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Sample records for thermodynamics quantum mechanics

  1. From Quantum Mechanics to Thermodynamics?

    E-print Network

    Steinhoff, Heinz-Jürgen

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

  2. NONEQUILIBRIUM QUANTUM STATISTICAL MECHANICS AND THERMODYNAMICS #

    E-print Network

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

  3. Quantum Thermodynamics

    E-print Network

    Ronnie Kosloff

    2013-05-10

    Quantum thermodynamics addresses the emergence of thermodynamical laws from quantum mechanics. The link is based on the intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts dynamics into thermodynamics giving a sound foundation to finite-time-thermodynamics. The emergence of the 0-law I-law II-law and III-law of thermodynamics from quantum considerations is presented. The emphasis is on consistence between the two theories which address the same subject from different foundations. We claim that inconsistency is the result of faulty analysis pointing to flaws in approximations.

  4. Emergent quantum mechanics as a classical, irreversible thermodynamics

    E-print Network

    Acosta, D; Isidro, J M; Santander, J L G

    2012-01-01

    We present an explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics as developed by Onsager, Prigogine et al. Our correspondence maps irreversible Gaussian Markov processes into the semiclassical approximation of quantum mechanics. Quantum-mechanical propagators are mapped into thermodynamical probability distributions. The Feynman path integral also arises naturally in this setup. The fact that quantum mechanics can be translated into thermodynamical language provides additional support for the conjecture that quantum mechanics is not a fundamental theory but rather an emergent phenomenon, i.e., an effective description of some underlying degrees of freedom.

  5. The Thermodynamic Arrow-of-time and Quantum Mechanics

    E-print Network

    Maccone, Lorenzo

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

  6. Black hole thermodynamics from near-horizon conformal quantum mechanics

    SciTech Connect

    Camblong, Horacio E.; Ordonez, Carlos R.

    2005-05-15

    The thermodynamics of black holes is shown to be directly induced by their near-horizon conformal invariance. This behavior is exhibited using a scalar field as a probe of the black hole gravitational background, for a general class of metrics in D spacetime dimensions (with D{>=}4). The ensuing analysis is based on conformal quantum mechanics, within a hierarchical near-horizon expansion. In particular, the leading conformal behavior provides the correct quantum statistical properties for the Bekenstein-Hawking entropy, with the near-horizon physics governing the thermodynamics from the outset. Most importantly: (i) this treatment reveals the emergence of holographic properties; (ii) the conformal coupling parameter is shown to be related to the Hawking temperature; and (iii) Schwarzschild-like coordinates, despite their 'coordinate singularity', can be used self-consistently to describe the thermodynamics of black holes.

  7. Thermodynamic Evidence for Water as a Quantum Mechanical Liquid

    E-print Network

    A. Widom; J. Swain; S. Sivasubramanian; D. Drosdoff; Y. N. Srivastava

    2015-12-10

    We consider general theoretical models of water and in particular the nature of the motions of the hydrogen nuclei. If the motion of hydrogen nuclei is classical, then the thermodynamic pressure equation of state for heavy water wherein the hydrogen nuclei are deuterons is identical to the pressure equation of state for light water wherein the hydrogen nuclei are protons. Since the experimental thermodynamic phase diagram for light water is clearly measurably different from the experimental thermodynamic phase diagram for heavy water, one may deduce that the motions of hydrogen nuclei are quantum mechanical in nature. This conclusion is in physical agreement with a recent analysis of X-ray, neutron and deep inelastic neutron scattering data.

  8. Quantum Thermodynamics

    E-print Network

    Sai Vinjanampathy; Janet Anders

    2015-08-25

    Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations, and with the full inclusion of quantum effects. Fuelled by experimental advances and the potential of future nanoscale applications this research effort is pursued by scientists with different backgrounds, including statistical physics, many-body theory, mesoscopic physics and quantum information theory, who bring various tools and methods to the field. A multitude of theoretical questions are being addressed ranging from issues of thermalisation of quantum systems and various definitions of "work", to the efficiency and power of quantum engines. This overview provides a perspective on a selection of these current trends accessible to postgraduate students and researchers alike.

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

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

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

  10. Similarity between quantum mechanics and thermodynamics: entropy, temperature, and Carnot cycle.

    PubMed

    Abe, Sumiyoshi; Okuyama, Shinji

    2011-02-01

    The similarity between quantum mechanics and thermodynamics is discussed. It is found that if the Clausius equality is imposed on the Shannon entropy and the analog of the quantity of heat, then the value of the Shannon entropy comes to formally coincide with that of the von Neumann entropy of the canonical density matrix, and pure-state quantum mechanics apparently transmutes into quantum thermodynamics. The corresponding quantum Carnot cycle of a simple two-state model of a particle confined in a one-dimensional infinite potential well is studied, and its efficiency is shown to be identical to the classical one. PMID:21405832

  11. Uncertainty and information in classical mechanics formulation. Common ground for thermodynamics and quantum mechanics

    E-print Network

    Adrian Faigon

    2007-11-01

    Mechanics can be founded on a principle relating the uncertainty delta-q in the trajectory of an observable particle to its motion relative to the observer. From this principle, p.delta-q=const., p being the q-conjugated momentum, mechanical laws are derived and the meaning of the Lagrangian and Hamiltonian functions are discussed. The connection between the presented principle and Hamilton's Least Action Principle is examined. Wave mechanics and Schrodinger equation appear without additional assumptions by choosing the representation for delta-q in the case the motion is not trajectory describable. The Cramer-Rao inequality serves that purpose. For a particle hidden from direct observation, the position uncertainty determined by the enclosing boundaries leads to thermodynamics in a straightforward extension of the presented formalism. The introduction of uncertainty in classical mechanics formulation enables the translation of mechanical laws into the wide ranging conceptual framework of information theory. The boundaries between classical mechanics, thermodynamics and quantum mechanics are defined in terms of informational changes associated with the system evolution. As a direct application of the proposed formulation upper bounds for the rate of information transfer are derived.

  12. Quantum thermodynamic cooling cycle.

    PubMed

    Palao, J P; Kosloff, R; Gordon, J M

    2001-11-01

    The quantum-mechanical and thermodynamic properties of a three-level molecular cooling cycle are derived. An inadequacy of earlier models is rectified in accounting for the spontaneous emission and absorption associated with the coupling to the coherent driving field via an environmental reservoir. This additional coupling need not be dissipative, and can provide a thermal driving force-the quantum analog of classical absorption chillers. The dependence of the maximum attainable cooling rate on temperature, at ultralow temperatures, is determined and shown to respect the recently established fundamental bound based on the second and third laws of thermodynamics. PMID:11736037

  13. Non-hermitian quantum thermodynamics

    E-print Network

    Bart?omiej Gardas; Sebastian Deffner; Avadh Saxena

    2015-11-19

    Thermodynamics is a phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum. This equality expresses the second law of thermodynamics for isothermal processes arbitrarily far from equilibrium. In the quasistatic limit however, the second law is reflected in the Carnot bound and it is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Furthermore, we propose a setup to test our predictions. The quantum system in question consists of strongly interacting excitons and photons in a semiconductor microcavity.

  14. Quantum Mechanics + Open Systems

    E-print Network

    Steinhoff, Heinz-Jürgen

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

  15. Set of molecular models based on quantum mechanical ab initio calculations and thermodynamic data.

    PubMed

    Eckl, Bernhard; Vrabec, Jadran; Hasse, Hans

    2008-10-01

    A parametrization strategy for molecular models on the basis of force fields is proposed, which allows a rapid development of models for small molecules by using results from quantum mechanical (QM) ab initio calculations and thermodynamic data. The geometry of the molecular models is specified according to the atom positions determined by QM energy minimization. The electrostatic interactions are modeled by reducing the electron density distribution to point dipoles and point quadrupoles located in the center of mass of the molecules. Dispersive and repulsive interactions are described by Lennard-Jones sites, for which the parameters are iteratively optimized to experimental vapor-liquid equilibrium (VLE) data, i.e., vapor pressure, saturated liquid density, and enthalpy of vaporization of the considered substance. The proposed modeling strategy was applied to a sample set of ten molecules from different substance classes. New molecular models are presented for iso-butane, cyclohexane, formaldehyde, dimethyl ether, sulfur dioxide, dimethyl sulfide, thiophene, hydrogen cyanide, acetonitrile, and nitromethane. Most of the models are able to describe the experimental VLE data with deviations of a few percent. PMID:18793022

  16. Coherence and measurement in quantum thermodynamics

    E-print Network

    Philipp Kammerlander; Janet Anders

    2015-09-18

    Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines and fridges to power plants and solar cells. With thermodynamics predating quantum theory, research now aims to uncover the thermodynamic laws that govern finite size systems which may in addition host quantum effects. Here we identify information processing tasks, the so-called "projections", that can only be formulated within the framework of quantum mechanics. We show that the physical realisation of such projections can come with a non-trivial thermodynamic work only for quantum states with coherences. This contrasts with information erasure, first investigated by Landauer, for which a thermodynamic work cost applies for classical and quantum erasure alike. Implications are far-reaching, adding a thermodynamic dimension to measurements performed in quantum thermodynamics experiments, and providing key input for the construction of a future quantum thermodynamic framework. Repercussions are discussed for quantum work fluctuation relations and thermodynamic single-shot approaches.

  17. Thermodynamic and Quantum Thermodynamic Analyses of Brownian Movement

    E-print Network

    Elias P. Gyftopoulos

    2006-07-06

    Thermodynamic and quantum thermodynamic analyses of Brownian movement of a solvent and a colloid passing through neutral thermodynamic equilibrium states only. It is shown that Brownian motors and E. coli do not represent Brownian movement.

  18. Reply to "Comment on 'Similarity between quantum mechanics and thermodynamics: Entropy, temperature, and Carnot cycle' ''.

    PubMed

    Abe, Sumiyoshi

    2015-05-01

    In their Comment on the paper [Abe and Okuyama, Phys. Rev. E 83, 021121 (2011)], González-Díaz and Díaz-Solórzano discuss that the initial state of the quantum-mechanical analog of the Carnot cycle should be not in a pure state but in a mixed state due to a projective measurement of the system energy. Here, first the Comment is shown to miss the point. Then, second, multiple projective measurements are discussed as a generalization of the Comment, although they are not relevant to the work commented. PMID:26066283

  19. Reply to ``Comment on `Similarity between quantum mechanics and thermodynamics: Entropy, temperature, and Carnot cycle' ''

    NASA Astrophysics Data System (ADS)

    Abe, Sumiyoshi

    2015-05-01

    In their Comment on the paper [Abe and Okuyama, Phys. Rev. E 83, 021121 (2011), 10.1103/PhysRevE.83.021121], González-Díaz and Díaz-Solórzano discuss that the initial state of the quantum-mechanical analog of the Carnot cycle should be not in a pure state but in a mixed state due to a projective measurement of the system energy. Here, first the Comment is shown to miss the point. Then, second, multiple projective measurements are discussed as a generalization of the Comment, although they are not relevant to the work commented.

