). Questions concerning mapping the TI onto the CI, of advanced waves as solutions to proper wave equations, of collapse and the QM formalism, and of the relation of quantum mechanical interpretations to experimental tests and results are discussed. 12 refs.

Cramer, J.G.

1987-01-01

383

Hidden-Variables Models of Quantum Mechanics (Noncontextual and Contextual)

In the following discussion of hidden variables models of quantum mechanics the ? Hilbert space formulation of quantum mechanics\\u000a and the standard interpretation of its notation and concepts will be taken to be initially understood, even though challenges\\u000a to the standard interpretation are implicit in the proposals of ? hidden variables.\\u000a \\u000a Very soon after the formulation of the new quantum

Abner Shimony

384

Two-dimensional quantum mechanical modeling of nanotransistors

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

385

Quantum Mechanical Black Holes: Towards a Unification of Quantum Mechanics and General Relativity

In this paper, starting from vortices we are finally lead to a treatment of\\u000aFermions as Kerr-Newman type Black Holes wherein we identify the horizon at the\\u000aparticle's Compton wavelength periphery. A naked singularity is avoided and the\\u000asingular processes inside the horizon of the Black Hole are identified with\\u000aQuantum Mechanical effects within the Compton wavelength. Inertial mass,\\u000agravitation,

B. G. Sidharth; B. M. Birla; Adarsh Nagar

1998-01-01

386

Depicting qudit quantum mechanics and mutually unbiased qudit theories

We generalize the ZX calculus to quantum systems of dimension higher than two. The resulting calculus is sound and universal for quantum mechanics. We define the notion of a mutually unbiased qudit theory and study two particular instances of these theories in detail: qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits. The calculus allows us to analyze the structure of qudit stabilizer quantum mechanics and provides a geometrical picture of qudit stabilizer theory using D-toruses, which generalizes the Bloch sphere picture for qubit stabilizer quantum mechanics. We also use our framework to describe generalizations of Spekkens toy theory to higher dimensional systems. This gives a novel proof that qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits are operationally equivalent in three dimensions. The qudit pictorial calculus is a useful tool to study quantum foundations, understand the relationship between qubit and qudit quantum mechanics, and provide a novel, high level description of quantum information protocols.

André Ranchin

2014-12-30

387

To look for high energy density materials (HEDM), the relationships between the structures and the performances of polynitroadamantanes (PNAs) were studied. The assigned infrared spectra of PNAs obtained at the density functional theory (DFT) B3LYP/6-31G level were used to compute the thermodynamic properties on the basis of the principle of statistical thermodynamics. The thermodynamic properties are linearly related with the number of nitro groups as well as with the temperatures. Detonation properties of PNAs were evaluated by using the Kamlet-Jacobs equation based on the calculated densities and heats of formation for titled compounds, and it is found that only when the number of nitro groups of PNA is equal to or more than eight can it be possible for PNAs to be used as HEDMs. The relative stabilities of PNAs were studied by the pyrolysis mechanism using the UHF-PM3 method. The homolysis of the C-NO2 bond is predicted to be the initial step of thermal decomposition. The activation energies (Ea) for the homolysis decrease with the number of nitro groups being increased on the whole. The stability order of dinitroadamantane isomers derived from the interactions among nitro groups is consistent with what is determined by Ea. The relations between the Ea's and the electronic structure parameters were discussed. In combination with the stability, PNA (1,2,3,4,5,6,7,8,9,10-) is recommended as the target of HEDM with insensitivity. PMID:16331911

Xu, Xiao Juan; Xiao, He Ming; Gong, Xue Dong; Ju, Xue Hai; Chen, Zhao Xu

2005-12-15

388

Quantum heat engines: A thermodynamic analysis of power and efficiency This article has been 2012 EPL, 99 (2012) 50005 www.epljournal.org doi: 10.1209/0295-5075/99/50005 Quantum heat engines that the operation and the output power of a quantum heat engine that converts incoherent thermal energy

Mukamel, Shaul

389

Highlighting the mechanism of the quantum speedup by time-symmetric and relational quantum mechanics

Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. We explain it by extending the usual representation of the quantum algorithm, limited to the process of solving the problem, to the process of setting the problem. The number of the drawer with the ball becomes a unitary transformation of the random outcome of the preparation measurement. This brings in relational quantum mechanics: the extension is with respect to Bob and cannot be with respect to Alice. It would tell her the drawer number before she opens any drawer. To Alice, the projection of the quantum state due to the preparation measurement should be retarded at the end of her search; in the input state of the search, the drawer number is determined to Bob and undetermined to Alice. A second consequence is the emergence of an ambiguity. Either the preparation measurement or the final one required to read the solution selects the solution. For reasons of symmetry, we assume that the selection shares evenly between the two measurements. All is as if Alice, by reading the solution, selected half of the information that specifies the drawer number. This selection leaves the input state to Bob unaltered and projects that to Alice on a state of lower entropy where she knows that half in advance. The quantum algorithm is a sum over histories in each of which Alice knows in advance that the ball is in a pair of drawers and locates it by opening one of the two. More in general, given an oracle problem, this explanation of the speedup predicts the number of queries required to solve it in an optimal quantum way.

Giuseppe Castagnoli

2014-12-11

390

BYU PHYS 731 Statistical Mechanics Chapter 7: Sethna Professor Manuel Berrondo Quantum Statistical #12;BYU PHYS 731 Statistical Mechanics Chapter 7: Sethna Professor Manuel Berrondo Quantum ensembles: = n pn |n n| density matrix 2 #12;BYU PHYS 731 Statistical Mechanics Chapter 7: Sethna Professor

Hart, Gus

391

A quantum mechanical version of Price's theorem for Gaussian states

This paper is concerned with integro-differential identities which are known in statistical signal processing as Price's theorem for expectations of nonlinear functions of jointly Gaussian random variables. We revisit these relations for classical variables by using the Frechet differentiation with respect to covariance matrices, and then show that Price's theorem carries over to a quantum mechanical setting. The quantum counterpart of the theorem is established for Gaussian quantum states in the framework of the Weyl functional calculus for quantum variables satisfying the Heisenberg canonical commutation relations. The quantum mechanical version of Price's theorem relates the Frechet derivative of the generalized moment of such variables with respect to the real part of their quantum covariance matrix with other moments. As an illustrative example, we consider these relations for quadratic-exponential moments which are relevant to risk-sensitive quantum control.

Igor G. Vladimirov

2014-09-15

392

Lectures on Black Hole Quantum Mechanics

NASA Astrophysics Data System (ADS)

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

Wilczek, Frank

393

The Born Rule in Quantum and Classical Mechanics

Considerable effort has been devoted to deriving the Born rule (e.g. that $|\\psi(x)|^2 dx$ is the probability of finding a system, described by $\\psi$, between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert space formulation of {\\it classical} mechanics as well. These results provide new insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.

Paul Brumer; Jiangbin Gong

2006-04-24

394

Cloning in nonlinear Hamiltonian quantum and hybrid mechanics

Possibility of state cloning is analyzed in two types of generalizations of quantum mechanics with nonlinear evolution. It is first shown that nonlinear Hamiltonian quantum mechanics does not admit cloning without the cloning machine. It is then demonstrated that the addition of the cloning machine, treated as a quantum or as a classical system, makes the cloning possible by nonlinear Hamiltonian evolution. However, a special type of quantum-classical theory, known as the mean-field Hamiltonian hybrid mechanics, does not admit cloning by natural evolution. The latter represents an example of a theory where it appears to be possible to communicate between two quantum systems at super-luminal speed, but at the same time it is impossible to clone quantum pure states.

