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1

From Quantum Mechanics to Thermodynamics?  

E-print Network

From Quantum Mechanics to Thermodynamics? Dresden, 22.11.2004 Jochen Gemmer Universit¨at Osnabr Description? Quantum Mechanics i¯h t = (- ¯h2 2m + V ) Classical Mechanics: m d2 dt2 x = - V Thermodynamics: dU = TdS - pdV dS dt > 0 #12;Fundamental Law or Emergent Description? Quantum Mechanics i

Steinhoff, Heinz-Jürgen

2

Nonequilibrium quantum statistical mechanics and thermodynamics  

E-print Network

The purpose of this work is to discuss recent progress in deriving the fundamental laws of thermodynamics (0th, 1st and 2nd-law) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and different reversible and irreversible thermodynamic processes are studied from the point of view of quantum statistical mechanics. Special emphasis is put on new adiabatic theorems for steady states close to and far from equilibrium, and on investigating cyclic thermodynamic processes using an extension of Floquet theory.

Walid K. Abou Salem

2006-01-23

3

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

NSDL National Science Digital Library

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

4

Exact fuzzy sphere thermodynamics in matrix quantum mechanics  

E-print Network

We study thermodynamical properties of a fuzzy sphere in matrix quantum mechanics of the BFSS type including the Chern-Simons term. Various quantities are calculated to all orders in perturbation theory exploiting the one-loop saturation of the effective action in the large-N limit. The fuzzy sphere becomes unstable at sufficiently strong coupling, and the critical point is obtained explicitly as a function of the temperature. The whole phase diagram is investigated by Monte Carlo simulation. Above the critical point, we obtain perfect agreement with the all order results. In the region below the critical point, which is not accessible by perturbation theory, we observe the Hagedorn transition. In the high temperature limit our model is equivalent to a totally reduced model, and the relationship to previously known results is clarified.

Naoyuki Kawahara; Jun Nishimura; Shingo Takeuchi

2007-04-24

5

Overview of some results in my thermodynamics, quantum mechanics, and molecular dynamics simulations research  

Microsoft Academic Search

Described here in sectional form are some simultaneous developments and results in [A] Continuum thermodynamics with applications, including electrochemical systems, [B] Statistical thermodynamics [C] Foundational studies in mechanics, quantum mechanics and radiation, and [D] Molecular dynamics and NEMD simulations of complex systems which are chemical reaction theories deduced from computer simulations. These topics were investigated over a two decade period

Christopher G. Jesudason

2009-01-01

6

Probing phase-space noncommutativity through quantum mechanics and thermodynamics of free particles and quantum rotors  

E-print Network

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

7

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.

8

An account on statistical mechanics and thermodynamics of quantum isolated horizons  

E-print Network

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

2013-11-30

9

Quantum Thermodynamic Cycles and Quantum Heat Engines (II)  

E-print Network

We study the quantum mechanical generalization of force or pressure, and then we extend the classical thermodynamic isobaric process to quantum mechanical systems. Based on these efforts, we are able to study the quantum version of thermodynamic cycles that consist of quantum isobaric process, such as quantum Brayton cycle and quantum Diesel cycle. We also consider the implementation of quantum Brayton cycle and quantum Diesel cycle with some model systems, such as single particle in 1D box and single-mode radiation field in a cavity. These studies lay the microscopic (quantum mechanical) foundation for Szilard-Zurek single molecule engine.

H. T. Quan

2008-11-17

10

Thermodynamical Quantum Gravity  

E-print Network

The canonically quantized 3+1 General Relativity with the global one dimensionality conjecture defines the model, which dimensionally reduced and secondary quantized yields the one-dimensional quantum field theory wherein the generic one-point correlations create a boson mass responsible for quantum gravity. In this paper, this simple model is developed in a wider sense. We propose to consider the thermodynamics of space quanta, constructed ab initio from the entropic formalism, as the quantum gravity phenomenology.

Lukasz Andrzej Glinka

2009-06-20

11

Thermodynamics of quantum lightspheres  

E-print Network

Lightspheres, surfaces where massless particles are confined in closed orbits, are expected to be common astrophysical structures surrounding ultra-compact objects. In this paper a semi-classical treatment to photons in a lightspheres is proposed. We consider the quantum Maxwell field and derive its energy spectra. A thermodynamic approach for the quantum lightsphere is explored. Within this treatment, an expression for the spectral energy density of the emitted radiation is presented. Our results suggest that lightspheres populated by photons, when thermalized with their environment, have non-usual thermodynamic properties, which could lead to distinct observational signatures.

Baldiotti, M C; Molina, C; Pereira, Thiago S

2014-01-01

12

Thermodynamics of quantum lightspheres  

E-print Network

Lightspheres, surfaces where massless particles are confined in closed orbits, are expected to be common astrophysical structures surrounding ultra-compact objects. In this paper a semi-classical treatment to photons in a lightspheres is proposed. We consider the quantum Maxwell field and derive its energy spectra. A thermodynamic approach for the quantum lightsphere is explored. Within this treatment, an expression for the spectral energy density of the emitted radiation is presented. Our results suggest that lightspheres populated by photons, when thermalized with their environment, have non-usual thermodynamic properties, which could lead to distinct observational signatures.

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

2014-10-07

13

Quantum Mechanics + Open Systems  

E-print Network

Quantum Mechanics + Open Systems = Thermodynamics ? Jochen Gemmer T¨ubingen, 09.02.2006 #12., World Scientific) #12;Fundamental Law or Emergent Description? Quantum Mechanics i t = (- 2 2m + V or Emergent Description? Quantum Mechanics i t = (- 2 2m + V ) "Heisenberg Cut" Classical Mechanics: m d2

Steinhoff, Heinz-Jürgen

14

Thermodynamic and quantum chemical study of the transformations and operation mechanism of molybdenum catalysts under hydrogenation conditions  

Microsoft Academic Search

Structural transformations and the mechanism of the operation of molybdenum-containing catalysts under hydrogenation conditions\\u000a have been studied by chemical thermodynamics and quantum chemistry methods, as well as the role of sulfur compounds in this\\u000a process. It has been shown that molybdenum disulfide, an effective hydrogenation catalyst, is produced via the reaction of\\u000a molybdenum oxide with hydrogen sulfide, not elemental sulfur.

Kh. M. Kadiev; A. M. Gyulmaliev; M. Ya. Shpirt; S. N. Khadzhiev

2010-01-01

15

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

E-print Network

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

16

Thermodynamics in Loop Quantum Cosmology  

E-print Network

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

17

Thermodynamics of quantum photon spheres  

E-print Network

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

18

Thermodynamics of quantum crystalline membranes  

NASA Astrophysics Data System (ADS)

We investigate the thermodynamic properties and the lattice stability of two-dimensional crystalline membranes, such as graphene and related compounds, in the low-temperature quantum regime T ?0. A key role is played by the anharmonic coupling between in-plane and out-of-plane lattice modes that, in the quantum limit, has very different consequences from those in the classical regime. The role of retardation, namely of frequency dependence, in the effective anharmonic interactions turns out to be crucial in the quantum regime. We identify a crossover temperature, T*, between the classical and quantum regimes, which is 70-90 K for graphene. Below T*, the heat capacity and thermal expansion coefficient decrease as power laws with decreasing temperature, tending to zero for T ?0 as required by the third law of thermodynamics.

Amorim, B.; Roldn, R.; Cappelluti, E.; Fasolino, A.; Guinea, F.; Katsnelson, M. I.

2014-06-01

19

Quantum Mechanics  

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 KleinGordon 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

20

Quantum Mechanics  

NSDL National Science Digital Library

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

De Raedt, Hans; Michielsen, Kristel

2010-03-25

21

Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics.  

PubMed

We perform a direct test of the gauge-gravity duality associated with the system of N D0-branes in type IIA superstring theory at finite temperature. Based on the fact that higher derivative corrections to the type IIA supergravity action start at the order of alpha;{'3}, we derive the internal energy in expansion around infinite 't Hooft coupling up to the subleading term with one unknown coefficient. The power of the subleading term is shown to be nicely reproduced by the Monte Carlo data obtained nonperturbatively on the gauge theory side at finite but large effective (dimensionless) 't Hooft coupling constant. This suggests, in particular, that the open strings attached to the D0-branes provide the microscopic origin of the black hole thermodynamics of the dual geometry including alpha;{'} corrections. The coefficient of the subleading term extracted from the fit to the Monte Carlo data provides a prediction for the gravity side. PMID:19518941

Hanada, Masanori; Hyakutake, Yoshifumi; Nishimura, Jun; Takeuchi, Shingo

2009-05-15

22

Thermodynamics of quantum heat engines  

NASA Astrophysics Data System (ADS)

We consider a recently proposed four-level quantum heat engine (QHE) model to analyze the role of quantum coherences in determining the thermodynamic properties of the engine, such as flux, output power, and efficiency. A quantitative analysis of the relative effects of the coherences induced by the two thermal baths is brought out. By taking account of the dissipation in the cavity mode, we define useful work obtained from the QHE and present some analytical results for the optimal values of relative coherences that maximizes flux (hence output power) through the engine. We also analyze the role of quantum effects in inducing population inversion (lasing) between the states coupled to the cavity mode. The universal behavior of the efficiency at maximum power (EMP) is examined. In accordance with earlier theoretical predictions, to leading order, we find that EMP?c/2, where ?c is Carnot efficiency. However, the next higher order coefficient is system dependent and hence nonuniversal.

Goswami, Himangshu Prabal; Harbola, Upendra

2013-07-01

23

Thermodynamics of discrete quantum processes  

E-print Network

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

24

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

25

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 5 problems LAST NAME FIRST NAME #12 with the effective electron mass at the band edges. #12;Applied quantum mechanics 3 (c) Write a computer program

Levi, Anthony F. J.

26

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 1 problems LAST NAME FIRST NAME #12 happens to the beat frequency if the airplane moves in an arc? #12;Applied quantum mechanics 3 Problem 1

Levi, Anthony F. J.

27

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 8 problems LAST NAME FIRST NAME #12;Applied quantum mechanics 3 (b) If the electron is in a semiconductor and has an effective mass m * 0.07 m

Levi, Anthony F. J.

28

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 10 problems LAST NAME FIRST NAME #12 ­( ) L/( )= L/ #12;Applied quantum mechanics 3 (d) Use the results of (b) an (c) to draw the electron

Levi, Anthony F. J.

29

Thermodynamics of space quanta models quantum gravity  

E-print Network

Canonically quantized 3+1 general relativity with the global one dimensionality (1D) conjecture defines the model, which dimensionally reduced and secondary quantized yields the 1D quantum field theory wherein generic one-point correlations create physical scales. This simple quantum gravity model, however, can be developed in a wider sense. In this paper we propose to consider ab initio thermodynamics of space quanta as the quantum gravity phenomenology. The thermodynamics is constructed in the entropic formalism.

Glinka, L A

2009-01-01

30

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 6 problems LAST NAME FIRST NAME #12 --- and that for a Poisson distribution of such photons #12; 1 2 n ---------------- Applied quantum mechanics 3 (c) Apply conditions is the quantum mechanical result m t 2 2 d d x xd d V x ­= the same Newton's second law in which

Levi, Anthony F. J.

31

Quantum Collapse and the Second Law of Thermodynamics  

E-print Network

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

32

Statistical Thermodynamics of Polymer Quantum Systems  

NASA Astrophysics Data System (ADS)

Polymer quantum systems are mechanical models quantized similarly as loop quantum gravity. It is actually in quantizing gravity that the polymer term holds proper as the quantum geometry excitations yield a reminiscent of a polymer material. In such an approach both non-singular cosmological models and a microscopic basis for the entropy of some black holes have arisen. Also important physical questions for these systems involve thermodynamics. With this motivation, in this work, we study the statistical thermodynamics of two one dimensional polymer quantum systems: an ensemble of oscillators that describe a solid and a bunch of non-interacting particles in a box, which thus form an ideal gas. We first study the spectra of these polymer systems. It turns out useful for the analysis to consider the length scale required by the quantization and which we shall refer to as polymer length. The dynamics of the polymer oscillator can be given the form of that for the standard quantum pendulum. Depending on the dominance of the polymer length we can distinguish two regimes: vibrational and rotational. The first occur for small polymer length and here the standard oscillator in Schrdinger quantization is recovered at leading order. The second one, for large polymer length, features dominant polymer effects. In the case of the polymer particles in the box, a bounded and oscillating spectrum that presents a band structure and a Brillouin zone is found. The thermodynamical quantities calculated with these spectra have corrections with respect to standard ones and they depend on the polymer length. When the polymer length is small such corrections resemble those coming from the phenomenological generalized uncertainty relation approach based on the idea of the existence of a minimal length. For generic polymer length, thermodynamics of both systems present an anomalous peak in their heat capacity CV. In the case of the polymer oscillators this peak separates the vibrational and rotati onal regimes, while in the ideal polymer gas it reflects the band structure which allows the existence of negative temperatures.

Chacn-Acosta, Guillermo; Manrique, Elisa; Dagdug, Leonardo; Morales-Tcotl, Hugo A.

2011-12-01

33

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 6 problems LAST NAME FIRST NAME #12 of the system. (b) Find . (c) Find and show that . Under what conditions is the quantum mechanical result( ) td d A t( ) t A td d A /= A B i 2 --- A^ B^,[ ] A^ B^ Et 2 --- n n 1 2 --- #12;Applied quantum

Levi, Anthony F. J.

34

quantum mechanics  

PubMed Central

-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matterantimatter 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

35

Bohmian mechanics contradicts quantum mechanics  

E-print Network

Bohmian mechanics contradicts quantum mechanics Arnold Neumaier Institut fur Mathematik, Universit and quantum mechanics predict values of opposite sign for certain time correlations. The discrepancy can no loophole for claiming that Bohmian mechanics reproduces all predictions of quantum mechanics exactly

Neumaier, Arnold

36

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 9 problems LAST NAME FIRST NAME #12 10 cm 1­ = 2 1? 0.2? µm 3 2 µm 100 µA #12;Applied quantum mechanics 3 Problem 9.4 Modify the computer

Levi, Anthony F. J.

37

Quantum Mechanics in Quantum Computing  

Microsoft Academic Search

Mathew Johnson is a Ball State junior majoring in Mathematics (Option 1) with a minor in Physics. In his sophomore year, he participated in the student- faculty colloquium, where he explored quantum com- puting with several other students and faculty. Quantum mechanics is a scientific theory that seeks to describe atomic and subatomic particles (or quantum particles) as well as

Mathew Johnson

2003-01-01

38

Quantum Mechanics Measurements, Mutually  

E-print Network

Quantum Mechanics Measurements, Mutually Unbiased Bases and Finite Geometry Or why six is the first) #12;Quantum Mechanics for Dummies Finite dimensional quantum states are represented by trace one,1 -icS1,1[ ] #12;Quantum systems evolve and are measured. The evolution of a quantum system using

Gruner, Daniel S.

39

Quantum Mechanics  

Microsoft Academic Search

We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with respect to a uniquely defined positive scalar product in a infinite dimensional (right) quaternionic Hilbert space. According to such results we obtain two alternative descriptions of a quantum

A. L. Stewart; G. Scolarici; L. Solombrino

1963-01-01

40

Quantum Mechanics  

NASA Astrophysics Data System (ADS)

A development of quantum theory that was initiated in the 1920s by Werner Heisenberg (1901-76) and Erwin Schrdinger (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

41

An entropic picture of emergent quantum mechanics  

E-print Network

Quantum mechanics emerges a la Verlinde from a foliation of space by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantised in units of Boltzmann's constant k. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on space. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant h from Boltzmann's constant k.

D. Acosta; P. Fernandez de Cordoba; J. M. Isidro; J. L. G. Santander

2011-07-10

42

Applied quantum mechanics 1 Applied Quantum Mechanics  

E-print Network

Applied quantum mechanics 1 Applied Quantum Mechanics Chapter 5 problems LAST NAME FIRST NAME #12 + --------------------------------------------- k = t 10/= t 1­= Ek 2t kxL( ) 2t 2kxL( )cos+cos= t 10/= t 1­= t 0.2­= #12;Applied quantum mechanics 3 (c) Write a computer program to plot the electron density of states for a square lat- tice

Levi, Anthony F. J.

43

Fractional quantum mechanics  

Microsoft Academic Search

A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Lvy 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 Lvy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and

Nikolai Laskin

2000-01-01

44

Thermodynamics of N-dimensional quantum walks  

E-print Network

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

45

Thermodynamics of N-dimensional quantum walks  

NASA Astrophysics Data System (ADS)

The entanglement between the position and the coin state of an N-dimensional quantum walker is shown to lead to a thermodynamic theory. The entropy, in this thermodynamics, is associated with 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, and Helmholz free energy. We study in detail the case of a two-dimensional quantum walk, in the case of two initial conditions: a nonseparable coin-position initial state and a separable one. The resulting entanglement temperature is presented as a function of the parameters of the system and those of the initial conditions.

Romanelli, Alejandro; Donangelo, Raul; Portugal, Renato; Marquezino, Franklin de Lima

2014-08-01

46

Quantum optical thermodynamic machines: lasing as relaxation.  

PubMed

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. PMID:20365140

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

2009-12-01

47

Astrophysics QuantumMechanics  

E-print Network

Astrophysics Geometry QuantumMechanics Stochasticanalysis DifferentialEquations A N N U A L R E P O report 2010 6 Geometry 6 Stochastic analysis 8 Differential Equations 9 Astrophysics 11 Quantum Mechanics

Johansen, Tom Henning

48

Quantum thermodynamic processes: a control theory for machine cycles  

NASA Astrophysics Data System (ADS)

The minimal set of thermodynamic control parameters consists of a statistical (thermal) and a mechanical one. These suffice to introduce all the pertinent thermodynamic variables; thermodynamic processes can then be defined as paths on this 2-dimensional control plane. Putting aside coherence we show that for a large class of quantum objects with discrete spectra and for the cycles considered the Carnot efficiency applies as a universal upper bound. In the dynamic (finite time) regime renormalized thermodynamic variables allow to include non-equilibrium phenomena in a systematic way. The machine function ceases to exist in the large speed limit; the way, in which this limit is reached, depends on the type of cycle considered.

Birjukov, J.; Jahnke, T.; Mahler, G.

2008-07-01

49

Introduction to Quantum Mechanics  

E-print Network

The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.

Eduardo J. S. Villaseor

2008-04-23

50

Elements of sub-quantum thermodynamics: quantum motion as ballistic diffusion  

E-print Network

By modelling quantum systems as emerging from a (classical) sub-quantum thermodynamics, the quantum mechanical "decay of the wave packet" is shown to simply result from sub-quantum diffusion with a specific diffusion coefficient varying in time due to a particle's changing thermal environment. It is thereby proven that free quantum motion strictly equals ballistic diffusion. The exact quantum mechanical trajectory distributions and the velocity field of the Gaussian wave packet are thus derived solely from classical physics. Moreover, also quantum motion in a linear (e.g., gravitational) potential is shown to equal said ballistic diffusion. Quantitative statements on the trajectories' characteristic behaviours are obtained which provide a detailed "micro-causal" explanation in full accordance with momentum conservation.

Gerhard Groessing; Siegfried Fussy; Johannes Mesa Pascasio; Herbert Schwabl

2010-05-06

51

Quantum theory of time and thermodynamics  

SciTech Connect

Quantum thermodynamics is introduced through a quantized relativistic trace equation. This equation describes the discrete and continuous spectra and eigenfunctions of macroscopic thermodynamic systems. For solids and quantum liquids this is equivalent to a set of coupled eigenvalue equations for the internal energy and Gruneisen parameter. Simultaneous eigenvalue equations are developed for internal energy, time, time dimension and space dimension. These equations determine the effects of real state equations on the rates and geometrical structures of physical processes such as chemical and nuclear reactions which occur in bulk matter. High-Tc superconductivity is suggested to be associated with the coherent spacetime state of electrons in Cooper pairs. A quantized relativistic thermodynamic trace equation for coherent spacetime is developed, and this equation in conjunction with the quantized coherent time, time dimension and space dimension equations are suggested to describe high-Tc superconductivity. The first order macroscopic quantum eigenvalue equations for time, time dimension and space dimension are the bulk matter equivalents of the Dirac equation which describes microscopic systems. The eigenvalue equations for time, time dimension and space dimension are solved and yield solutions that predict structured energy and pressure.

Weiss, R. A.

1992-03-01

52

Quantum Mechanics II (Undergraduate)  

E-print Network

, 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.

53

Introduction to Quantum Mechanics  

NSDL National Science Digital Library

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

Griffiths, David J.

2005-04-16

54

Friction Force: From Mechanics to Thermodynamics  

ERIC Educational Resources Information Center

We study some mechanical problems in which a friction force is acting on a system. Using the fundamental concepts of state, time evolution and energy conservation, we explain how to extend Newtonian mechanics to thermodynamics. We arrive at the two laws of thermodynamics and then apply them to investigate the time evolution and heat transfer of

Ferrari, Christian; Gruber, Christian

2010-01-01

55

Ph 125 Quantum Mechanics  

NSDL National Science Digital Library

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

Mabuchi, Hideo

2005-12-05

56

Ph 125 Quantum Mechanics  

NSDL National Science Digital Library

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

Mabuchi, Hideo

2011-01-21

57

Covariant quantum mechanics and quantum symmetries  

E-print Network

Covariant quantum mechanics and quantum symmetries Josef JanyŸska 1 , Marco Modugno 2 , Dirk Saller: quantum mechanics, classical mechanics, general relativity, infinitesimal symmetries. 2000 MSC: 81P99, 81Q Introduction 2 2 Covariant quantum mechanics 5 2.1 Classical background

Jany?ka, Josef

58

An introduction to quantum probability, quantum mechanics, and quantum computation  

E-print Network

An introduction to quantum probability, quantum mechanics, and quantum computation Greg Kuperberg". Recently quantum computation has entered as a new reason for both mathematicians and computer scientists deterministic algorithms for some computational problems, quantum algorithms can be moderately faster

Thomases, Becca

59

Low-temperature thermodynamics with quantum coherence  

E-print Network

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

60

Quantum Statistical Mechanics and Quantum Computation  

E-print Network

Quantum Statistical Mechanics and Quantum Computation 22-23 March 2012 Room 111, Jadwin Hall, focused meeting to explore the intersection between quantum statistical mechanics and quantum computation, specifically quantum complexity theory. Advances in complexity theory have interesting implications for physics

61

EK424 THERMODYNAMICS AND STATISTICAL MECHANICS Boston University  

E-print Network

EK424 THERMODYNAMICS AND STATISTICAL MECHANICS Boston University Fall 2012 Thermodynamics. The subject of statistical mechanics is concerned with expressing thermodynamics and the macroscopic behavior Wednesday, October 17, 2012 Statistical Mechanics and Partition Functions 12 Monday, October 22, 2012

62

Time in quantum mechanics  

E-print Network

The role of time in quantum mechanics has been and is still very controversial. The purpose of this paper was to explore the historical interpretation of time in quantum mechanics, to determine the current status of this problem-L and to investigate...

Chapin, Kimberly R.

2012-06-07

63

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

64

Geometrization of Quantum Mechanics  

E-print Network

We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.

J. F. Carinena; J. Clemente-Gallardo; G. Marmo

2007-01-19

65

Membrane Quantum Mechanics  

E-print Network

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

2014-01-01

66

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

67

Is quantum mechanics exact?  

SciTech Connect

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 [California Institute of Technology, Pasadena, California 91125 (United States)] [California Institute of Technology, Pasadena, California 91125 (United States)

2013-06-15

68

Constructibility in Quantum Mechanics  

E-print Network

We propose a set theoretical foundation including an axiom of constructibility and derive a generalized quantum mechanics by postulating symmetry of action. The Schroedinger equation proves to be a special case of a nonlinear sigma model. Quantum mechanics is obtained here without the requirement for presupposing the statistical interpretation of the wave function; thus this derivation becomes continuous with prior physics. In this theory we also see space-time as relational and the fields as free of singularities.