  20. Quantum thermodynamics of general quantum processes

    NASA Astrophysics Data System (ADS)

    Binder, Felix; Vinjanampathy, Sai; Modi, Kavan; Goold, John

    2015-03-01

    Accurately describing work extraction from a quantum system is a central objective for the extension of thermodynamics to individual quantum systems. The concepts of work and heat are surprisingly subtle when generalizations are made to arbitrary quantum states. We formulate an operational thermodynamics suitable for application to an open quantum system undergoing quantum evolution under a general quantum process by which we mean a completely positive and trace-preserving map. We derive an operational first law of thermodynamics for such processes and show consistency with the second law. We show that heat, from the first law, is positive when the input state of the map majorizes the output state. Moreover, the change in entropy is also positive for the same majorization condition. This makes a strong connection between the two operational laws of thermodynamics.

  1. Quantum thermodynamics of general quantum processes.

    PubMed

    Binder, Felix; Vinjanampathy, Sai; Modi, Kavan; Goold, John

    2015-03-01

    Accurately describing work extraction from a quantum system is a central objective for the extension of thermodynamics to individual quantum systems. The concepts of work and heat are surprisingly subtle when generalizations are made to arbitrary quantum states. We formulate an operational thermodynamics suitable for application to an open quantum system undergoing quantum evolution under a general quantum process by which we mean a completely positive and trace-preserving map. We derive an operational first law of thermodynamics for such processes and show consistency with the second law. We show that heat, from the first law, is positive when the input state of the map majorizes the output state. Moreover, the change in entropy is also positive for the same majorization condition. This makes a strong connection between the two operational laws of thermodynamics. PMID:25871066

  2. Thermodynamics in Loop Quantum Cosmology

    E-print Network

    Li-Fang Li; Jian-Yang Zhu

    2008-12-18

    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.

  3. Thermodynamics and statistical mechanics. [thermodynamic properties of gases

    NASA Technical Reports Server (NTRS)

    1976-01-01

    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.

  4. Comment on "Similarity between quantum mechanics and thermodynamics: Entropy, temperature, and Carnot cycle"

    NASA Astrophysics Data System (ADS)

    González-Díaz, L. A.; Díaz-Solórzano, S.

    2015-05-01

    In the paper by Abe and Okuyama [Phys. Rev. E 83, 021121 (2011), 10.1103/PhysRevE.83.021121], the quantum Carnot cycle of a simple two-state model of a particle confined in a one-dimensional infinite potential well is discussed. It is claimed that the state at the beginning of the quantum Carnot cycle is pure. After that, it is apparently transmuted to a mixed state if Clausius equality is imposed. We prove that this statement is incorrect. In particular, we prove that the state at the beginning of the cycle is mixed due to the process of measuring energy.

  5. Comment on "Similarity between quantum mechanics and thermodynamics: Entropy, temperature, and Carnot cycle".

    PubMed

    González-Díaz, L A; Díaz-Solórzano, S

    2015-05-01

    In the paper by Abe and Okuyama [Phys. Rev. E 83, 021121 (2011)], the quantum Carnot cycle of a simple two-state model of a particle confined in a one-dimensional infinite potential well is discussed. It is claimed that the state at the beginning of the quantum Carnot cycle is pure. After that, it is apparently transmuted to a mixed state if Clausius equality is imposed. We prove that this statement is incorrect. In particular, we prove that the state at the beginning of the cycle is mixed due to the process of measuring energy. PMID:26066282

  6. Quantum dynamics in the thermodynamic limit

    SciTech Connect

    Wezel, Jasper van

    2008-08-01

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

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

    E-print Network

    Masanori Hanada; Yoshifumi Hyakutake; Jun Nishimura; Shingo Takeuchi

    2009-03-09

    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, which can be checked once the complete form of the O(\\alpha'^3) corrections to the supergravity action is obtained.

  8. Thermodynamics of quantum feedback cooling

    E-print Network

    Liuzzo-Scorpo, Pietro; Schmidt, Rebecca; Adesso, Gerardo

    2015-01-01

    The ability to initialize quantum registers in pure states lies at the core of many applications of quantum technologies, from sensing to quantum information processing and computation. In this paper we tackle the problem of increasing the polarization bias of an ensemble of two-level register spins by means of joint coherent manipulations, involving a second ensemble of ancillary spins, and energy dissipation into an external heat bath. We formulate this spin refrigeration protocol, akin to algorithmic cooling, in the general language of quantum feedback control, and identify the relevant thermodynamic variables involved. Our analysis is twofold: On the one hand, we assess the optimality of the protocol by means of suitable figures of merit, accounting for both its work cost and effectiveness. On the other hand, we characterise the nature of correlations built up between the register and the ancilla. In particular, we observe that neither the amount of classical correlations nor the quantum entanglement seem...

  9. Quantum Maxwell's Demon in Thermodynamic Cycles

    E-print Network

    H. Dong; D. Z. Xu; C. P. Sun

    2010-09-14

    We study the physical mechanism of Maxwell's Demon (MD) helping to do extra work in thermodynamic cycles, by describing measurement of position, insertion of wall and information erasing of MD in a quantum mechanical fashion. The heat engine is exemplified with one molecule confined in an infinitely deep square potential inserted with a movable solid wall, while the MD is modeled as a two-level system (TLS) for measuring and controlling the motion of the molecule. It is discovered that the the MD with quantum coherence or on a lower temperature than that of the heat bath of the particle would enhance the ability of the whole work substance formed by the system plus the MD to do work outside. This observation reveals that the role of the MD essentially is to drive the whole work substance being off equilibrium, or equivalently working with an effective temperature difference. The elaborate studies with this model explicitly reveal the effect of finite size off the classical limit or thermodynamic limit, which contradicts the common sense on Szilard heat engine (SHE). The quantum SHE's efficiency is evaluated in detail to prove the validity of second law of thermodynamics.

  10. Statistical Thermodynamics of Polymer Quantum Systems

    E-print Network

    Guillermo Chacón-Acosta; Elisa Manrique; Leonardo Dagdug; Hugo A. Morales-Técotl

    2011-12-02

    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 {\\em 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 Schr\\"odinger 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. For generic polymer length, thermodynamics of both systems present an anomalous peak in their heat capacity $C_V$.

  11. Thermodynamics of quantum systems under dynamical control

    E-print Network

    D. Gelbwaser-Klimovsky; Wolfgang Niedenzu; Gershon Kurizki

    2015-03-04

    In this review the debated rapport between thermodynamics and quantum mechanics is addressed in the framework of the theory of periodically-driven/controlled quantum-thermodynamic machines. The basic model studied here is that of a two-level system (TLS), whose energy is periodically modulated while the system is coupled to thermal baths. When the modulation interval is short compared to the bath memory time, the system-bath correlations are affected, thereby causing cooling or heating of the TLS, depending on the interval. In steady state, a periodically-modulated TLS coupled to two distinct baths constitutes the simplest quantum heat machine (QHM) that may operate as either an engine or a refrigerator, depending on the modulation rate. We find their efficiency and power-output bounds and the conditions for attaining these bounds. An extension of this model to multilevel systems shows that the QHM power output can be boosted by the multilevel degeneracy. These results are used to scrutinize basic thermodynamic principles: (i) Externally-driven/modulated QHMs may attain the Carnot efficiency bound, but when the driving is done by a quantum device ("piston"), the efficiency strongly depends on its initial quantum state. Such dependence has been unknown thus far. (ii) The refrigeration rate effected by QHMs does not vanish as the temperature approaches absolute zero for certain quantized baths, e.g., magnons, thous challenging Nernst's unattainability principle. (iii) System-bath correlations allow more work extraction under periodic control than that expected from the Szilard-Landauer principle, provided the period is in the non-Markovian domain. Thus, dynamically-controlled QHMs may benefit from hitherto unexploited thermodynamic resources.

  12. Towards quantum thermodynamics in electronic circuits

    NASA Astrophysics Data System (ADS)

    Pekola, Jukka P.

    2015-02-01

    Electronic circuits operating at sub-kelvin temperatures are attractive candidates for studying classical and quantum thermodynamics: their temperature can be controlled and measured locally with exquisite precision, and they allow experiments with large statistical samples. The availability and rapid development of devices such as quantum dots, single-electron boxes and superconducting qubits only enhance their appeal. But although these systems provide fertile ground for studying heat transport, entropy production and work in the context of quantum mechanics, the field remains in its infancy experimentally. Here, we review some recent experiments on quantum heat transport, fluctuation relations and implementations of Maxwell's demon, revealing the rich physics yet to be fully probed in these systems.

  13. The role of quantum information in thermodynamics --- a topical review

    E-print Network

    John Goold; Marcus Huber; Arnau Riera; Lídia del Rio; Paul Skrzypczyk

    2015-06-23

    This topical review article gives an overview of the interplay between quantum information theory and thermodynamics of quantum systems. We focus on several trending topics including the foundations of statistical mechanics, resource theories, entanglement in thermodynamic settings, fluctuation theorems and thermal machines. This is not a comprehensive review of the diverse field of quantum thermodynamics; rather, it is a convenient entry point for the thermo-curious information theorist. Furthermore this review should facilitate the unification and understanding of different interdisciplinary approaches emerging in research groups around the world.

  14. Thermodynamics of discrete quantum processes

    E-print Network

    Janet Anders; Vittorio Giovannetti

    2012-11-01

    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.