D. Arsenovic; N. Buric; D. B. Popovic; M. Radonjic; S. Prvanovic

2014-11-17

395

Quantum Mechanics as a Classical Theory III: Epistemology

The two previous papers developed quantum mechanical formalism from classical mechanics and two additional postulates. In the first paper it was also shown that the uncertainty relations possess no ontological validity and only reflect the formalism's limitations. In this paper, a Realist Interpretation of quantum mechanics based on these results is elaborated and compared to the Copenhagen Interpretation. We demonstrate that von Neumann's proof of the impossibility of a hidden variable theory is not correct, independently of Bell's argumentation. A local hidden variable theory is found for non-relativistic quantum mechanics, which is nothing else than newtonian mechanics itself. We prove that Bell's theorem does not imply in a non-locality of quantum mechanics, and also demonstrate that Bohm's theory cannot be considered a true hidden variable theory.

L. S. F. Olavo

1995-03-31

396

QUANTUM STATISTICAL MECHANICS OVER FUNCTION FIELDS CATERINA CONSANI AND MATILDE MARCOLLI

QUANTUM STATISTICAL MECHANICS OVER FUNCTION FIELDS CATERINA CONSANI AND MATILDE MARCOLLI 1 interplay between quantum statistical mechanics and arithmetic. In the case of number fields, the symmetries]. Moreover, very recently Benoit Jacob constructed an interesting quantum statistical mechanical system

Marcolli, Matilde

397

EEE 434 Quantum Mechanics for Engineers (3) [F] Course (Catalog) Description

EEE 434 Quantum Mechanics for Engineers (3) [F] Course (Catalog) Description: Angular momentum. Ferry, Quantum Mechanics: An Introduction for Device Physicists and Electrical Engineers, Institute Objective: Students are conversant with the concepts of quantum mechanics as they apply to semiconductors

Zhang, Junshan

398

Information flow in quantum mechanics: The Quantum Maxwell Demon

Quantum information can be lost only when a quantum system is placed in contact with a heat bath, and then only in proportion to the entropy generated. Applied to the universe as a whole this suggests that the universe is in an algorithmically simple nearly pure quantum state. This could be verified by squeezing'' the vacuum state, and it is quite plausible that this is exactly what is happening inside black holes. 14 refs.

Chapline, G.F.

1990-08-09

399

Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics

NASA Astrophysics Data System (ADS)

In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called quantum annealing. The most typical instance is quantum adiabatic computation based on the adiabatic theorem. The quantum adiabatic computation as discussed in the other chapter, unfortunately, has a crucial bottleneck for a part of the optimization problems. We here introduce several recent trials to overcome such a weakpoint by use of developments in statistical mechanics. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.

Ohzeki, Masayuki

2013-09-01

400

Is string interaction the origin of quantum mechanics?

NASA Astrophysics Data System (ADS)

String theory was developed by demanding consistency with quantum mechanics. In this paper we wish to reverse the reasoning. We pretend that open string field theory is a fully consistent definition of the theory - it is at least a self-consistent sector. Then we find in its structure that the rules of quantum mechanics emerge from the non-commutative nature of the basic string joining/splitting interactions. Thus, rather than assuming the quantum commutation rules among the usual canonical variables we derive them from the physical process of string interactions. Morally we could apply such an argument to M-theory to cover quantum mechanics for all physics. If string or M-theory really underlies all physics, it seems that the door has been opened to an explanation of the origins of quantum mechanics from the physical processes point of view.

Bars, Itzhak; Rychkov, Dmitry

2014-12-01

401

Is Holographic Entropy and Gravity the result of Quantum Mechanics?

In this paper we suggest a connection between quantum mechanics and Verlinde's recently proposed entropic force theory for the laws of Newton. We propose an entropy based on the quantum mechanical probability density distribution. With the assumption that the holographic principle holds we propose that our suggested quantum entropy generalizes the Bekenstein entropy used by Verlinde in his approach. Based on this assumption we suggest that Verlinde's entropic theory of gravity has a quantum mechanical origin. We establish a reformulation of the Newtonian potential for gravity based on this quantum mechanical entropy. We also discuss the notion of observation and the correspondence to classical physics. Finally we give a discussion, a number of open problems and some concluding remarks.

Joakim Munkhammar

2010-03-05

402

Statistical Mechanics of Quantum-Classical Systems with Holonomic Constraints

The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained system arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear response function of constrained quantum-classical systems contains non-trivial additional terms which are absent in the response of unconstrained systems.

Alessandro Sergi

2005-11-15

403

More on Exact $\\CP$-Symmetric Quantum Mechanics

In this article, we discussed certain properties of non-Hermitian $\\CP$-symmetry Hamiltonian, and it is shown that a consistent physical theory of quantum mechanics can be built on a ${\\cal C} \\CP$-symmetry Hamiltonian. In particular, we show that these theories have unitary time evolution, and conservation probability. Furthermore, transition from quantum mechanics to classical mechanics is investigate and it is found that the Ehrenfest theorem is satisfied.

Khaled Saaidi

2003-09-15

404

Are quantum-mechanical-like models possible, or necessary, outside quantum physics?

NASA Astrophysics Data System (ADS)

This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.

Plotnitsky, Arkady

2014-12-01

405

Quantum statistical mechanics on infinitely ramified fractals

NASA Astrophysics Data System (ADS)

I present the thermodynamics of identical particles confined in infinitely ramified, exactly self-similar fractals, such as the Sierpinski carpet (in 2D) and the Menger sponge (in 3D). Recent results from analysis on fractals have established that the heat kernel associated with the Laplacian on such fractals satisfy, in the short-time regime, a scaling relation with exponent dS/2 (where dS is the spectral dimension) modulated by log-periodic oscillations. I explain how such a scaling affects the partition function, and the resultant thermodynamics associated with blackbody radiation [1], Casimir effect, and electrons in the fractal box.

Chen, Joe P.

2011-03-01

406

Potentiality and Contradiction in Quantum Mechanics

Following J.-Y.B\\'eziau in his pioneer work on non-standard interpretations of the traditional square of opposition, we have applied the abstract structure of the square to study the relation of opposition between states in superposition in orthodox quantum mechanics in \\cite{are14}. Our conclusion was that such states are \\ita{contraries} (\\ita{i.e.} both can be false, but both cannot be true), contradicting previous analyzes that have led to different results, such as those claiming that those states represent \\ita{contradictory} properties (\\ita{i. e.} they must have opposite truth values). In this chapter we bring the issue once again into the center of the stage, but now discussing the metaphysical presuppositions which underlie each kind of analysis and which lead to each kind of result, discussing in particular the idea that superpositions represent potential contradictions. We shall argue that the analysis according to which states in superposition are contrary rather than contradictory is still more plausible.

Jonas R. B. Arenhart; Décio Krause

2014-06-07

407

A Process Algebra Approach to Quantum Mechanics

The process approach to NRQM offers a fourth framework for the quantization of physical systems. Unlike the standard approaches (Schrodinger-Heisenberg, Feynman, Wigner-Gronewald-Moyal), the process approach is not merely equivalent to NRQM and is not merely a re-interpretation. The process approach provides a dynamical completion of NRQM. Standard NRQM arises as a asymptotic quotient by means of a set-valued process covering map, which links the process algebra to the usual space of wave functions and operators on Hilbert space. The process approach offers an emergentist, discrete, finite, quasi-non-local and quasi-non-contextual realist interpretation which appears to resolve many of the paradoxes and is free of divergences. Nevertheless, it retains the computational power of NRQM and possesses an emergent probability structure which agrees with NRQM in the asymptotic quotient. The paper describes the process algebra, the process covering map for single systems and the configuration process covering map for multiple systems. It demonstrates the link to NRQM through a toy model. Applications of the process algebra to various quantum mechanical situations - superpositions, two-slit experiments, entanglement, Schrodinger's cat - are presented along with an approach to the paradoxes and the issue of classicality.

William H. Sulis

2014-09-07

408

The representation of numbers in quantum mechanics.