D. J. Bendaniel

2008-06-06

69

Supersymmetry in quantum mechanics  

Microsoft Academic Search

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical\\u000a problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable. In\\u000a this lecture I review the theoretical formulation of supersymmetric quantum mechanics and discuss many of its applications.\\u000a I show that the well-known exactly solvable

Avinash Khare

1997-01-01

70

Evading quantum mechanics  

E-print Network

Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement back action often limit the precision of conventional classical information-processing devices, such as sensors and atomic clocks. Here we show that by engineering the dynamics of coupled quantum systems, it is possible to construct a subsystem that evades the measurement back action of quantum mechanics, at all times of interest, and obeys any classical dynamics, linear or nonlinear, that we choose. We call such a system a quantum-mechanics-free subsystem (QMFS). All of the observables of a QMFS are quantum-nondemolition (QND) observables; moreover, they are dynamical QND observables, thus demolishing the widely held belief that QND observables are constants of motion. QMFSs point to a new strategy for designing classical information-processing devices in regimes where quantum noise is detrimental, unifying previous approaches that employ QND observables, back-action evasion, and quantum noise cancellation. Potential applications include gravitational-wave detection, optomechanical force sensing, atomic magnetometry, and classical computing. Demonstrations of dynamical QMFSs include the generation of broad-band squeezed light for use in interferometric gravitational-wave detection, experiments using entangled atomic spin ensembles, and implementations of the quantum Toffoli gate.

Mankei Tsang; Carlton M. Caves

2012-03-11

71

Graduate Quantum Mechanics Reform  

NSDL National Science Digital Library

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

Carr, Lincoln D.; Mckagan, Sam B.

2009-05-06

72

The Teaching of Quantum Mechanics  

NSDL National Science Digital Library

This website has tips and techniques for teaching quantum mechanics. It presents and outlines central ideas in quantum mechanics and includes descriptions of textbooks and software that can be helpful in quantum classes.

Styer, Dan

2003-10-10

73

Mechanics and thermodynamics in lubrication  

NASA Technical Reports Server (NTRS)

The causes for breakdown in the lubricant film of mineral oils are discussed. It is stated that the critical point is caused by desorption of the naturally occurring surface active agent and can be described by thermodynamic analysis. The effect of different metals in lubrication is surveyed. The problem of breakdown in elastohydrodynamic lubrication is treated phenomenologically by studying traction. The topics considered are classical and non-Newtonian explanations, anomalous film thickness and viscosity effects, surface roughness contributions, and solidification of the lubricant. Reasons for the apparent granular traction characteristics are examined.

Cameron, A.; Gentle, C. R.

1973-01-01

74

Quantum Mechanics From the Cradle?  

ERIC Educational Resources Information Center

States that the major problem in learning quantum mechanics is often the student's ignorance of classical mechanics and that one conceptual hurdle in quantum mechanics is its statistical nature, in contrast to the determinism of classical mechanics. (MLH)

Martin, John L.

1974-01-01

75

QUANTUM MECHANICS II Physics 342  

E-print Network

QUANTUM MECHANICS II Physics 342 KPTC 103 9:00 ­ 10:20 a.m. 1 Tues., Thurs. ­ Winter Quarter 2011 quantum mechanics at the graduate level. The text for Quantum Mechanics II will be J. J. Sakurai and Jim Napolitano, Modern Quantum Mechanics, Second Edition (Addison-Wesley, San Francisco, 2011). For supplemental

Rosner, Jonathan L.

76

Quantum mechanics over sets  

E-print Network

In the tradition of toy models of quantum mechanics in vector spaces over finite fields (e.g., Schumacher and Westmoreland's "modal quantum theory"), one finite field stands out, 2, since vectors over 2 have an interpretation as natural mathematical objects, i.e., sets. This engages a sets-to-vector-spaces bridge that is part of the mathematical folklore to translate both ways between set concepts and vector space concepts. Using that bridge, the mathematical framework of (finite-dimensional) quantum mechanics can be transported down to sets resulting in quantum mechanics over sets or QM/sets. This approach leads to a different treatment of Dirac's brackets than in "modal quantum theory" (MQT), and that gives a full probability calculus (unlike MQT that only has zero-one modalities of impossible and possible). That, in turn, leads to a rather fulsome theory of QM over sets that includes "logical" models of the double-slit experiment, Bell's Theorem, quantum information theory, quantum computing, and much else. Indeed, QM/sets is proposed as the "logic" of QM in the old-fashioned sense of "logic" as giving the simplified essentials of a theory. QM/sets is also a key part of a broader research program to provide an interpretation of QM based on the notion of "objective indefiniteness," a program that grew out the recent development of the logic of partitions mathematically dual to the usual Boolean logic of subsets.

David Ellerman

2013-10-30

77

Periodic thermodynamics of isolated quantum systems.  

PubMed

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 adhoc methods. PMID:24785013

Lazarides, Achilleas; Das, Arnab; Moessner, Roderich

2014-04-18

78

What is quantum mechanics?  

Microsoft Academic Search

We discuss the arguments for suspecting that there exists a classical, i.e. deterministic theory underlying quantum mechanics. A difficulty is that an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in

Gerard't Hooft

2007-01-01

79

Probability in Quantum Mechanics  

Microsoft Academic Search

The concept of probability played an important role in the very beginning of ? quantum theory, when Max Planck (18581947)\\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

80

Black Hole Thermodynamics and Statistical Mechanics  

E-print Network

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

81

Nonlinear thermodynamic quantum master equation: Properties and examples  

SciTech Connect

The quantum master equation obtained from two different thermodynamic arguments is seriously nonlinear. We argue that, for quantum systems, nonlinearity occurs naturally in the step from reversible to irreversible equations and we analyze the nature and consequences of the nonlinear contribution. The thermodynamic nonlinearity naturally leads to canonical equilibrium solutions and extends the range of validity to lower temperatures. We discuss the Markovian character of the thermodynamic quantum master equation and introduce a solution strategy based on coupled evolution equations for the eigenstates and eigenvalues of the density matrix. The general ideas are illustrated for the two-level system and for the damped harmonic oscillator. Several conceptual implications of the nonlinearity of the thermodynamic quantum master equation are pointed out, including the absence of a Heisenberg picture and the resulting difficulties with defining multitime correlations.

Oettinger, Hans Christian [ETH Zuerich, Department of Materials, Polymer Physics, HCI H 543, CH-8093 Zuerich (Switzerland)

2010-11-15

82

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

83

Dual Quantum Mechanics  

E-print Network

We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position or in the momentum representation. As a way to support this complementation, starting from the action that describes conformal gravity in the world-line formalism, we show that there are duality transformations that relate the dynamics in the presence of position dependent vector and tensor fields to the dynamics in the presence of momentum dependent vector and tensor fields.

W. Chagas-Filho

2009-05-11

84

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

E-print Network

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

85

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

E-print Network

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

86

Lorentz covariant statistical mechanics and thermodynamics of the relativistic ideal gas and preferred frame  

E-print Network

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 consistent, free of paradoxes description of tachyons. The thermodynamic functions within the covariant approach are obtained both in classical and quantum case.

K. Kowalski; J. Rembielinski; K. A. Smolinski

2007-12-17

87

Lorentz covariant statistical mechanics and thermodynamics of the relativistic ideal gas and preferred frame  

SciTech Connect

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

88

Relational Quantum Mechanics  

E-print Network

We suggest that the inner syntax of Quantum Mechanics is relational logic, a form of logic developed by C. S. Peirce during the years 1870 - 1880. The Peircean logic has the structure of category theory, with relation serving as an arrow (or morphism). At the core of the relational logical system is the law of composition of relations. This law leads to the fundamental quantum rule of probability as the square of an amplitude. Our study of a simple discrete model, extended to the continuum, indicates that a finite number of degrees of freedom can live in phase space. This "granularity" of phase space is determined by Planck's constant h. We indicate also the broader philosophical ramifications of a relational quantum mechanics.

Nicolaidis, Argyris

2012-01-01

89

Relational Quantum Mechanics  

E-print Network

We suggest that the inner syntax of Quantum Mechanics is relational logic, a form of logic developed by C. S. Peirce during the years 1870 - 1880. The Peircean logic has the structure of category theory, with relation serving as an arrow (or morphism). At the core of the relational logical system is the law of composition of relations. This law leads to the fundamental quantum rule of probability as the square of an amplitude. Our study of a simple discrete model, extended to the continuum, indicates that a finite number of degrees of freedom can live in phase space. This "granularity" of phase space is determined by Planck's constant h. We indicate also the broader philosophical ramifications of a relational quantum mechanics.

Argyris Nicolaidis

2012-11-09

90

QUANTUM MECHANICS I Physics 341  

E-print Network

QUANTUM MECHANICS I Physics 341 KPTC 103 9:00 ­ 10:20 a.m. 1 Tues., Thurs. ­ Fall Quarter 1999 mechanics at the graduate level. The text for Quantum mechanics I and II will be J. J. Sakurai and Jim Napolitano, Modern Quantum Mechanics, Second Edition (Addison- Wesley, 2011). We will cover the first three

Rosner, Jonathan L.

91

Quantum Mechanics and Gravitation  

E-print Network

In summer 1999 an experiment at ILL, Grenoble was conducted. So-called ultra-cold neutrons (UCN) were trapped in the vertical direction between the Fermi-potential of a smooth mirror below and the gravitational potential of the earth above [Ne00, Ru00]. If quantum mechanics turns out to be a sufficiently correct description of the phenomena in the regime of classical, weak gravitation, one should observe the forming of quantized bound states in the vertical direction above a mirror. Already in a simplified view, the data of the experiment provides strong evidence for the existence of such gravitationally bound quantized states. A successful quantum-mechanical description would then provide a convincing argument, that the socalled first quantization can be used for gravitation as an interaction potential, as this is widely expected. Furthermore, looking at the characteristic length scales of about 10 mikron of such bound states formed by UCN, one sees, that a complete quantum mechanical description of this experiment additionally would enable one to check for possible modifications of Newtonian gravitation on distance scales being one order of magnitude below currently available tests [Ad00]. The work presented here deals mainly with the development of a quantum mechanical description of the experiment.

A. Westphal

2002-08-21

92

Interpretation of quantum mechanics  

Microsoft Academic Search

New axioms are proposed for the interpretation of quantum mechanics. They rest on a kind of calculus allowing to select meaningful physical statements and giving rules to check a given physical reasoning containing implications. Measurement theory is reformulated. Laboratoire associ au Centre National de la Recherche Scientifique.

Roland Omns

1987-01-01

93

Supersymmetry and quantum mechanics  

Microsoft Academic Search

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of

Fred Cooper; Avinash Khare; Uday Sukhatme

1995-01-01

94

Thermodynamics and Universality for Mean Field Quantum Spin Glasses  

E-print Network

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

95

Physicalism versus quantum mechanics  

E-print Network

In the context of theories of the connection between mind and brain, physicalism is the demand that all is basically purely physical. But the concept of "physical" embodied in this demand is characterized essentially by the properties of the physical that hold in classical physical theories. Certain of these properties contradict the character of the physical in quantum mechanics, which provides a better, more comprehensive, and more fundamental account of phenomena. It is argued that the difficulties that have plaged physicalists for half a century, and that continue to do so, dissolve when the classical idea of the physical is replaced by its quantum successor. The argument is concretized in a way that makes it accessible to non-physicists by exploiting the recent evidence connecting our conscious experiences to macroscopic measurable synchronous oscillations occurring in well-separated parts of the brain. A specific new model of the mind-brain connection that is fundamentally quantum mechanical but that ties conscious experiences to these macroscopic synchronous oscillations is used to illustrate the essential disparities between the classical and quantum notions of the physical, and in particular to demonstrate the failure in the quantum world of the principle of the causal closure of the physical, a failure that goes beyond what is entailed by the randomness in the outcomes of observations, and that accommodates the efficacy in the brain of conscious intent.

Henry P. Stapp

2008-03-11

96

Fields and Quantum Mechanics  

E-print Network

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

2013-12-09

97

Epigenetics: Biology's Quantum Mechanics  

PubMed Central

The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene the molecular biological view and the epigenetic view are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider. PMID:22639577

Jorgensen, Richard A.

2011-01-01

98

On Randomness in Quantum Mechanics  

E-print Network

The quantum mechanical probability densities are compared with the probability densities treated by the theory of random variables. The relevance of their difference for the interpretation of quantum mechanics is commented.

Alberto C. de la Torre

2007-07-19

99

Does Quantum Mechanics Need Interpretation?  

E-print Network

Since the beginning, quantum mechanics has raised major foundational and interpretative problems. Foundational research has been an important factor in the development of quantum cryptography, quantum information theory and, perhaps one day, practical quantum computers. Many believe that, in turn, quantum information theory has bearing on foundational research. This is largely related to the so-called epistemic view of quantum states, which maintains that the state vector represents information on a system and has led to the suggestion that quantum theory needs no interpretation. I will argue that this and related approaches fail to take into consideration two different explanatory functions of quantum mechanics, namely that of accounting for classically unexplainable correlations between classical phenomena and that of explaining the microscopic structure of classical objects. If interpreting quantum mechanics means answering the question, "How can the world be for quantum mechanics to be true?", there seems to be no way around it.

Louis Marchildon

2009-02-17

100

Bohmian quantum mechanics with quantum trajectories  

NASA Astrophysics Data System (ADS)

The quantum trajectory method in the hydrodynamical formulation of Madelung-Bohm-Takabayasi quantum mechanics is an example of showing the cognitive importance of scientific illustrations and metaphors, especially, in this case, in computational quantum chemistry and electrical engineering. The method involves several numerical schemes of solving a set of hydrodynamical equations of motion for probability density fluids, based on the propagation of those probability density trajectories. The quantum trajectory method gives rise to, for example, an authentic quantum electron transport theory of motion to, among others, classically-minded applied scientists who probably have less of a commitment to traditional quantum mechanics. They were not the usual audience of quantum mechanics and simply choose to use a non-Copenhagen type interpretation to their advantage. Thus, the metaphysical issues physicists had a trouble with are not the main concern of the scientists. With the advantages of a visual and illustrative trajectory, the quantum theory of motion by Bohm effectively bridges quantum and classical physics, especially, in the mesoscale domain. Without having an abrupt shift in actions and beliefs from the classical to the quantum world, scientists and engineers are able to enjoy human cognitive capacities extended into the quantum mechanical domain.

Jeong, Yeuncheol

101

Can Quantum Cryptography Imply Quantum Mechanics?  

E-print Network

It has been suggested that the ability of quantum mechanics to allow secure distribution of secret key together with its inability to allow bit commitment or communicate superluminally might be sufficient to imply the rest of quantum mechanics. I argue using a toy theory as a counterexample that this is not the case. I further discuss whether an additional axiom (key storage) brings back the quantum nature of the theory.

John A. Smolin

2003-10-10

102

Syllabus Physics 531 (PHY 531) Thermodynamics and Statistical Mechanics  

E-print Network

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

103

Relativity and quantum mechanics  

Microsoft Academic Search

Conditions under which quantum mechanics can be made compatible with the curved space-time of gravitation theories is investigated. A postulate is imposed in the formv=vg wherev is the kinematical Hamilton-Jacobi (geometric optic limit) velocity andvg is the group velocity of the waves. This imposes a severe condition on the possible coordinates in which the Schrdinger form (the coordinate realization) of

Hseyin Yilmaz

1982-01-01

104

Quantum thermodynamics for a model of an expanding universe  

E-print Network

We investigate the thermodynamical properties of quantum fields in curved spacetime. Our approach is to consider quantum fields in curved spacetime as a quantum system undergoing an out-of-equilibrium transformation. The non-equilibrium features are studied by using a formalism which has been developed to derive fluctuation relations and emergent irreversible features beyond the linear response regime. We apply these ideas to an expanding universe scenario, therefore avoiding assumptions on the relation between entropy and quantum matter. We provide a fluctuation theorem which allows us to understand particle production due to the expansion of the universe as an entropic increase. Our results pave the way towards a different understanding of the thermodynamics of relativistic and quantum systems in our universe.

Liu, Nana; Fuentes, Ivette; Vedral, Vlatko; Modi, Kavan; Bruschi, David Edward

2014-01-01

105

Quantum Mechanics Survey (QMS)  

NSDL National Science Digital Library

This 31-question research-based multiple-choice test is designed to evaluate students conceptual understanding of quantum mechanics in junior-level courses. The survey is based on investigations of students 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 students 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

106

Quantum Mechanics and Representation Theory Columbia University  

E-print Network

Quantum Mechanics and Representation Theory Peter Woit Columbia University Texas Tech, November 21 2013 Peter Woit (Columbia University) Quantum Mechanics and Representation Theory November 2013 1 / 30 #12;Does Anyone Understand Quantum Mechanics? "No One Understands Quantum Mechanics" "I think

Woit, Peter

107

Principles of Fractional Quantum Mechanics  

E-print Network

A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum mechanics, hermiticity of the Hamilton operator, parity conservation law and the current density. Applications of fractional quantum mechanics cover dynamics of a free particle, new representation for a free particle quantum mechanical kernel, infinite potential well, bound state in {\\delta}-potential well, linear potential, fractional Bohr atom and fractional oscillator. We also review fundamentals of the L\\'evy path integral approach to fractional statistical mechanics.

Nick Laskin

2010-09-28

108

Nonlinear friction in quantum mechanics  

E-print Network

The effect of nonlinear friction forces in quantum mechanics is studied via dissipative Madelung hydrodynamics. A new thermo-quantum diffusion equation is derived, which is solved for the particular case of quantum Brownian motion with a cubic friction. It is extended also by a chemical reaction term to describe quantum reaction-diffusion systems with nonlinear friction as well.

Roumen Tsekov

2010-03-01

109

On the Quantum-Corrected Black Hole Thermodynamics  

E-print Network

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

2005-04-21

110

Quantum chemical approach to estimating the thermodynamics of metabolic reactions.  

PubMed

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, Aln

2014-01-01

111

What is quantum mechanics?  

NASA Astrophysics Data System (ADS)

We discuss the arguments for suspecting that there exists a classical, i.e. deterministic theory underlying quantum mechanics. A difficulty is that an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes is further elucidated, as it follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model. An example of a deterministic dissipative model producing exact quantum mechanics is provided for the case of a finite-dimensional vector space. These lecture notes have been produced partly from material published earlier, and as such contain more material than what could be presented in the talk.

't Hooft, Gerard

2007-04-01

112

Logical foundation of quantum mechanics  

Microsoft Academic Search

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

E. W. Stachow; Theoretische Physik

1980-01-01

113

Non-equilibrium thermodynamics approach to open quantum systems  

E-print Network

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

114

Octonic relativistic quantum mechanics  

E-print Network

In this paper we represent the generalization of relativistic quantum mechanics on the base of eght-component values "octons", generating associative noncommutative spatial algebra. It is shown that the octonic second-order equation for the eight-component octonic wave function, obtained from the Einshtein relation for energy and momentum, describes particles with spin of 1/2. It is established that the octonic wave function of a particle in the state with defined spin projection has the specific spatial structure in the form of octonic oscillator with two spatial polarizations: longitudinal linear and transversal circular. The relations between bispinor and octonic descriptions of relativistic particles are established. We propose the eight-component spinors, which are octonic generalisation of two-component Pauli spinors and four-component Dirac bispinors. It is shown that proposed eight-component spinors separate the states with different spin projection, different particle-antiparticle state as well as different polarization of the octonic oscillator. We demonstrate that in the frames of octonic relativistic quantum mechanics the second-order equation for octonic wave function can be reformulated in the form of the system of first-order equations for quantum fields, which is analogous to the system of Maxwell equations for the electromagnetic field. It is established that for the special type of wave functions the second-order equation can be reduced to the single first-order equation, which is analogous to the Dirac equation. At the same time it is shown that this first-order equation describes particles, which do not create quantum fields.

V. L. Mironov; S. V. Mironov

2008-03-04

115

Einstein gravity as the thermodynamic limit of an underlying quantum statistics  

E-print Network

The black hole area theorem suggests that classical general relativity is the thermodynamic limit of a quantum statistics. The degrees of freedom of the statistical theory cannot be the spacetime metric. We argue that the statistical theory should be constructed from a noncommutative gravity, whose classical, and thermodynamic, approximation is Einstein gravity. The noncommutative gravity theory exhibits a duality between quantum fields and macroscopic black holes, which is used to show that the black hole possesses an entropy of the order of its area. The principle on which this work is based also provides a possible explanation for the smallness of the cosmological constant, and for the quantum measurement problem, indicating that this is a promising avenue towards the merger of quantum mechanics and gravity.

T. P. Singh

2009-05-15

116

Conformal Orthosymplectic Quantum Mechanics  

E-print Network

We present the most general curvature obstruction to the deformed parabolic orthosymplectic symmetry subalgebra of the supersymmetric quantum mechanical models recently developed to describe Lichnerowicz wave operators acting on arbitrary tensors and spinors. For geometries possessing a hypersurface-orthogonal homothetic conformal Killing vector we show that the parabolic subalgebra is enhanced to a (curvature-obstructed) orthosymplectic algebra. The new symmetries correspond to time-dependent conformal symmetries of the underlying particle model. We also comment on generalizations germane to three dimensions and new Chern--Simons-like particle models.

J. Burkart; A. Waldron

2008-12-20

117

Conformal orthosymplectic quantum mechanics  

NASA Astrophysics Data System (ADS)

We present the most general curvature obstruction to the deformed parabolic orthosymplectic symmetry subalgebra of the supersymmetric quantum mechanical models recently developed to describe Lichnerowicz wave operators acting on arbitrary tensors and spinors. For geometries possessing a hypersurface-orthogonal homothetic conformal Killing vector we show that the parabolic subalgebra is enhanced to a (curvature-obstructed) orthosymplectic algebra. The new symmetries correspond to time-dependent conformal symmetries of the underlying particle model. We also comment on generalizations germane to three dimensions and new Chern-Simons-like particle models.

Burkart, Joshua; Waldron, Andrew

2009-05-01

118

Supersymmetric Quantum Mechanics  

SciTech Connect

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

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

2010-10-11

119

Diffusion-Schrdinger Quantum Mechanics  

NASA Astrophysics Data System (ADS)

A quantum solution of a nonlinear differential equation of diffusion type with a potential term has been found. Diffusion-Schrdinger quantum mechanics can find wide application in quantum biology, biological electronics, synthetic biology, nanomedicine, the quantum theory of consciousness, cosmology, and other fields of science and technology. One consequence of the macroscopic nature of diffusion-Schrdinger quantum mechanics is the possibility of generation of hard photons. The dust plasma in the Universe can generate cosmic rays with ultra-relativistic energies in a galactic magnetic field via a diffusion mechanism.

Lasukov, V. V.; Lasukova, T. V.; Lasukova, O. V.; Novoselov, V. V.

2014-08-01

120

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

SciTech Connect

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

121

Quantum Mechanics as Dualism  

NASA Astrophysics Data System (ADS)

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

Jones, Robert

2011-03-01

122

Thermodynamics and Statistical Mechanics of Induced Liouville Gravity  

E-print Network

In this paper we describe a Liouville gravity which is induced by a set of quantum fields (constituents) and represents a two-dimensional analog of Sakharov's induced gravity. The important feature of the considered theory is the presence of massless constituents which are responsible for the appearance of the induced Liouville field. The role of the massive constituents is only to induce the cosmological constant. We consider the instanton solutions of the Euclidean Liouville gravity with negative and zero cosmological constants, some instantons being interpreted as two-dimensional anti-de Sitter $AdS_2$ black holes. We study thermodynamics of all the solutions and conclude that their entropy is completely determined by the statistical-mechanical entropy of the massless constituents. This shows, in particular, that the constituents of the induced gravity are the true degrees of freedom of $AdS_2$ black holes. Special attention is also paid to the induced Liouville gravity with zero cosmological constant on a torus. We demonstrate the equivalence of its thermodynamics to the thermodynamics of BTZ black holes and comment on computations of the BTZ black hole entropy.

V. Frolov; D. Fursaev; J. Gegenberg; G. Kunstatter

1999-01-20

123

Kindergarten Quantum Mechanics  

E-print Network

These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in quant-ph/0402130 and [4]) which subsumes my Logic of Entanglement quant-ph/0402014. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes quant-ph/0506132. In a last section we provide some pointers to the body of technical literature on the subject.

Bob Coecke

2005-10-04

124

PT quantum mechanics.  