  15. Quantum collapse and the second law of thermodynamics.

    PubMed

    Hormoz, Sahand

    2013-02-01

    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 composed 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. PMID:23496481

  16. Thermodynamic universality of quantum Carnot engines.

    PubMed

    Gardas, Bart?omiej; Deffner, Sebastian

    2015-10-01

    The Carnot statement of the second law of thermodynamics poses an upper limit on the efficiency of all heat engines. Recently, it has been studied whether generic quantum features such as coherence and quantum entanglement could allow for quantum devices with efficiencies larger than the Carnot efficiency. The present study shows that this is not permitted by the laws of thermodynamics-independent of the model. We will show that rather the definition of heat has to be modified to account for the thermodynamic cost of maintaining non-Gibbsian equilibrium states. Our theoretical findings are illustrated for two experimentally relevant examples. PMID:26565187

  17. Thermodynamic universality of quantum Carnot engines

    NASA Astrophysics Data System (ADS)

    Gardas, Bart?omiej; Deffner, Sebastian

    2015-10-01

    The Carnot statement of the second law of thermodynamics poses an upper limit on the efficiency of all heat engines. Recently, it has been studied whether generic quantum features such as coherence and quantum entanglement could allow for quantum devices with efficiencies larger than the Carnot efficiency. The present study shows that this is not permitted by the laws of thermodynamics—independent of the model. We will show that rather the definition of heat has to be modified to account for the thermodynamic cost of maintaining non-Gibbsian equilibrium states. Our theoretical findings are illustrated for two experimentally relevant examples.

  18. Thermodynamic universality of quantum Carnot engines

    SciTech Connect

    Gardas, Bart?omiej; Deffner, Sebastian

    2015-10-12

    The Carnot statement of the second law of thermodynamics poses an upper limit on the efficiency of all heat engines. Recently, it has been studied whether generic quantum features such as coherence and quantum entanglement could allow for quantum devices with efficiencies larger than the Carnot efficiency. The present study shows that this is not permitted by the laws of thermodynamic —independent of the model. We will show that rather the definition of heat has to be modified to account for the thermodynamic cost of maintaining non-Gibbsian equilibrium states. As a result, our theoretical findings are illustrated for two experimentally relevant examples.

  19. Thermodynamic universality of quantum Carnot engines

    DOE PAGESBeta

    Gardas, Bart?omiej; Deffner, Sebastian

    2015-10-12

    The Carnot statement of the second law of thermodynamics poses an upper limit on the efficiency of all heat engines. Recently, it has been studied whether generic quantum features such as coherence and quantum entanglement could allow for quantum devices with efficiencies larger than the Carnot efficiency. The present study shows that this is not permitted by the laws of thermodynamic —independent of the model. We will show that rather the definition of heat has to be modified to account for the thermodynamic cost of maintaining non-Gibbsian equilibrium states. As a result, our theoretical findings are illustrated for two experimentallymore »relevant examples.« less

  20. Bohmian mechanics contradicts quantum mechanics

    E-print Network

    Neumaier, Arnold

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

  1. A quantum-mechanical Maxwell's demon

    E-print Network

    Seth Lloyd

    1996-12-12

    A Maxwell's demon is a device that gets information and trades it in for thermodynamic advantage, in apparent (but not actual) contradiction to the second law of thermodynamics. Quantum-mechanical versions of Maxwell's demon exhibit features that classical versions do not: in particular, a device that gets information about a quantum system disturbs it in the process. In addition, the information produced by quantum measurement acts as an additional source of thermodynamic inefficiency. This paper investigates the properties of quantum-mechanical Maxwell's demons, and proposes experimentally realizable models of such devices.

  2. Copenhagen Quantum Mechanics

    E-print Network

    Timothy J. Hollowood

    2015-11-03

    In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950's development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrodinger cat states are the norm rather than curiosities generated in physicists' laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr's quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.

  3. quantum mechanics

    PubMed Central

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

    2013-01-01

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

  4. Quantum mechanics calculations of the thermodynamically controlled coverage and structure of alkyl monolayers on Si(111) surfaces.

    PubMed

    Nemanick, E Joseph; Solares, Santiago D; Goddard, William A; Lewis, Nathan S

    2006-08-01

    The heat of formation, Delta E, for silicon (111) surfaces terminated with increasing densities of the alkyl groups CH3- (methyl), C2H5- (ethyl), (CH3)2CH- (isopropyl), (CH3)3C- (tert-butyl), CH3(CH2)5- (hexyl), CH3(CH2)7- (octyl), and C6H5- (phenyl) was calculated using quantum mechanics (QM) methods, with unalkylated sites being H-terminated. The free energy, Delta G, for the formation of both Si-C and Si-H bonds from Si-Cl model compounds was also calculated using QM, with four separate Si-H formation mechanisms proposed, to give overall Delta G(S) values for the formation of alkylated Si(111) surfaces through a two step chlorination/alkylation method. The data are in good agreement with measurements of the packing densities for alkylated surfaces formed through this technique, for Si-H free energies of formation, Delta G(H), corresponding to a reaction mechanism including the elimination of two H atoms and the formation of a C=C double bond in either unreacted alkyl Grignard groups or tetrahydrofuran solvent. PMID:16869594

  5. Friction Force: From Mechanics to Thermodynamics

    ERIC Educational Resources Information Center

    Ferrari, Christian; Gruber, Christian

    2010-01-01

    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…

  6. Quantum Mechanics of Black Holes

    NASA Astrophysics Data System (ADS)

    Witten, Edward

    2012-08-01

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

  7. Quantum mechanics of black holes.

    PubMed

    Witten, Edward

    2012-08-01

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

  8. Introduction: quantum resonances Classical and quantum mechanics

    E-print Network

    Ramond, Thierry

    : quantum resonances Classical and quantum mechanics Microlocal analysis Resonances associated;..... . .... . .... . ..... . .... . .... . .... . ..... . .... . .... . .... . ..... . .... . .... . .... . ..... . .... . ..... . .... . .... . Introduction: quantum resonances Classical and quantum mechanics Microlocal analysis Resonances associated with homoclinic orbits Outline Introduction: quantum resonances Classical and quantum mechanics Microlocal

  9. Thermodynamics of weakly measured quantum systems

    E-print Network

    Jose Joaquin Alonso; Eric Lutz; Alessandro Romito

    2015-08-03

    We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superpositions of energy eigenstates. We use these quantities to extend the first and second laws of stochastic thermodynamics to the quantum domain. We illustrate our results with the case of a weakly measured driven two-level system and show how to distinguish between quantum work and heat contributions. We finally employ quantum feedback control to suppress detector backaction and determine the work statistics.

  10. An entropic picture of emergent quantum mechanics

    E-print Network

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

    2011-09-20

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

  11. Analogy between Thermodynamics and Mechanics.

    ERIC Educational Resources Information Center

    Peterson, Mark A.

    1979-01-01

    Establishes and illustrates a formal analogy between the motion of a particle and the "motion" of the equilibrium state of a homogeneous system in a quasistatic process. The purpose is to show that there is a much larger set of natural coordinate transformations in thermodynamics. (GA)

  12. Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Murdin, P.

    2000-11-01

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

  13. Thermodynamics of N-dimensional quantum walks

    NASA Astrophysics Data System (ADS)

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

    2014-08-01

    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.

  14. Learning in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Gardner, David E.

    This thesis describes qualitative research conducted to understand the problems students have when learning quantum mechanics. It differs from previous studies on educational issues associated with quantum mechanics in that I have examined the difficulties from the students' perspective. Three questions guided this research: What are the experiences of students learning quantum mechanics? What conceptual difficulties do students have with quantum mechanics? and, How do students approach learning quantum mechanics? From these questions, two themes emerged. First, students do not consider the quantum mechanical concepts of wave-particle duality or the uncertainty principle to be important sources of difficulties for them. Second, many of the difficulties students encounter are not related to conceptual understanding of specific topics, but stem from a mindset that is incongruent with the nature and structure of quantum mechanics. The implications for teaching are that the nature and structure of quantum mechanics should be emphasized and be an explicit part of instruction.

  15. Introduction to Quantum Mechanics

    E-print Network

    Eduardo J. S. Villaseñor

    2008-04-23

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

  16. Black Hole Thermodynamics and Statistical Mechanics

    E-print Network

    Steven Carlip

    2008-07-28

    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.

  17. Statistical mechanics based on fractional classical and quantum mechanics

    SciTech Connect

    Korichi, Z.; Meftah, M. T.

    2014-03-15

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

  18. Testing Nonassociative Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Bojowald, Martin; Brahma, Suddhasattwa; Büyükçam, Umut

    2015-11-01

    The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to nonassociative algebras. Their quantum physics has remained obscure. This Letter presents the first derivation of potentially testable physical results in nonassociative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.

  19. Quantum walk, entanglement and thermodynamic laws

    NASA Astrophysics Data System (ADS)

    Romanelli, Alejandro

    2015-09-01

    We consider a special dynamics of a quantum walk (QW) on a line. The walker, initially localized at the origin of the line with arbitrary chirality, evolves to an asymptotic stationary state. In this stationary state a measurement is performed and the state resulting from this measurement is used to start a second QW evolution to achieve a second asymptotic stationary state. In previous works, we developed the thermodynamics associated with the entanglement between the coin and position degrees of freedom in the QW. Here we study the application of the first and second laws of thermodynamics to the process between the two stationary states mentioned above. We show that: (i) the entropy change has upper and lower bounds that are obtained analytically as functions of the initial conditions. (ii) the energy change is associated to a heat-transfer process.

  20. Out-of-equilibrium Thermodynamics of Quantum Optomechanical Systems

    E-print Network

    M. Brunelli; A. Xuereb; A. Ferraro; G. De Chiara; N. Kiesel; M. Paternostro

    2014-12-15

    We address the out-of-equilibrium thermodynamics of an isolated quantum system consisting of a cavity optomechanical device. We explore the dynamical response of the system when driven out of equilibrium by a sudden quench of the coupling parameter and compute analytically the full distribution of the work generated by the process. We consider linear and quadratic optomechanical coupling, where the cavity field is parametrically coupled to either the position or the square of the position of a mechanical oscillator, respectively. In the former case we find that the average work generated by the quench is zero, whilst the latter leads to a non-zero average value. Through fluctuations theorems we access the most relevant thermodynamical figures of merit, such as the free energy difference and the amount of irreversible work generated. We thus provide a full characterization of the out-of-equilibrium thermodynamics in the quantum regime for nonlinearly coupled bosonic modes. Our study is the first due step towards the construction and full quantum analysis of an optomechanical machine working fully out of equilibrium.