Earlier work on modular arithmetic of k-ary representations of length L of the natural numbers in quantum mechanics is extended here to k-ary representations of all natural numbers, and to integers and rational numbers. Since the length L is indeterminate, representations of states and operators using creation and annihilation operators for bosons and fermions are defined. Emphasis is on definitions and properties of operators corresponding to the basic operations whose properties are given by the axioms for each type of number. The importance of the requirement of efficient implementability for physical models of the axioms is emphasized. Based on this, successor operations for each value of j corresponding to addition of k {l_brace}j-1{r_brace} if j>0 and k {l_brace}j{r_brace} if j<0 are defined. It follows from the efficient implementability of these successors, which is the case for all computers, that implementation of the addition and multiplication operators, which are defined in terms of polynomially many iterations of the successors, should be efficient. This is not the case for definitions based on the successor for j=1 only. This is the only successor defined in the usual axioms of arithmetic.

Benioff, P.; Physics

2002-12-01

409

Quantum mechanical studies of DNA and LNA.

Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies of the electrostatic potentials were compared among model oligonucleotides, and it was observed that small structural modifications induce global changes in the molecular structure and surface potentials. Since ligand structure and electrostatic potential complementarity with a receptor is a determinant for the bonding pattern between molecules, minor chemical modifications may have profound changes in the interaction profiles of oligonucleotides, possibly leading to changes in pharmacological properties. The QM modeling data can be used to understand earlier observations of antisense oligonucleotide properties, that is, the observation that small structural changes in oligonucleotide composition may lead to dramatic shifts in phenotypes. These observations should be taken into account in future oligonucleotide drug discovery, and by focusing more on non RNA target interactions it should be possible to utilize the exhibited property diversity of oligonucleotides to produce improved antisense drugs. PMID:24491259

Koch, Troels; Shim, Irene; Lindow, Morten; Ørum, Henrik; Bohr, Henrik G

2014-04-01

410

PT-Symmetric Matrix Quantum Mechanics

Recently developed methods for PT-symmetric models are applied to quantum-mechanical matrix models. We consider in detail the case of potentials of the form $V=-(g/N^{p/2-1})Tr(iM)^{p}$ and show how the calculation of all singlet wave functions can be reduced to solving a one-dimensional PT-symmetric model. The large-N limit of this class of models exists, and properties of the lowest-lying singlet state can be computed using WKB. For $p=3,4$, the energy of this state for small values of $N$ appears to show rapid convergence to the large-N limit. For the special case of $p=4$, we extend recent work on the $-gx^{4}$ potential to the matrix model: we show that the PT-symmetric matrix model is equivalent to a hermitian matrix model with a potential proportional to $+(4g/N)Tr\\Pi^{4}$. However, this hermitian equivalent model includes an anomaly term $\\hbar\\sqrt{2g/N}Tr\\Pi$. In the large-N limit, the anomaly term does not contribute at leading order to the properties of singlet states.

Peter N. Meisinger; Michael C. Ogilvie

2007-01-23

411

Atomistic modeling of thermodynamic properties of Pu-Ga alloys based on the Invar mechanism

NASA Astrophysics Data System (ADS)

We present an atomistic model that accounts for a range of anomalous thermodynamic properties of the fcc ? phase of Pu-Ga alloys in terms of the Invar mechanism. Two modified embedded atom method potentials are employed to represent competing electronic states in ?-Pu, each of which has an individual configuration dependence as well as distinct interactions with gallium. Using classical Monte Carlo simulations, we compute the temperature dependence of various thermodynamic properties for different dilute gallium concentrations. The model reproduces the observed effects of excessive volume reduction along with a rapid shift in thermal expansion from negative to positive values with increasing gallium concentration. It also predicts progressive stiffening upon dilute-gallium alloying, while the calculated thermal softening is nearly independent of the gallium concentration in agreement with resonant ultrasound spectroscopy measurements in the literature. Analysis of the local structure predicted by the model indicates that the distribution of the gallium atoms is not completely random in the ? phase due to the presence of short-range order associated with the Invar mechanism. This effect is consistent with the nanoscale heterogeneity in local gallium concentration which is observed in recent extended x-ray absorption fine structure spectroscopy experiments. Implications of the Invar effect for phase stability and physical interpretations of the two states are also discussed.

Lee, Tongsik; Taylor, Christopher D.; Lawson, A. C.; Conradson, Steven D.; Chen, Shao Ping; Caro, A.; Valone, Steven M.; Baskes, Michael I.

2014-05-01

412

Thermodynamic and mechanical properties of crystalline CoSb3: A molecular dynamics simulation study

NASA Astrophysics Data System (ADS)

Molecular dynamics simulations have been performed to study the fundamental thermodynamic and mechanical properties of single-crystalline skutterudite CoSb3 in the nanometric scale. The several interesting thermodynamic predictions, including linear thermal expansion coefficient, specific heat capacity, thermal conductivity, and temperature dependence of elastic constants, show excellent agreement with data available in the literature. The classic mechanical tests of uniaxial tension and compression are performed respectively at constant temperatures. The CoSb3 single-crystal exhibits nonlinear elastic response during the deformation process and the sustainable stress is very high, demonstrating its outstanding stability. An interesting phenomenon occurs at compression that the stress-strain curve undergoes a transition. The cause of the transition is an atomic reconstruction, which is observed and interpreted on the basis of interatomic interactions. Both of the failure patterns under tension and compression reveal brittleness of the material. The increasing of temperature would result in a linear degradation of the effective Young's modulus and ultimate strength, but its effect on Poisson's ratio is negligible. The results provide the groundwork for future studies of service behavior of the skutterudites-based thermoelectric devices.

Yang, Xu-qiu; Zhai, Peng-cheng; Liu, Li-sheng; Zhang, Qing-jie

2011-06-01

413

Quantum mechanical theory of dynamic nuclear polarization in solid dielectrics

Microwave driven dynamic nuclear polarization (DNP) is a process in which the large polarization present in an electron spin reservoir is transferred to nuclei, thereby enhancing NMR signal intensities. In solid dielectrics there are three mechanisms that mediate this transfer—the solid effect (SE), the cross effect (CE), and thermal mixing (TM). Historically these mechanisms have been discussed theoretically using thermodynamic parameters and average spin interactions. However, the SE and the CE can also be modeled quantum mechanically with a system consisting of a small number of spins and the results provide a foundation for the calculations involving TM. In the case of the SE, a single electron–nuclear spin pair is sufficient to explain the polarization mechanism, while the CE requires participation of two electrons and a nuclear spin, and can be used to understand the improved DNP enhancements observed using biradical polarizing agents. Calculations establish the relations among the electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) frequencies and the microwave irradiation frequency that must be satisfied for polarization transfer via the SE or the CE. In particular, if ?, ????0I?>??, the CE dominates the polarization transfer. This two-electron process is optimized when ?0S1??0S2=?0I and ?M??0S1 or?0S2, where ?0S1 and ?0S2 are the EPR Larmor frequencies of the two electrons. Using these matching conditions, we calculate the evolution of the density operator from electron Zeeman order to nuclear Zeeman order for both the SE and the CE. The results provide insights into the influence of the microwave irradiation field, the external magnetic field, and the electron?electron and electron?nuclear interactions on DNP enhancements. PMID:21456705

Hu, Kan-Nian; Debelouchina, Galia T.; Smith, Albert A.; Griffin, Robert G.

2011-01-01

414

Quantum mechanical theory of dynamic nuclear polarization in solid dielectrics.