PubMed

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

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

2013-04-28

125

On the Quantum Correction For Thermodynamic Equilibrium  

Microsoft Academic Search

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

126

On Finite $J$-Hermitian Quantum Mechanics  

E-print Network

In his recent paper arXiv:1312.7738, the author discussed $J$-Hermitian quantum mechanics and showed that $PT$-symmetric quantum mechanics is essentially $J$-Hermitian quantum mechanics. In this paper, the author discusses finite $J$-Hermitian quantum mechanics which is derived naturally from its continuum one and its relationship with finite $PT$-symmetric quantum mechanics.

Sungwook Lee

2014-01-21

127

Invariance in adelic quantum mechanics  

E-print Network

Adelic quantum mechanics is form invariant under an interchange of real and p-adic number fields as well as rings of p-adic integers. We also show that in adelic quantum mechanics Feynman's path integrals for quadratic actions with rational coefficients are invariant under changes of their entries within nonzero rational numbers.

Branko Dragovich

2006-12-07

128

Decoherence in quantum mechanics and quantum cosmology  

NASA Technical Reports Server (NTRS)

A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.

Hartle, James B.

1992-01-01

129

Thermodynamic properties of Th xU 1-xO 2 (0 < x < 1) based on quantum-mechanical calculations and Monte-Carlo simulations  

NASA Astrophysics Data System (ADS)

Th xU 1-xO 2+y binary compositions occur in nature, uranothorianite, and as a mixed oxide nuclear fuel. As a nuclear fuel, important properties, such as the melting point, thermal conductivity, and the thermal expansion coefficient change as a function of composition. Additionally, for direct disposal of Th xU 1-xO 2, the chemical durability changes as a function of composition, with the dissolution rate decreasing with increasing thoria content. UO 2 and ThO 2 have the same isometric structure, and the ionic radii of 8-fold coordinated U 4+ and Th 4+ are similar (1.14 nm and 1.19 nm, respectively). Thus, this binary is expected to form a complete solid solution. However, atomic-scale measurements or simulations of cation ordering and the associated thermodynamic properties of the Th xU 1-xO 2 system have yet to be determined. A combination of density-functional theory, Monte-Carlo methods, and thermodynamic integration are used to calculate thermodynamic properties of the Th xU 1-xO 2 binary (? H mix, ? G mix, ? S mix, phase diagram). The Gibbs free energy of mixing (? G mix) shows a miscibility gap at equilibration temperatures below 1000 K (e.g., E exsoln = 0.13 kJ/(mol cations) at 750 K). Such a miscibility gap may indicate possible exsolution (i.e., phase separation upon cooling). A unique approach to evaluate the likelihood and kinetics of forming interfaces between U-rich and Th-rich has been chosen that compares the energy gain of forming separate phases with estimated energy losses of forming necessary interfaces. The result of such an approach is that the thermodynamic gain of phase separation does not overcome the increase in interface energy between exsolution lamellae for thin exsolution lamellae (10 ). Lamella formation becomes energetically favorable with a reduction of the interface area and, thus, an increase in lamella thickness to >45 . However, this increase in lamellae thickness may be diffusion limited. Monte-Carlo simulations converge to an exsolved structure [lamellae || (2 1 1)] only for very low equilibration temperatures (below room temperature). In addition to the weak tendency to exsolve, there is an ordered arrangement of Th and U in the solid solution [alternating U and Th layers || {1 0 0}] that is energetically favored for the homogeneously mixed 50% Th configurations. Still, this tendency to order is so weak that ordering is seldom reached due to kinetic hindrances. The configurational entropy of mixing (? S mix) is approximately equal to the point entropy at all temperatures, indicating that the system is not ordered.

Shuller, Lindsay C.; Ewing, Rodney C.; Becker, Udo

2011-05-01

130

Playing Games in Quantum Mechanical Settings:. Features of Quantum Games  

Microsoft Academic Search

In this lecture note, we present the implications of playing classical games in quantum mechanical settings where the quantum mechanical toolbox consisting of entanglement, quantum operations and measurement is used. After a brief introduction to the concepts of classical game theory and quantum mechanics, we study quantum games and their corresponding classical analogues to determine the novelties. In addition, we

Sahin Kaya zdemir; Junichi Shimamura; Nobuyuki Imoto

2008-01-01

131

Radiation spectrum and the thermodynamics of quantum cubic cavities  

NASA Astrophysics Data System (ADS)

In this paper, the density of modes in quantum cubic cavities is calculated taking into account the small number of modes. Then the `spatial quantization' fluctuations, which appear as a correction factor in the mode density, are introduced in the Planck law. The discrete form of the Planck radiation spectrum is demonstrated and the limits of this double-quantum regime of the cubic cavity are set for the product of cavity size by temperature. LT(epsilon) (0.1, 1). A reciprocity rule for the cavity size and the temperature is shown. Calculating the total energy in the quantum cubic cavities (QCC), we found out a `corrected' Stefan-Boltzmann law for the double-quantum regime. Furthermore, the corrections for all thermodynamic functions of the photon gas in QCC are given.

Vlad, Valentin I.; Ionescu-Pallas, Nicholas

1998-07-01

132

Quantum Mechanics 1 for graduate students  

E-print Network

Course 606 Quantum Mechanics 1 for graduate students Fall 2010 Instructor Valery Pokrovsky 1 electromagnetic field. Gauge invariance. Landau levels. 7. Semiclassical approximation. 8. Quantum mechanics. Scattering. The main textbook is E. Merzbacher, Quantum Mechanics, third edition, Wiley. Additional

133

Thermodynamic and quantum bounds on nonlinear DC thermoelectric transport  

E-print Network

I consider the non-equilibrium DC transport of electrons through a quantum system with a thermoelectric response. This system may be any nanostructure or molecule modeled by the nonlinear scattering theory which includes Hartree-like electrostatic interactions exactly, and certain dynamic interaction effects (decoherence and relaxation) phenomenologically. This theory is believed to be a reasonable model when single-electron charging effects are negligible. I derive three fundamental bounds for such quantum systems coupled to multiple macroscopic reservoirs, one of which may be superconducting. These bounds affect nonlinear heating (such as Joule heating), work and entropy production. Two bounds correspond to the first law and second law of thermodynamics in classical physics. The third bound is quantum (wavelength dependent), and is as important as the thermodynamic ones in limiting the capabilities of mesoscopic heat-engines and refrigerators. The quantum bound also leads to Nernst's unattainability principle that the quantum system cannot cool a reservoir to absolute zero in a finite time, although it can get exponentially close.

Robert S. Whitney

2012-11-20

134

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

135

Quantum Mechanics as Classical Physics  

E-print Network

Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds.

Charles Sebens

2014-02-27

136

Noninertial quantum mechanical fluctuations  

E-print Network

Zero point quantum fluctuations as seen from non-inertial reference frames are of interest for several reasons. In particular, because phenomena such as Unruh radiation (acceleration radiation) and Hawking radiation (quantum leakage from a black hole) depend intrinsically on both quantum zero-point fluctuations and some appropriate notion of an accelerating vacuum state, any experimental test of zero-point fluctuations in non-inertial frames is implicitly a test of the foundations of quantum field theory, and the Unruh and Hawking effects

H. C. Rosu

2000-12-20

137

Communication: Quantum mechanics without wavefunctions  

SciTech Connect

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

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

2012-01-21

138

Scattering Relativity in Quantum Mechanics  

E-print Network

Transforming from one reference frame to another yields an equivalent physical description. If quantum fields are transformed one way and quantum states transformed a different way then the physics changes. We show how to use the resulting changed physical description to obtain the equations of motion of charged, massive particles in electromagnetic and gravitational fields. The derivation is based entirely on special relativity and quantum mechanics.

Richard Shurtleff

2011-08-09

139

Phase Space Quantum Mechanics - Direct  

E-print Network

Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of non commuting observables. Further conceptual and practical merits of the formalism are demonstrated throughout the text.

S. Nasiri; Y. Sobouti; F. Taati

2006-05-15

140

Topological quantum mechanics  

SciTech Connect

The quantum theory of a type of generally covariant field theory, that has no local degrees of freedom, is described. Physical observables that capture topological properties of the manifold are identified and a representation of their Poisson algebra is constructed to obtain the quantum theory. A non-Abelian generalization to SU(2) is also discussed in a similar way.

Husain, V. (Department of Physics, University of Utah, Salt Lake City, Utah 84112 (US))

1991-03-15

141

Quantum mechanical description of waveguides  

E-print Network

In this paper, applying the spinor representation of the electromagnetic field, we present a quantum-mechanical description of waveguides. As an example of application, a potential qubit generated via photon tunneling is discussed.

Zhi-Yong Wang; Cai-Dong Xiong; Bing He

2006-11-02

142

Free will and quantum mechanics  

E-print Network

A simple example is provided showing that violation of free will allows to reproduce the quantum mechanical predictions, and that the Clauser-Horne parameter can take the maximum value 4 for a proper choice.

Antonio Di Lorenzo

2011-05-05

143

Quantum mechanics writ large  

E-print Network

Some two centuries before the quantum revolution, Newton (1) suggested that corpuscles of light generate waves in an aethereal medium like skipping stones generate waves in water, with their motion then being affected by ...

Bush, John W. M.

144

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

145

From Quantum Mechanics to String Theory  

E-print Network

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics) New Particles anti-particles (combining special relativity and quantum mechanics pions (mediator/momentum/mass discrepancy must fit inside the quantum mechanical uncertainty p, E E2 - p2 c2 = 0 Thursday, May 7, 2009 #12

146

Chem 793 Quantum Mechanics I Chemistry 793  

E-print Network

Chem 793 Quantum Mechanics I Chemistry 793 Quantum Mechanics I Fall 2000 Course outline 1 formulation. · Constants of the motion. 2. Probability in classical and quantum mechanics · Probability University #12;Chem 793 Quantum Mechanics I 7. Separable problems in 2D and 3D · Direct product functions

147

From mechanics to thermodynamics -- analysis of selected examples  

E-print Network

We present and discuss a selected set of problems of classical mechanics and thermodynamics. The discussion is based on the use of the impulse-momentum equation simultaneously with the centre-of-mass (pseudo-work) equation or with the first law of thermodynamics, depending on the nature of the problem. Thermodynamical aspects of classical mechanics, namely problems involving non-conservative forces or variation of mechanical energy are discussed, in different reference frames, in connection with the use of one or the other energy equation, and with the compliance of the Principle of Relativity.

Gmez, Julio

2014-01-01

148

Sampling with quantum mechanics  

E-print Network

A new algorithm for estimating the fraction of numbers that is present in a superpositional state which satisfies a given condition,is introduced.This algorithm is conceptually simple and does not require quantum Fourier transform.Also the number of steps required does not depend on the size of the data base to be searched.

M. P John

2003-06-26

149

Quantum mechanics needs no interpretation  

E-print Network

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule, probability density current, commutation relations, momentum operator, uncertainty relations, rules for including the scalar and vector potentials and existence of antiparticles can be derived from the definition of the mean values of the space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schroedinger equation and Dirac equation are obtained from requirement of the relativistic invariance of the theory. Limit case of localized probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many particle systems are also discussed.

L. Skala; V. Kapsa

2004-12-22

150

Work Cost of Thermal Operations in Quantum and Nano Thermodynamics  

E-print Network

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

151

Semiclassical Loop Quantum Gravity and Black Hole Thermodynamics  

NASA Astrophysics Data System (ADS)

In this article we explore the origin of black hole thermodynamics using semiclassical states in loop quantum gravity. We re-examine the case of entropy using a density matrix for a coherent state and describe correlations across the horizon due to SU(2) intertwiners. We further show that Hawking radiation is a consequence of a non-Hermitian term in the evolution operator, which is necessary for entropy production or depletion at the horizon. This non-unitary evolution is also rooted in formulations of irreversible physics.

Dasgupta, Arundhati

2013-02-01

152

Canonical Transformations in Quantum Mechanics  

E-print Network

Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can, in principle, be realized quantum mechanically as a product of these transformations. It is found that the intertwining of two super-Hamiltonians is equivalent to there being a canonical transformation between them. A consequence is that the procedure for solving a differential equation can be viewed as a sequence of elementary canonical transformations trivializing the super-Hamiltonian associated to the equation. It is proposed that the quantum integrability of a system is equivalent to the existence of such a sequence.

Arlen Anderson

1992-05-22

153

PT quantum mechanics - Recent results  

SciTech Connect

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

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

2012-09-26

154

Quantum Mechanics (QM) Measurement Package  

NSDL National Science Digital Library

This set of tutorial worksheets, based on the OSP Quantum Mechanics Simulations, help students explore the effects of position, momentum, and energy measurements on quantum state wavepackets. The probabilistic change in the wavefunction upon measurements and the time propagation of the states are illustrated. Similar worksheets are available for measurements of single and superpositions of energy eigenstates. The worksheets can be run online or downloaded as a pdf (attached).

Belloni, Mario; Christian, Wolfgang

2010-01-07

155

Kowalevski top in quantum mechanics  

SciTech Connect

The quantum mechanical Kowalevski top is studied by the direct diagonalization of the Hamiltonian. The spectra show different behaviors depending on the region divided by the bifurcation sets of the classical invariant tori. Some of these spectra are nearly degenerate due to the multiplicity of the invariant tori. The Kowalevski top has several symmetries and symmetry quantum numbers can be assigned to the eigenstates. We have also carried out the semiclassical quantization of the Kowalevski top by the EBK formulation. It is found that the semiclassical spectra are close to the exact values, thus the eigenstates can be also labeled by the integer quantum numbers. The symmetries of the system are shown to have close relations with the semiclassical quantum numbers and the near-degeneracy of the spectra. -- Highlights: Quantum spectra of the Kowalevski top are calculated. Semiclassical quantization is carried out by the EBK formulation. Quantum states are labeled by the semiclassical integer quantum numbers. Multiplicity of the classical torus makes the spectra nearly degenerate. Symmetries, quantum numbers and near-degenerate spectra are closely related.

Matsuyama, A., E-mail: spamatu@ipc.shizuoka.ac.jp

2013-09-15

156

Contributions in Non-Equilibrium Statistical Mechanics and Thermodynamics.  

National Technical Information Service (NTIS)

Apart from a thermodynamic study of the hydromagnetic stability problem for a system far from equilibrium, the essential matter of this report consists in a number of applications and extensions of the general statistical mechanical theory of irreversible...

I. Prigogine

1964-01-01

157

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.

158

Quantum Statistical Mechanics and Quantum Computation Thursday, 22 March 2012  

E-print Network

Quantum Statistical Mechanics and Quantum Computation Thursday, 22 March 2012 8:50 am Welcoming:30 ­ 5:30 "Criticality without frustration for quantum spin-1 chains" Sergey Bravyi 6:30 pm Dinner at Triumph Brewery 138 Nassau Street Princeton, NJ 08542 609-924-7855 Quantum Statistical Mechanics

159

A Criterion for Holism in Quantum Mechanics  

E-print Network

A Criterion for Holism in Quantum Mechanics # M.P Seevinck # # Utrecht University, The Netherlands, June 2003. # 1 #12; # Motivation # . The question whether or not quantum mechanics (QM) gives rise. Orthodox Quantum Mechanics . Criterion for Holism in the Quantum Formalism . Orthodox QM is Holistic

Seevinck, Michiel

160

A Criterion for Holism in Quantum Mechanics  

E-print Network

A Criterion for Holism in Quantum Mechanics M.P Seevinck Utrecht University, The Netherlands, June 2003. 1 #12; Motivation · The question whether or not quantum mechanics (QM) gives rise to some. Orthodox Quantum Mechanics · Criterion for Holism in the Quantum Formalism · Orthodox QM is Holistic

Seevinck, Michiel

161

ccsd00002942, ON SUPERSYMMETRIC QUANTUM MECHANICS  

E-print Network

ccsd­00002942, version 1 ­ 25 Sep 2004 ON SUPERSYMMETRIC QUANTUM MECHANICS M.R. KIBLER Institut de Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl supersymmetric Quantum Mechanics corresponds to k = 2. A connection between fractional supersymmetric Quantum

162

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

163

Algebraic Quantum Mechanics and Pregeometry  

E-print Network

We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points" we suggest an approach that may make it possible to dispense with an a priori given space manifold. In this approach the algebra itself would carry the symmetries of translation, rotation, etc. Our suggestion is illustrated in a preliminary way by using a particular generalized Clifford Algebra proposed originally by Weyl, which approaches the ordinary Heisenberg algebra in a suitable limit. We thus obtain a certain insight into how quantum mechanics may be regarded as a purely algebraic theory, provided that we further introduce a new set of "neighbourhood operators", which remove an important kind of arbitrariness that has thus far been present in the attempt to treat quantum mechanics solely in terms of a Heisenberg algebra.

D. J. Bohm; P. G. Davies; B. J. Hiley

2006-11-30

164

THE OBJECTIVE INDEFINITENESS INTERPRETATION OF QUANTUM MECHANICS: Partition logic, logical information theory, and quantum mechanics  

E-print Network

THE OBJECTIVE INDEFINITENESS INTERPRETATION OF QUANTUM MECHANICS: Partition logic, logical information theory, and quantum mechanics David Ellerman University of California at Riverside www ago that quantum mechanics was not compatible with Boolean logic, then the natural thing to do would

Wüthrich, Christian

165

Remarks on osmosis, quantum mechanics, and gravity  

E-print Network

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

166

Remarks on osmosis, quantum mechanics, and gravity  

E-print Network

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

167

Faster than Hermitian quantum mechanics.  

PubMed

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

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

2007-01-26

168

Canonical Transformations in Quantum Mechanics  

E-print Network

Quantum canonical transformations are defined algebraically outside of a Hilbert space context. This generalizes the quantum canonical transformations of Weyl and Dirac to include non-unitary transformations. The importance of non-unitary transformations for constructing solutions of the Schr\\"odinger equation is discussed. Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can be realized quantum mechanically as a product of these transformations. Each transformation corresponds to a familiar tool used in solving differential equations, and the procedure of solving a differential equation is systematized by the use of the canonical transformations. Several examples are done to illustrate the use of the canonical transformations. [This is an extensively revised version of hep-th-9205080: the first third of the paper is new material; the notation has been simplified, and further discussion has been added to the remainder.

Arlen Anderson

1993-05-13

169

Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in General Covariant Quantum Theories  

E-print Network

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

170

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

171

Quantum Mechanics and Physical Reality  

Microsoft Academic Search

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

N. Bohr

1935-01-01

172

Quantum Mechanics Of Consciousness  

E-print Network

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

173

Effective equations for the quantum pendulum from momentous quantum mechanics  

SciTech Connect

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

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

2012-08-24

174

Thermodynamics and Mechanical Equivalent of Heat  

NASA Astrophysics Data System (ADS)

This paper is the first part of a three-part project `How the principle of energy conservation evolved between 1842 and 1870: the view of a participant'. This paper aims at showing how the new ideas of Mayer and Joule were received, what constituted the new theory in the period under study, and how it was supported experimentally. A connection was found between the new theory and thermodynamics which benefited both of them. Some considerations are offered about the desirability of taking a historical approach to teaching energy and its conservation.

Kipnis, Nahum

2014-10-01

175

Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology  

Microsoft Academic Search

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

176

The Grammatical Universe and the Laws of Thermodynamics and Quantum Entanglement  

SciTech Connect

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

177

Delay Time in Quaternionic Quantum Mechanics  

E-print Network

In looking for quaternionic violations of quantum mechanics, we discuss the delay time for pure quaternionic potentials. The study shows in which energy region it is possible to amplify the difference between quaternionic and complex quantum mechanics.

Stefano De Leo; Gisele Ducati

2012-04-11

178

Star Products for Relativistic Quantum Mechanics  

E-print Network

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

179

Irreversible work and inner friction in quantum thermodynamic processes  

E-print Network

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

2014-07-13

180

Quantum quenches in the thermodynamic limit. II. Initial ground states  

NASA Astrophysics Data System (ADS)

A numerical linked-cluster algorithm was recently introduced to study quantum quenches in the thermodynamic limit starting from thermal initial states [M. Rigol, Phys. Rev. Lett. 112, 170601 (2014), 10.1103/PhysRevLett.112.170601]. Here, we tailor that algorithm to quenches starting from ground states. In particular, we study quenches from the ground state of the antiferromagnetic Ising model to the XXZ chain. Our results for spin correlations are shown to be in excellent agreement with recent analytical calculations based on the quench action method. We also show that they are different from the correlations in thermal equilibrium, which confirms the expectation that thermalization does not occur in general in integrable models even if they cannot be mapped to noninteracting ones.

Rigol, Marcos

2014-09-01

181

Driven spin systems as quantum thermodynamic machines: fundamental limits.  

PubMed

We show that coupled two-level systems like qubits studied in quantum-information processing can be used as a thermodynamic machine. At least three qubits or spins are necessary and they must be arranged in a chain. The system is interfaced between two split baths and the working spin in the middle is externally driven. The machine performs Carnot-type cycles and is able to work as a heat pump or engine depending on the temperature difference of the baths, DeltaT , and the energy difference in the spin system, DeltaE . It can be shown that the efficiency is a function of DeltaT and DeltaE . PMID:17677033

Henrich, Markus J; Mahler, Gnter; Michel, Mathias

2007-05-01

182

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

183

Quantum Mechanics Joachim Burgdorfer and Stefan Rotter  

E-print Network

1 1 Quantum Mechanics Joachim Burgd¨orfer and Stefan Rotter 1.1 Introduction 3 1.2 Particle and Quantization 8 1.5 Angular Momentum in Quantum Mechanics 9 1.6 Formalism of Quantum Mechanics 12 1.7 Solution Quantization 33 1.9.3 Gutzwiller Trace Formula 34 1.10 Conceptual Aspects of Quantum Mechanics 35 1

Rotter, Stefan

184

Entanglement and Disentanglement in Relativistic Quantum Mechanics  

E-print Network

Entanglement and Disentanglement in Relativistic Quantum Mechanics Jeffrey A. Barrett August 16, 2014 Abstract A satisfactory formulation of relativistic quantum mechanics re- quires that one be able in relativistic quantum mechanics must ultimately depend on the details of one's strategy for addressing

Stanford, Kyle

185

Quantum Mechanics: From Realism to Intuitionism  

E-print Network

Quantum Mechanics: From Realism to Intuitionism A mathematical and philosophical investigation with the idea for this thesis I didn't know very much about the funda- ments of quantum mechanics. Discussions that the incomprehensibility of quantum mechanics is not easily stepped over. This became clearer to me when I followed

Bosma, Wieb

186

Quantum Mechanics Revisited Jean Claude Dutailly  

E-print Network

Quantum Mechanics Revisited Jean Claude Dutailly Paris (France) August 20, 2014 Abstract The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general a new theoretical foundation. ii) The quantum mechanics (QM) which is presented in all the books

Boyer, Edmond

187

From Quantum Mechanics to String Theory  

E-print Network

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Dimensions Strings and the Strong Force Thursday, May 7, 2009 #12;Particle Interaction Summary quantum mechanics and special relativity together imply the existence of anti-particles forces are mediated

188

Quantum Mechanics for Mathematicians: Introduction and Overview  

E-print Network

Quantum Mechanics for Mathematicians: Introduction and Overview Peter Woit Department Richard Feynman goes "I think it is safe to say that no one understands quantum mechanics."[1 was contrasting quantum mechanics with the theory of general relativity, a supposedly equally hard to understand

Woit, Peter

189

Probability in modal interpretations of quantum mechanics  

E-print Network

Probability in modal interpretations of quantum mechanics Dennis Dieks Institute for the History interpretations have the ambition to construe quantum mechanics as an ob- jective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix

Seevinck, Michiel

190

Quantum Mechanics: Structures, Axioms and Paradoxes  

E-print Network

Quantum Mechanics: Structures, Axioms and Paradoxes Diederik Aerts Center Leo Apostel, Brussels present an analysis of quantum mechanics and its problems and para- doxes taking into account the results a genuine incomplete- ness of standard quantum mechanics, however not an incompleteness that means

Aerts, Diederik

191

A Criterion for Holism in Quantum Mechanics  

E-print Network

A Criterion for Holism in Quantum Mechanics M.P Seevinck E-mail: M.P.Seevinck@phys.uu.nl Utrecht University, The Netherlands, August 2003. 1 #12; Motivation · The question whether or not quantum mechanics is it that makes quantum mechanics a holistic theory (if so), and other physical theories not (if so). · I propose

Seevinck, Michiel

192

On a realistic interpretation of quantum mechanics  

E-print Network

On a realistic interpretation of quantum mechanics Arnold Neumaier Institut fur Mathematik respecting the indeter- ministic nature of quantum mechanics, allows to speak of de#12;nite values for all], there are at least two levels of inter- preting quantum mechanics: the statistical interpretation in the narrower

Neumaier, Arnold

193

Visualizing quantum mechanics in phase space  

E-print Network

We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner function formalism resembles the mathematical language of classical mechanics of non-interacting particles. Thus, it allows a more direct comparison between classical and quantum dynamical features.