  1. Introduction to Thermodynamics and Statistical Mechanics Professor Sergey Buldyrev

    E-print Network

    Buldyrev, Sergey

    Introduction to Thermodynamics and Statistical Mechanics Professor Sergey Buldyrev An introductory in a state of constant motion. The study of this behavior is known as thermodynamics. Thermodynamics is based of thermodynamics, which states that the degree of disorder in any closed system cannot decrease. #12;These two laws

  2. Low-temperature thermodynamics with quantum coherence

    E-print Network

    Varun Narasimhachar; Gilad Gour

    2015-08-09

    Thermal operations are an operational model of non-equilibrium quantum thermodynamics. In the absence of coherence between energy levels, exact state transition conditions under thermal operations are known in terms of a mathematical relation called thermo-majorization. But incorporating coherence has turned out to be challenging, even under the relatively tractable model wherein all Gibbs state-preserving quantum channels are included. Here we find a mathematical generalization of thermal operations at low temperatures, "cooling maps", for which we derive the necessary and sufficient state transition condition. Cooling maps that saturate recently-discovered bounds on coherence transfer are realizable as thermal operations, motivating us to conjecture that all cooling maps are thermal operations. Cooling maps, though a less conservative generalization to thermal operations, are more tractable than Gibbs-preserving operations, suggesting that cooling map-like models at general temperatures could be of use in gaining insight about thermal operations.

  3. The thermodynamics of quantum spacetime histories

    E-print Network

    Smolin, Lee

    2015-01-01

    We show that the simplicity constraints, which define the dynamics of spin foam models, imply, and are implied by, the first law of thermodynamics, when the latter is applied to causal diamonds in the quantum spacetime. This result reveals an intimate connection between the holographic nature of gravity, as reflected by the Bekenstein entropy, and the fact that general relativity and other gravitational theories can be understood as constrained topological field theories. To state and derive this correspondence we describe causal diamonds in the causal structure of spin foam histories and generalize arguments given for the near horizon region of black holes by Frodden, Gosh and Perez and Bianchi. This allows us to apply a recent argument of Jacobson to show that if a spin foam history has a semiclassical limit described in terms of a smooth metric geometry, that geometry satisfies the Einstein equations. These results suggest also a proposal for a quantum equivalence principle.

  4. The thermodynamics of quantum spacetime histories

    E-print Network

    Lee Smolin

    2015-10-13

    We show that the simplicity constraints, which define the dynamics of spin foam models, imply, and are implied by, the first law of thermodynamics, when the latter is applied to causal diamonds in the quantum spacetime. This result reveals an intimate connection between the holographic nature of gravity, as reflected by the Bekenstein entropy, and the fact that general relativity and other gravitational theories can be understood as constrained topological field theories. To state and derive this correspondence we describe causal diamonds in the causal structure of spin foam histories and generalize arguments given for the near horizon region of black holes by Frodden, Gosh and Perez and Bianchi. This allows us to apply a recent argument of Jacobson to show that if a spin foam history has a semiclassical limit described in terms of a smooth metric geometry, that geometry satisfies the Einstein equations. These results suggest also a proposal for a quantum equivalence principle.

  5. Low-temperature thermodynamics with quantum coherence

    PubMed Central

    Narasimhachar, Varun; Gour, Gilad

    2015-01-01

    Thermal operations are an operational model of non-equilibrium quantum thermodynamics. In the absence of coherence between energy levels, exact state transition conditions under thermal operations are known in terms of a mathematical relation called thermo-majorization. But incorporating coherence has turned out to be challenging, even under the relatively tractable model wherein all Gibbs state-preserving quantum channels are included. Here we find a mathematical generalization of thermal operations at low temperatures, ‘cooling maps', for which we derive the necessary and sufficient state transition condition. Cooling maps that saturate recently discovered bounds on coherence transfer are realizable as thermal operations, motivating us to conjecture that all cooling maps are thermal operations. Cooling maps, though a less-conservative generalization to thermal operations, are more tractable than Gibbs-preserving operations, suggesting that cooling map-like models at general temperatures could be of use in gaining insight about thermal operations. PMID:26138621

  6. Geometrization of Quantum Mechanics

    E-print Network

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

    2007-03-23

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

  7. Time in quantum mechanics 

    E-print Network

    Chapin, Kimberly R.

    1997-01-01

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

  8. Thermodynamics of Quantum Gases for the Entire Range of Temperature

    ERIC Educational Resources Information Center

    Biswas, Shyamal; Jana, Debnarayan

    2012-01-01

    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…

  9. Nonthermal Quantum Channels as a Thermodynamical Resource.

    PubMed

    Navascués, Miguel; García-Pintos, Luis Pedro

    2015-07-01

    Quantum thermodynamics can be understood as a resource theory, whereby thermal states are free and the only allowed operations are unitary transformations commuting with the total Hamiltonian of the system. Previous literature on the subject has just focused on transformations between different state resources, overlooking the fact that quantum operations which do not commute with the total energy also constitute a potentially valuable resource. In this Letter, given a number of nonthermal quantum channels, we study the problem of how to integrate them in a thermal engine so as to distill a maximum amount of work. We find that, in the limit of asymptotically many uses of each channel, the distillable work is an additive function of the considered channels, computable for both finite dimensional quantum operations and bosonic channels. We apply our results to bound the amount of distillable work due to the natural nonthermal processes postulated in the Ghirardi-Rimini-Weber (GRW) collapse model. We find that, although GRW theory predicts the possibility of extracting work from the vacuum at no cost, the power which a collapse engine could, in principle, generate is extremely low. PMID:26182086

  10. Nonthermal Quantum Channels as a Thermodynamical Resource

    NASA Astrophysics Data System (ADS)

    Navascués, Miguel; García-Pintos, Luis Pedro

    2015-07-01

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

  11. Covariant quantum mechanics and quantum symmetries

    E-print Network

    JanyÂ?ka, Josef

    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

  12. Dissipative and quantum mechanics

    E-print Network

    Roumen Tsekov

    2015-06-08

    Three existing interpretations of quantum mechanics, given by Heisenberg, Bohm and Madelung, are examined to describe dissipative quantum systems as well. It is found that the Madelung quantum hydrodynamics is the only correct approach. A new stochastic reinterpretation of the quantum mechanics is proposed, which represents the microscopic face of the Madelung hydrodynamics. The main idea is that the vacuum fluctuates permanently, which explains the probabilistic character of the quantum mechanics. Thus, it is an objective theory independent of the human beings and their measurements. The effect of the thermal fluctuations in the surrounding is also accounted for via a heuristic Langevin equation with two random forces. Some statistical characteristics of these quantum and thermal noises are determined by reproducing known results for the system phase-space dynamics.

  13. Complete Quantum Thermodynamics of the Black Body Photon Gas

    E-print Network

    Pankovic, Vladan

    2011-01-01

    Kelly and Leff demonstrated and discussed formal and conceptual similarities between basic thermodynamic formulas for the classical ideal gas and black body photon gas. Leff pointed out that thermodynamic formulas for the photon gas cannot be deduced completely by thermodynamic methods since these formulas hold two characteristic parameters, {\\it r} and {\\it b}, whose accurate values can be obtained exclusively by accurate methods of the quantum statistics (by explicit use of the Planck's or Bose-Einstein distribution). In this work we prove that the complete quantum thermodynamics of the black body photon gas can be done by simple, thermodynamic (non-statistical) methods. We prove that both mentioned parameters and corresponding variables (photons number and pressure) can be obtained very simply and practically exactly (with relative error about few percent), by non-statistical (without any use of the Planck's or Bose-Einstein distribution), quantum thermodynamic methods. Corner-stone of these methods repres...

  14. Is quantum mechanics exact?

    SciTech Connect

    Kapustin, Anton

    2013-06-15

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

  15. Quantum Mechanics Without Observers

    E-print Network

    W. H. Sulis

    2013-03-03

    The measurement problem and the role of observers have plagued quantum mechanics since its conception. Attempts to resolve these have introduced anthropomorphic or non-realist notions into physics. A shift of perspective based upon process theory and utilizing methods from combinatorial games, interpolation theory and complex systems theory results in a novel realist version of quantum mechanics incorporating quasi-local, nondeterministic hidden variables that are compatible with the no-hidden variable theorems and relativistic invariance, and reproduce the standard results of quantum mechanics to a high degree of accuracy without invoking observers.

  16. Numerical continuation in classical mechanics and thermodynamics

    NASA Astrophysics Data System (ADS)

    Gimenez, Aleix; Chausse, Victor; Meseguer, Alvaro

    2015-01-01

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

  17. Quantum Mechanics From the Cradle?

    ERIC Educational Resources Information Center

    Martin, John L.

    1974-01-01

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

  18. Universal quantum mechanics

    SciTech Connect

    Giddings, Steven B.

    2008-10-15

    If gravity respects quantum mechanics, it is important to identify the essential postulates of a quantum framework capable of incorporating gravitational phenomena. Such a construct likely requires elimination or modification of some of the 'standard' postulates of quantum mechanics, in particular, those involving time and measurement. This paper proposes a framework that appears sufficiently general to incorporate some expected features of quantum gravity. These include the statement that space and time may only emerge approximately and relationally. One perspective on such a framework is as a sort of generalization of the S-matrix approach to dynamics. Within this framework, more dynamical structure is required to fully specify a theory; this structure is expected to lack some of the elements of local quantum field theory. Some aspects of this structure are discussed, both in the context of scattering of perturbations about a flat background, and in the context of cosmology.

  19. Complete Quantum Thermodynamics of the Black Body Photon Gas

    E-print Network

    Vladan Pankovic; Darko V. Kapor

    2011-03-16

    Kelly and Leff demonstrated and discussed formal and conceptual similarities between basic thermodynamic formulas for the classical ideal gas and black body photon gas. Leff pointed out that thermodynamic formulas for the photon gas cannot be deduced completely by thermodynamic methods since these formulas hold two characteristic parameters, {\\it r} and {\\it b}, whose accurate values can be obtained exclusively by accurate methods of the quantum statistics (by explicit use of the Planck's or Bose-Einstein distribution). In this work we prove that the complete quantum thermodynamics of the black body photon gas can be done by simple, thermodynamic (non-statistical) methods. We prove that both mentioned parameters and corresponding variables (photons number and pressure) can be obtained very simply and practically exactly (with relative error about few percent), by non-statistical (without any use of the Planck's or Bose-Einstein distribution), quantum thermodynamic methods. Corner-stone of these methods represents a quantum thermodynamic stability condition that is, in some degree, very similar to quantum stability condition in the Bohr quantum atomic theory (de Broglie's interpretation of the Bohr quantization postulate). Finally, we discuss conceptual similarities between black body photon gas entropy and Bekenstein-Hawking black hole entropy.