Microwave driven dynamic nuclear polarization (DNP) is a process in which the large polarization present in an electron spin reservoir is transferred to nuclei, thereby enhancing NMR signal intensities. In solid dielectrics there are three mechanisms that mediate this transfer--the solid effect (SE), the cross effect (CE), and thermal mixing (TM). Historically these mechanisms have been discussed theoretically using thermodynamic parameters and average spin interactions. However, the SE and the CE can also be modeled quantum mechanically with a system consisting of a small number of spins and the results provide a foundation for the calculations involving TM. In the case of the SE, a single electron-nuclear spin pair is sufficient to explain the polarization mechanism, while the CE requires participation of two electrons and a nuclear spin, and can be used to understand the improved DNP enhancements observed using biradical polarizing agents. Calculations establish the relations among the electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) frequencies and the microwave irradiation frequency that must be satisfied for polarization transfer via the SE or the CE. In particular, if ?, ? < ?(0I), where ? and ? are the homogeneous linewidth and inhomogeneous breadth of the EPR spectrum, respectively, we verify that the SE occurs when ?(M) = ?(0S) ± ?(0I), where ?(M), ?(0S) and ?(0I) are, respectively, the microwave, and the EPR and NMR frequencies. Alternatively, when ? > ?(0I) > ?, the CE dominates the polarization transfer. This two-electron process is optimized when ?(0S(1))-?(0S(2)) = ?(0I) and ?(M)~?(0S(1)) or ?(0S(2)), where ?(0S(1)) and ?(0S(2)) are the EPR Larmor frequencies of the two electrons. Using these matching conditions, we calculate the evolution of the density operator from electron Zeeman order to nuclear Zeeman order for both the SE and the CE. The results provide insights into the influence of the microwave irradiation field, the external magnetic field, and the electron-electron and electron-nuclear interactions on DNP enhancements. PMID:21456705

Hu, Kan-Nian; Debelouchina, Galia T; Smith, Albert A; Griffin, Robert G

2011-03-28

415

Clausius' statement of the second law of thermodynamics reads: Heat will flow spontaneously from a hot to cold reservoir. This statement should hold for transport of energy through a quantum network composed of small subsystems each coupled to a heat reservoir. When the coupling between nodes is small, it seems reasonable to construct a local master equation for each node in contact with the local reservoir. The energy transport through the network is evaluated by calculating the energy flux after the individual nodes are coupled. We show by analysing the most simple network composed of two quantum nodes coupled to a hot and cold reservoir, that the local description can result in heat flowing from cold to hot reservoirs, even in the limit of vanishing coupling between the nodes. A global derivation of the master equation which prediagonalizes the total network Hamiltonian, and within this framework derives the master equation, is always consistent with the second-law of thermodynamics.

Amikam Levy; Ronnie Kosloff

2014-02-16

416

A Novel Radiation to Test Foundations of Quantum Mechanics

We point out that a new mechanism for radiation should exist if the Bohm theory of quantum mechanics is taken seriously. By traversing a quantum potential, an electron will necessarily be accelerated and radiate. For an illustration, we show that in the double-slit experiment this radiation yields a characteristic spectrum and a distinct pattern on the screen that is complementary to the pattern of the electrons. Experimentally, either the existence or the nonexistence of such a radiation would have important implications for the foundations of quantum mechanics.

Pisin Chen

2014-03-05

417

Entanglement swapping in the transactional interpretation of quantum mechanics

NASA Astrophysics Data System (ADS)

The transactional interpretation (TI) of quantum mechanics, which uses retarded and advanced solutions of the Schrödinger equation and its complex conjugate, offers an original way to visualize and understand quantum processes. After a brief review, we show how it can be applied to different quantum situations, emphasizing the importance of specifying a complete configuration of absorbers. We consider in more detail the phenomenon of entanglement swapping, and see how the apparent retroactive enforcement of entanglement can be understood in the TI.

Marchildon, Louis

2014-12-01

418

Lectures on Black Hole Quantum Mechanics

The lectures that follow were originally given in 1992, and written up only slightly later. Since then there have been dramatic developments in the quantum theory of black holes, especially in the context of string theory. None of these are reflected here. The concept of quantum hair, which is discussed at length in the lectures, is certainly of permanent interest,

Frank Wilczek

1998-01-01

419

Quantum Mechanical Models of Turing Machines That Dissipate No Energy

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

420

NARST 1999: Research on Teaching and Learning Quantum Mechanics

NSDL National Science Digital Library

This is a collection of nine papers from a session at the 1999 NARST conference on teaching and learning in quantum mechanics. Topics covered include conceptual understanding of students, computers and visualization, curriculum, and the relations between classical and quantum understanding.

2004-03-10

421

QUANTUM MECHANICS When German physicist Max Planck became the

QUANTUM MECHANICS When German physicist Max Planck became the father of quantum theory in 1900, he and recentlyofGermany'sMaxPlanckInstitute.Ateam of computational scientists led by Dr. Roscilde is using the Oak under your arm. Planck had a much more modest and immediate need

Haas, Stephan

422

The auxiliary field method in quantum mechanics

The auxiliary field method is a new technique to obtain closed formulae for the solutions of eigenequations in quantum mechanics. The idea is to replace a Hamiltonian $H$ for which analytical solutions are not known by another one $\\tilde H$, including one or more auxiliary fields. For instance, a potential $V(r)$ not solvable is replaced by another one $P(r)$ more familiar, or a semirelativistic kinetic part is replaced by an equivalent nonrelativistic one. The approximation comes from the replacement of the auxiliary fields by pure real constants. The approximant solutions for $H$, eigenvalues and eigenfunctions, are then obtained by the solutions of $\\tilde H$ in which the auxiliary parameters are eliminated by an extremization procedure for the eigenenergies. If $H=T(\\bm p)+V(r)$ and if $P(r)$ is a power law, the approximate eigenvalues can be written $T(p_0)+V(r_0)$, where the mean impulsion $p_0$ is a function of the mean distance $r_0$ and where $r_0$ is determined by an equation which is linked to the generalized virial theorem. The general properties of the method are studied and the connections with the envelope theory presented. This method is first applied to nonrelativistic and semirelativistic two-body systems, with a great variety of potentials. Closed formulae are produced for energies, eigenstates, various observables and critical constants, with sometimes a very good accuracy. The method is then used to solve nonrelativistic and semirelativistic many-body systems with one-body and two-body interactions. For such cases, analytical solutions can only be obtained for systems of identical particles, but several systems of interest for atomic and hadronic physics are studied. General results concerning the many-body critical constants are presented, as well as duality relations existing between approximate and exact eigenvalues.

Bernard Silvestre-Brac; Claude Semay; Fabien Buisseret

2011-01-27

423

Interpretation of Quantum Mechanics. A view of our universe

of bright young scientists, Werner Heisenberg, Wolfgang Pauli and others (Fig. 2). THE COPENHAGEN the foundation of quantum mechanics at the Bohr Institute with Werner Heisenberg (middle) and Wolfgang Pauli

Lindgren, Ingvar

424

Quantum mechanics helps in learning for more intelligent robot

A learning algorithm based on state superposition principle is presented. The physical implementation analysis and simulated experiment results show that quantum mechanics can give helps in learning for more intelligent robot.

Dao-Yi Dong; Chun-Lin Chen; Zong-Hai Chen; Chen-Bin Zhang

2005-06-18

425

Interference with correlated photons: Five quantum mechanics experiments for undergraduates

setting. The experiments use correlated photons produced by parametric down conversion to generate for doing experiments with single photons have stimulated studies of the fundamen- tals of quantum mechanics

Galvez, Enrique J. "Kiko"

426

A Simplified Quantum Mechanical Model of Diatomic Molecules

ERIC Educational Resources Information Center

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

Nielsen, Lars Drud

1978-01-01

427

A Computational Model for Observation in Quantum Mechanics

A computational model of observation in quantum mechanics is presented. The model provides a clean and simple computational paradigm which can be used to illustrate and possibly explain some of the unintuitive and ...