Heiko Bauke; Noya Ruth Itzhak

2011-01-11

194

The Postulates of Quantum Mechanics (from Quantum Mechanics by Claude Cohen-Tannoudji, Bernard Diu, and  

E-print Network

The Postulates of Quantum Mechanics (from Quantum Mechanics by Claude Cohen-Tannoudji, Bernard Diu, and Franck Lalo¨e) Introduction The postulates of quantum mechanics are the theory. Their physical content to the following questions: (i) How is the state of a quantum mechanical system at a given time described

Nielsen, Steven O.

195

Supersymmetric Quantum Mechanics with Reflections  

E-print Network

We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q-> -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wave functions of extended Scarf I potentials with different parameters are presented.

S. Post; L. Vinet; A. Zhedanov

2011-07-28

196

Supersymmetric Quantum Mechanics with Reflections  

E-print Network

A novel realization of supersymmetric quantum mechanics is obtained by using as supercharges, differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q-> -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wave functions of extended Scarf I potentials with different parameters are presented.

Post, S; Zhedanov, A

2011-01-01

197

Game Theory in Categorical Quantum Mechanics  

E-print Network

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

198

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

199

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

200

Facets of contextual realism in quantum mechanics  

SciTech Connect

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

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

2011-09-23

201

Helping Students Learn Quantum Mechanics for Quantum Computing  

NSDL National Science Digital Library

Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research in quantum computing because there is a lack of emphasis in the current curriculum on quantum formalism and dynamics. We are investigating the difficulties students have with quantum mechanics and are developing and evaluating quantum interactive learning tutorials (QuILTs) to reduce the difficulties. Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. We discuss the implications of our research and development project on helping students learn quantum mechanics relevant for quantum computing.

Singh, Chandralekha

2007-11-25

202

Playing Games in Quantum Mechanical Settings:. Features of Quantum Games  

NASA Astrophysics Data System (ADS)

In this lecture note, we present the implications of playing classical games in quantum mechanical settings where the quantum mechanical toolbox consisting of entanglement, quantum operations and measurement is used. After a brief introduction to the concepts of classical game theory and quantum mechanics, we study quantum games and their corresponding classical analogues to determine the novelties. In addition, we introduce a benchmark which attempts to make a fair comparison of classical games and their quantum extensions. This benchmark exploits the fact that in special settings a classical game should be reproduced as a subgame of its quantum extension. We obtained a rather surprising result that this requirement prevents the use of a large set of entangled states in quantum extension of classical games.

zdemir, ?ahin Kaya; Shimamura, Junichi; Imoto, Nobuyuki

2008-04-01

203

A concise introduction to quantum probability, quantum mechanics, and quantum computation  

E-print Network

A concise introduction to quantum probability, quantum mechanics, and quantum computation Greg called "non-commutative probability". Recently quantum computation has entered as a new reason for both mathematicians and computer scientists to learn the precepts of quantum mechan- ics. Just as randomized

Thomases, Becca

204

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 Gottfrieds 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 Bells 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. Gottfrieds 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 Gottfrieds 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 Gottfrieds treatment little more than the cruder collapse idea of von Neumann, and when, shortly before Bells 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 Lifshitzs classic Quantum Mechanics, pilloried for its advocacy of old-fashioned collapse, and a paper by van Kampen in Physica, but also Gottfrieds 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 Bells work, for example editing the section on quantum foundations in the World Scientific edition of Bells collected works. Thus it is exceedingly interesting to disco

Whitaker, A.

2004-02-01

205

Status of the Fundamental Laws of Thermodynamics  

E-print Network

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

206

Teaching Quantum Mechanics on an Introductory Level.  

ERIC Educational Resources Information Center

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

Muller, Rainer; Wiesner, Hartmut

2002-01-01

207

Treating time travel quantum mechanically  

NASA Astrophysics Data System (ADS)

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

Allen, John-Mark A.

2014-10-01

208

Treating Time Travel Quantum Mechanically  

E-print Network

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

209

Orthodox Quantum Mechanics Free from Paradoxes  

E-print Network

A formulation of quantum mechanics based on an operational definition of state is presented. This formulation, which includes explicitly the macroscopic systems, assumes the probabilistic interpretation and is nevertheless objective. The classical paradoxes of quantum mechanics are analyzed and their origin is found to be the fictitious properties that are usually attributed to quantum-mechanical states. The hypothesis that any mixed state can always be considered as an incoherent superposition of pure states is found to contradict quantum mechanics. A solution of EPR paradox is proposed. It is shown that entanglement of quantum states is compatible with realism and locality of events, but implies non-local encoding of information.

Rodrigo Medina

2005-08-02

210

Quantum Mechanics of Proca Fields  

E-print Network

We construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time-translations with the Hamiltonian, we obtain a unitary quantum system that describes first-quantized Proca fields and does not involve the conventional restriction to the positive-frequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity ($\\cP$), generalized time-reversal ...

Zamani, Farhad

2008-01-01

211

Quantum mechanics: Myths and facts  

E-print Network

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.

H. Nikolic

2006-09-21

212

Quantum mechanics: Myths and facts  

E-print Network

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.

Nikolic, H

2006-01-01

213

Quantum Mechanics: Myths and Facts  

NASA Astrophysics Data System (ADS)

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of myths, that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.

Nikoli?, Hrvoje

2007-11-01

214

Thermodynamic and mechanical properties of model mitochondrial membranes  

E-print Network

an electrochemical potential for substrate transport and ATP synthesis [1,2]. The human inner mitochondrial membraneThermodynamic and mechanical properties of model mitochondrial membranes Stephanie Nichols membrane, and is thought to be influential in determining membrane potential and permeability. To determine

Kuhl, Tonya L.

215

A quantum mechanical model of "dark matter"  

E-print Network

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

216

Web-based Quantum Mechanics I Course  

NSDL National Science Digital Library

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

Breinig, Marianne

2009-09-17

217

Errors and paradoxes in quantum mechanics  

E-print Network

Errors and paradoxes in quantum mechanics, entry in the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, ed. F. Weinert, K. Hentschel, D. Greenberger and B. Falkenburg (Springer), to appear

D. Rohrlich

2007-08-28

218

Prolegomena to a non-equilibrium quantum statistical mechanics  

Microsoft Academic Search

We suggest that the framework of quantum information theory, which has been developing rapidly in recent years due to intense activity in quantum computation and quantum communication, is a reasonable starting point to study non-equilibrium quantum statistical phenomena. As an application, we discuss the non-equilibrium quantum thermodynamics of black hole formation and evaporation.

C. Adami; N. J. Cerf

1999-01-01

219

Thermodynamics and Statistical Mechanics of dense granular media  

E-print Network

By detailed Molecular Dynamics and Monte Carlo simulations %of a realistic model we show that granular materials at rest can be described as thermodynamics systems. First we show that granular packs can be characterized by few parameters, as much as fluids or solids. Then, in a second independent step, we demonstrate that these states can be described in terms of equilibrium distributions which coincide with the Statistical Mechanics of powders first proposed by Edwards. We also derive the system equation of state as a function of the ``configurational temperature'', its new intensive thermodynamic parameter.

Massimo Pica Ciamarra; Antonio Coniglio; Mario Nicodemi

2006-03-16

220

Exploration of similarities between classical wave mechanics and quantum mechanics  

Microsoft Academic Search

This dissertation explores classical analogs of one particle wave mechanics and multiparticle quantum entanglement by using classical wave optics. We develop classical measurement techniques to simulate one particle wave mechanics and quantum entanglement for up to four particles. Classical simulation of multi-particle entanglement is useful for quantum information processing (QIP) because much of the QIP does not require collapse and

Kim Fook Lee

2002-01-01

221

Multiverse interpretation of quantum mechanics  

NASA Astrophysics Data System (ADS)

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

Bousso, Raphael; Susskind, Leonard

2012-02-01

222

Transfer of Learning in Quantum Mechanics  

NSDL National Science Digital Library

We investigate the difficulties that undergraduate students in quantum mechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting individual interviews. Quantum mechanics is abstract and its paradigm is very different from the classical one. A good grasp of the principles of quantum mechanics requires creating and organizing a knowledge structure consistent with the quantum postulates. Previously learned concepts such as the principle of superposition and probability can be useful in quantum mechanics if students are given opportunity to build associations between new and prior knowledge. We also discuss the need for better alignment between quantum mechanics and modern physics courses taken previously because semi-classical models can impede internalization of the quantum paradigm in more advanced courses.

Singh, Chandralekha

2010-01-18

223

Optimizing adiabaticity in quantum mechanics  

E-print Network

A condition on the Hamiltonian of a time-dependent quantum mechanical system is derived which, if satisfied, implies optimal adiabaticity (defined below). The condition is expressed in terms of the Hamiltonian and in terms of the evolution operator related to it. Since the latter depends in a complicated way on the Hamiltonian, it is not yet clear how the condition can be used to extract useful information about the optimal Hamiltonian. The condition is tested on an exactly-soluble time-dependent problem (a spin in a magnetic field), where perfectly adiabatic evolution can be easily identified.

MacKenzie, R; Renaud-Desjardins, L

2011-01-01

224

Optimizing adiabaticity in quantum mechanics  

E-print Network

A condition on the Hamiltonian of a time-dependent quantum mechanical system is derived which, if satisfied, implies optimal adiabaticity (defined below). The condition is expressed in terms of the Hamiltonian and in terms of the evolution operator related to it. Since the latter depends in a complicated way on the Hamiltonian, it is not yet clear how the condition can be used to extract useful information about the optimal Hamiltonian. The condition is tested on an exactly-soluble time-dependent problem (a spin in a magnetic field), where perfectly adiabatic evolution can be easily identified.

R. MacKenzie; M. Pineault; L. Renaud-Desjardins

2011-09-12

225

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

226

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

227

I. BASICS OF STATISTICAL MECHANICS AND QUANTUM MECHANICS Markus Holzmann  

E-print Network

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

228

Quantum mechanics without state vectors  

NASA Astrophysics Data System (ADS)

Because the state vectors of isolated systems can be changed in entangled states by processes in other isolated systems, keeping only the density matrix fixed, it is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying only on density matrices. The density matrix is defined here by the formula giving the mean values of physical quantities, which implies the same properties as the usual definition in terms of state vectors and their probabilities. This change in the description of physical states opens up a large variety of new ways that the density matrix may transform under various symmetries, different from the unitary transformations of ordinary quantum mechanics. Such new transformation properties have been explored before, but so far only for the symmetry of time translations into the future, treated as a semigroup. Here, new transformation properties are studied for general symmetry transformations forming groups, not just semigroups. Arguments that such symmetries should act on the density matrix as in ordinary quantum mechanics are presented, but all of these arguments are found to be inconclusive.

Weinberg, Steven

2014-10-01

229

Identical Particles in Quantum Mechanics  

E-print Network

If, in a system of identical particles, the one particle state is defined by the partial trace to one of the component spaces of the total Hilbert space, then all one particle states are identical. The particles are indistinguishable. This is often thought to be a typical quantum mechanical phenomenon. I will show however that an analogous procedure to define particle states exists in classical mechanics, which results in classical indistinguishable identical particles. From this analogy it follows that the indistinguishability of identical particles depends on how we define particle states. It is not an inevitable result of the symmetry postulate. Indeed, if particles are defined by partial traces, consistent use of the symmetry postulate leads to the conclusion that all identical particles in the universe are indistinguishable, so that particles can never be pointed at, not even in the classical limit. This does not correspond to the way the term particle is actually used in practice. I will argue that a particle should be defined in such a way that in the classical limit the quantum particle state becomes the state of a classical particle. This will lead us to a definition of particles which is in line with the way the term particle is actually used by physicists.

Andrea Lubberdink

2009-10-24

230

Bananaworld: Quantum Mechanics for Primates  

E-print Network

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

2012-11-13

231

Thermodynamic Optimization of Flow Geometry in Mechanical and Civil Engineering  

NASA Astrophysics Data System (ADS)

Recent developments in thermodynamic optimization are reviewed by focusing on the generation of optimal geometric form (shape, structure, topology) in flow systems. The flow configuration is free to vary. The principle that generates geometric form is the pursuit of maximum global performance (e.g., minimum flow resistance, minimum irreversibility) subject to global finiteness constraints (volume, weight, time). The resulting structures constructed in this manner have been named constructal designs. The thought that the same objective and constraints principle accounts for the optimally shaped flow paths that occur in natural systems (animate and inanimate) has been named constructal theory. Examples of large classes of applications are drawn from various sectors of mechanical and civil engineering: the distribution of heat transfer area in power plants, optimal sizing and shaping of flow channels and fins, optimal aspect ratios of heat exchanger core structures, aerodynamic and hydrodynamic shapes, tree-shaped assemblies of convective fins, treeshaped networks for fluid flow and other currents, optimal configurations for streams that undergo bifurcation or pairing, insulated pipe networks for the distribution of hot water and exergy over a fixed territory, and distribution networks for virtually everything that moves in society (goods, currency, information). The principle-based generation of flow geometry unites the thermodynamic optimization developments known in mechanical engineering with lesser known applications in civil engineering and social organization. This review extends thermodynamics, because it shows how thermodynamic principles of design optimization account for the development of optimal configurations in civil engineering and social organization.

Bejan, Adrian; Lorente, Sylvie

2001-12-01

232

Quantum Mechanics and Closed Timelike Curves  

E-print Network

General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal region of space-time are investigated. If the correspondence principle is true, then all generalizations of quantum mechanics on acausal manifolds are not renormalizable. Therefore quantum mechanics can only be defined on global hyperbolic manifolds and all general relativity solutions exhibiting time travel are unphysical.

Florin Moldoveanu

2007-04-23

233

Bohmian particle trajectories contradict quantum mechanics  

E-print Network

The Bohmian interpretation of quantum mechanics adds particle trajectories to the wave function and ensures that the probability distribution of the particle positions agrees with quantum mechanics at any time. This is not sufficient to avoid contradictions with quantum mechanics. There are correlations between particle positions at different times which cannot be reproduced with real particle trajectories. A simple rearrangement of an experimental test of the Bell-CHSH inequality demonstrates this.

Michael Zirpel

2009-03-23

234

Quantum Statistical Mechanics. III. Equilibrium Probability  

E-print Network

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

235

A Process Model of Quantum Mechanics  

E-print Network

A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise through a non-uniform interpolation process. Standard non-relativistic quantum mechanics emerges under the limit of infinite information (the causal space grows to infinity) and infinitesimal scale (the separation between points goes to zero). The model has the potential to address several paradoxes in quantum mechanics while remaining computationally powerful.

William Sulis

2014-04-13

236

Time dependent quantum thermodynamics of a coupled quantum oscillator system in a small thermal environment  

SciTech Connect

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

237

Time dependent quantum thermodynamics of a coupled quantum oscillator system in a small thermal environment.  

PubMed

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. PMID:24320365

Barnes, George L; Kellman, Michael E

2013-12-01

238

Quantum Mechanics Dung-Hai Lee  

E-print Network

Quantum Mechanics Dung-Hai Lee Summer 2000 #12;Contents 1 A brief reminder of linear Algebra 3 1.5 Bell's inequality . . . . . . . . . . . . . . . . . . . . . . . 20 3 Quantum dynamics 23 3 . . . . . . . . . . . . . . . . . . . 43 3.12 Classical approximation . . . . . . . . . . . . . . . . . . 45 3.13 Quantum statistical

Murayama, Hitoshi

239

A Modern Approach to Quantum Mechanics  

NSDL National Science Digital Library

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

Townsend, John

2004-03-04

240

Thermodynamically Stable Dispersions of Quantum Dots in a Nematic Liquid Crystal  

E-print Network

- conductors, quantum dots (QD) or rods,3-5,23-40 dispersed in liquid crystal hosts also affect mesogenicThermodynamically Stable Dispersions of Quantum Dots in a Nematic Liquid Crystal Maksym F. Prodanov surfactant were readily dispersed in nematic liquid crystal (LC) to form stable colloids. The mixture

Reznikov, Yuri

241

Improving Students' Understanding of Quantum Mechanics  

NSDL National Science Digital Library

Richard Feynman once famously stated that nobody understands quantum mechanics. He was, of course, referring to the many strange, unintuitive foundational aspects of quantum theory such as its inherent indeterminism and state reduction during measurement according to the Copenhagen interpretation. But despite its underlying fundamental mysteries, the theory has remained a cornerstone of modern physics. Most physicists, as students, are introduced to quantum mechanics in a modern-physics course, take quantum mechanics as advanced undergraduates, and then take it again in their first year of graduate school. One might think that after all this instruction, students would have become certified quantum mechanics, able to solve the Schrödinger equation, manipulate Dirac bras and kets, calculate expectation values, and, most importantly, interpret their results in terms of real or thought experiments. That sort of functional understanding of quantum mechanics is quite distinct from the foundational issues alluded to by Feynman.

Singh, Chandralekha; Belloni, Mario; Christian, Wolfgang

2008-06-23

242

Interactive Learning Tutorials on Quantum Mechanics  

NSDL National Science Digital Library

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

Singh, Chandralekha

2013-08-08

243

Kindergarten Quantum Mechanics lectures notes  

E-print Network

These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in quant-ph/0402130 and [4]) which subsumes my Logic of Entanglement quant-ph/0402014. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes quant-ph/0506132. In a last section we provide some pointers to the body of technical literature on the subject.

Coecke, B

2005-01-01

244

Kindergarten Quantum Mechanics: Lecture Notes  

SciTech Connect

These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns 'doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I which subsumes my Logic of Entanglement. For a survey on the 'what', the 'why' and the 'hows' I refer to a previous set of lecture notes. In a last section we provide some pointers to the body of technical literature on the subject.

Coecke, Bob [Oxford University Computing Laboratory, Wolfson Building, Parks rd, OX1 3QD Oxford (United Kingdom)

2006-01-04

245

Tests of CPT and Quantum Mechanics: experiment  

NASA Astrophysics Data System (ADS)

Neutral kaons provide one of the systems most sensitive to quantum mechanics and CPT violation. Models predicting quantum mechanics violation, also related to CPT violation, have been tested at the CPLEAR and KLOE experiments. In this report results of CPLEAR obtained by studying the time evolution of single and two entangled kaons are reviewed. New or improved limits on decoherence and CPT violation parameters have been obtained by KLOE studying the quantum interference in the channel ??KK?????. No deviations from the expectations of quantum mechanics and CPT symmetry have been observed.

Ambrosino, F.; Antonelli, A.; Antonelli, M.; Bacci, C.; Barva, M.; Beltrame, P.; Bencivenni, G.; Bertolucci, S.; Bini, C.; Bloise, C.; Bocchetta, S.; Bocci, V.; Bossi, F.; Bowring, D.; Branchini, P.; Bulychjov, S. A.; Caloi, R.; Campana, P.; Capon, G.; Capussela, T.; Carboni, G.; Ceradini, F.; Cervelli, F.; Chi, S.; Chiefari, G.; Ciambrone, P.; Conetti, S.; De Lucia, E.; De Santis, A.; De Simone, P.; De Zorzi, G.; Dell'Agnello, S.; Denig, A.; Di Domenico, A.; Di Donato, C.; Di Falco, S.; Di Micco, B.; Doria, A.; Dreucci, M.; Farilla, A.; Felici, G.; Ferrari, A.; Ferrer, M. L.; Finocchiaro, G.; Fiore, S.; Forti, C.; Franzini, P.; Gatti, C.; Gauzzi, P.; Giovannella, S.; Gorini, E.; Graziani, E.; Incagli, M.; Kluge, W.; Kulikov, V.; Lacava, F.; Lanfranchi, G.; Lee-Franzini, J.; Leone, D.; Martemianov, M.; Martini, M.; Massarotti, P.; Matsyuk, M.; Mei, W.; Meola, S.; Messi, R.; Miscetti, S.; Moulson, M.; Mller, S.; Murtas, F.; Napolitano, M.; Nguyen, F.; Palutan, M.; Pasqualucci, E.; Passalacqua, L.; Passeri, A.; Patera, V.; Perfetto, F.; Pontecorvo, L.; Primavera, M.; Santangelo, P.; Santovetti, E.; Saracino, G.; Schamberger, R. D.; Sciascia, B.; Sciubba, A.; Scuri, F.; Sfiligoi, I.; Sibidanov, A.; Spadaro, T.; Spiriti, E.; Tabidze, M.; Testa, M.; Tortora, L.; Valente, P.; Valeriani, B.; Venanzoni, G.; Veneziano, S.; Ventura, A.; Ventura, S.; Versaci, R.; Villella, I.; Xu, G.; KLOE Collaboration

2007-05-01

246

PERSPECTIVE Quantum Mechanics of Black Holes  

E-print Network

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

247

QUANTUM MECHANICS AND DUALISM JEFFREY A. BARRETT  

E-print Network

mechanics, a strong variety of mind-body dualism provides a natural criterion for when collapses occur record. We will also consider options for avoiding a commitment to at least mind-body dualism. 1. Quantum of quantum mechanics requires one to endorse a strong variety of mind-body dualism. In particular, he argued

Stanford, Kyle

248

Pseudospectra in non-Hermitian quantum mechanics  

E-print Network

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT-symmetric quantum mechanics.

D. Krejcirik; P. Siegl; M. Tater; J. Viola

2014-02-05

249

Quaternionic Formulation of Supersymmetric Quantum Mechanics  

E-print Network

Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions. Supercharges, superpartner Hamiltonians and energy eigenvalues are discussed and it has been shown that the results are consistent with the results of quantum mechanics.

Seema Rawat; O. P. S. Negi

2007-03-18

250

On the quantum mechanics of supermembranes  

Microsoft Academic Search

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

Bernard de Wit; J. Hoppe; H. Nicolai

1988-01-01

251

From Quantum Mechanics to String Theory  

E-print Network

of location Over time, the spike will often spread out again into a wave similar to the one it startedFrom Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics lengths and times to change depending on reference frame Any physical observable (the result

252

From Quantum Mechanics to String Theory  

E-print Network

From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Quarks and the Strong Force Symmetry and Unification String Theory: a different kind of unification from the interaction energy Thursday, June 4, 2009 #12;String Theory: A different kind of unification

253

From Quantum Mechanics to String Theory  

E-print Network

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

254

From Quantum Mechanics to String Theory  

E-print Network

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

255

Quantum Mechanics: Bell and Quantum Entropy for the Classroom  

E-print Network

In this article we are willing to give some first steps to quantum mechanics and a motivation of quantum mechanics and its interpretation for undergraduate students not from physics. After a short historical review in the development we discuss philosophical, physical and mathematical interpretation. We define local realism, locality and hidden variable theory which ends up in the EPR paradox, a place where questions on completeness and reality comes into play. The fundamental result of the last century was maybe Bell's that states that local realism is false if quantum mechanics is true. From this fact we can obtain the so called Bell inequalities. After a didactic example of the fact what these inequalities means we describe the key concept of quantum entanglement motivated here by quantum information theory. Also classical entropy and von Neuman entropy is discussed.