  20. Symplectic Quantum Mechanics

    E-print Network

    J. LaChapelle

    2015-08-10

    We propose $Sp(8,\\mathbb{R})$ and $SO(9,\\mathbb{R})$ as dynamical groups for closed quantum systems. Restricting here to $Sp(8,\\mathbb{R})$, the quantum theory is constructed and investigated. The functional Mellin transform plays a prominent role in defining the quantum theory as it provides a bridge between the quantum algebra of observables and the algebra of operators on Hilbert spaces furnishing unitary representations that are induced from a distinguished parabolic subgroup of $Sp(8,\\mathbb{R})$. As well, the parabolic subgroup furnishes a fiber bundle construction that models what can be described as a matrix quantum gauge theory. The formulation is strictly quantum mechanics: no a priori space-time is assumed and the only geometrical input comes from the group manifold. But, what appears on the surface to be a fairly simple model, turns out to have a capacious structure suggesting some surprising physical interpretations.

  1. QUANTUM MECHANICS II Physics 342

    E-print Network

    Rosner, Jonathan L.

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

  2. Periodic thermodynamics of isolated quantum systems.

    PubMed

    Lazarides, Achilleas; Das, Arnab; Moessner, Roderich

    2014-04-18

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

  3. Statistical Mechanics and Thermodynamics of Viral Evolution

    PubMed Central

    Jones, Barbara A.; Lessler, Justin; Bianco, Simone; Kaufman, James H.

    2015-01-01

    This paper uses methods drawn from physics to study the life cycle of viruses. The paper analyzes a model of viral infection and evolution using the "grand canonical ensemble" and formalisms from statistical mechanics and thermodynamics. Using this approach we enumerate all possible genetic states of a model virus and host as a function of two independent pressures–immune response and system temperature. We prove the system has a real thermodynamic temperature, and discover a new phase transition between a positive temperature regime of normal replication and a negative temperature “disordered” phase of the virus. We distinguish this from previous observations of a phase transition that arises as a function of mutation rate. From an evolutionary biology point of view, at steady state the viruses naturally evolve to distinct quasispecies. This paper also reveals a universal relationship that relates the order parameter (as a measure of mutational robustness) to evolvability in agreement with recent experimental and theoretical work. Given that real viruses have finite length RNA segments that encode proteins which determine virus fitness, the approach used here could be refined to apply to real biological systems, perhaps providing insight into immune escape, the emergence of novel pathogens and other results of viral evolution. PMID:26422205

  4. From mechanics to thermodynamics: an example of how to build the thermodynamics laws

    E-print Network

    Ferrari, Christian

    2009-01-01

    We study a mechanical problem in which a friction force is acting on the system. We explain how to extend Newtonian mechanics to thermodynamics using the fundamental concept of state, time evolution and energy conservation. We derive the two law of thermodynamics and then apply them to significant examples.

  5. Quantum mechanics without measurements

    E-print Network

    Robert B. Griffiths

    2006-12-08

    Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic probabilities in quantum theory requires setting up appropriate sample spaces taking proper account of quantum incompatibility. When this is done the Schrodinger equation can be used to calculate probabilities independent of whether a system is or is not being measured, and the results usually ascribed to wave function collapse are obtained in a less misleading way through conditional probabilities. Toy models that include measurement apparatus as part of the total quantum system make this approach accessible to students. Some comments are made about teaching this material.

  6. Grassmann Matrix Quantum Mechanics

    E-print Network

    Anninos, Dionysios; Monten, Ruben

    2015-01-01

    We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kahler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit. We discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.

  7. Grassmann Matrix Quantum Mechanics

    E-print Network

    Dionysios Anninos; Frederik Denef; Ruben Monten

    2015-12-11

    We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kahler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit. We discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.

  8. Quantum Corrected Schwarzschild Black Hole: Inner Horizon Thermodynamic Behaviors

    E-print Network

    Mandal, Abhijit

    2015-01-01

    The thermodynamic properties of Cauchy horizon is a matter of interest. Event horizon and Cauchy horizon together can enlighten us about the micro-states of a black hole. In addition, if we consider a black hole metric modified with quantum terms, which is not forcing the geodesics to focus at a singularity, the study of horizons becomes much more interesting. The spacelike behavior inside the Cauchy horizon has a deep impact on the related thermodynamics. We analyze different thermodynamic product to check whether a right left string theory mode's addition type representation for the concerned thermodynamic parameters is possible or not. Stability of Cauchy horizon is studied.

  9. Quantum Coherence, Time-Translation Symmetry, and Thermodynamics

    NASA Astrophysics Data System (ADS)

    Lostaglio, Matteo; Korzekwa, Kamil; Jennings, David; Rudolph, Terry

    2015-04-01

    The first law of thermodynamics imposes not just a constraint on the energy content of systems in extreme quantum regimes but also symmetry constraints related to the thermodynamic processing of quantum coherence. We show that this thermodynamic symmetry decomposes any quantum state into mode operators that quantify the coherence present in the state. We then establish general upper and lower bounds for the evolution of quantum coherence under arbitrary thermal operations, valid for any temperature. We identify primitive coherence manipulations and show that the transfer of coherence between energy levels manifests irreversibility not captured by free energy. Moreover, the recently developed thermomajorization relations on block-diagonal quantum states are observed to be special cases of this symmetry analysis.

  10. Quantum coherence, time-translation symmetry and thermodynamics

    E-print Network

    Matteo Lostaglio; Kamil Korzekwa; David Jennings; Terry Rudolph

    2015-04-13

    The first law of thermodynamics imposes not just a constraint on the energy-content of systems in extreme quantum regimes, but also symmetry-constraints related to the thermodynamic processing of quantum coherence. We show that this thermodynamic symmetry decomposes any quantum state into mode operators that quantify the coherence present in the state. We then establish general upper and lower bounds for the evolution of quantum coherence under arbitrary thermal operations, valid for any temperature. We identify primitive coherence manipulations and show that the transfer of coherence between energy levels manifests irreversibility not captured by free energy. Moreover, the recently developed thermo-majorization relations on block-diagonal quantum states are observed to be special cases of this symmetry analysis.

  11. Dual Quantum Mechanics

    E-print Network

    W. Chagas-Filho

    2009-05-11

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

  12. Noncommutative quantum mechanics

    NASA Astrophysics Data System (ADS)

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

    2001-09-01

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

  13. PHYSICS 482, QUANTUM MECHANICS II Introductory Quantum Mechanics contd.

    E-print Network

    Akerib, Daniel S.

    PHYSICS 482, QUANTUM MECHANICS II Introductory Quantum Mechanics contd. 1. Time dependent methods. Quantum Many-body physics: 1. Variational principle, simple applications. 2. Many body wave, ferromagnetism of the electron gas, Wigner crystals and quantum phase transitions. 4. Second quantization

  14. Chaos and Quantum Mechanics

    E-print Network

    Habib, S; Greenbaum, B; Jacobs, K; Shizume, K; Sundaram, B; Habib, Salman; Bhattacharya, Tanmoy; Greenbaum, Benjamin; Jacobs, Kurt; Shizume, Kosuke; Sundaram, Bala

    2005-01-01

    The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our starting point here is that a complete dynamical description requires a full understanding of the evolution of measured systems, necessary to explain actual experimental results. This is of course true, both classically and quantum mechanically. Because the evolution of the physical state is now conditioned on measurement results, the dynamics of such systems is intrinsically nonlinear even at the level of distribution functions. Due to this feature, the physically more complete treatment reveals the existence of dynamical regimes -- such as chaos -- that have no direct counterpart in the linear (unobserved) case. Moreover, this treatment allows for understanding how an effective classical behavior can result from the dynamics of an observed quantum system, both at the level of t...

  15. Relational Quantum Mechanics

    E-print Network

    Nicolaidis, Argyris

    2012-01-01

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

  16. Relational Quantum Mechanics

    E-print Network

    Argyris Nicolaidis

    2012-11-09

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

  17. Quantum Mechanics in Phase Space

    E-print Network

    Ali Mohammad Nassimi

    2008-06-11

    The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.

  18. Thermodynamics and Universality for Mean Field Quantum Spin Glasses

    E-print Network

    Nick Crawford

    2006-10-13

    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.

  19. Internal dissipation and heat leaks in quantum thermodynamic cycles

    NASA Astrophysics Data System (ADS)

    Correa, Luis A.; Palao, José P.; Alonso, Daniel

    2015-09-01

    The direction of the steady-state heat currents across a generic quantum system connected to multiple baths may be engineered to realize virtually any thermodynamic cycle. In spite of their versatility, such continuous energy-conversion systems are generally unable to operate at maximum efficiency due to non-negligible sources of irreversible entropy production. In this paper we introduce a minimal model of irreversible absorption chiller. We identify and characterize the different mechanisms responsible for its irreversibility, namely heat leaks and internal dissipation, and gauge their relative impact in the overall cooling performance. We also propose reservoir engineering techniques to minimize these detrimental effects. Finally, by looking into a known three-qubit embodiment of the absorption cooling cycle, we illustrate how our simple model may help to pinpoint the different sources of irreversibility naturally arising in more complex practical heat devices.

  20. Internal dissipation and heat leaks in quantum thermodynamic cycles.

    PubMed

    Correa, Luis A; Palao, José P; Alonso, Daniel

    2015-09-01

    The direction of the steady-state heat currents across a generic quantum system connected to multiple baths may be engineered to realize virtually any thermodynamic cycle. In spite of their versatility, such continuous energy-conversion systems are generally unable to operate at maximum efficiency due to non-negligible sources of irreversible entropy production. In this paper we introduce a minimal model of irreversible absorption chiller. We identify and characterize the different mechanisms responsible for its irreversibility, namely heat leaks and internal dissipation, and gauge their relative impact in the overall cooling performance. We also propose reservoir engineering techniques to minimize these detrimental effects. Finally, by looking into a known three-qubit embodiment of the absorption cooling cycle, we illustrate how our simple model may help to pinpoint the different sources of irreversibility naturally arising in more complex practical heat devices. PMID:26465455

  1. Quantum Rényi relative entropies affirm universality of thermodynamics

    NASA Astrophysics Data System (ADS)

    Misra, Avijit; Singh, Uttam; Bera, Manabendra Nath; Rajagopal, A. K.