Rozas, Guillermo Juan

1987-03-01

428

Everett's Relative-State Formulation of Quantum Mechanics

NSDL National Science Digital Library

This encyclopedia entry 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, Jeff

2005-04-16

429

QUANTUM MECHANICAL CARRIER OF THE IMPRINTS OF GRAVITATION a

QUANTUM MECHANICAL CARRIER OF THE IMPRINTS OF GRAVITATION invariance of spacetime in the absence of gravitation* *. This car- rier consists of the phase Einstein actually started o* *n the path which led towards his formulation of gravitation (general

Gerlach, Ulrich

430

Some Novel Thought Experiments Involving Foundations of Quantum Mechanics and Quantum Information

NASA Astrophysics Data System (ADS)

In this thesis, we have proposed some novel thought experiments involving foundations of quantum mechanics and quantum information theory, using quantum entanglement property. Concerning foundations of quantum mechanics, we have suggested some typical systems including two correlated particles which can distinguish between the two famous theories of quantum mechanics, i.e. the standard and Bohmian quantum mechanics, at the individual level of pair of particles. Meantime, the two theories present the same predictions at the ensemble level of particles. Regarding quantum information theory, two theoretical quantum communication schemes including quantum dense coding and quantum teleportation schemes have been proposed by using entangled spatial states of two EPR particles shared between two parties. It is shown that the rate of classical information gain in our dense coding scheme is greater than some previously proposed multi-qubit protocols by a logarithmic factor dependent on the dimension of Hilbert space. The proposed teleportation scheme can provide a complete wave function teleportation of an object having other degrees of freedom in our three-dimensional space, for the first time. All required unitary operators which are necessary in our state preparation and Bell state measurement processes are designed using symmetric normalized Hadamard matrix, some basic gates and one typical conditional gate, which are introduced here for the first time.

Akhavan, Omid

2004-02-01

431

Vortex Line Fluctuations in Superconductors from Elementary Quantum Mechanics

Concepts from elementary quantum mechanics can be used to understand vortex\\u000aline fluctuations in high-temperature superconductors. Flux lines are\\u000aessentially classical objects, described by a string tension, their mutual\\u000arepulsion, and interactions with pinning centers. The classical partition\\u000afunction, however, is isomorphic to the imaginary time path integral\\u000adescription of quantum mechanics. This observation is used to determine the\\u000athermal

David R. Nelson

1993-01-01

432

On the geometry of the energy operator in quantum mechanics

We analyze the different ways to define the energy operator in geometric theories of quantum mechanics. In some formulations the operator contains the scalar curvature as a multiplicative term. We show that such term can be canceled or added with an arbitrary constant factor, both in the mainstream Geometric Quantization and in the Covariant Quantum Mechanics, developed by Jadczyk and Modugno with several contributions from many authors.

Carlos Tejero Prieto; Raffaele Vitolo

2014-08-26

433

Combined quantum and molecular mechanics (QM/MM).

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

Friesner, Richard A

2004-12-01

434

Exactly solvable quantum mechanical models with Stückelberg divergences

We consider an exactly solvable quantum mechanical model with an infinite number of degrees of freedom that is an analogue\\u000a of the model of N scalar fields (?\\/N)(?a\\u000a a)2 in the leading order in 1\\/N. The model involves vacuum and S-matrix divergences and also the Stckelberg divergences, which\\u000a are absent in other known renormalizable quantum mechanical models with, divergences (such

O. Yu. Shvedov; Shvedov I

2000-01-01

435

Three Essential Reasons Why Nature Chose Quantum Mechanics

We discuss the reason why quantum mechanics is chosen as the most basic law of nature. Probability amplitude, which becomes a probability density after square it, is considered as one of the most essential ingredient of quantum mechanics. Code transfer experiments based on the probability amplitude is proved to be i) error of code transfer is minimum, ii) that error is independent of coding parameters and iii) non-trivial and non-local correlation is possible.

Yoshimasa Kurihara

2013-04-21

436

Contribution to understanding the mathematical structure of quantum mechanics

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed.\\u000a It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, the Born rule, commutation\\u000a and uncertainty relations, probability density current, momentum operator, and rules for including the scalar and vector potentials\\u000a and antiparticles can be obtained from the probabilistic description

L. Skála; V. Kapsa

2007-01-01

437

Scalable quantum mechanical simulation of large polymer systems

We describe a program for quantum mechanical calculations of very large hydrocarbon polymer systems. It is based on a new algorithmic approach to the quantum mechanical tight binding equations that naturally leads to a very efficient parallel implementation and that scales linearly with respect to the number of atoms. We get both very high single node performance as well as a significant parallel speedup on the SGI Origin 2000 parallel computer.

Goedecker, S. [Max-Planck Institute for Solid State Research, Stuttgart (Germany); Hoisie, A.; Kress, J.; Lubeck, O.; Wasserman, H. [Los Alamos National Lab., NM (United States)

1997-08-01

438

Nonlinear Phenomenology from Quantum Mechanics: Soliton in a Lattice

We study a soliton in an optical lattice holding bosonic atoms quantum mechanically using both an exact numerical solution and quantum Monte Carlo simulations. The computation of the state is combined with an explicit account of the measurements of the numbers of the atoms at the lattice sites. In particular, importance sampling in the quantum Monte Carlo method arguably produces faithful simulations of individual experiments. Even though the quantum state is invariant under lattice translations, an experiment may show a noisy version of the localized classical soliton.

Juha Javanainen; Uttam Shrestha

2009-03-29

439

Quantum fragile matter: mechanical excitations of a Reggeon ion chain

This paper proposes to study quantum fragile materials with small linear elasticity and a strong response to zero-point fluctuations. As a first model, we consider a non-unitary (but PT-symmetric) massive quantum chain with a Reggeon-type cubic nonlinearity. At the critical point, the chain supports neither the ordinary quantum phonons of a Luttinger liquid, nor the supersonic solitons that arise in classical fragile critical points in the absence of fluctuations. Quantum fluctuations, approximately captured within a one-loop renormalization group, give rise to mechanical excitations with a nonlinear dispersion relation and dissipative spectral behavior. Models of similar complexity should be realizable with trapped ions.

Strack, Philipp

2013-01-01

440

Is Quantum Mechanics Incompatible with Newton's First Law of Motion

Quantum mechanics (QM)clearly violates Newton's First Law of Motion (NFLM) in the quantum domain. This paper examines an apparent incompatibility between the predictions of QM in the classical limit, and that of classical mechanics (CM) with respect to NFLM. In the process, a general argument is made that such a disparity may be found commonly for a wide variety of quantum predictions in the classical limit. The meaning of the classical limit is examined. Critical views regarding QM by Schrodinger, Bohm, Bell, Clauser, and others are presented as a perspective for the motivation of the present work.

Rabinowitz, Mario

2007-01-01

441

Characterizing mixing and measurement in quantum mechanics

What fundamental constraints characterize the relationship between a mixture $\\rho = \\sum_i p_i \\rho_i$ of quantum states, the states $\\rho_i$ being mixed, and the probabilities $p_i$? What fundamental constraints characterize the relationship between prior and posterior states in a quantum measurement? In this paper we show that there are many surprisingly strong constraints on these mixing and measurement processes that can be expressed simply in terms of the eigenvalues of the quantum states involved. These constraints capture in a succinct fashion what it means to say that a quantum measurement acquires information about the system being measured, and considerably simplify the proofs of many results about entanglement transformation.

M. A. Nielsen

2000-08-16

442

Assessing the Montevideo Interpretation of Quantum Mechanics

This paper gives a philosophical assessment of the Montevideo interpretation of quantum theory, advocated by Gambini, Pullin and co-authors. This interpretation has the merit of linking its proposal about how to solve the measurement problem to the search for quantum gravity: namely by suggesting that quantum gravity makes for fundamental limitations on the accuracy of clocks, which imply a type of decoherence that "collapses the wave-packet". I begin (Section 2) by sketching the topics of decoherence, and quantum clocks, on which the interpretation depends. Then I expound the interpretation, from a philosopher's perspective (Sections 3, 4 and 5). Finally, in Section 6, I argue that the interpretation, at least as developed so far, is best seen as a form of the Everett interpretation: namely with an effective or approximate branching, that is induced by environmental decoherence of the familiar kind, and by the Montevideans' "temporal decoherence".

Jeremy Butterfield

2014-06-17

443

Quantum mechanical version of the classical Liouville theorem

NASA Astrophysics Data System (ADS)

In terms of the coherent state evolution in phase space, we present a quantum mechanical version of the classical Liouville theorem. The evolution of the coherent state from |z> to |sz - rz*> corresponds to the motion from a point z (q,p) to another point sz - rz* with |s|2 - |r|2 = 1. The evolution is governed by the so-called Fresnel operator U(s,r) that was recently proposed in quantum optics theory, which classically corresponds to the matrix optics law and the optical Fresnel transformation, and obeys group product rules. In other words, we can recapitulate the Liouville theorem in the context of quantum mechanics by virtue of coherent state evolution in phase space, which seems to be a combination of quantum statistics and quantum optics.