Pluch, Philipp

2014-01-01

256

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

257

EK424 THERMODYNAMICS AND STATISTICAL MECHANICS (Fall 2013) Thermodynamics is the study of processes (e.g., expansion of a gas, boiling of water, or diffusion  

E-print Network

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

258

EK424 THERMODYNAMICS AND STATISTICAL MECHANICS (Spring 2013) Thermodynamics is the study of processes (e.g., expansion of a gas, boiling of water, or diffusion  

E-print Network

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

259

Relationship between quantum walks and relativistic quantum mechanics  

SciTech Connect

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

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

2010-06-15

260

Nonequilibrium Statistical Mechanics and Thermodynamics from Darwinian Dynamics: a Primer  

E-print Network

We present here an exploration on on the physical implications of the Darwinian dynamics. We first show that how the nonequilibrium statistical mechanics emerges naturally. We then show that the first three laws of the thermodynamics, the Zeroth Law, the First Law and the Second Law can be followed from the Darwinian dynamics, except the Third Law. The inability to derive the Third Law indicates that the Darwinian dynamics belongs to the "classical" domain. Specifically, the Second Law is proved from the dynamical point of view. Two types of current dynamical equalities are explicitly discussed in the paper: one is based on Feynman-Kac formula and one is a generalization of the Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that the Darwinian dynamics is logically a simple and straightforward starting point to get into thermodynamics and is complementary to the conservative dynamics dominated in physics.

Ao, P

2005-01-01

261

Collimation processes in quantum mechanics interpreted in quantum real numbers  

Microsoft Academic Search

We reexamine the theory of quantum mechanics using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from entities in the standard Hilbert space formulation of the theory. Our motivation is to elucidate certain apparently paradoxical features of the standard theory by enlarging the class of real numbers that physical quantities can take as numerical values. The concept

John Vincent Corbett; Thomas Durt

2009-01-01

262

Polymer Quantum Mechanics and its Continuum Limit  

E-print Network

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

Alejandro Corichi; Tatjana Vukasinac; Jose A. Zapata

2007-03-31

263

Polymer quantum mechanics and its continuum limit  

SciTech Connect

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

264

Improving Students' Understanding of Quantum Mechanics  

NSDL National Science Digital Library

Learning physics is challenging at all levels. Students difficulties in the introductory level physics courses have been widely studied and many instructional strategies have been developed to help students learn introductory physics. However, research shows that there is a large diversity in students preparation and skills in the upper-level physics courses and it is necessary to provide scaffolding support to help students learn advanced physics. This thesis explores issues related to students common difficulties in learning upper-level undergraduate quantum mechanics and how these difficulties can be reduced by research-based learning tutorials and peer instruction tools. We investigated students difficulties in learning quantum mechanics by administering written tests and surveys to many classes and conducting individual interviews with a subset of students. Based on these investigations, we developed Quantum Interactive Learning Tutorials (QuILTs) and peer instruction tools to help students build a hierarchical knowledge structure of quantum mechanics through a guided approach. Preliminary assessments indicate that students understanding of quantum mechanics is improved after using the research-based learning tools in the junior-senior level quantum mechanics courses. We also designed a standardized conceptual survey that can help instructors better probe students understanding of quantum mechanics concepts in one spatial dimension. The validity and reliability of this quantum mechanics survey is discussed.

Zhu, Guangtian

2011-07-31

265

Causal wave mechanics and the advent of complexity; 5, quantum field mechanics  

E-print Network

The physical consequences of the analysis performed in parts I-IV are summarised within a tentative scheme of the complete quantum (wave) mechanics called quantum field mechanics and complementing the original de Broglie ideas by the dynamic complexity concept. It includes the obtained formally complete description at the level of the "average" wave function of Schr\\"odinger type showing dynamically chaotic behaviour, and in particular, causal quantum indeterminacy and wave reduction. This level is only an approximation, though rather perfect and usually acceptable, to a lower, and the last, level containing the unreduced, essentially nonlinear de Broglie double solution. The latter describes the state of a nonlinear material field and includes the unstable soliton-like high-intensity "hump" moving chaotically within the embedding smooth wave. The involvement of chaos, understood within the same concept of the fundamental dynamic uncertainty, provides, at this lower level, "hidden thermodynamics" of de Brogli...

Kirilyuk, A P

1995-01-01

266

Is Quantum Mechanics Falsifiable? A computational perspective on the foundations of Quantum Mechanics  

E-print Network

Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity. We describe how QM can be tested in this regime by extending the usual scientific paradigm to include {\\it interactive experiments}.

Dorit Aharonov; Umesh Vazirani

2012-06-16

267

NON-COMMUTATIVE SPHERES AND NUMERICAL QUANTUM MECHANICS  

E-print Network

NON-COMMUTATIVE SPHERES AND NUMERICAL QUANTUM MECHANICS basic issues that arise when one attempts to mo* *del quantum mechanical systems on a computer, quantum mechanics. Contributed to the proceedings of a NATO conference on operator algebras, ma

Arveson, William

268

Quantum-mechanical analysis of single molecule quantum electronic devices  

Microsoft Academic Search

This paper documents the need to coherently apply quantum mechanics in order to analyze microscopic devices. We examine device physics and study characteristics of single-molecule processing devices. The device physics of the proposed single-molecule device is based on the controlled propagation of electrons. By applying quantum mechanics and advanced numeric schemes, we perform the device-level analysis researching electron propagation (motion),

Sergey Edward Lyshevski

2011-01-01

269

OPTI 570A-Quantum Mechanics Course Description  

E-print Network

OPTI 570A- Quantum Mechanics Course Description: This is a one-semester course designed to provide students with a solid understanding of quantum mechanics formalism, techniques, and important example physics, quantum optics, relativistic quantum mechanics and other advanced quantum mechanics topics

Arizona, University of

270

Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics-I  

E-print Network

The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics could prove to be valuable for larger objectives such as understanding of gravity.

Aalok Pandya

2008-09-08

271

Quantum Physics Online: Wave Mechanics  

NSDL National Science Digital Library

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

Joffre, Manuel

2004-03-28

272

A Quantum Mechanical Travelling Salesman  

E-print Network

A quantum simulation of a travelling salesman is described. A vector space for a graph is defined together with a sequence of operators which transform a special initial state into a superposition states representing Hamiltonian tours. The quantum amplitude for any tour is a function of the classical cost of travelling along the edges in that tour. Tours with the largest quantum amplitude may be different than those with the smallest classically-computed cost.

Ravindra N. Rao

2011-08-23

273

Playing Games with Quantum Mechanics  

E-print Network

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

274

Topological Strings from Quantum Mechanics  

E-print Network

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. Phys...

Grassi, Alba; Marino, Marcos

2014-01-01

275

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+vfnl(s)), n=1,2,3,..., l=0,1,2,..., where the ``kinetic potentials'' fnl(s) associated with f(r) are defined by fnl(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)( fnl(i)(s)). This nice behavior of the kinetic potentials leads to a constructive global approximation theory for Schrdinger 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

276

Strange Bedfellows: Quantum Mechanics and Data Mining  

NASA Astrophysics Data System (ADS)

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

2010-02-01

277

Strange Bedfellows: Quantum Mechanics and Data Mining  

E-print Network

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.

Weinstein, Marvin

2009-01-01

278

Strange Bedfellows: Quantum Mechanics and Data Mining  

SciTech Connect

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

Weinstein, Marvin; /SLAC

2009-12-16

279

Strange Bedfellows: Quantum Mechanics and Data Mining  

E-print Network

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

280

Active Quantum Mechanics: Tutorials and Writing Assignments  

NSDL National Science Digital Library

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

Timberlake, Todd

2011-08-01

281

Canonical distribution and incompleteness of quantum mechanics  

E-print Network

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

2012-01-04

282

Four-dimensional understanding of quantum mechanics  

E-print Network

In this paper I will try to convince that quantum mechanics does not have to lead to indeterminism, but is just a natural consequence of four-dimensional nature of our world - that for example particles shouldn't be imagined as 'moving points' in space, but as their trajectories in the spacetime like in optimizing action formulation of Lagrangian mechanics. There will be analyzed simplified model - Boltzmann distribution among trajectories occurs to give quantum mechanic like behavior - for example electron moving in proton's potential would make some concrete trajectory which average exactly to the probability distribution of the quantum mechanical ground state. We will use this model to build intuition about quantum mechanics and discuss its generalizations to get some effective approximation of physics. We will see that topological excitations of the simplest model obtained this way already creates known from physics particle structure, their decay modes and electromagnetic/gravitational interactions between them.

Jarek Duda

2009-10-14

283

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.

284

Space time symmetry in quantum mechanics  

E-print Network

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

285

Can Quantum Mechanics Heal Classical Singularities?  

NASA Astrophysics Data System (ADS)

We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. We show that a large subset of classically singular spacetimes is nevertheless nonsingular quantum mechanically, in that the Hamiltonian operator is essentially self-adjoint so the evolution of quantum wave packets lacks the ambiguity associated with scattering off singularities.

Helliwell, T. M.; Konkowski, D. A.

2008-09-01

286

Quantum Mechanics and the Generalized Uncertainty Principle  

E-print Network

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

2006-10-11

287

Quantum Mechanics and Multiply Connected Spaces  

E-print Network

t is well known that the difference between Quantum Mechanics and Classical Theory appears most crucially in the non Classical spin half of the former theory and the Wilson-Sommerfelt quantization rule. We argue that this is symptomatic of the fact that Quantum Theory is actually a theory in multiply connected space while Classical Theory operates in simply connected space.

B. G. Sidharth

2006-05-16

288

Local quantum mechanics with finite Planck mass  

E-print Network

In this paper the motion of quantum particles with initial mass m is investigated. The quantum mechanics equation is formulated and solved. It is shown that the wave function contains the component which is depended on the gravitation fine structure constant

M Kozlowski; J. Marciak -Kozlowska; M. pelc

2007-04-20

289

Web-based Quantum Mechanics II Course  

NSDL National Science Digital Library

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

Breinig, Marianne

2005-04-16

290

Macrostates thermodynamics and its stable classical limit in Global One-Dimensional Quantum General Relativity  

E-print Network

Global One--Dimensional Quantum General Relativity is the toy model with nontrivial field theoretical content, describing classical one-dimensional massive bosonic fields related to any 3+1 metric, where the dimension is a volume of three-dimensional embedding. In fact it constitutes the midisuperspatial Quantum Gravity model. We use one-particle density operator method in order to building macrostates thermodynamics related with any 3+1 metric. Taking the Boltzmann gas limit, which is given by the energy equipartition law for the Bose-Einstein gas of space quantum states generated from the Bogoliubov vacuum, we receive consistent with General Relativity thermodynamical degrees of freedom number. It confirms that the proposed Quantum Gravity toy model has well-defined classical limit in accordance with classical gravity theory.

Glinka, L A

2008-01-01

291

Macrostates thermodynamics and its stable classical limit in Global One-Dimensional Quantum General Relativity  

E-print Network

Global One--Dimensional Quantum General Relativity is the toy model with nontrivial field theoretical content, describing classical one-dimensional massive bosonic fields related to any 3+1 metric, where the dimension is a volume of three-dimensional embedding. In fact it constitutes the midisuperspatial Quantum Gravity model. We use one-particle density operator method in order to building macrostates thermodynamics related with any 3+1 metric. Taking the Boltzmann gas limit, which is given by the energy equipartition law for the Bose-Einstein gas of space quantum states generated from the Bogoliubov vacuum, we receive consistent with General Relativity thermodynamical degrees of freedom number. It confirms that the proposed Quantum Gravity toy model has well-defined classical limit in accordance with classical gravity theory.

L. A. Glinka

2008-09-30

292

Gerbes, Quantum Mechanics and Gravity  

E-print Network

We prove that invariance of a quantum theory under the semiclassical vs. strong-quantum duality $S/\\hbar\\longleftrightarrow\\hbar/S$, where S is the classical action, is equivalent to noncommutativity (of the Heisenberg-algebra type) of the coordinates of the space on which S is defined. We place these facts in correspondence with gerbes and Neveu-Schwarz B-fields and discuss their implications for a quantum theory of gravity. Feynman's propagator turns out to be closely related to the trivialisation of a gerbe on configuration space.

J. M. Isidro

2005-10-10

293

CLNS 96/1399 Peculiarities of Quantum Mechanics  

E-print Network

CLNS 96/1399 Peculiarities of Quantum Mechanics: Origins and Meaning Yuri F. Orlov Floyd R. Newman, specifically quantum, features of quantum mechanics --- quan­ tum nonlocality, indeterminism, interference are quantum observables themselves and are represented in quantum mechanics by density matrices of pure states

294

On a New Form of Quantum Mechanics (II)  

E-print Network

The correspondence of a new form of quantum mechanics based on a quantum version of the action principle, which was proposed earlier [arXiv:0807.3508], with the ordinary quantum mechanics is established. New potentialities of the quantum action principle in the interpretation of quantum mechanics are considered.

N. Gorobey; A. Lukyanenko; I. Lukyanenko

2009-12-16

295

Supersymmetric q-deformed quantum mechanics  

SciTech Connect

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

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

2012-06-27

296

Lecture Notes in Quantum Mechanics Doron Cohen  

E-print Network

, scattering resonances · The Aharonov-Bohm effect · Magnetic field (Landau levels, Hall effect) · Motion · Spherical geometry, phase shifts · Cross section, optical theorem, resonances Quantum mechanics in practice

Cohen, Doron

297

Student Difficulties in Learning Quantum Mechanics.  

ERIC Educational Resources Information Center

Reports on a preliminary project that uses a phenomenographic approach to explore the ways in which a small number of fundamental ideas are conceptualized by students who are judged to have mastered quantum mechanics material. (DDR)

Johnston, I. D.; Crawford, K.; Fletcher, P. R.

1998-01-01

298

Quantum mechanical streamlines. I - Square potential barrier  

NASA Technical Reports Server (NTRS)

Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.

Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.

1974-01-01

299

Student difficulties in learning quantum mechanics  

NSDL National Science Digital Library

Reports on a preliminary project that uses a phenomenographic approach to explore the ways in which a small number of fundamental ideas are conceptualized by students who are judged to have mastered quantum mechanics material.

Johnston, Ian D.; Crawford, K.; Fletcher, P. R.

2006-06-19

300

Beyond Quantum Mechanics and General Relativity  

E-print Network

In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.

Andrea Gregori

2010-02-24

301

Quantum mechanics in de Sitter space  

E-print Network

We consider some possible phenomenological implications of the extended uncertainty principle, which is believed to hold for quantum mechanics in de Sitter spacetime. The relative size of the corrections to the standard results is however of the order of the ratio between the length scale of the quantum mechanical system and the de Sitter radius, and therefore exceedingly small. Nevertheless, the existence of effects due to the large scale curvature of spacetime in atomic experiments has a theoretical relevance.

Subir Ghosh; Salvatore Mignemi

2009-11-30

302

SEI: Quantum Mechanics I Course Materials  

NSDL National Science Digital Library

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

Goldhaber, Steve; Pollock, Steven J.

2010-01-29

303

2T Physics and Quantum Mechanics  

E-print Network

We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit described by the same Hamiltonian. One of these formulations is used as a basis for a complementation of the usual quantum mechanics when in the presence of gravity.

W. Chagas-Filho

2008-02-20

304

Quantum Mechanics: Rigid Rotator Applet  

NSDL National Science Digital Library

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

Falstad, Paul

2004-05-17

305

Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics-II  

E-print Network

The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of probability in Quantum Mechanics and its interpretations. We give yet another interpretation to the notion of Faraday lines and loops as the locus of probability flow. Also, the possibilities of visualization of spectra of area operators by means of classical geometric forms and conventional Quantum Mechanics are explored.

Aalok Pandya

2009-01-19

306

Interpretations of Quantum Mechanics: a critical survey  

E-print Network

This brief survey analyzes the epistemological implications about the role of observer in the interpretations of Quantum Mechanics. As we know, the goal of most interpretations of quantum mechanics is to avoid the apparent intrusion of the observer into the measurement process. In the same time, there are implicit and hidden assumptions about his role. In fact, most interpretations taking as ontic level one of these fundamental concepts as information, physical law and matter bring us to new problematical questions. We think, that no interpretation of the quantum theory can avoid this intrusion until we do not clarify the nature of observer.

Michele Caponigro

2008-11-24

307

Interpretations of Quantum Mechanics: a critical survey  

E-print Network

This brief survey analyzes the epistemological implications about the role of observer in the interpretations of Quantum Mechanics. As we know, the goal of most interpretations of quantum mechanics is to avoid the apparent intrusion of the observer into the measurement process. In the same time, there are implicit and hidden assumptions about his role. In fact, most interpretations taking as ontic level one of these fundamental concepts as information, physical law and matter bring us to new problematical questions. We think, that no interpretation of the quantum theory can avoid this intrusion until we do not clarify the nature of observer.

Caponigro, Michele

2008-01-01

308

What is Time in Quantum Mechanics?  

E-print Network

Time of arrival in quantum mechanics is discussed in two versions: the classical axiomatic "time of arrival operator" introduced by J. Kijowski and the EEQT method. It is suggested that for free particles the two methods may lead to the same result. On the other hand the EEQT method can be easily geometrized within the framework of Galilei-Newton general relativistic quantum mechanics developed by M. Modugno and collaborators, and it can be applied to non-free evolutions. The way of geometrization of irreversible quantum dynamics based on dissipative Liouville equation is suggested.

Arkadiusz Jadczyk

2014-02-25

309

Testing foundations of quantum mechanics with photons  

NASA Astrophysics Data System (ADS)

Quantum mechanics continues to predict effects at odds with a classical understanding of nature. Experiments with light at the single-photon level have historically been at the forefront of fundamental tests of quantum theory and the current developments in photonic technologies enable the exploration of new directions. Here we review recent photonic experiments to test two important themes in quantum mechanics: wave-particle duality, which is central to complementarity and delayed-choice experiments; and Bell nonlocality, where the latest theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different experiments.

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

2014-04-01

310

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

311

Symmetry and the thermodynamics of currents in open quantum systems  

E-print Network

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

2013-10-28

312

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

E-print Network

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

313

Thermodynamics of Quantum Ultra-Cold Neutron Gas under Gravity of the Earth  

NASA Astrophysics Data System (ADS)

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.

Kaneko, H.; Tohsaki, A.; Hosaka, A.

2012-09-01

314

Thermodynamics of quantum jump trajectories in systems driven by classical fluctuations  

E-print Network

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 transit...

Budini, Adrian A

2010-01-01

315

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

E-print Network

MS/ME 505 Thermodynamics and Statistical Mechanics of Materials Instructor: Prof. Uday B. Pal University Press Syndicate, Cambridge 3. David Chandler, Introduction to Modern Statistical Mechanics, Oxford to Modern Statistical Mechanics, Oxford University Press, Oxford, New York. #12;

316

DNA cytosine methylation: Structural and thermodynamic characterization of the epigenetic marking mechanism  

PubMed Central

DNA cytosine methyltransferases regulate the expression of the genome through the precise epigenetic marking of certain cytosines with a methyl group, and aberrant methylation is a hallmark of human diseases including cancer. Targeting these enzymes for drug design is currently a high priority. We have utilized ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations to extensively investigate the reaction mechanism of the representative DNA methyltransferase HhaI (M.HhaI) from prokaryotes, whose overall mechanism is shared with the mammalian enzymes. We obtain for the first time full free energy profiles for the complete reaction, together with reaction dynamics in atomistic detail. Our results show an energetically preferred mechanism in which nucleophilic attack of cytosine C5 on the S-adenosyl-L-methionine (AdoMet) methyl group is concerted with formation of the Michael adduct between a conserved Cys in the active site with cytosine C6. Spontaneous and reversible proton transfer between a conserved Glu in the active site and cytosine N3 at the transition state was observed in our simulations, revealing the chemical participation of this Glu residue in the catalytic mechanism. Subsequently, the ?-elimination of the C5 proton utilizes as base an OH? derived from a conserved crystal water that is part of a proton wire water channel, and this syn ?-elimination reaction is the rate-limiting step. Design of novel cytosine methylation inhibitors would be advanced by our structural and thermodynamic characterization of the reaction mechanism. PMID:23528166

Yang, Jin; Lior-Hoffmann, Lee; Wang, Shenglong; Zhang, Yingkai; Broyde, Suse

2013-01-01

317

Treating Time Travel Quantum Mechanically  

E-print Network

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: D-CTCs and 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 T-CTCs, is fully developed. The theory of T-CTCs is shown to not have undesirable features--...

Allen, John-Mark A

2014-01-01

318

Mechanics and chemical thermodynamics of a temperature-sensitive hydrogel  

NASA Astrophysics Data System (ADS)

A temperature-sensitive hydrogel is a network of polymers containing monomers, whose interaction with water molecules can be tuned dramatically by changing temperature. In most cases, the swelling ratio of a temperature-sensitive hydrogel changes discontinuously upon heating above or cooling below a critical temperature, which is called volume phase transition. Interestingly, the coexistence of swollen phases and shrunk phases are frequently observed in the experiments for temperature-sensitive hydrogels and additionally, people have also discovered that a uniaxial force can induce phase transition in a temperature-sensitive gel bar .In order to understand these phenomena, we studied the mechanics and chemical thermodynamics of a temperature-sensitive hydrogel bar, by using the free-energy landscape of a bar made from PNIPAM gel. Following Gibbs, we plot the phase diagram of a temperature-sensitive hydrogel bar under uniaxial force.

Cai, Shengqiang; Suo, Zhigang

2011-03-01

319

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/spacetimethese phenomena arise to represent changes of the reference frame in the relevant Hilbert space. This can be viewed as an extension of the Poincar transformation in the quantum gravitational context. Given an initial condition, the evolution of the multiverse state obeys the laws of quantum mechanicsit evolves deterministically and unitarily. The beginning of the multiverse, however, is still an open issue.

Nomura, Yasunori

2013-08-01

320

A quantum information approach to statistical mechanics  

E-print Network

We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all classical spin models (including models in different dimensions, different types of many-body interactions, different symmetries, etc) can be mapped to the partition function of a single model. Second, we give efficient quantum algorithms to estimate the partition function of various classical spin models, such as the Ising or the Potts model. The proofs of these two results are based on a mapping from partition functions to quantum states and to quantum circuits, respectively. Finally, we show how classical spin models can be used to describe certain fluctuating lattices appearing in models of discrete quantum gravity.

Gemma De las Cuevas

2013-12-20

321

Quantum mechanics and the equivalence principle  

E-print Network

A quantum particle moving in a gravitational field may penetrate the classically forbidden region of the gravitational potential. This raises the question of whether the time of flight of a quantum particle in a gravitational field might deviate systematically from that of a classical particle due to tunnelling delay, representing a violation of the weak equivalence principle. I investigate this using a model quantum clock to measure the time of flight of a quantum particle in a uniform gravitational field, and show that a violation of the equivalence principle does not occur when the measurement is made far from the turning point of the classical trajectory. I conclude with some remarks about the strong equivalence principle in quantum mechanics.

P. C. W. Davies

2004-03-03

322

1 Introduction to quantum mechanics Quantum mechanics is the basic tool needed to describe, understand and devise  

E-print Network

1­1 1 Introduction to quantum mechanics Quantum mechanics is the basic tool needed to describe, understand and devise NMR experiments. Fortunately for NMR spectroscopists, the quantum mechanics of nuclear mathematical concepts frequently encountered in quantum mechanics and NMR. 0DWKHPDWLFDO FRQFHSWV 1.1.1 Complex

Foster, Mark P.

323

Quantum mechanics as applied mathematical statistics  

SciTech Connect

Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.

Skala, L., E-mail: Lubomir.Skala@mff.cuni.cz [Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2 (Czech Republic); University of Waterloo, Department of Applied Mathematics, Waterloo, Ontario, Canada N2L 3G1 (Canada); Cizek, J. [Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2 (Czech Republic); University of Waterloo, Department of Applied Mathematics, Waterloo, Ontario, Canada N2L 3G1 (Canada); Kapsa, V. [Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2 (Czech Republic)

2011-05-15

324

Notes on Quantum Mechanics and Consciousness  

E-print Network

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

325

Quantum mechanics: last stop for reductionism  

E-print Network

The state space of a homogeneous body is derived under two different assumptions: infinitesimal reducibility and irreducibility. The first assumption leads to a real vector space, used in classical mechanics, while the second one leads to a complex vector space, used in quantum mechanics.