    2015-10-01

    We formulate a complete theory of quantum thermodynamics in the Rényi entropic formalism exploiting the Rényi relative entropies, starting from the maximum entropy principle. In establishing the first and second laws of quantum thermodynamics, we have correctly identified accessible work and heat exchange in both equilibrium and nonequilibrium cases. The free energy (internal energy minus temperature times entropy) remains unaltered, when all the entities entering this relation are suitably defined. Exploiting Rényi relative entropies we have shown that this "form invariance" holds even beyond equilibrium and has profound operational significance in isothermal process. These results reduce to the Gibbs-von Neumann results when the Rényi entropic parameter ? approaches 1. Moreover, it is shown that the universality of the Carnot statement of the second law is the consequence of the form invariance of the free energy, which is in turn the consequence of maximum entropy principle. Further, the Clausius inequality, which is the precursor to the Carnot statement, is also shown to hold based on the data processing inequalities for the traditional and sandwiched Rényi relative entropies. Thus, we find that the thermodynamics of nonequilibrium state and its deviation from equilibrium together determine the thermodynamic laws. This is another important manifestation of the concepts of information theory in thermodynamics when they are extended to the quantum realm. Our work is a substantial step towards formulating a complete theory of quantum thermodynamics and corresponding resource theory.

  2. On Randomness in Quantum Mechanics

    E-print Network

    Alberto C. de la Torre

    2007-07-19

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

  3. Quantum mechanics over sets

    NASA Astrophysics Data System (ADS)

    Ellerman, David

    2014-03-01

    In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantum mechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.

  4. TRANSIENT QUANTUM MECHANICAL PROCESSES

    SciTech Connect

    L. COLLINS; J. KRESS; R. WALKER

    1999-07-01

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

  5. Three Pictures of Quantum Mechanics

    E-print Network

    Olszewski Jr., Edward A.

    Three Pictures of Quantum Mechanics Thomas R. Shafer April 17, 2009 #12;Outline of the Talk · Brief review of (or introduction to) quantum mechanics. · 3 different viewpoints on calculation. · Schrödinger the Stage: Quantum Mechanics in Five Minutes #12;The Wave Function · A particle or system is described

  6. Chaos and quantum mechanics.

    PubMed

    Habib, Salman; Bhattacharya, Tanmoy; Greenbaum, Benjamin; Jacobs, Kurt; Shizume, Kosuke; Sundaram, Bala

    2005-06-01

    The relationship between chaos and quantum mechanics has been somewhat uneasy--even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our starting point here is that a complete dynamical description requires a full understanding of the evolution of measured systems, necessary to explain actual experimental results. This is of course true, both classically and quantum mechanically. Because the evolution of the physical state is now conditioned on measurement results, the dynamics of such systems is intrinsically nonlinear even at the level of distribution functions. Due to this feature, the physically more complete treatment reveals the existence of dynamical regimes--such as chaos--that have no direct counterpart in the linear (unobserved) case. Moreover, this treatment allows for understanding how an effective classical behavior can result from the dynamics of an observed quantum system, both at the level of trajectories as well as distribution functions. Finally, we have the striking prediction that time-series from measured quantum systems can be chaotic far from the classical regime, with Lyapunov exponents differing from their classical values. These predictions can be tested in next-generation experiments. PMID:15980320

  7. Chaos and Quantum Mechanics

    E-print Network

    Salman Habib; Tanmoy Bhattacharya; Benjamin Greenbaum; Kurt Jacobs; Kosuke Shizume; Bala Sundaram

    2005-05-11

    The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our starting point here is that a complete dynamical description requires a full understanding of the evolution of measured systems, necessary to explain actual experimental results. This is of course true, both classically and quantum mechanically. Because the evolution of the physical state is now conditioned on measurement results, the dynamics of such systems is intrinsically nonlinear even at the level of distribution functions. Due to this feature, the physically more complete treatment reveals the existence of dynamical regimes -- such as chaos -- that have no direct counterpart in the linear (unobserved) case. Moreover, this treatment allows for understanding how an effective classical behavior can result from the dynamics of an observed quantum system, both at the level of trajectories as well as distribution functions. Finally, we have the striking prediction that time-series from measured quantum systems can be chaotic far from the classical regime, with Lyapunov exponents differing from their classical values. These predictions can be tested in next-generation experiments.

  8. Time Asymmetric Quantum Mechanics

    E-print Network

    Arno R. Bohm; Manuel Gadella; Piotr Kielanowski

    2011-09-03

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

  9. Discrete Quantum Mechanics

    E-print Network

    Odake, Satoru

    2011-01-01

    A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, the unified theory of exact and quasi-exact solvability based on the sinusoidal coordinates, the infinite families of new orthogonal (the exceptional) polynomials. Two new infinite families of orthogonal polynomials, the X_\\ell Meixner-Pollaczek and the X_\\ell Meixner polynomials are reported.

  10. Discrete Quantum Mechanics

    E-print Network

    Satoru Odake; Ryu Sasaki

    2011-08-11

    A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, the unified theory of exact and quasi-exact solvability based on the sinusoidal coordinates, the infinite families of new orthogonal (the exceptional) polynomials. Two new infinite families of orthogonal polynomials, the X_\\ell Meixner-Pollaczek and the X_\\ell Meixner polynomials are reported.

  11. Discrete quantum mechanics

    NASA Astrophysics Data System (ADS)

    Odake, Satoru; Sasaki, Ryu

    2011-09-01

    A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorized Hamiltonians, the general structure of the solution spaces of the Schrödinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schrödinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, the unified theory of exact and quasi-exact solvability based on the sinusoidal coordinates, and the infinite families of new orthogonal (the exceptional) polynomials. Two new infinite families of orthogonal polynomials, the X? Meixner-Pollaczek and the X? Meixner polynomials, are reported.

  12. Work extraction and thermodynamics for individual quantum systems

    NASA Astrophysics Data System (ADS)

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

    2014-06-01

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

  13. Quantum conformal mechanics

    E-print Network

    K. Andrzejewski

    2015-06-18

    The quantum mechanics of one degree of freedom exhibiting the exact conformal SL(2,R) symmetry is presented. The starting point is the classification of the unitary irreducible representations of the SL(2,R) group (or, to some extent, its universal covering). The coordinate representation is defined as the basis diagonalizing the special conformal generator K. It is indicated how the resulting theory emerges from the canonical/geometric quantization of the Hamiltonian dynamics on the relevant coadjoint orbits.

  14. Quantum conformal mechanics

    E-print Network

    Andrzejewski, K

    2015-01-01

    The quantum mechanics of one degree of freedom exhibiting the exact conformal SL(2,R) symmetry is presented. The starting point is the classification of the unitary irreducible representations of the SL(2,R) group (or, to some extent, its universal covering). The coordinate representation is defined as the basis diagonalizing the special conformal generator K. It is indicated how the resulting theory emerges from the canonical/geometric quantization of the Hamiltonian dynamics on the relevant coadjoint orbits.

  15. Quantum Mechanics and Representation Theory Columbia University

    E-print Network

    Woit, Peter

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

  16. Quantum Mechanics, Nonlinear Dynamics, and Correlated Statistical Mechanics

    NASA Astrophysics Data System (ADS)

    McHarris, Wm. C.

    2007-02-01

    Many of the so-called paradoxes of orthodox quantum mechanics can be shown to have parallel, more logical interpretations in the realm of nonlinear dynamics and chaos theory. Among these are violations of Bell-type inequalities, which in comparing "classical" mechanics with quantum mechanics implicitly compare uncorrelated and correlated statistics. During the past decade research in the field of nonextensive thermodynamics (including Tsallis entropy) has demonstrated the existence of many statistical correlations in classical, nonlinear systems. When such correlations exist, the conventional classical upper limit on statistical correlations in Bell-type experiments can easily be raised to overlap with quantum mechanical predictions involving correlated states such as the Bell singlet state, a favorite for deriving Bell inequalities. Thus, arguments based on experimental violations of Bell-type inequalities, which rule out the existence of "local reality," become moot. Perhaps quantum mechanics does have a deterministic, ontological basis, albeit one based in nonlinear dynamics and chaos theory. If so, deterministic chaos could provide Einstein's longed-for fundamental determinism, but because chaotic systems must be interpreted statistically, this also fits in quite well with the ideas of Bohr — Einstein and Bohr both could have been correct! It should be emphasized that the concept of nonlinear dynamics and chaos underpinning quantum mechanics does not involve hidden variables, nor does the fact that chaos is deterministic interlope on the existence of free will.

  17. Nonequilibrium-thermodynamics approach to open quantum systems

    NASA Astrophysics Data System (ADS)

    Semin, Vitalii; Petruccione, Francesco

    2014-11-01

    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 for dynamical and thermodynamical properties of open quantum systems. The power of the approach is illustrated by the application to the damped harmonic oscillator and the damped driven two-level system, resulting in analytical expressions for the non-Markovian and nonequilibrium entropy and inverse temperature.

  18. The second laws of quantum thermodynamics.

    PubMed

    Brandão, Fernando; Horodecki, Micha?; Ng, Nelly; Oppenheim, Jonathan; Wehner, Stephanie

    2015-03-17

    The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are approximately cyclic, the second law for microscopic systems takes on a different form compared to the macroscopic scale, imposing not just one constraint on state transformations, but an entire family of constraints. We find a family of free energies which generalize the traditional one, and show that they can never increase. The ordinary second law relates to one of these, with the remainder imposing additional constraints on thermodynamic transitions. We find three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparent violation of the usual second law, through a process of embezzling work from a large system which remains arbitrarily close to its original state. These second laws are relevant for small systems, and also apply to individual macroscopic systems interacting via long-range interactions. By making precise the definition of thermal operations, the laws of thermodynamics are unified in this framework, with the first law defining the class of operations, the zeroth law emerging as an equivalence relation between thermal states, and the remaining laws being monotonicity of our generalized free energies. PMID:25675476

  19. The second laws of quantum thermodynamics

    PubMed Central

    Brandão, Fernando; Horodecki, Micha?; Ng, Nelly; Oppenheim, Jonathan; Wehner, Stephanie

    2015-01-01

    The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are approximately cyclic, the second law for microscopic systems takes on a different form compared to the macroscopic scale, imposing not just one constraint on state transformations, but an entire family of constraints. We find a family of free energies which generalize the traditional one, and show that they can never increase. The ordinary second law relates to one of these, with the remainder imposing additional constraints on thermodynamic transitions. We find three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparent violation of the usual second law, through a process of embezzling work from a large system which remains arbitrarily close to its original state. These second laws are relevant for small systems, and also apply to individual macroscopic systems interacting via long-range interactions. By making precise the definition of thermal operations, the laws of thermodynamics are unified in this framework, with the first law defining the class of operations, the zeroth law emerging as an equivalence relation between thermal states, and the remaining laws being monotonicity of our generalized free energies. PMID:25675476

  20. Nonlinear friction in quantum mechanics

    E-print Network

    Roumen Tsekov

    2013-03-10

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

  1. Copenhagen Quantum Mechanics

    E-print Network

    Hollowood, Timothy J

    2015-01-01

    In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950's development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrodinger cat states are the norm rather than curiosities generat...