Xie, Chuan-Mei; Fan, Hong-Yi

2013-03-01

444

From Quantum Mechanics to Quantum Field Theory: The Hopf route

NASA Astrophysics Data System (ADS)

We show that the combinatorial numbers known as Bell numbers are generic in quantum physics. This is because they arise in the procedure known as Normal ordering of bosons, a procedure which is involved in the evaluation of quantum functions such as the canonical partition function of quantum statistical physics, inter alia. In fact, we shall show that an evaluation of the non-interacting partition function for a single boson system is identical to integrating the exponential generating function of the Bell numbers, which is a device for encapsulating a combinatorial sequence in a single function. We then introduce a remarkable equality, the Dobinski relation, and use it to indicate why renormalisation is necessary in even the simplest of perturbation expansions for a partition function. Finally we introduce a global algebraic description of this simple model, giving a Hopf algebra, which provides a starting point for extensions to more complex physical systems.

Solomon, A. I.; Duchamp, G. H. E.; Blasiak, P.; Horzela, A.; Penson, K. A.

2011-03-01

445

Coal Chemistry for Mechanical Engineers: From Macromolecular Thermodynamics to Reservoir Simulation

In pilot trials and commercial scale field demonstrations of CO2 storage in coal seams, quite often unexpected problems with coal swelling around injector and reducing injection efficiency (e.g., Allison unit in the San Juan Basin, RECOPOL in Poland, Hokkaido project in Japan, etc.) can stall or even terminate the site development. To avoid the costly mistakes with the prospective site evaluation, the state of the art in reservoir modeling needs to be improved by taking into account coal properties at the macromolecular level. The current models are based on the rock mechanics, which ignores decades of experimental and theoretical studies of interaction between coal and injected fluids. A pseudopolymer approach is introduced to the modelers as a viable alternative, especially, at medium to high fluid pressures. Further, it is discussed how the thermodynamics of CO2 dissolution in the macromolecular network of the coal matrix can be incorporated into geomechanical models.

Romanov, V.

2007-05-01

446

Coal chemistry for mechanical engineers: from macromolecular thermodynamics to reservoir simulation

In pilot trials and commercial scale field demonstrations of CO{sub 2} storage in coal seams, quite often unexpected problems with coal swelling around injector and reducing injection efficiency (e.g., Allison unit in the San Juan Basin, RECOPOL in Poland, Hokkaido project in Japan, etc.) can stall or even terminate the site development. To avoid the costly mistakes with the prospective site evaluation, the state of the art in reservoir modeling needs to be improved by taking into account coal properties at the macromolecular level. The current models are based on the rock mechanics, which ignores decades of experimental and theoretical studies of interaction between coal and injected fluids. A pseudopolymer approach is introduced to the modelers as a viable alternative, especially, at medium to high fluid pressures. Further, it is discussed how the thermodynamics of CO{sub 2} dissolution in the macromolecular network of the coal matrix can be incorporated into geomechanical models. 96 refs., 4 figs.

Vyacheslav Romanov [U.S. Department of Energy, Pittsburgh, PA (United States). National Energy Technology Laboratory

2007-06-15

447

Whether quantum mechanics can be almighty even in information science

We discuss that there is a crucial contradiction within quantum mechanics. We derive a proposition concerning a quantum expectation value under the assumption of the existence of the directions in a spin-1/2 system. The quantum predictions within the formalism of von Neumann's projective measurement cannot coexist with the proposition concerning the existence of the directions. Therefore, we have to give up either the existence of the directions or the formalism of von Neumann's projective measurement. Hence there is a crucial contradiction within the Hilbert space formalism of the quantum theory. This implies that there is no axiomatic system for the quantum theory. This also reveals that we need new physical theories in order to explain the handing of raw experimental data. We discuss that this crucial contradiction makes the quantum-theoretical formulation of Deutsch's algorithm questionable.

Koji Nagata; Tadao Nakamura

2008-11-28

448

Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaotic nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover`s and Kubo-Fox-Keizer`s approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty.

Lee, Sang-Bong

1993-09-01

449

Can PT-Symmetric Quantum Mechanics be a Viable Alternative Quantum Theory?

Update: A time-independent $n\\times n$ PT-symmetric (and symmetric) Hamiltonian is diagonalizable since it has all distinct real eigenvalues and the resulting diagonal matrix is a real symmetric matrix. The diagonalization results an isometry so there shouldn't be any issue with unitarity and unfortunately this very elementary mathematical fact somehow did not draw the authors' attention. However, PT-symmetric quantum mechanics is not out of trouble. For time-dependent PT-symmetric (and symmetric) Hamiltonians (even $2\\times 2$ ones) the authors observed that there is a violation of unitarity. Moreover, the first named author showed in his recent article arXiv:1312.7738 that PT-symmetric quantum mechanics is indeed a certain kind of Hermitian quantum mechanics and that in order for time-evolution to be unitary with respect to $J$-inner product (one that gives rise to a Hilbert space structure on the space of state functions), the potential energy operator $V(x)$ must be real. This means that those complex PT-symmetric Hamiltonians that have been studied by physicists are unfortunately unphysical. The first named author discussed in a subsequent article arXiv:1401.5149 that while finite-state PT-symmetric quantum mechanics with time-independent Hamiltonians is not physically any different from Hermitian quantum mechanics, PT-symmetric quantum mechanics exhibits a distinctive symmetry from that of Hermitian quantum mechanics.

Sungwook Lee; Lawrence R. Mead

2014-05-18

450

A Practical Quantum Mechanism for the Public Goods Game

Quantum generalizations of conventional games broaden the range of available strategies, which can help improve outcomes for the participants. With many players, such quantum games can involve entanglement among many states which is difficult to implement, especially if the states must be communicated over some distance. This paper describes a quantum mechanism for the economically significant $n$-player public goods game that requires only two-particle entanglement and is thus much easier to implement than more general quantum mechanisms. In spite of the large temptation to free ride on the efforts of others in this game, two-particle entanglement is sufficient to give near optimal expected payoff when players use a simple mixed strategy for which no player can benefit by making different choices. This mechanism can also address some heterogeneous preferences among the players.

Kay-Yut Chen; Tad Hogg; Raymond Beausoleil

2003-01-06

451

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

NASA Astrophysics Data System (ADS)

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

Mahler, G.

2004-07-01

452

Quantum mechanics and reality: An interpretation of Everett's theory

NASA Astrophysics Data System (ADS)

The central part of Everett's formulation of quantum mechanics is a quantum mechanical model of memory and of observation as the recording of information in a memory. To use this model as an answer to the measurement problem, Everett has to assume that a conscious observer can be in a superposition of such memory states and be unaware of it. This assumption has puzzled generations of readers. The fundamental aim of this dissertation is to find a set of simpler assumptions which are sufficient to show that Everett's model is empirically adequate. I argue that Everett's model needs three assumptions to account for the process of observation: an assumption of decoherence of observers as quantum mechanical systems; an assumption of supervenience of mental states (qualities) over quantum mechanical properties; and an assumption about the interpretation of quantum mechanical states in general: quantum mechanical states describe ensembles of states of affairs coexisting in the same system. I argue that the only plausible understanding of such ensembles is as ensembles of possibilities, and that all standard no-collapse interpretations agree in this reading of quantum mechanical states. Their differences can be understood as different theories about what marks the real state within this ensemble, and Everett's theory as the claim that no additional 'mark of reality' is necessary. Using the three assumptions, I argue that introspection cannot determine the objective quantum mechanical state of an observer. Rather, the introspective qualities of a quantum mechanical state can be represented by a (classical) statistical ensemble of subjective states. An analysis of these subjective states and their dynamics leads to the conclusion that they suffice to give empirically correct predictions. The argument for the empirical adequacy of the subjective state entails that knowledge of the objective quantum mechanical state is impossible in principle. Empirical reality for a conscious observer is not described by the objective state, but by a Everettian relative state conditional on the subjective state, and no theoretical 'mark of reality' is necessary for this concept of reality. I compare the resulting concept of reality to Kant's distinction between empirical and transcendental reality.