Gabriele Carcassi

2012-03-16

326

Pseudo-Hermitian Representation of Quantum Mechanics  

E-print Network

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review of the basic ideas and techniques responsible for the recent developments in this subject. We provide a critical assessment of the role of the geometry of the Hilbert space in conventional quantum mechanics to reveal the basic physical principle motivating our study. We then offer a survey of the necessary mathematical tools and elaborate on a number of relevant issues of fundamental importance. In particular, we discuss the role of the antilinear symmetries such as PT, the true meaning and significance of the charge operators C and the CPT-inner products, the nature of the physical observables, the equivalent description of such models using ordinary Hermitian quantum mechanics, the pertaining duality between local-non-Hermitian versus nonlocal-Hermitian descriptions of their dynamics, the corresponding classical systems, the pseudo-Hermitian canonical quantization scheme, various methods of calculating the (pseudo-) metric operators, subtleties of dealing with time-dependent quasi-Hermitian Hamiltonians and the path-integral formulation of the theory, and the structure of the state space and its ramifications for the quantum Brachistochrone problem. We also explore some concrete physical applications of the abstract concepts and tools that have been developed in the course of this investigation. These include applications in nuclear physics, condensed matter physics, relativistic quantum mechanics and quantum field theory, quantum cosmology, electromagnetic wave propagation, open quantum systems, magnetohydrodynamics, quantum chaos, and biophysics.

Ali Mostafazadeh

2008-10-31

327

Quantum electro-mechanical systems (QEMS)  

NASA Astrophysics Data System (ADS)

We give a quantum description of a Quantum Electro-Mechanical System (QEMS) comprising a single quantum dot harmonically bound between two electrodes and facilitating a tunnelling current between them. An example of such a system is a fullerene molecule between two metal electrodes. The description is based on a quantum master equation for the density operator of the electronic and vibrational degrees of freedom and thus incorporates the dynamics of both diagonal (population) and off diagonal (coherence) terms. We derive coupled equations of motion for the electron occupation number of the dot and the vibrational degrees of freedom, including damping of the vibration and thermo-mechanical noise, and give a semiclassical description of the dynamics under a variety of bias conditions. This dynamical description is related to observable features of the system including the stationary conductance as a function of bias voltage.

Utami, Dian W.; Goan, Hsi-Sheng; Milburn, Gerard J.

2004-04-01

328

Optimal guidance law in quantum mechanics  

SciTech Connect

Following de Broglies 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 particles motion is just the wavefunction ?(t,x), a solution to the Schrdinger equation; meanwhile, the closed-loop guidance system forms a complex statespace 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 BroglieBohms idea of a pilot wave. The optimal pilot wave is shown to be a wavefunction solved from Schrdinger equation.

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

2013-11-15

329

Objective and Subjective Probabilities in Quantum Mechanics  

E-print Network

The concept of probability was prominent in the original foundations of quantum mechanics, and continues to be so today. Indeed, the controversies regarding objective and subjective interpretations of probability have again become active. I argue that, although both objective and subjective probabilities have domains of relevance in QM, their roles are quite distinct. Even where both are legitimate, the objective and subjective probabilities differ, both conceptually and numerically. There are quantum probabilities that have no useful subjective interpretations, and there are subjective probabilities that cannot be realized as quantum probabilities.

Leslie Ballentine

2007-10-31

330

Quantum mechanical counterpart of nonlinear optics  

E-print Network

Raman-type laser excitation of a trapped atom allows one to realize the quantum mechanical counterpart of phenomena of nonlinear optics, such as Kerr-type nonlinearities, parametric amplification, and multi-mode mixing. Additionally, huge nonlinearities emerge from the interference of the atomic wave function with the laser waves. They lead to a partitioning of the phase space accompanied by a significantly different action of the time evolution in neighboring phase-space zones. For example, a nonlinearly modified coherent "displacement" of the motional quantum state may induce strong amplitude squeezing and quantum interferences.

S. Wallentowitz; W. Vogel

1997-05-15

331

On Time. 6b: Quantum Mechanical Time  

E-print Network

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

332

A Primer on Resonances in Quantum Mechanics  

E-print Network

After a pedagogical introduction to the concept of resonance in classical and quantum mechanics, some interesting applications are discussed. The subject includes resonances occurring as one of the effects of radiative reaction, the resonances involved in the refraction of electromagnetic waves by a medium with a complex refractive index, and quantum decaying systems described in terms of resonant states of the energy. Some useful mathematical approaches like the Fourier transform, the complex scaling method and the Darboux transformation are also reviewed.

O. Rosas-Ortiz; N. Fernandez-Garcia; Sara Cruz y Cruz

2009-02-24

333

A Primer on Resonances in Quantum Mechanics  

E-print Network

After a pedagogical introduction to the concept of resonance in classical and quantum mechanics, some interesting applications are discussed. The subject includes resonances occurring as one of the effects of radiative reaction, the resonances involved in the refraction of electromagnetic waves by a medium with a complex refractive index, and quantum decaying systems described in terms of resonant states of the energy. Some useful mathematical approaches like the Fourier transform, the complex scaling method and the Darboux transformation are also reviewed.

Rosas-Ortiz, O; Cruz, Sara Cruz y; 10.1063/1.3040259

2009-01-01

334

Testing the limits of quantum mechanical superpositions  

NASA Astrophysics Data System (ADS)

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 past decades inspires hope that this debate may be settled by table-top experiments.

Arndt, Markus; Hornberger, Klaus

2014-04-01

335

Testing the limits of quantum mechanical superpositions  

E-print Network

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

336

The Mechanism of Quantum Computation  

Microsoft Academic Search

I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine\\u000a whose coordinates are submitted to a nonfunctional relation representing all the problem constraints; moving an input part,\\u000a reversibly and nondeterministically produces a solution through a many body interaction. The machine can be considered the\\u000a many body generalization of another perfect machine, the

Giuseppe Castagnoli

2008-01-01

337

The effects of the size of nanocrystalline materials on their thermodynamic and mechanical properties  

PubMed Central

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

338

Quantum Mechanics and the Principle of Least Radix Economy  

E-print Network

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 Schroedinger, Dirac and Klein-Gordon 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 to interpret dynamical processes 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 thousand. Finally, it is shown how the principle of least-radix economy leads to establish Boltzmann's principle of classical statistical thermodynamics and the Second Law of thermodynamics. A new expression for a general (path-dependent) nonequilibrium entropy is derived showing that it satisfies the Second Law.

Vladimir Garcia-Morales

2014-01-06

339

CLNS 96/1443 Peculiarities of Quantum Mechanics  

E-print Network

CLNS 96/1443 REVISED Peculiarities of Quantum Mechanics: Origins and Meaning 1 Yuri F. Orlov Floyd The most peculiar, specifically quantum, features of quantum mechanics --- quan­ tum nonlocality of pure states. Structurally, quantum mechanics is a result of applying non­Abelian symmetries to truth

340

Green's Functions and Their Applications to Quantum Mechanics  

E-print Network

Green's Functions and Their Applications to Quantum Mechanics Jeff Schueler June 2, 2011 Contents 1 Green's Functions in Quantum Mechanics and Many-body Theory 8 3.1 Time Independent Green's Fuctions, specifically in how they apply to quantum mechan- ics. I plan to introduce some of the fundamentals of quantum

Morrow, James A.

341

Quantum mechanics as "space-time statistical mechanics"?  

E-print Network

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 Mnsson

2005-01-24

342

Statistical mechanics of confined quantum particles  

E-print Network

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

343

Diffusion-based DNA target colocalization by thermodynamic mechanisms  

E-print Network

In eukaryotic cell nuclei, a variety of DNA interactions with nuclear elements occur, which, in combination with intra- and inter- chromosomal cross-talks, shape a functional 3D architecture. In some cases they are organized by active, i.e. actin/myosin, motors. More often, however, they have been related to passive diffusion mechanisms. Yet, the crucial questions on how DNA loci recognize their target and are reliably shuttled to their destination by Brownian diffusion are still open. Here, we complement the current experimental scenario by considering a physics model, in which the interaction between distant loci is mediated by diffusing bridging molecules. We show that, in such a system, the mechanism underlying target recognition and colocalization is a thermodynamic switch-like process (a phase transition) that only occurs if the concentration and affinity of binding molecules is above a threshold, or else stable contacts are not possible. We also briefly discuss the kinetics of this "passive-shuttling" process, as produced by random diffusion of DNA loci and their binders, and derive predictions based on the effects of genomic modifications and deletions.

Antonio Scialdone; Mario Nicodemi

2011-05-04

344

Space and time from quantum mechanics  

SciTech Connect

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

Chew, G.F.

1992-09-16

345

Space and time from quantum mechanics  

NASA Astrophysics Data System (ADS)

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

Chew, G. F.

1992-09-01

346

First-Person Plural Quantum Mechanics  

E-print Network

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.

Mohrhoff, Ulrich

2014-01-01

347

First-Person Plural Quantum Mechanics  

E-print Network

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

348

Two basic Uncertainty Relations in Quantum Mechanics  

SciTech Connect

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

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

2011-04-07

349

Transport and thermodynamic properties of mesoscopic quantum systems  

Microsoft Academic Search

The transport properties of three-dimensional quantum microconstrictions in field-free conditions and under the influence of magnetic fields of arbitrary strengths and directions are studied via a generalized Buttiker model. It is shown that conductance quantization is influenced by the geometry of the microconstriction (that is, its length and the shape of its transverse cross-section). In a weak longitudinal magnetic field,

Andrew Germanovich Scherbakov

1997-01-01

350

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

351

A proof of von Neumann's postulate in Quantum Mechanics  

SciTech Connect

A Clifford algebraic analysis is explained. It gives proof of von Neumann's postulate on quantum measurement. It is of basic significance to explain the problem of quantum wave function reduction in quantum mechanics.

Conte, Elio [Department of Pharmacology and Human Physiology, TIRES-Center for Innovative Technologies for Signal Detection and Processing, Department of Physics, University of Bari (Italy) and School of Advanced International Studies for Applied Theoretical and Non Linear Methodologies of Physics, Bari (Italy)

2010-05-04

352

Quantum mechanics of time travel through post-selected teleportation  

E-print Network

This paper discusses the quantum mechanics of closed-timelike curves (CTCs) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based ...

Maccone, Lorenzo

353

Deformation Quantization: From Quantum Mechanics to Quantum Field Theory  

E-print Network

The aim of this paper is to give a basic overview of Deformation Quantization (DQ) to physicists. A summary is given here of some of the key developments over the past thirty years in the context of physics, from quantum mechanics to quantum field theory. Also, we discuss some of the conceptual advantages of DQ and how DQ may be related to algebraic quantum field theory. Additionally, our previous results are summarized which includes the construction of the Fedosov star-product on dS/AdS. One of the goals of these results was to verify that DQ gave the same results as previous analyses of these spaces. Another was to verify that the formal series used in the conventional treatment converged by obtaining exact and nonperturbative results for these spaces.

P. Tillman

2006-10-31

354

Partitions and Objective Indefiniteness in Quantum Mechanics  

E-print Network

Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual to one another and which are developed in two mathematical logics, the usual Boolean logic of subsets and the more recent logic of partitions. Our sense-making strategy is "follow the math" by showing how the logic and mathematics of set partitions can be transported in a natural way to Hilbert spaces where it yields the mathematical machinery of QM--which shows that the mathematical framework of QM is a type of logical system over the complex numbers. And then we show how the machinery of QM can be transported the other way down to the set-like vector spaces over Z_2 showing how the classical logical finite probability calculus (in a "non-commutative" version) is a type of "quantum mechanics" over Z_2, i.e., over sets. In this way, we try to make sense out of objective indefiniteness and thus to interpret quantum mechanics.

David Ellerman

2014-01-10

355

Macroscopic Quantum Mechanics in a Classical Spacetime  

E-print Network

We apply the many-particle Schr\\"{o}dinger-Newton equation, which describes the co-evolution of an many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schr\\"odinger-Newton equation for their centers of mass, which are degrees of freedom that can be monitored and manipulated at the quantum mechanical levels by state-of-the-art optoemchanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, we found that its quantum uncertainty evolves in a different frequency from its classical eigenfrequency --- with a difference that depends on the internal structure of the object, and can be observable using current technology. For several objects, the Schr\\"odinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet they do not allow quantum uncertainty to be transferred from one object to another through gravity.

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

2012-10-01

356

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

357

On Time in Quantum Mechanics  

E-print Network

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

358

CPT and Quantum Mechanics Tests with Kaons  

E-print Network

In this review we first discuss the theoretical motivations for possible CPT violation and deviations from ordinary quantum-mechanical behavior of field-theoretic systems in the context of an extended class of quantum-gravity models. Then we proceed to a description of precision tests of CPT symmetry using mainly neutral kaons. We emphasize the possibly unique role of neutral meson factories in providing specific tests of models where the quantum-mechanical CPT operator is not well-defined, leading to modifications of Einstein-Podolsky-Rosen particle correlators. Finally, we present tests of CPT, T, and CP using charged kaons, and in particular K_l4 decays, which are interesting due to the high statistics attainable in experiments.

Jose Bernabeu; John Ellis; Nick E. Mavromatos; Dimitri V. Nanopoulos; Joannis Papavassiliou

2006-07-28

359

A Euclidean formulation of relativistic quantum mechanics  

E-print Network

In this paper we discuss a formulation of relativistic quantum mechanics that uses Euclidean Green functions or generating functionals as input. This formalism has a close relation to quantum field theory, but as a theory of linear operators on a Hilbert space, it has many of the advantages of quantum mechanics. One interesting feature of this approach is that matrix elements of operators in normalizable states on the physical Hilbert space can be calculated directly using the Euclidean Green functions without performing an analytic continuation. The formalism is summarized in this paper. We discuss the motivation, advantages and difficulties in using this formalism. We discuss how to compute bound states, scattering cross sections, and finite Poincare transformations without using analytic continuation. A toy model is used to demonstrate how matrix elements of exp(-beta H) in normalizable states can be used to construct-sharp momentum transition matrix elements.

Philip Kopp; Wayne Polyzou

2011-06-21

360

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

361

Transport and thermodynamic properties of mesoscopic quantum systems  

NASA Astrophysics Data System (ADS)

The transport properties of three-dimensional quantum microconstrictions in field-free conditions and under the influence of magnetic fields of arbitrary strengths and directions are studied via a generalized Buttiker model. It is shown that conductance quantization is influenced by the geometry of the microconstriction (that is, its length and the shape of its transverse cross-section). In a weak longitudinal magnetic field, when rsb{c}? d, where rsb{c} is the cyclotron radius and d the effective transverse size of the narrowing of the microconstriction, the conductance exhibits Aharonov-Bohm type behavior. This behavior transforms in the strong field limit, rsb{c}? d, into Shubnikov-de Haas oscillations with a superimposed Aharonov-Bohm fine-structure. The dependence of the Aharonov-Bohm type features on the length of the microconstriction and on temperature are demonstrated. Effects of the shapes of the cross sections of three-dimensional nanowires on electronic conductance quantization are studied for both hard- and soft-wall potentials. In both models the quantum conductance is determined by both the area and shape of the narrowmost part of the nanowire. For the hard-wall potential the semiclassical (Weyl) correction to the Sharvin formula provides an adequate approximation to the average quantized conductance. For nanowires modeled by soft-wall potentials the average quantum conductance may be well estimated using a classical approximation. Magnetic field switching and blockade of quantum transport through three-dimensional metallic and semimetallic nanowires with a small number of conducting channels are proposed. Temperature enhancement of magnetotransport in such wires is predicted. Thermoelectric properties of nanowires in a magnetic field are studied. Magnetic splitting of thermopower peaks associated with electronic energy levels which are degenerate at zero field, leading to the development of separate thermopower peaks at larger fields, are predicted. A method for numerical calculation of the conductance through microconstrictions based on the time-dependent Schrodinger equation is developed, allowing investigations of electronic transport in complex situations. An algorithm for conductance calculations via propagation of wave packets is presented, and results for electronic transport through various constrictions are given, including model calculations of the conductance of a one-atom contact in the scanning tunneling microscope.

Scherbakov, Andrew Germanovich

362

Quantum and thermodynamic properties of spontaneous and low-energy induced fission of nuclei  

Microsoft Academic Search

It is shown that A. Bohrs concept of transition fission states can be matched with the properties of Coriolis interaction\\u000a if an axisymmetric fissile nucleus near the scission point remains cold despite a nonadiabatic character of nuclear collective\\u000a deformation motion. The quantum and thermodynamic properties of various stages of binary and ternary fission after the descent\\u000a of a fissile nucleus

S. G. Kadmensky

2005-01-01

363

Converting fructose to 5-hydroxymethylfurfural: A quantum mechanics/molecular mechanics study of the mechanism and energetics  

SciTech Connect

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

364

Quantum statistical mechanics, L-series, Anabelian Geometry  

E-print Network

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

365

Subjective and Objective Probabilities in Quantum Mechanics  

E-print Network

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

Mark Srednicki

2005-01-03

366

WEAK MEASUREMENT IN QUANTUM MECHANICS ABRAHAM NEBEN  

E-print Network

WEAK MEASUREMENT IN QUANTUM MECHANICS ABRAHAM NEBEN PHYS 342 Final Project March 10, 2011 Contents of Postselection 4 4. Impossible Spin Measurements 5 5. Hardy's Paradox 5 6. Controversy over Weak Measurement 8 7 of a Measurement of a Component of the Spin of a Spin-1/2 Particle Can Turn Out to be 100." [1] The topic

Rosner, Jonathan L.

367

Is Quantum Mechanics needed to explain consciousness ?  

E-print Network

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

368

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

369

Quantum mechanical model for Maya Blue  

Microsoft Academic Search

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

Mara E. Fuentes; Brisa Pea; Csar Contreras; Ana L. Montero; Russell Chianelli; Manuel Alvarado; Ramn Olivas; Luz M. Rodrguez; Hctor Camacho; Luis A. Montero-Cabrera

2008-01-01

370

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

371

Control of quantum thermodynamic behavior of a charged magneto-oscillator with momentum dissipation  

NASA Astrophysics Data System (ADS)

In this work we expose the role of environment, confinement, and external magnetic field B in determining the low-temperature thermodynamic behavior in the context of cyclotron motion of a charged oscillator with anomalous dissipative coupling involving momentum instead of the much studied coordinate coupling. Explicit expressions for different quantum thermodynamic functions (QTFs) are obtained at low temperatures for different quantum heat baths characterized by the spectral density function ? (?). The power-law fall of different QTFs is in conformity with the third law of thermodynamics; however, the sensitivity of decay, i.e., the power of the power-law decay, explicitly depends on ? (?). We also discuss separately the influence of confinement and magnetic field on the low-temperature behavior of different QTFs. In this process we demonstrate how to control the low-temperature behavior of anomalous dissipative quantum systems by varying the confining length a, B, and the temperature T. Momentum dissipation reduces the effective mass of the system and we also discuss its effect on different QTFs at low temperatures.

Rajesh, Asam; Bandyopadhyay, Malay

2014-06-01

372

Control of quantum thermodynamic behaviour of a charged magneto oscillator with momentum dissipation  

E-print Network

In this work, we expose the role of environment, confinement and external magnetic field ($B$) in determining the low temperature thermodynamic behaviour in the context of cyclotron motion of a charged oscillator with anomalous dissipative coupling involving the momentum instead of the much studied coordinate coupling. Explicit expressions for different quantum thermodynamic functions (QTF) are obtained at low temperatures for different quantum heat bath characterized by spectral density function, $\\mu(\\omega)$. The power law fall of different QTF are in conformity with third law of thermodynamics. But, the sensitiveness of decay i.e. the power of the power law decay explicitly depends on $\\mu(\\omega)$. We also separately discuss the influence of confinement and magnetic field on the low temperature behavior of different QTF. In this process we demonstrate how to control low temperature behaviour of anomalous dissipative quantum systems by varying confining length $a$, $B$ and the temperature $T$. Momentum dissipation reduces effective mass of the system and we also discuss its effect on different QTF at low temperatures.

Asam Rajesh; Malay Bandyopadhyay

2014-05-07

373

Exchange symmetry, fluctuation-compressibility relation, and thermodynamic potentials of quantum liquids.  

PubMed

Liquid helium does not obey the Gibbs fluctuation-compressibility relation, which was noted more than six decades ago. However, still missing is a clear explanation of the reason for the deviation or the correct fluctuation-compressibility relation for the quantum liquid. Here we present the fluctuation-compressibility relation valid for any grand canonical system. Our result shows that the deviation from the Gibbs formula arises from a nonextensive part of thermodynamic potentials. The particle-exchange symmetry of many-body wave function of a strongly degenerate quantum gas is related to the thermodynamic extensivity of the system; a Bose gas does not always obey the Gibbs formula, while a Fermi gas does. Our fluctuation-compressibility relation works for classical systems as well as quantum systems. This work demonstrates that the application range of the Gibbs-Boltzmann statistical thermodynamics can be extended to encompass nonextensive open systems without introducing any postulate other than the principle of equal a priori probability. PMID:25019748

Lim, Yu Rim; Park, Seong Jun; Song, Sanggeun; Yang, Gil-Suk; Yoon, Young-Gui; Kim, Ji-Hyun; Sung, Jaeyoung

2014-06-01

374

Spin Glass: A Bridge between quantum computation and statistical mechanics  

E-print Network

We show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Second, we show another interesting technique to employ quantum nature, quantum annealing. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.

Masayuki Ohzeki

2012-04-13

375

Doubly special quantum and statistical mechanics from quantum $?$-Poincar algebra  

E-print Network

Recently Amelino--Camelia proposed a ``Doubly Special Relativity'' theory with two observer independent scales (of speed and mass) that could replace the standard Special Relativity at energies close to the Planck scale. Such a theory might be a starting point in construction of quantum theory of space-time. In this paper we investigate the quantum and statistical mechanical consequences of such a proposal. We construct the generalized Newton--Wigner operator and find relations between energy/momentum and frequency/wavevector for position eigenstates of this operator. These relations indicate the existence of a minimum length scale. Next we analyze the statistical mechanics of the corresponding systems. We find that depending on the value of a parameter defining the canonical commutational algebra one has to do either with system with maximal possible temperature or with the one, which in the high temperature limit becomes discrete.

J. Kowalski-Glikman

2001-11-12

376

Riemann hypothesis and Quantum Mechanics  

E-print Network

In their 1995 paper, Jean-Beno\\^{i}t Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function $\\zeta(\\beta)$, where $\\beta$ 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 $N_q=\\prod_{k=1}^qp_k$ is the primorial number of order $q$ and $ \\psi_b $ a generalized Dedekind $\\psi$ function depending on one real parameter $b$ as $$ \\psi_b (q)=q \\prod_{p \\in \\mathcal{P,}p \\vert q}\\frac{1-1/p^b}{1-1/p}.$$ Fix a large inverse temperature $\\beta >2.$ The Riemann hypothesis is then shown to be equivalent to the inequality $$ N_q |\\phi_\\beta (N_q)|\\zeta(\\beta-1) >e^\\gamma \\log \\log N_q, $$ for $q$ large enough. Under RH, extra formulas for high temperatures KMS states ($1.5< \\beta <2$) are derived.

Michel Planat; Patrick Sol; Sami Omar

2010-12-21

377

Thermodynamics of quantum jump trajectories in systems driven by classical fluctuations  

E-print Network

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

378

Quantum mechanical coherence, resonance, and mind  

SciTech Connect

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

379

Indistinguishable Particles in Quantum Mechanics: An Introduction  

E-print Network

In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This is, for electrons, the Pauli Exclusion Principle, or in general, the Symmetrization Postulate. Then, we introduce fermions and bosons and the distributions respectively describing their statistical behaviour in indistinguishable situations. Following that, we discuss the spin-statistics connection, as well as alternative statistics and experimental evidence for all these results, including the use of bunching and antibunching of particles emerging from a beam splitter as a signature for some bosonic or fermionic states.

Y. Omar

2005-11-01

380

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

381

Quantum Hypothesis Testing Non-Equilibrium Statistical Mechanics  

E-print Network

Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics V. Jaksi´c1 , Y. Ogata2 , C with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large

Boyer, Edmond

382

Quantum Entanglement and Decoherence: Beyond Particle Models. A Farewell to Quantum Mechanics's Weirdness  

E-print Network

Combining abstract to laboratory projected quantum states a general analysis of headline quantum phenomena is presented. Standard representation mode is replaced; instead quantum states sustained by elementary material constituents occupy its place. Renouncing to assign leading roles to language originated in classical physics when describing genuine quantum processes, together with sustainment concept most, if not all weirdness associated to Quantum Mechanics vanishes.