  2. Bohmian quantum mechanics with quantum trajectories

    NASA Astrophysics Data System (ADS)

    Jeong, Yeuncheol

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

  3. Moyal quantum mechanics

    E-print Network

    Osborn, T A

    1997-01-01

    The Moyal--Weyl description of quantum mechanics provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in \\hbar. Its semiclassical expansion `coefficients,' acting on symbols that represent observables, are simple, globally defined differential operators constructed in terms of the classical flow. Two methods of constructing this expansion are discussed. The first introduces a cluster-graph expansion for the symbol of an exponentiated operator, which extends Groenewold's formula for the Weyl product of symbols. This Poisson bracket based cluster expansion determines the Jacobi equations for the semiclassical expansion of `quantum trajectories.' Their Green function solutions construct the regular \\hbar\\downarrow0 asymptotic series for the Heisenberg--Weyl evolution map. The second method directly substitutes such a series into the Moyal equation of motion and determines the \\hbar coefficients recursively. The Heisenberg--...

  4. On Non-Equilibrium Thermodynamics of Space-Time and Quantum Gravity

    E-print Network

    Joakim Munkhammar

    2015-07-02

    Based on recent results from general relativistic statistical mechanics and black hole information transfer limits a space-time entropy-action equivalence is proposed as a generalization of the holographic principle. With this conjecture, the action principle can be replaced by the second law of thermodynamics, and for the Einstein-Hilbert action the Einstein field equations are conceptually the result of thermodynamic equilibrium. For non-equilibrium situations Jaynes' information-theoretic approach to maximum entropy production is adopted instead of the second law of thermodynamics. As it turns out, for appropriate choices of constants quantum gravity is obtained. For the special case of a free particle the Bekenstein-Verlinde entropy-to-displacement relation of holographic gravity, and thus the traditional holographic principle, emerges. Although Jacobson's original thermodynamic equilibrium approach proposed that gravity might not necessarily be quantized, this particular non-equilibrium treatment might require it.

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

    PubMed

    Fresch, Barbara; Moro, Giorgio J

    2010-07-21

    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 Schrodinger 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. PMID:20649339

  6. Thermodynamic analogy for quantum phase transitions at zero temperature

    SciTech Connect

    Cejnar, Pavel; Heinze, Stefan; Dobes, Jan

    2005-01-01

    We propose a relationship between thermodynamic phase transitions and ground-state quantum phase transitions in systems with variable Hamiltonian parameters. It is based on a link between zeros of the canonical partition function at complex temperatures and branch points of a quantum Hamiltonian in the complex-extended parameter space. This approach is applied in the interacting boson model, where it is shown to properly distinguish the first- and second-order phase transitions.

  7. Gravitomagnetism in quantum mechanics

    SciTech Connect

    Adler, Ronald J.; Chen Pisin

    2010-07-15

    We give a systematic treatment of the quantum mechanics of a spin zero particle in a combined electromagnetic field and a weak gravitational field that is produced by a slow moving matter source. The analysis is based on the Klein-Gordon equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The Klein-Gordon equation is recast into Schroedinger equation form, which we then analyze in the nonrelativistic limit. We include a discussion of some rather general observable physical effects implied by the Schroedinger equation form, concentrating on gravitomagnetism. Of particular interest is the interaction of the orbital angular momentum of the particle with the gravitomagnetic field.

  8. Principles of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Landé, Alfred

    2013-10-01

    Preface; Introduction: 1. Observation and interpretation; 2. Difficulties of the classical theories; 3. The purpose of quantum theory; Part I. Elementary Theory of Observation (Principle of Complementarity): 4. Refraction in inhomogeneous media (force fields); 5. Scattering of charged rays; 6. Refraction and reflection at a plane; 7. Absolute values of momentum and wave length; 8. Double ray of matter diffracting light waves; 9. Double ray of matter diffracting photons; 10. Microscopic observation of ? (x) and ? (p); 11. Complementarity; 12. Mathematical relation between ? (x) and ? (p) for free particles; 13. General relation between ? (q) and ? (p); 14. Crystals; 15. Transition density and transition probability; 16. Resultant values of physical functions; matrix elements; 17. Pulsating density; 18. General relation between ? (t) and ? (?); 19. Transition density; matrix elements; Part II. The Principle of Uncertainty: 20. Optical observation of density in matter packets; 21. Distribution of momenta in matter packets; 22. Mathematical relation between ? and ?; 23. Causality; 24. Uncertainty; 25. Uncertainty due to optical observation; 26. Dissipation of matter packets; rays in Wilson Chamber; 27. Density maximum in time; 28. Uncertainty of energy and time; 29. Compton effect; 30. Bothe-Geiger and Compton-Simon experiments; 31. Doppler effect; Raman effect; 32. Elementary bundles of rays; 33. Jeans' number of degrees of freedom; 34. Uncertainty of electromagnetic field components; Part III. The Principle of Interference and Schrödinger's equation: 35. Physical functions; 36. Interference of probabilities for p and q; 37. General interference of probabilities; 38. Differential equations for ?p (q) and Xq (p); 39. Differential equation for ?? (q); 40. The general probability amplitude ??' (Q); 41. Point transformations; 42. General theorem of interference; 43. Conjugate variables; 44. Schrödinger's equation for conservative systems; 45. Schrödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantum mechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantum mechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.

  9. Advanced Concepts in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

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

    2014-11-01

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

  10. Gaussian effective potential: Quantum mechanics

    NASA Astrophysics Data System (ADS)

    Stevenson, P. M.

    1984-10-01

    We advertise the virtues of the Gaussian effective potential (GEP) as a guide to the behavior of quantum field theories. Much superior to the usual one-loop effective potential, the GEP is a natural extension of intuitive notions familiar from quantum mechanics. A variety of quantum-mechanical examples are studied here, with an eye to field-theoretic analogies. Quantum restoration of symmetry, dynamical mass generation, and "quantum-mechanical resuscitation" are among the phenomena discussed. We suggest how the GEP could become the basis of a systematic approximation procedure. A companion paper will deal with scalar field theory.

  11. Diffusion-Schrödinger Quantum Mechanics

    NASA Astrophysics Data System (ADS)

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

    2014-08-01

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

  12. Gamification of Quantum Mechanics Teaching

    E-print Network

    Ole Eggers Bjælde; Mads Kock Pedersen; Jacob Sherson

    2015-06-26

    In this small scale study we demonstrate how a gamified teaching setup can be used effectively to support student learning in a quantum mechanics course. The quantum mechanics games were research games, which were played during lectures and the learning was measured with a pretest/posttest method with promising results. The study works as a pilot study to guide the planning of quantum mechanics courses in the future at Aarhus University in Denmark.

  13. Thermodynamics of discrete-charge quantum circuits

    NASA Astrophysics Data System (ADS)

    Utreras-Díaz, C. A.; Laroze, D.

    2015-11-01

    We study a dilute gas made of quantum circuits with discrete charge, interacting with a thermal reservoir at absolute temperature T, using Boltzmann statistics. This system is described by a quantum Hamiltonian that explicitly includes the effect of the discrete nature of the electric charge within a circuit approach. The eigenfunctions can be expressed as solutions of the Mathieu equation, and the energy spectrum is related to its characteristic values. We also make a comparative numerical study of the thermal properties, between the quantum case with discrete charge, and the so-called semiclassical approximation.

  14. Principles of thermodynamics and statistical mechanics

    SciTech Connect

    Lawden, D.F.

    1987-01-01

    This book gives a careful examination of the principles and concepts on which thermodynamics theories are based. It provides a foundation for understanding how theory is applied to many situations in physics and engineering. Applications to such areas as gases, crystals, and magnets are developed to illustrate general methods of analysis, giving the reader the background knowledge needed to pursue any particular area through further reading. The author's experience has allowed him to take special care with concepts that are most difficult for students. Numerous sets of exercises are included.

  15. Thermodynamics and Mechanical Equivalent of Heat

    NASA Astrophysics Data System (ADS)

    Kipnis, Nahum

    2014-10-01

    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.

  16. PT quantum mechanics.

    PubMed

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

    2013-04-28

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

  17. QUANTUM MECHANICS WITHOUT STATISTICAL POSTULATES

    SciTech Connect

    G. GEIGER; ET AL

    2000-11-01

    The Bohmian formulation of quantum mechanics describes the measurement process in an intuitive way without a reduction postulate. Due to the chaotic motion of the hidden classical particle all statistical features of quantum mechanics during a sequence of repeated measurements can be derived in the framework of a deterministic single system theory.

  18. Invariance in adelic quantum mechanics

    E-print Network

    Branko Dragovich

    2006-12-07

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

  19. Quantum phase transitions without thermodynamic limits

    E-print Network

    Macrina, Andrea

    at finite temperatures. Keywords: microcanonical equilibrium; continuous phase transition 1. Introduction at about 267 K, a temperature that is some 104 K greater than the melting point of bulk sodium (Schmidt et, London WC2R 2LS, UK A new microcanonical equilibrium state is introduced for quantum systems with finite

  20. Scan Quantum Mechanics: Quantum Inertia Stops Superposition

    E-print Network

    Gato-Rivera, Beatriz

    2015-01-01

    A novel interpretation of the quantum mechanical superposition is put forward. Quantum systems scan all possible available states and switch randomly and very rapidly among them. The longer they remain in a given state, the larger the probability of the system to be found in that state during a measurement. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia $I_q$ reaches a critical value $I_{cr}$ for an observable, the switching among the different eigenvalues of that observable stops and the corresponding superposition comes to an end. Consequently, increasing the mass, temperature, gravitational force, etc. of a quantum system increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. The process could be reversible decreasing the size, temperature, gravitational force, etc. leading to...