Lehner, Christoph Albert

453

The mechanism of hydrolysis of deprotonated methyl triphosphate (MTP) to methyl diphosphate (MDP) and inorganic phosphate\\u000a (Pi) in water clusters in the presence and absence of magnesium cations has been modeled. Modeling has been performed by the\\u000a effective fragment potential-based quantum mechanical\\/molecular mechanical method. The energies and energy derivatives in\\u000a the quantum subsystem including MTP, reacting water molecules, and Mg2+

A. V. Rogov; B. L. Grigorenko; A. V. Bochenkova; A. A. Granovskii; A. V. Nemukhin

2007-01-01

454

Deformation quantization: Quantum mechanics lives and works in phase space

NASA Astrophysics Data System (ADS)

Wigner's 1932 quasi-probability Distribution Function in phase-space, his first paper in English, is a special (Weyl) representation of the density matrix. It has been useful in describing quantum flows in semiclassical limits; quantum optics; nuclear and physics; decoherence (eg, quantum computing); quantum chaos; "Welcher Weg" puzzles; molecular Talbot-Lau interferometry; atomic measurements. It is further of great importance in signal processing (time-frequency analysis). Nevertheless, a remarkable aspect of its internal logic, pioneered by H. Groenewold and J. Moyal, has only blossomed in the last quarter-century: It furnishes a third, alternate, formulation of Quantum Mechanics, independent of the conventional Hilbert Space (the gold medal), or Path Integral (the silver medal) formulations, and perhaps more intuitive, since it shares language with classical mechanics: one need not choose sides between coordinate or momentum space variables, since it is formulated simultaneously in terms of position and momentum. This bronze medal formulation is logically complete and self-standing, and accommodates the uncertainty principle in an unexpected manner, so that it offers unique insights into the classical limit of quantum theory. The observables in this formulation are cnumber functions in phase space instead of operators, with the same interpretation as their classical counterparts, only now composed together in novel algebraic ways using star products. One might then envision an imaginary world in which this formulation of quantum mechanics had preceded the conventional Hilbert-space formulation, and its own techniques and methods had arisen independently, perhaps out of generalizations of classical mechanics and statistical mechanics. A sampling of such intriguing techniques and methods has already been published in C. K. Zachos, Int Jou Mod Phys A17 297-316 (2002), and T. L. Curtright, D. B. Fairlie, and C. K. Zachos, A Concise Treatise on Quantum Mechanics in Phase Space, (Imperial Press & World Scientific, 2014).

Zachos, Cosmas K.

2014-09-01

455

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

NASA Astrophysics Data System (ADS)

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

Goff, Allan

2006-11-01

456

Mangosteen is a tropical fruit that presents beneficial effects on human health since it is rich in anthocyanins and xanthones, which are considered bioactive compounds that have been described as good free radical scavengers. One of its most active compounds is ?-mangostin. In this report, a theoretical study on the free radical scavenger capacity of ?-mangostin and its monoanion is analyzed using the density functional theory approximation. Two well-known reaction mechanisms are investigated: the hydrogen atom transfer (HAT) and the radical adduct formation (RAF). Two other mechanisms are also considered: sequential electron proton Transfer (SEPT) and proton coupled electron transfer (PCET). According to thermodynamics and kinetics, ?-mangostin and its deprotonated form are good free radical scavenger through the HAT mechanism, with the anionic (deprotonated) form being more reactive than the neutral one. Their capacity to scavenge OOH free radical is similar to that of carotenes, higher than that of allicin, much higher than that of melatonin and N-acetylcysteine amide, and about 15 times lower than that of 2-propenesulfenic acid. PMID:21936544

Martínez, Ana; Galano, Annia; Vargas, Rubicelia

2011-11-01

457

Anomalous capacitance-voltage profiles in quantum wells explained by a quantum mechanical model

We have developed a quantum mechanical model for understanding and explaining the capacitance–voltage (C–V) carrier profiles observed in quantum wells (QW). The external field imposed on the QW during C–V profiling changes the carrier distribution of the system. This model considers the effects of field and quantum confinement of the carriers in the well. The results obtained by iterative solutions

Sudakshina Kundu; Dipankar Biswas; Reshmi Datta

1997-01-01

458

Electron exchange-correlation in quantum mechanics

It is shown that Fermi-Dirac statistics is guaranteed by the Dirac current, from which spin-dependent quantum velocity fields and spin-dependent quantum trajectories can be inferred. Pauli's exclusion principle is demonstrated using the spin-dependent quantum trajectories. The Dirac current, unlike the Schroedinger current, is nonzero for stationary bound states due to the permanent magnetic moment of the electron. It is of order c{sup 0} in agreement with observation that Fermi-Dirac statistics is independent of electronic velocity. In summary the physical basis for exchange-correlation is found in Dirac's equation, although Schroedinger's equation may be used to evaluate the Dirac current in the nonrelativistic regime of electronic velocity.

Ritchie, B

2009-01-30

459

Multiple-event probability in general-relativistic quantum mechanics

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

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

2007-04-15

460

Fault Models for Quantum Mechanical Switching Networks

The difference between faults and errors is that, unlike faults, errors can be corrected using control codes. In classical test and verification one develops a test set separating a correct circuit from a circuit containing any considered fault. Classical faults are modelled at the logical level by fault models that act on classical states. The stuck fault model, thought of as a lead connected to a power rail or to a ground, is most typically considered. A classical test set complete for the stuck fault model propagates both binary basis states, 0 and 1, through all nodes in a network and is known to detect many physical faults. A classical test set complete for the stuck fault model allows all circuit nodes to be completely tested and verifies the function of many gates. It is natural to ask if one may adapt any of the known classical methods to test quantum circuits. Of course, classical fault models do not capture all the logical failures found in quantum circuits. The first obstacle faced when using methods from classical test is developing a set of realistic quantum-logical fault models. Developing fault models to abstract the test problem away from the device level motivated our study. Several results are established. First, we describe typical modes of failure present in the physical design of quantum circuits. From this we develop fault models for quantum binary circuits that enable testing at the logical level. The application of these fault models is shown by adapting the classical test set generation technique known as constructing a fault table to generate quantum test sets. A test set developed using this method is shown to detect each of the considered faults.

Jacob Biamonte; Jeff S. Allen; Marek A. Perkowski

2010-01-19

461

Scattering and reflection positivity in relativistic Euclidean quantum mechanics

Scattering and reflection positivity in relativistic Euclidean quantum mechanics W. N. Polyzou The University of Iowa, Iowa City, IA 52242 Abstract In this paper I exhibit a class of reflection positive mechanics where the dynamics is introduced through a collection of reflection positive Euclidean "Green

Polyzou, Wayne

462

Scattering and reflection positivity in relativistic Euclidean quantum mechanics

Scattering and reflection positivity in relativistic Euclidean quantum mechanics W. N. Polyzou The University of Iowa, Iowa City, IA 52242 Abstract In this paper I exhibit a class of reflection positive mechanics where the dynamics is introduced through a collection of reflection positive Euclidean ``Green

Polyzou, Wayne

463

Thermodynamic and fluid mechanic analysis of rapid pressurization in a dead-end tube

NASA Technical Reports Server (NTRS)

Three models have been applied to very rapid compression of oxygen in a dead-ended tube. Pressures as high as 41 MPa (6000 psi) leading to peak temperatures of 1400 K are predicted. These temperatures are well in excess of the autoignition temperature (750 K) of teflon, a frequently used material for lining hoses employed in oxygen service. These findings are in accord with experiments that have resulted in ignition and combustion of the teflon, leading to the combustion of the stainless steel braiding and catastrophic failure. The system analyzed was representative of a capped off-high-pressure oxygen line, which could be part of a larger system. Pressurization of the larger system would lead to compression in the dead-end line, and possible ignition of the teflon liner. The model consists of a large plenum containing oxygen at the desired pressure (500 to 6000 psi). The plenum is connected via a fast acting valve to a stainless steel tube 2 cm inside diameter. Opening times are on the order of 15 ms. Downstream of the valve is an orifice sized to increase filling times to around 100 ms. The total length from the valve to the dead-end is 150 cm. The distance from the valve to the orifice is 95 cm. The models describe the fluid mechanics and thermodynamics of the flow, and do not include any combustion phenomena. A purely thermodynamic model assumes filling to be complete upstream of the orifice before any gas passes through the orifice. This simplification is reasonable based on experiment and computer modeling. Results show that peak temperatures as high as 4800 K can result from recompression of the gas after expanding through the orifice. An approximate transient model without an orifice was developed assuming an isentropic compression process. An analytical solution was obtained. Results indicated that fill times can be considerably shorter than valve opening times. The third model was a finite difference, 1-D transient compressible flow model. Results from the code show the recompression effect but predict much lower peak temperatures than the thermodynamic model.