O. Tapia

2014-04-02

383

1/n expansion in quantum mechanics  

SciTech Connect

The classical approximation (/ell/ = n - 1 /yields/ /infinity/) for the energy /var epsilon/(/sup 0/) and the semiclassical expansion in problems of quantum mechanics are discussed. A recursive method is proposed for calculating the quantum corrections of arbitrary order to /var epsilon/ (/sup 0/), this being valid for both bound and quasistationary states. The generalization of the method to states with an arbitrary number of nodes and the possibility of a more general choice of the parameter of the semiclassical expansion are considered. The method is illustrated by the example of the Yukawa and funnel potentials and for the Stark effect in the hydrogen atom. These examples demonstrate the rapid convergence of the 1/n expansion even for small quantum numbers.

Vainberg, V.M.; Mur, V.D.; Popov, V.S.; Sergeev, A.V.; Shcheblykin, A.V.

1988-09-01

384

Calculation of Mechanical, Thermodynamic and Transport Properties of Metalic Glass formers  

E-print Network

Calculation of Mechanical, Thermodynamic and Transport Properties of Metalic Glass formers Tahir C properties of pure metals and binary alloys in solid, liquid and glass phases. Here, we will describe the kinetics and thermodynamics of supercooled bulk metallic glass forming liquids is of critical importance

?agin, Tahir

385

Quantum Mechanics Joachim Burgd orfer and Stefan Rotter  

E-print Network

1 1 Quantum Mechanics Joachim Burgd? orfer and Stefan Rotter 1.1 Introduction 3 1.2 Particle and Quantization 8 1.5 Angular Momentum in Quantum Mechanics 9 1.6 Formalism of Quantum Mechanics 12 1.7 Solution Quantization 33 1.9.3 Gutzwiller Trace Formula 34 1.10 Conceptual Aspects of Quantum Mechanics 35 1

Rotter, Stefan

386

Introduction to Nonequilibrium Statistical Mechanics with Quantum Field  

E-print Network

In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson's equation. The aims are threefold: (i) to explain the fundamentals of nonequilibrium quantum field theory as simple as possible on the basis of the knowledge of the equilibrium counterpart; (ii) to elucidate the hierarchy in describing nonequilibrium systems from Dyson's equation on the Keldysh contour to the Navier-Stokes equation in fluid mechanics via quantum transport equations and the Boltzmann equation; (iii) to derive an expression of nonequilibrium entropy that evolves with time. In stage (i), we introduce nonequilibrium Green's function and the self-energy uniquely on the round-trip Keldysh contour, thereby avoiding possible confusions that may arise from defining multiple Green's functions at the very beginning. We try to present the Feynman rules for the perturbation expansion as simple as possible. In particular, we focus on the self-consistent perturbation expansion with the Luttinger-Ward thermodynamic functional, i.e., Baym's Phi-derivable approximation, which has a crucial property for nonequilibrium systems of obeying various conservation laws automatically. We also show how the two-particle correlations can be calculated within the Phi-derivable approximation, i.e., an issue of how to handle the "Bogoliubov-Born-Green-Kirkwood-Yvons (BBGKY) hierarchy".

Takafumi Kita

2010-05-03

387

The Objective Inde...niteness Interpretation of Quantum Mechanics  

E-print Network

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

Wüthrich, Christian

388

Quantum statistical mechanics, L-series, Anabelian Geometry  

E-print Network

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

389

Quantum statistical mechanics, L-series, Anabelian Geometry  

E-print Network

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

390

Harvard University Physics 143b: Quantum Mechanics II  

E-print Network

Harvard University Physics 143b: Quantum Mechanics II Instructor : Subir Sachdev, Lyman 343@fas.harvard.edu This is the second half of an introductory course on quantum mechanics. The course will complete the text book: the photon 5. Relativistic quantum mechanics: the Dirac equation 6. Einstein-Podolsky-Rosen "paradox", Bell

391

Harvard University Physics 143b: Quantum Mechanics II  

E-print Network

Harvard University Physics 143b: Quantum Mechanics II Instructor : Subir Sachdev, Lyman 343@physics.harvard.edu This is the second half of an introductory course on quantum mechanics. The course will complete the text book: the photon 5. Relativistic quantum mechanics: the Dirac equation 6. Scattering theory. 7. Einstein

392

Faculty Disagreement about the Teaching of Quantum Mechanics  

E-print Network

Faculty Disagreement about the Teaching of Quantum Mechanics Michael Dubson1 , Steve Goldhaber1 (matter wave vs. information wave vs. something else). Keywords: upper-division quantum mechanics, curriculum reform, faculty survey, quantum mechanics textbooks PACS: 01.40.-d, 01.40.Fk, 01.40.gb, 01.40.G

Colorado at Boulder, University of

393

Physica D 145 (2000) 330348 Lyapunov exponent in quantum mechanics.  

E-print Network

Physica D 145 (2000) 330­348 Lyapunov exponent in quantum mechanics. A phase-space approach V extension of the notion of Lyapunov exponent to quantum mechanics, the method that is developed is also trajectories in phase-space, it is not obvious what the corresponding quantities in quantum mechanics should be

Vilela Mendes, Rui

394

The syllabus of the Course 624 Quantum Mechanics 2  

E-print Network

The syllabus of the Course 624 Quantum Mechanics 2 Spring 2009. Instructor V.L. Pokrovsky. 1. Many-body quantum mechanics. Second quantization. Spin and statistics. Bose- Einstein condensation. 6's phase. Landau-Zener theory. Principal textbook: E. Merzbacher, Quantum Mechanics, 3-d edition, Wiley

395

Quantum Mechanics as a Science -Religion Bridge By Stanley Klein  

E-print Network

Quantum Mechanics as a Science - Religion Bridge By Stanley Klein (May 1, 2002) Stanley Klein and for fitting contact lenses. Klein's interest in quantum mechanics and brain research has led him to explore of more than 20 years, DUALITY, summarizes his theme that the duality of quantum mechanics provides

Klein, Stanley

396

Quantum Mechanics Summary/Review Spring 2009 Compton Lecture Series  

E-print Network

time, the spike will generally spread out again, and the information about position will be lost one component at a time. · Planck's constant determines the scale at which quantum mechanical effectsQuantum Mechanics Summary/Review Spring 2009 Compton Lecture Series: From Quantum Mechanics

397

A Chaotic, Deterministic Model for Quantum Mechanics  

E-print Network

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

398

Diffusion Waves in Sub-Quantum Thermodynamics: Resolution of Einstein's 'Particle-in-a-box' Objection  

E-print Network

Einstein's objection against both the completeness claim of the orthodox version and the Bohmian interpretation of quantum theory, using the example of a 'particle in a box', is reiterated and resolved. This is done by proving that the corresponding quantum mechanical states exactly match classical analogues. The latter are shown to result from the recently elaborated physics of diffusion waves.

Gerhard Groessing

2008-06-27

399

Neutrino oscillations: Quantum mechanics vs. quantum field theory  

SciTech Connect

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

Akhmedov, Evgeny Kh.; Kopp, Joachim; ,

2010-01-01

400

Thermodynamic theory of two-dimensional to three-dimensional growth transition in quantum dots self-assembly.  

PubMed

A thermodynamic model has been proposed to address the transition from the two-dimensional to three-dimensional growth modes in the quantum dots self-assembly. It was found that the surface energy density of substrates and the mismatch between quantum dots and substrates play key roles in the transition of the growth modes. The high (low) surface energy density of substrate and the low (high) mismatch between quantum dots and substrate result in the large (small) critical thickness of the wetting layer, which further determines the growth mode of quantum dots. These findings suggested that we could control the transition of the quantum dots growth mode by substrate manipulation. The theoretical results were consistent with experimental observations, which implied that the established thermodynamic theory could be expected to be a general approach for pursuing the evolution of the growth mode in the quantum dots self-assembly. PMID:20428557

Li, Xinlei; Cao, Yuanyuan; Yang, Guowei

2010-05-14

401

Clocks And Dynamics In Quantum Mechanics  

E-print Network

We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of quantum uncertainty lies with the absence of infinities or infinitesimals in observational data and that our concept of time derives from observing changing data (events). We argue that the fundamentally important content of the Superposition Principle is not the "probability amplitude" of posterior state observation but future state availability conditional only on prior information. Since event detection also implies posterior conditions (e.g. a specific type of detectable event occurred) as well as prior conditions, the probabilities of detected outcomes are also conditional on properties of the posterior properties of the observation. Such posterior conditions cannot affect the prior state availabilities and this implies violation of counter-factual definiteness. A componen...

York, Michael

2014-01-01

402

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

403

The preparation of states in quantum mechanics  

E-print Network

The important problem of how to prepare a quantum mechanical system, $S$, in a specific initial state of interest - e.g., for the purposes of some experiment - is addressed. Three distinct methods of state preparation are described. One of these methods has the attractive feature that it enables one to prepare $S$ in a preassigned initial state with certainty; i.e., the probability of success in preparing $S$ in a given state is unity. This method relies on coupling $S$ to an open quantum-mechanical environment, $E$, in such a way that the dynamics of $S \\vee E$ pulls the state of $S$ towards an "attractor", which is the desired initial state of $S$. This method is analyzed in detail.

Juerg Froehlich; Baptiste Schubnel

2014-09-28

404

Quantum Mechanics, Gravity, and the Multiverse  

NASA Astrophysics Data System (ADS)

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

Nomura, Yasunori

2012-04-01

405

Physical Interpretations of Nilpotent Quantum Mechanics  

E-print Network

Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit construction of vacuum. Physical interpretation of the nilpotent formalism is discussed with respect to boson and baryon structures, the mass-gap problem, zitterbewgung, Berry phase, renormalization, and related issues.

Peter Rowlands

2010-04-09

406

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

407

Chiral quantum mechanics (CQM) for antihydrogen systems  

E-print Network

A first deception of QM on antiH already appears in one-center integrals for two-center systems (G. Van Hooydonk, physics/0511115). In reality, full QM is a theory for chiral systems but the QM establishment was wrong footed with a permutation of reference frames. With chiral quantum mechanics (CQM), the theoretical ban on natural antiH must be lifted as soon as possible.

G. Van Hooydonk

2005-12-03

408

Quantum Mechanics and Motion: A Modern Perspective  

E-print Network

This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum, yields a world-line. If a force acts on the particle, its probability distribution is accordingly modified. This must also be true for macroscopic objects, although now the description is far more complicated by the structure of matter and associated surface physics.

Gerald E. Marsh

2009-12-27

409

Sixty years of quantum wave mechanics  

NASA Astrophysics Data System (ADS)

We present an inaugural lecture, originally given by the author on 2 June 1987 at the Queen's University of Belfast, but in an edited version, on the topic "Sixty years of quantum wave mechanics". A short historical survey is given as an introduction to some of the author's own personal research in the theory of atomic collisions, notably heavy-particle collisions and semiclassical methods.

Crothers, D. S. F.

1989-11-01

410

Euclidean Quantum Mechanics and Universal Nonlinear Filtering  

Microsoft Academic Search

An important problem in applied science is the continuous nonlinear filtering\\u000aproblem, i.e., the estimation of a Langevin state that is observed indirectly.\\u000aIn this paper, it is shown that Euclidean quantum mechanics is closely related\\u000ato the continuous nonlinear filtering problem. The key is the configuration\\u000aspace Feynman path integral representation of the fundamental solution of a\\u000aFokker-Planck type

Bhashyam Balaji

2009-01-01

411

Relativistic Non-Hermitian Quantum Mechanics  

E-print Network

We develop relativistic wave equations in the framework of the new non-hermitian ${\\cal PT}$ quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of ${\\cal PT}$-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 $\\cal{PT}$ symmetric mass matrix, describes a single relativistic particle that can have massless dispersion relation even though the mass matrix is non-zero.The ${\\cal PT}$-generalized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a non-interacting theory it violates ${\\cal P}$ and ${\\cal T}$ 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 new possibilities permitted by the non-hermiticity parameter $m_2$.

Katherine Jones-Smith; Harsh Mathur

2009-08-28

412

Quantum mechanics and low energy nucleon dynamics  

E-print Network

We discuss the problem of consistency of quantum mechanics as applied to low energy nucleon dynamics with the symmetries of QCD. It is shown that the dynamics consistent with these symmetries is not governed by the Schrodinger equation. We present a new way to formulate the effective theory of nuclear forces as an inevitable consequence of the basic principles of quantum mechanics and the symmetries of strong interactions. We show that being formulated in this way the effective theory of nuclear forces can be put on the same firm theoretical grounds as the quantum mechanics of atomic phenomena. In this case the effective theory allows one to describe with a given accuracy not only two-nucleon scattering, but also the evolution of nucleon systems, and places the constraints on the off-shell behavior of the two-nucleon interaction. In this way we predict the off-shell behavior of the S wave two-nucleon T-matrix at very low energies when the pionless theory is applicable. Further extensions and applications of this approach are discussed.

Renat Kh. Gainutdinov; Aigul A. Mutygullina

2003-04-03

413

Hunting for Snarks in Quantum Mechanics  

SciTech Connect

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

414

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

415

Quantum selfish gene (biological evolution in terms of quantum mechanics)  

E-print Network

I propose to treat the biological evolution of genoms by means of quantum mechanical tools. We start with the concept of meta- gene, which specifies the "selfish gene" of R.Dawkins. Meta- gene encodes the abstract living unity, which can live relatively independently of the others, and can contain a few real creatures. Each population of living creatures we treat as the wave function on meta- genes, which module squared is the total number of creatures with the given meta-gene, and the phase is the sum of "aspirations" to change the classical states of meta- genes. Each individual life thus becomes one of possible outcomes of the virtual quantum measurement of this function. The evolution of genomes is described by the unitary operator in the space of psi-functions or by Kossovsky-Lindblad equation in the case of open biosystems. This operator contains all the information about specific conditions under which individuals are, and how "aspirations" of their meta- genes may be implemented at the biochemical level. We show the example of quantum description of the population with two parts of meta-gene: "wolves" and "deer", which can be simultaneously in the same abstract living unity. "Selfish gene" reconciled with the notion of individuality of alive beings that gives possibility to consider evolutionary scenarios and their possible physical causes from the single position.

Yuri I. Ozhigov

2013-12-07

416

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

E-print Network

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

417

FIG. 1: Size-dependent color emission of quantum dots. This is a purely quantum mechanical FIG. 2: Size-dependent color emission of quantum dots. This is a purely quantum mechanical  

E-print Network

FIG. 1: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect. FIG. 2: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect. 1 #12;FIG. 3: Size-dependent color emission of quantum dots. This is a purely quantum mechanical effect

Nielsen, Steven O.

418

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

E-print Network

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

419

Optimal guidance law in quantum mechanics  

NASA Astrophysics Data System (ADS)

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 Schrdinger 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 ???.

Yang, Ciann-Dong; Cheng, Lieh-Lieh

2013-11-01

420

Shaping the composition profiles in heteroepitaxial quantum dots: Interplay of thermodynamic and kinetic effects  

NASA Astrophysics Data System (ADS)

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.; Leontiou, T.; Kelires, P. C.

2014-07-01

421

Quantum mechanics with coordinate dependent noncommutativity  

SciTech Connect

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 Andr, SP (Brazil)] [CMCC, Universidade Federal do ABC, Santo Andr, SP (Brazil)

2013-11-15

422

Advances in relativistic molecular quantum mechanics  

NASA Astrophysics Data System (ADS)

A quantum mechanical equation H?=E? is composed of three components, viz., Hamiltonian H, wave function ?, and property E(?), each of which is confronted with fundamental issues in the relativistic regime, e.g., (1) What is the most appropriate relativistic many-body Hamiltonian? How to solve the resulting equation? (2) How does the relativistic wave function behave at the coalescence of two electrons? How to do relativistic explicit correlation? (3) How to formulate relativistic properties properly?, to name just a few. It is shown here that the charge-conjugated contraction of Fermion operators, dictated by the charge conjugation symmetry, allows for a bottom-up construction of a relativistic Hamiltonian that is in line with the principles of quantum electrodynamics (QED). Various approximate but accurate forms of the Hamiltonian can be obtained based entirely on physical arguments. In particular, the exact two-component Hamiltonians can be formulated in a general way to cast electric and magnetic fields, as well as electron self-energy and vacuum polarization, into a unified framework. While such algebraic two-component Hamiltonians are incompatible with explicit correlation, four-component relativistic explicitly correlated approaches can indeed be made fully parallel to the nonrelativistic counterparts by virtue of the extended no-pair projection and the coalescence conditions. These findings open up new avenues for future developments of relativistic molecular quantum mechanics. In particular, molecular QED will soon become an active and exciting field.

Liu, Wenjian

2014-04-01

423

Surveying Students Understanding of Quantum Mechanics  

NSDL National Science Digital Library

Development of research-based multiple-choice tests about quantum mechanics is important for assessing students difficulties and for evaluating curricula and pedagogies that strive to reduce the difficulties. We explore the difficulties that the undergraduate and graduate students have with non-relativistic quantum mechanics of one particle in one spatial dimension. We developed a research-based conceptual multiple-choice survey that targets these issues to obtain information about the common difficulties and administered it to more than a hundred students from seven different institutions. The issues targeted in the survey include the set of possible wavefunctions, bound and scattering states, quantum measurement, expectation values, the role of the Hamiltonian, time-dependence of wavefunction and time-dependence of expectation value. We find that the advanced undergraduate and graduate students have many common difficulties with these concepts and that research-based tutorials and peer-instruction tools can significantly reduce these difficulties. The survey can be administered to assess the effectiveness of various intructional strategies.

Singh, Chandralekha; Zhu, Guangtian

2010-12-31

424

An approach to nonstandard quantum mechanics  

E-print Network

We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to non-relativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the M{\\o}ller wave operators and the S-Matrix.

Andreas Raab

2006-12-27

425

Path integration in relativistic quantum mechanics  

E-print Network

The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple relativistic action proportional to its proper time. This propagator is nonvanishing outside the light cone, implying that spacelike trajectories must be included in the path integral. The propagator matches the WKB approximation to the corresponding configuration-space path integral far from the light cone; outside the light cone that approximation consists of the contribution from a single spacelike geodesic. This propagator also has the unusual property that its short-time limit does not coincide with the WKB approximation, making the construction of a concrete skeletonized version of the path integral more complicated than in nonrelativistic theory.

Ian H. Redmount; Wai-Mo Suen

1992-10-28

426

Quantum Mechanics of a Rotating Billiard  

E-print Network

Integrability of a square billiard is spontaneously broken as it rotates about one of its corners. The system becomes quasi-integrable where the invariant tori are broken with respect to a certain parameter, $\\lambda = 2E/\\omega^{2}$ where E is the energy of the particle inside the billiard and $\\omega$ is the angular frequency of rotation of billiard. We study the system classically and quantum mechanically in view of obtaining a correspondence in the two descriptions. Classical phase space in Poincar\\'{e} surface of section shows transition from regular to chaotic motion as the parameter $\\lambda$ is decreased. In the Quantum counterpart, the spectral statistics shows a transition from Poisson to Wigner distribution as the system turns chaotic with decrease in $\\lambda$. The wavefunction statistics however show breakdown of time-reversal symmetry as $\\lambda$ decreases.

Nandan Jha; Sudhir R. Jain

2014-06-12

427

Quantum Mechanics la Langevin and Supersymmetry  

E-print Network

We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under ${\\mathcal N}=1$ SUSY, but can be obtained from a, manifestly, supersymmetric expression, upon fixing a local fermionic symmetry, called $\\kappa-$symmetry. The kinetic term for the fermions is a total derivative and can contribute only on the boundaries. We define combinations that scale appropriately, as the lattice spacing is taken to zero and the lattice size to infinity and provide evidence, by numerical simulations, that the correlation functions of the auxiliary field do satisfy Wick's theorem. We show, in particular, that simulations can be carried out using a purely bosonic action. The physical import is that the classical trajectory, $\\phi(\\tau)$, becomes a (chiral) superfield, $(\\phi(\\tau),\\psi_{\\alpha}(\\tau),F(\\tau))$, when quantum fluctuations are taken into account.

S. Nicolis

2013-11-14

428

BYU PHYS 731 Statistical Mechanics Chapter 1: Sethna Professor Manuel Berrondo Quick Review Thermodynamics  

E-print Network

BYU PHYS 731 Statistical Mechanics Chapter 1: Sethna Professor Manuel Berrondo Quick Review #12;BYU PHYS 731 Statistical Mechanics Chapter 1: Sethna Professor Manuel Berrondo Thermodynamic = L P RT2 P (T) = P0e- L RT L = latent heat Arrhenius form 3 #12;BYU PHYS 731 Statistical Mechanics

Hart, Gus

429

5.74 Introductory Quantum Mechanics II, Spring 2005  

E-print Network

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

430

5.74 Introductory Quantum Mechanics II, Spring 2007  

E-print Network

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

431

5.74 Introductory Quantum Mechanics II, Spring 2003  

E-print Network

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

432

Quantum mechanism helps agents combat "bad" social choice rules  

E-print Network

Quantum strategies have been successfully applied to game theory for years. However, as a reverse problem of game theory, the theory of mechanism design is ignored by physicists. In this paper, the theory of mechanism design is generalized to a quantum domain. The main result is that by virtue of a quantum mechanism, agents who satisfy a certain condition can combat "bad" social choice rules instead of being restricted by the traditional mechanism design theory.

Haoyang Wu

2010-02-23

433

Estimation of the thermodynamic properties of functional groups and biomolecules using quantum chemical/statistical thermodynamic calculations  

NASA Astrophysics Data System (ADS)

The scarcity and sustainability of energy sources have always been a concern while seeking for alternative fuels. Biofuels have drawn the attention of various researchers due to their abundancy and renewability. Understanding the physical and chemical properties of these molecules is essential to determining their potential as alternative fuels or fuel additives. In this work, the properties of these molecules are predicted through methods developed from quantum mechanics and statistical mechanics theories. The heats of formations are calculated with the Gaussian program and combined with the Benson group contribution method to predict the Benson parameters of unknown functional groups in a molecule. The methods developed are used to expand the Benson database and improve the practicability of the group contribution method. The heats of formations are also used to predict and correlate heat capacities across a range of temperatures and energy densities in this study.

Chai, Weisin

434

Clocks And Dynamics In Quantum Mechanics  

E-print Network

We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of quantum uncertainty lies with the absence of infinities or infinitesimals in observational data and that our concept of time derives from observing changing data (events). We argue that the fundamentally important content of the Superposition Principle is not the "probability amplitude" of posterior state observation but future state availability conditional only on prior information. Since event detection also implies posterior conditions (e.g. a specific type of detectable event occurred) as well as prior conditions, the probabilities of detected outcomes are also conditional on properties of the posterior properties of the observation. Such posterior conditions cannot affect the prior state availabilities and this implies violation of counter-factual definiteness. A component of a quantum system may be chosen to represent a clock and changes in other components can then be expected to be correlated with clocks with which they are entangled. Instead of traditional time-dependent equations of motion we provide a specific mechanism whereby evolution of data is instead quasi-causally related to the relative \\availability\\ of states and equations of motion are expressed in terms of quantized clock variables. We also suggest that time-reversal symmetry-breaking in weak interactions is an artifice of a conventional choice of co-ordinate time-function. Analysis of a "free" particle suggests that conventional co-ordinate space-time emerges from how we measure the separation of objects and events.

Michael York

2014-05-05

435

Renormalization group invariance of quantum mechanics  

NASA Astrophysics Data System (ADS)

We propose a framework to renormalize the nonrelativistic quantum mechanics with arbitrary singular interactions. The scattering equation is written to have one or more subtraction in the kernel at a given energy scale. The scattering amplitude is the solution of a nth order derivative equation in respect to the renormalization scale, which is the nonrelativistic counterpart of the Callan-Symanzik formalism. Scaled running potentials for the subtracted equations keep the physics invariant for a sliding subtraction point. An example of a singular potential, that requires more than one subtraction to renormalize the theory is shown.