Leslie, Ian H.

1989-01-01

464

Comments on continuous observation in quantum mechanics

It is shown that in open quantum systems the so-called Zeno paradox is not valid. The equations of ideal continuous measurement for Markovian open systems are elaborated and applied to Pauli's simple open system, the actual energy level of which is shown to be monitorable by a continuous nondemolition measurement.

L. Diósi

1986-01-01

465

A quantum mechanical model of adaptive mutation

The principle that mutations occur randomly with respect to the direction of evolutionary change has been challenged by the phenomenon of adaptive mutations. There is currently no entirely satisfactory theory to account for how a cell can selectively mutate certain genes in response to environmental signals. However, spontaneous mutations are initiated by quantum events such as the shift of a

Johnjoe McFadden; Jim Al-Khalili

1999-01-01

466

NASA Astrophysics Data System (ADS)

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

Aspelmeyer, Markus; Schwab, Keith

2008-09-01

467

New Understandings of Quantum Mechanics Based on Interaction

The interaction between two parts in a compound quantum system may be reconsidered more completely than before and some new understandings and conclusions different from current quantum mechanics are obtained, including the conservation law in the evolution in an isolated quantum system, new understandings of duality of particle and wave and the superposition principle of states, three laws corresponding to Newton's laws, new understandings of measurement and the uncertainty relation, arguments against the non-locality of any entangled state and a simple criterion of coherence which is obtained for the experimenter to examine the correctness of the non-locality. These may make quantum mechanics be easily understood intuitively and some strange properties will not appear.

Tian-Hai Zeng

2010-08-10

468

From principles of mechanics to quantum mechanics - a survey on fuzziness in scientific theories

In this paper we discuss the principles of two fundamental theories of physics: mechanics and quantum mechanics. First, we consider two philosophical positions of the German physicist Heinrich Hertz. He established one of the both in the introduction of his well known Principles of Mechanics. This view - Hertz's \\

Rudolf Seising

2008-01-01

469

Hybrid quantum mechanical\\/molecular mechanical potentials have proved to be powerful tools for the simulation of many processes in condensed phase systems and, as a result, there is much current research into how they can be improved. An area of recent attention has been the inclusion of polarization effects on the atoms in the molecular mechanical region which have been shown

Martin J. Field

1997-01-01

470

Quantum mechanical model for two-state jump Markovian process

A quantum mechanical model is given which is equivalent to the stochastic dephasing subject to the two-state jump Markovian process. The stochastic variable corresponds to a Hermitian operator of a spin-1\\/2 system which is embedded in a thermal reservoir, where the time-evolution of the spin-1\\/2 system is described by the quantum master equation of the Lindblad form.

Masashi Ban; Sachiko Kitajima; Kishiko Maruyama; Fumiaki Shibata

2008-01-01

471

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

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

472

Quantum mechanical signature in exclusive coherent pion production

NASA Technical Reports Server (NTRS)

We calculate the coherent production of pions from subthreshold to relativistic energies in heavy-ion collisions using a quantum, microscopic, many-body model. For the first time, in this approach, we use harmonic oscillator wave functions to describe shell-model information. The theoretical quantum mechanical results obtained for the pion spectra represent an important improvement over our previous microscopic, many-body calculations.

Deutchman, P. A.; Buvel, R. L.; Maung, K. M.; Norbury, J. W.; Townsend, L. W.

1986-01-01

473

Supersymmetric Quantum Mechanics for Bianchi Class A models

In this work we present cosmological quantum solutions for all Bianchi Class A cosmological models obtained by means of supersymmetric quantum mechanics . We are able to write one general expression for all bosonic components occuring in the Grassmann expansion of the wave function of the Universe for this class of models. These solutions are obtained by means of a more general ansatz for the so-called master equations.

J. Socorro; E. R. Medina

1999-12-13

474

Quantum mechanics emerges from information theory applied to causal horizons

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

Jae-Weon Lee

2010-05-16

475

Quantum Mechanics Emerges from Information Theory Applied to Causal Horizons

It is suggested that quantum mechanics is not fundamental but emerges from classical information theory applied to causal\\u000a horizons. The path integral quantization and quantum randomness can be derived by considering information loss of fields or\\u000a particles crossing Rindler horizons for accelerating observers. This implies that information is one of the fundamental roots\\u000a of all physical phenomena. The connection between

Jae-Weon Lee

2011-01-01

476

The holographic principle states that the information about a volume of a system is encoded on the boundary surface of the volume. Holography appears in many branches of physics, such as optics, electromagnetism, many-body physics, quantum gravity, and string theory. Here we show that holography is also an underlying principle in thermodynamics, a most important foundation of physics. The thermodynamics of a system is fully determined by its partition function. We prove that the partition function of a physical system is an analytic function of all the physical parameters, and therefore its values in any area on the complex plane of a physical parameter are uniquely determined by its values along the boundary. The thermodynamic holography has applications in studying thermodynamics of nano-scale systems (such as molecule engines, nano-generators and macromolecules) and provides a new approach to many-body physics.

Bo-Bo Wei; Zhan-Feng Jiang; Ren-Bao Liu

2014-11-24

477

Imitating quantum mechanics: qubit-based model for simulation

We present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations of different frequencies results in exponential growth of the state space similar to the tensor-product composition of qubit spaces in quantum mechanics. Individual qubits remain accessible in a composite system, which is represented as a complex function of a single variable, though entanglement imposes a demand on resources that scales exponentially with the number of entangled qubits. We carry out a simulation of Shor's algorithm and discuss a simpler implementation in this classical model.

Steven Peil

2009-06-29

478

Aspects of the Decoherent Histories Approach to Quantum Mechanics

I give an informal overview of the decoherent histories approach to quantum mechanics, due to Griffiths, to Omn\\`es, and to Gell-Mann and Hartle is given. Results on the connections between decoherence, records, correlation and entropy are described. The emphasis of the presentation is on understanding the broader meaning of the conditions of consistency and decoherence, and in particular, the extent to which they permit one to assign definite properties to the system. The quantum Brownian motion model is briefly discussed. (To appear in proceedings of the workshop, "Stochastic Evolution of Quantum States in Open Systems and Measurement Processes", Budapest, March, 1993, edited by L.Diosi).

J. J. Halliwell

1993-08-06

479

Classical Representations of Quantum Mechanics Related to Statistically Complete Observables

We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding is the existence of so-called statistically complete observables and the duality between the state spaces and the spaces of the observables, the latter holding in the quantum as well as in the classical case. In the phase-space context, we further discuss joint position-momentum observables, Hilbert spaces of infinitely differentiable functions on phase space, and dequantizations. Finally, the relation of quantum dynamics to the classical Liouville dynamics is investigated.

Werner Stulpe

2006-10-16

480

Comment on 'Nonlocality, Counterfactuals and Quantum Mechanics'

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

Stapp, H.P.

1999-04-14