Frederico, T.; Delfino, A.; Tomio, L.

2000-05-01

436

Hidden geometric character of relativistic quantum mechanics  

SciTech Connect

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

437

Vector Models in PT Quantum Mechanics  

E-print Network

We present two examples of non-Hermitian Hamiltonians which consist of an unperturbed part plus a perturbation that behaves like a vector, in the framework of PT quantum mechanics. The first example is a generalization of the recent work by Bender and Kalveks, wherein the E2 algebra was examined; here we consider the E3 algebra representing a particle on a sphere, and identify the critical value of coupling constant which marks the transition from real to imaginary eigenvalues. Next we analyze a model with SO(3) symmetry, and in the process extend the application of the Wigner-Eckart theorem to a non-Hermitian setting.

Katherine Jones-Smith; Rudolph Kalveks

2013-04-21

438

Improved lattice actions for supersymmetric quantum mechanics  

E-print Network

We analyze the Euclidean version of supersymmetric quantum mechanics on the lattice by means of a numerical path integral. We consider two different lattice derivatives and improve the actions containing them with respect to supersymmetry by systematically adding interaction terms with non-zero extent. To quantize this improvement, we measure boson and fermion masses and Ward identities for the naive as well as the improved models. The masses are degenerate in all models, but the magnitude of the Ward identities decreases significantly for both derivative operators using the improved actions. This is a clear sign that the breaking of supersymmetry due to lattice artifacts is reduced.

Sebastian Schierenberg; Falk Bruckmann

2012-10-19

439

Euclidean Quantum Mechanics and Universal Nonlinear Filtering  

E-print Network

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

440

Wigner Measures in Noncommutative Quantum Mechanics  

E-print Network

We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner measure, for a Gaussian to be a noncommutative Wigner measure, and derive certain properties of the marginal distributions which are not shared by ordinary Wigner measures. Moreover, we derive the Robertson-Schr\\"odinger uncertainty principle. Finally, we show explicitly how the set of noncommutative Wigner measures relates to the sets of Liouville and (commutative) Wigner measures.

C. Bastos; N. C. Dias; J. N. Prata

2009-07-25

441

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 Schrdinger 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

442

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

443

Bhomian Mechanics vs. Standard Quantum Mechanics: a Difference in Experimental Predictions  

E-print Network

Standard Quantum Mechanics (QM) predicts an anti-intuitive fenomenon here referred to as "quantum autoscattering", which is excluded by Bhomian Mechanics. The scheme of a gedanken experiment testing the QM prediction is briefly discussed.

Artur Szczepanski

2010-02-08

444

Black hole thermodynamics  

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

445

Black Hole Thermodynamics  

E-print Network

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.

Carlip, S

2014-01-01

446

Black Hole Thermodynamics  

E-print Network

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

447

Nonlinear Riccati equations as a unifying link between linear quantum mechanics and other fields of physics  

NASA Astrophysics Data System (ADS)

Theoretical physics seems to be in a kind of schizophrenic state. Many phenomena in the observable macroscopic world obey nonlinear evolution equations, whereas the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. I claim that linearity in quantum mechanics is not as essential as it apparently seems since quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown where complex Riccati equations appear in time-dependent quantum mechanics and how they can be treated and compared with similar space-dependent Riccati equations in supersymmetric quantum mechanics. Furthermore, the time-independent Schrdinger equation can also be rewritten as a complex Riccati equation. Finally, it will be shown that (real and complex) Riccati equations also appear in many other fields of physics, like statistical thermodynamics and cosmology.

Schuch, Dieter

2014-04-01

448

Smallest Relational Mechanics Model of Quantum Cosmology  

E-print Network

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

449

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

450

The formal path integral and quantum mechanics  

SciTech Connect

Given an arbitrary Lagrangian function on R{sup d} and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.

Johnson-Freyd, Theo [Department of Mathematics, University of California - Berkeley, 970 Evans Hall, Berkeley, California 94720 (United States)

2010-11-15

451

Assessing the Nonequilibrium Thermodynamics in a Quenched Quantum Many-Body System via Single Projective Measurements  

NASA Astrophysics Data System (ADS)

We analyze the nature of the statistics of the work done on or by a quantum many-body system brought out of equilibrium. We show that, for the sudden quench and for an initial state that commutes with the initial Hamiltonian, it is possible to retrieve the whole nonequilibrium thermodynamics via single projective measurements of observables. We highlight, in a physically clear way, the qualitative implications for the statistics of work coming from considering processes described by operators that either commute or do not commute with the unperturbed Hamiltonian of a given system. We consider a quantum many-body system and derive an expression that allows us to give a physical interpretation, for a thermal initial state, to all of the cumulants of the work in the case of quenched operators commuting with the unperturbed Hamiltonian. In the commuting case, the observables that we need to measure have an intuitive physical meaning. Conversely, in the noncommuting case, we show that, although it is possible to operate fully within the single-measurement framework irrespectively of the size of the quench, some difficulties are faced in providing a clear-cut physical interpretation to the cumulants. This circumstance makes the study of the physics of the system nontrivial and highlights the nonintuitive phenomenology of the emergence of thermodynamics from the fully quantum microscopic description. We illustrate our ideas with the example of the Ising model in a transverse field showing the interesting behavior of the high-order statistical moments of the work distribution for a generic thermal state and linking them to the critical nature of the model itself.

Fusco, L.; Pigeon, S.; Apollaro, T. J. G.; Xuereb, A.; Mazzola, L.; Campisi, M.; Ferraro, A.; Paternostro, M.; De Chiara, G.

2014-07-01

452

Thermodynamics of liquid metal  

SciTech Connect

The thermodynamics of a liquid metal based on quantum-mechanical models of the crystal, electronic, and nuclear structures of the metal are derived in this paper. The models are based on such formulations as the Bohr radius, the Boltzmann constant, the Planck Law, the Fermi surface, and the Pauli principle.

Kushnirenko, A.N.

1988-01-01

453

Mind, Matter and Quantum Mechanics (2nd edition)  

Microsoft Academic Search

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

G Mahler

2004-01-01

454

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

Microsoft Academic Search

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

H. P. Stapp

2004-01-01

455

A note on the Landauer principle in quantum statistical mechanics  

E-print Network

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

Boyer, Edmond

456

CHE 210A: Thermodynamics and Statistical Mechanics (F13) UCSB Department of Chemical Engineering  

E-print Network

lecture notes provided on the course website. Other recommended texts Molecular Driving Forces) A classic statistical mechanics text, with clear, concise explanations of the subject material. It servesCHE 210A: Thermodynamics and Statistical Mechanics (F13) UCSB Department of Chemical Engineering

Shell, M. Scott

457

Generalization of Classical Statistical Mechanics to Quantum Mechanics and Stable Property of Condensed Matter  

E-print Network

Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new general continuous eigenvalue equation and a general discrete eigenvalue equation in quantum mechanics, and discover that a eigenvalue of quantum mechanics is just an extreme value of an operator in possibility distribution, the eigenvalue f is just classical observable quantity. A general classical statistical uncertain relation is further given, the general classical statistical uncertain relation is generally generalized to quantum uncertainty principle, the two lost conditions in classical uncertain relation and quantum uncertainty principle, respectively, are found. We generally expound the relations among uncertainty principle, singularity and condensed matter stability, discover that quantum uncertainty principle prevents from the appearance of singularity of the electromagnetic potential between nucleus and electrons, and give the failure conditions of quantum uncertainty principle. Finally, we discover that the classical limit of quantum mechanics is classical statistical mechanics, the classical statistical mechanics may further be degenerated to classical mechanics, and we discover that only saying that the classical limit of quantum mechanics is classical mechanics is mistake. As application examples, we deduce both Shrodinger equation and state superposition principle, deduce that there exist decoherent factor from a general mathematical representation of state superposition principle, and the consistent difficulty between statistical interpretation of quantum mechanics and determinant property of classical mechanics is overcome.

Y. C. Huang; F. C. Ma; N. Zhang

2005-06-09

458

Surveying Instructors' Attitudes and Approaches to Teaching Quantum Mechanics  

NASA Astrophysics Data System (ADS)

Understanding instructors' attitudes and approaches to teaching quantum mechanics can be helpful in developing research-based learning tools. Here we discuss the findings from a survey in which 13 instructors reflected on issues related to quantum mechanics teaching. Topics included opinions about the goals of a quantum mechanics course, general challenges in teaching the subject, students' preparation for the course, comparison between their own learning of quantum mechanics vs. how they teach it and the extent to which contemporary topics are incorporated into the syllabus.

Siddiqui, Shabnam; Singh, Chandralekha

2010-10-01

459

Surveying Instructors Attitudes and Approaches to Teaching Quantum Mechanics  

NSDL National Science Digital Library

Understanding instructors attitudes and approaches to teaching quantum mechanics can be helpful in developing research-based learning tools. Here we discuss the findings from a survey in which 13 instructors reflected on issues related to quantum mechanics teaching. Topics included opinions about the goals of a quantum mechanics course, general challenges in teaching the subject, students preparation for the course, comparison between their own learning of quantum mechanics vs. how they teach it and the extent to which contemporary topics are incorporated into the syllabus.

Siddiqui, Shabnam; Singh, Chandralekha

2010-12-31

460

Fundamental phenomena of quantum mechanics explored with neutron interferometers  

E-print Network

Ongoing fascination with quantum mechanics keeps driving the development of the wide field of quantum-optics, including its neutron-optics branch. Application of neutron-optical methods and, especially, neutron interferometry and polarimetry has a long-standing tradition for experimental investigations of fundamental quantum phenomena. We give an overview of related experimental efforts made in recent years.

J. Klepp; S. Sponar; Y. Hasegawa

2014-07-09

461

On The Relation of Weyl Geometry and Bohmian Quantum Mechanics  

E-print Network

It is shown that the recently geometric formulation of quantum mechanics implies the use of Weyl geometry. It is discussed that the natural framework for both gravity and quantum is Weyl geometry. At the end a Weyl invariant theory is built, and it is shown that both gravity and quantum are present at the level of equations of motion.

Fatimah Shojai; Ali Shojai

2003-06-22

462

Thermodynamic compressibility and spin-splitting in one-dimensional quantum wires  

NASA Astrophysics Data System (ADS)

We study spin-splitting and the much-debated 0.7 structure in GaAs quantum wires using compressibility measurements that directly probe the thermodynamic density of states. Two quantum wires are simultaneously defined in the upper and lower well of a GaAs/AlGaAs double quantum well heterostructure, using midline-gated split-gate devices [1]. The lower wire probes the ability of the upper wire to screen the electric field from a biased surface gate. The technique is sensitive enough to resolve spin splitting of the 1D subbands in the presence of an in-plane magnetic field. The compressibility response of the 0.7 structure is measured, and its evolution with increasing temperature and magnetic field is studied [2]. Despite the sensitivity of our measurements we see no evidence of the formation of the quasibound state predicted by the Kondo model of the 0.7 structure. Instead our data are more consistent with theories which predict that the 0.7 structure arises as a result of spontaneous spin polarization. [4pt] [1] I.M. Castleton et al, Physica B 249, 157 (1998).[0pt] [2] L.W. Smith et al, Phys. Rev. Lett. 107, 126801 (2011)

Smith, Luke W.; Hamilton, A. R.; Thomas, K. J.; Pepper, M.; Farrer, I.; Anderson, D.; Jones, G. A. C.; Ritchie, D. A.

2012-02-01

463

Thermodynamics is more powerful than the role to it reserved by Boltzmann-Gibbs statistical mechanics  

NASA Astrophysics Data System (ADS)

We briefly review the connection between statistical mechanics and thermodynamics. We show that, in order to satisfy thermo-dynamics and its Legendre transformation mathematical frame, the celebrated Boltzmann-Gibbs (BG) statistical mechanics is sufficient but not necessary. Indeed, the N ?? limit of statistical mechanics is expected to be consistent with thermodynamics. For systems whose elements are generically independent or quasi-independent in the sense of the theory of probabilities, it is well known that the BG theory (based on the additive BG entropy) does satisfy this expectation. However, in complete analogy, other thermostatistical theories (e.g., q-statistics), based on nonadditive entropic functionals, also satisfy the very same expectation. We illustrate this standpoint with systems whose elements are strongly correlated in a specific manner, such that they escape the BG realm.

Tsallis, C.; Cirto, L. J. L.

2014-10-01

464

Quantum Mechanics with Basic Field Theory  

NASA Astrophysics Data System (ADS)

Preface; 1. Basic formalism; 2. Fundamental commutator and time evolution of state vectors and operators; 3. Dynamical equations; 4. Free particles; 5. Particles with spin 1/2; 6. Gauge invariance, angular momentum and spin; 7. Stern-Gerlach experiments; 8. Some exactly solvable bound state problems; 9. Harmonic oscillator; 10. Coherent states; 11. Two-dimensional isotropic harmonic oscillator; 12. Landau levels and quantum Hall effect; 13. Two-level problems; 14. Spin 1/2 systems in the presence of magnetic field; 15. Oscillation and regeneration in neutrino and neutral K-mesons as two-level systems; 16. Time-independent perturbation for bound states; 17. Time-dependent perturbation; 18. Interaction of charged particles and radiation in perturbation theory; 19. Scattering in one dimension; 20. Scattering in three dimensions - a formal theory; 21. Partial wave amplitudes and phase shifts; 22. Analytic structure of the S-matrix; 23. Poles of the Green's function and composite systems; 24. Approximation methods for bound states and scattering; 25. Lagrangian method and Feynman path integrals; 26. Rotations and angular momentum; 27. Symmetry in quantum mechanics and symmetry groups; 28. Addition of angular momenta; 29. Irreducible tensors and Wigner-Eckart theorem; 30. Entangled states; 31. Special theory of relativity: Klein Gordon and Maxwell's equation; 32. Klein Gordon and Maxwell's equation; 33. Dirac equation; 34. Dirac equation in the presence of spherically symmetric potentials; 35. Dirac equation in a relativistically invariant form; 36. Interaction of Dirac particle with electromagnetic field; 37. Multiparticle systems and second quantization; 38. Interactions of electrons and phonons in condensed matter; 39. Superconductivity; 40. Bose Einstein condensation and superfluidity; 41. Lagrangian formulation of classical fields; 42. Spontaneous symmetry breaking; 43. Basic quantum electrodynamics and Feynman diagrams; 44. Radiative corrections; 45. Anomalous magnetic moment and Lamb shift; Appendix; References; Index.

Desai, Bipin R.

2009-12-01

465

Tampering detection system using quantum-mechanical systems  

DOEpatents

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

466

Existence of the thermodynamic limit and asymptotic behavior of some irreversible quantum dynamical systems  

NASA Astrophysics Data System (ADS)

This dissertation discusses the properties of two open quantum systems with a general class of irreversible quantum dynamics. First we study Lieb-Robinson bounds in a quantum lattice systems. This bound gives an estimate for the speed of growth of the support of an evolved local observable up to an exponentially small error. In a second model we study the properties of a leaking cavity pumped by a random atomic beam. We begin by describing quantum systems on an infinite lattice with associated finite or infinite dimensional Hilbert space. The generator of the dynamics of this system is of the Lindblad-Kossakowski type and consists of two parts: the Hamiltonian interactions and the dissipative terms. We allow both of them to be time-dependent. This generator satisfies some suitable decay condition in space. We show that the dynamics with a such generator on a finite system is a well-defined quantum dynamics in a sense of a norm-continuous cocycle of unit preserving completely positive maps. Lieb-Robinson bounds for irreversible dynamics were first considered in the classical context and in for a class of quantum lattice systems with finite-range interactions. We extend those results by proving a Lieb-Robinson bound for lattice models with a more general class of quantum dynamics. Then we use Lieb-Robinson bounds for a finite lattice systems to prove the existence of the thermodynamic limit of the dynamics. We show that in a strong limit there exits a strongly continuous cocycle of unit preserving completely positive maps. Which means that the dynamics exists in an infinite system, where Lieb-Robinson bounds also holds. In the second part of the dissertation we consider a system that consists of a beam of two-level atoms that pass one by one through the microwave cavity. The atoms are randomly excited and there is exactly one atom present in the cavity at any given moment. We consider both the ideal and leaky cavity and study the time asymptotic behavior of the state of the cavity. We show that the number of photons increases indefinitely in the case of the ideal cavity. In the case of the leaking cavity the limiting state is independent of the initial state, it is not quasi-free and it is a non-equilibrium steady state. We also compute the associated energy flow.

Vershynina, Anna

467

Twist deformation of rotationally invariant quantum mechanics  

SciTech Connect

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

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

2010-11-15

468

On geometric aspects of topological quantum mechanics  

NASA Astrophysics Data System (ADS)

We construct a Chern-Simons gauge theory for dg Lie and L-infinity algebras on any one-dimensional manifold and quantize this theory using the Batalin-Vilkovisky formalism and Costello's renormalization techniques. Koszul duality and derived geometry allow us to encode topological quantum mechanics, a nonlinear sigma model of maps from a 1-manifold into a cotangent bundle T* X, as such a Chern-Simons theory. Our main result is that the partition function of this theory is naturally identified with the A genus of X. From the perspective of derived geometry, our quantization constructs a volume form on the derived loop space which can be identified with the A class.

Grady, Ryan E.

469

Quantum mechanical calculations to chemical accuracy  

NASA Technical Reports Server (NTRS)

The accuracy of current molecular-structure calculations is illustrated with examples of quantum mechanical solutions for chemical problems. Two approaches are considered: (1) the coupled-cluster singles and doubles (CCSD) with a perturbational estimate of the contribution of connected triple excitations, or CCDS(T); and (2) the multireference configuration-interaction (MRCI) approach to the correlation problem. The MRCI approach gains greater applicability by means of size-extensive modifications such as the averaged-coupled pair functional approach. The examples of solutions to chemical problems include those for C-H bond energies, the vibrational frequencies of O3, identifying the ground state of Al2 and Si2, and the Lewis-Rayleigh afterglow and the Hermann IR system of N2. Accurate molecular-wave functions can be derived from a combination of basis-set saturation studies and full configuration-interaction calculations.

Bauschlicher, Charles W., Jr.; Langhoff, Stephen R.

1991-01-01

470

Supersymmetric quantum mechanics and Painlev 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 Painlev IV (PIV) and Painlev 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; Fernndez C., David J.

2014-01-01

471

A causal net approach to relativistic quantum mechanics  

NASA Astrophysics Data System (ADS)

In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on Reichenbach-like conjunctive forks in proper time we can exactly derive the 1+1 dimension Dirac equation for a relativistic fermion and correctly model quantum mechanical statistics. Symmetries of the net provide various quantum mechanical effects such as quantum uncertainty and wavefunction, phase, spin, negative energy states and the effect of a potential. The causal net can be embedded in 3+1 dimensions and is consistent with the conventional Dirac equation. In the low velocity limit the causal net approximates to the Schrodinger equation and Pauli equation for an electromagnetic field. Extending to different momentum states the net is compatible with the Feynman path integral approach to quantum mechanics that allows calculation of well known quantum phenomena such as diffraction.

Bateson, R. D.

2012-05-01

472

A Causal Net Approach to Relativistic Quantum Mechanics  

E-print Network

In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on Reichenbach-like conjunctive forks in proper time we can exactly derive the 1+1 dimension Dirac equation for a relativistic fermion and correctly model quantum mechanical statistics. Symmetries of the net provide various quantum mechanical effects such as quantum uncertainty and wavefunction, phase, spin, negative energy states and the effect of a potential. The causal net can be embedded in 3+1 dimensions and is consistent with the conventional Dirac equation. In the low velocity limit the causal net approximates to the Schrodinger equation and Pauli equation for an electromagnetic field. Extending to different momentum states the net is compatible with the Feynman path integral approach to quantum mechanics that allows calculation of well known quantum phenomena such as diffraction.

R. D. Bateson

2010-07-14

473

Quantum mechanics, matter waves, and moving clocks  

E-print Network

This paper is divided into three parts. In the first (section 1), we demonstrate that all of quantum mechanics can be derived from the fundamental property that the propagation of a matter wave packet is described by the same gravitational and kinematic time dilation that applies to a clock. We will do so in several steps, first deriving the Schroedinger equation for a nonrelativistic particle without spin in a weak gravitational potential, and eventually the Dirac equation in curved space-time describing the propagation of a relativistic particle with spin in strong gravity. In the second part (sections 2-4), we present interesting consequences of the above quantum mechanics: that it is possible to use wave packets as a reference for a clock, to test general relativity, and to realize a mass standard based on a proposed redefinition of the international system of units, wherein the Planck constant would be assigned a fixed value. The clock achieved an absolute accuracy of 4 parts per billion (ppb). The experiment yields the fine structure constant $\\alpha = 7.297\\,352\\,589(15) \\times 10^{-3}$ with 2.0 ppb accuracy. We present improvements that have reduced the leading systematic error about 8-fold and improved the statistical uncertainty to 0.33 ppb in 6 hours of integration time, referred to $\\alpha$. In the third part (sections 5-7), we present possible future experiments with atom interferometry: A gravitational Aharonov-Bohm experiment and its application as a measurement of Newton's gravitational constant, antimatter interferometry, interferometry with charged particles, and interferometry in space. We will give a review of previously published material when appropriate, but will focus on new aspects that haven't been published before.

Holger Mueller

2013-12-23

474

Biological applications of hybrid quantum mechanics/molecular mechanics calculation.  

PubMed

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

475

Physlets and Open Source Physics for Quantum Mechanics: Visualizing Quantum-mechanical Revivals  

NSDL National Science Digital Library

In this paper we describe our five-year effort to create interactive curricular material for upper-level quantum mechanics courses. This material uses both Physlets and newly created Open Source Physics applets and applications to make the teaching of quantum mechanics visual and interactive. These exercises and tools address both quantitative and conceptual difficulties experienced by many students. Because the materials are Web based, they are extremely flexible and are appropriate for use with various pedagogies, such as the Just-in-Time Teaching technique. We briefly outline the features of Physlets and Open Source Physics programs and then describe our suite of Java programs that solve and visualize the problem of a wave packet in an infinite square well. The materials described in this paper can be found on the Open Source Physics Web site and on the MERLOT and ComPADRE digital libraries.

Belloni, Mario; Christian, Wolfgang

2011-02-01

476

The relation between quantum mechanics and higher brain functions: Lessons from quantum computation and  

E-print Network

of QM (the best we can make in non-relativistic atomic physics and quantum computation (Mermin 20031 The relation between quantum mechanics and higher brain functions: Lessons from quantum computation and neurobiology Christof Koch1,2 and Klaus Hepp1 April 2. 2007 1 Institute for Neuroinformatics

Koch, Christof

477

Algorithmic Information Theoretic Issues in Quantum Mechanics  

E-print Network

.1 The unpublished ideas of Sidney Coleman and Andrew Lesniewski210 6.2 Karl Svozil's invention of Quantum 248 6.6 Peter Gacs' quantum algorithmic entropy . . . . . . . . . . . . . 248 6.7 The algorithmic

478

Quantum mechanical reaction probabilities with a power series Green's function  

E-print Network

Quantum mechanical reaction probabilities with a power series Green's function Scott M. Auerbach for use in the calculation of quantum mechanical reaction probabilities. This is an iterative technique Green's function to the calculation of the cumulative reaction probability for the benchmark collinear H

Miller, William H.

479

Design and Validation of the Quantum Mechanics Conceptual Survey  

ERIC Educational Resources Information Center

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

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

2010-01-01

480

Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems  

ERIC Educational Resources Information Center

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

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

2009-01-01

481

In Defense of a Heuristic Interpretation of Quantum Mechanics  

ERIC Educational Resources Information Center

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

Healy, Eamonn F.

2010-01-01

482

New Potentials for Old: The Darboux Transformation in Quantum Mechanics  

ERIC Educational Resources Information Center

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

Williams, Brian Wesley; Celius, Tevye C.

2008-01-01

483

Environment-Induced Decoherence in Noncommutative Quantum Mechanics  

E-print Network

We address the question of the appearence of ordinary quantum mechanics in the context of noncommutative quantum mechanics. We obtain the noncommutative extension of the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators. We consider the particular case of an Ohmic regime.

Joao Nuno Prata; Nuno Costa Dias