  1. Quantum uncertainty in distance measurement: Holography and black hole thermodynamics

    E-print Network

    Michael Maziashvili

    2006-04-01

    Exact conditions on the clock parameters corresponding to the minimal uncertainty in distance measurement are derived in uniform manner for any number of space time dimensions. The result espouses the holography principle no matter what the number of space time dimensions is. In this context the ADD braneworld model is considered. Some remarks are made on deviation of holography as well as of special relativity at the scales provided by the cosmological constant. We also comment on the potential influence of the background radiation on the uncertainty in length measurement. The presence of unavoidable quantum uncertainty in length measurement results in fluctuations of the black hole thermodynamics that can be interested to address the information loss problem. The quantum corrections to the black hole entropy obtained in various scenarios are imperceptible because of these fluctuations. At the Planck scale the fluctuations destroy the thermodynamic picture of the black hole.

  2. Galilei general relativistic quantum mechanics revisited

    E-print Network

    JanyÂ?ka, Josef

    Galilei general relativistic quantum mechanics revisited Arkadiusz Jadczyk Institute of Theoretical of Galilei relativistic quantum mechanics. The main concepts used are Galilei­Newton space­time, Newtonian : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 22 1.9 Classical particle mechanics : : : : : : : : : : : : : : : : : : : : : : : : 22 2 Quantum

  3. 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

  4. Thermodynamics of spherically symmetric spacetimes in loop quantum gravity

    NASA Astrophysics Data System (ADS)

    Mäkelä, Jarmo

    2015-06-01

    The choice of the area operator in loop quantum gravity is by no means unique. In addition to the area operator commonly used in loop quantum gravity there is also an area operator introduced by Krasnov in 1998, which gives uniformly spaced area spectra for the horizons of spacetime. Using Krasnov's area operator we consider the thermodynamics of spherically symmetric spacetimes equipped with horizons in loop quantum gravity. Among other things, our approach implies, in a pretty simple manner, that every horizon of spacetime emits thermal radiation and possesses entropy which, in the natural units, is one-quarter of its area. When applied to the de Sitter spacetime loop quantum gravity provides an explanation both to the presence and the smallness of the cosmological constant.

  5. Thermodynamic and quantum bounds on nonlinear DC thermoelectric transport

    E-print Network

    Robert S. Whitney

    2013-03-05

    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.

  6. Quantum Mechanics as Classical Physics

    E-print Network

    Charles Sebens

    2015-04-02

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

  7. Quantum Mechanics of the Einstein-Hopf Model.

    ERIC Educational Resources Information Center

    Milonni, P. W.

    1981-01-01

    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)

  8. Thermodynamic Derivation of the Equilibrium Distribution Functions of Statistical Mechanics.

    ERIC Educational Resources Information Center

    Stoeckly, Beth

    1979-01-01

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

  9. Phase space quantum mechanics - Direct

    SciTech Connect

    Nasiri, S.; Sobouti, Y.; Taati, F.

    2006-09-15

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

  10. Decoherence in quantum mechanics and quantum cosmology

    NASA Technical Reports Server (NTRS)

    Hartle, James B.

    1992-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Campisi, Michele

    2007-10-01

    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.

  12. Communication: Quantum mechanics without wavefunctions

    SciTech Connect

    Schiff, Jeremy; Poirier, Bill

    2012-01-21

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

  13. Foundations of Quantum Mechanics and Quantum Computation

    NASA Astrophysics Data System (ADS)

    Aspect, Alain; Leggett, Anthony; Preskill, John; Durt, Thomas; Pironio, Stefano

    2013-03-01

    I ask the question: What can we infer about the nature and structure of the physical world (a) from experiments already done to test the predictions of quantum mechanics (b) from the assumption that all future experiments will agree with those predictions? I discuss existing and projected experiments related to the two classic paradoxes of quantum mechanics, named respectively for EPR and Schrödinger's Cat, and show in particular that one natural conclusion from both types of experiment implies the abandonment of the concept of macroscopic counterfactual definiteness.

  14. Generalizations of Quantum Mechanics

    E-print Network

    Philip Pearle; Antony Valentini

    2005-10-14

    We review realistic models that reproduce quantum theory in some limit and yield potentially new physics outside that limit. In particular, we consider deterministic hidden-variables theories (such as the pilot-wave model) and their extension to 'quantum nonequilibrium', and we consider the continuous spontaneous localization model of wave function collapse. Other models are briefly discussed.

  15. Quantum mechanical description of waveguides

    E-print Network

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

    2008-05-12

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

  16. Free will and quantum mechanics

    E-print Network

    Antonio Di Lorenzo

    2011-05-05

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

  17. Quantum mechanics from invariance principles

    NASA Astrophysics Data System (ADS)

    Moldoveanu, Florin

    2015-07-01

    Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.

  18. Quantum mechanics from invariance principles

    E-print Network

    Florin Moldoveanu

    2015-10-25

    Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell inequalities.

  19. Quantum mechanics for relativistic bosons

    E-print Network

    Soon-Tae Hong

    2015-11-12

    We construct a relativistic quantum mechanics for a boson. To do this we exploit two component wave functions in Dirac type equations of motion. In our formalism we fix the pathological aspect of particle probability density which appears in Klein-Gordon theory. Our solutions possess a negative solution as well as a positive one. We also formulate a diagonal Hamiltonian of the relativistic quantum mechanics for the boson.

  20. Thermodynamic Optimization of Flow Geometry in Mechanical and Civil Engineering

    NASA Astrophysics Data System (ADS)

    Bejan, Adrian; Lorente, Sylvie

    2001-12-01

    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.

  1. Quantum mechanics writ large

    E-print Network

    Bush, John W. M.

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

  2. Quantum Mechanics in Insulators

    SciTech Connect

    Aeppli, G.

    2009-08-20

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

  3. Scan Quantum Mechanics: Quantum Inertia Stops Superposition

    E-print Network

    Beatriz Gato-Rivera

    2015-12-11

    A novel interpretation of the quantum mechanical superposition is put forward. Quantum systems scan all possible available states and switch randomly and very rapidly among them. The longer they remain in a given state, the larger the probability of the system to be found in that state during a measurement. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia $I_q$ reaches a critical value $I_{cr}$ for an observable, the switching among the different eigenvalues of that observable stops and the corresponding superposition comes to an end. Consequently, increasing the mass, temperature, gravitational force, etc. of a quantum system increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. The process could be reversible decreasing the size, temperature, gravitational force, etc. Entanglement can only occur between quantum systems, not between a quantum system and a classical one, because an exact synchronization between the switchings of the systems involved must be established in the first place and classical systems do not have any switchings to start with. Future experiments might determine the critical inertia $I_{cr}$ corresponding to different observables. In addition, our proposal implies a new radiation mechanism in strong gravitational fields, giving rise to non-thermal emission, that could contribute to neutron star formation and provides new insight into the information loss paradox and the firewall. Superconductivity, superfluidity, Bose-Einstein condensates, and any other physical phenomena at very low temperatures must be reanalyzed in the light of this interpretation, as well as mesoscopic systems in general.

  4. Double quantum dot coupled to a quantum point contact: a stochastic thermodynamics approach

    NASA Astrophysics Data System (ADS)

    Bulnes Cuetara, Gregory; Esposito, Massimiliano

    2015-09-01

    We study the nonequilibrium properties of an electronic circuit composed of a double quantum dot (DQD) channel capacitively coupled to a quantum point contact (QPC) within the framework of stochastic thermodynamics. We show that the transition rates describing the dynamics satisfy a nontrivial local detailed balance and that the statistics of energy and particle currents across both channels obeys a fluctuation theorem. We analyze two regimes where the device operates as a thermodynamic machine and study its output power and efficiency fluctuations. We show that the electrons tunneling through the QPC without interacting with the DQD have a strong effect on the device efficiency.

  5. The thermodynamic cost of driving quantum systems by their boundaries.

    PubMed

    Barra, Felipe

    2015-01-01

    The laws of thermodynamics put limits to the efficiencies of thermal machines. Analogues of these laws are now established for quantum engines weakly and passively coupled to the environment providing a framework to find improvements to their performance. Systems whose interaction with the environment is actively controlled do not fall in that framework. Here we consider systems actively and locally coupled to the environment, evolving with a so-called boundary-driven Lindblad equation. Starting from a unitary description of the system plus the environment we simultaneously obtain the Lindblad equation and the appropriate expressions for heat, work and entropy-production of the system extending the framework for the analysis of new, and some already proposed, quantum heat engines. We illustrate our findings in spin 1/2 chains and explain why an XX chain coupled in this way to a single heat bath relaxes to thermodynamic-equilibrium while and XY chain does not. Additionally, we show that an XX chain coupled to a left and a right heat baths behaves as a quantum engine, a heater or refrigerator depending on the parameters, with efficiencies bounded by Carnot efficiencies. PMID:26445899

  6. The thermodynamic cost of driving quantum systems by their boundaries

    NASA Astrophysics Data System (ADS)

    Barra, Felipe

    2015-10-01

    The laws of thermodynamics put limits to the efficiencies of thermal machines. Analogues of these laws are now established for quantum engines weakly and passively coupled to the environment providing a framework to find improvements to their performance. Systems whose interaction with the environment is actively controlled do not fall in that framework. Here we consider systems actively and locally coupled to the environment, evolving with a so-called boundary-driven Lindblad equation. Starting from a unitary description of the system plus the environment we simultaneously obtain the Lindblad equation and the appropriate expressions for heat, work and entropy-production of the system extending the framework for the analysis of new, and some already proposed, quantum heat engines. We illustrate our findings in spin 1/2 chains and explain why an XX chain coupled in this way to a single heat bath relaxes to thermodynamic-equilibrium while and XY chain does not. Additionally, we show that an XX chain coupled to a left and a right heat baths behaves as a quantum engine, a heater or refrigerator depending on the parameters, with efficiencies bounded by Carnot efficiencies.

  7. The thermodynamic cost of driving quantum systems by their boundaries

    PubMed Central

    Barra, Felipe

    2015-01-01

    The laws of thermodynamics put limits to the efficiencies of thermal machines. Analogues of these laws are now established for quantum engines weakly and passively coupled to the environment providing a framework to find improvements to their performance. Systems whose interaction with the environment is actively controlled do not fall in that framework. Here we consider systems actively and locally coupled to the environment, evolving with a so-called boundary-driven Lindblad equation. Starting from a unitary description of the system plus the environment we simultaneously obtain the Lindblad equation and the appropriate expressions for heat, work and entropy-production of the system extending the framework for the analysis of new, and some already proposed, quantum heat engines. We illustrate our findings in spin 1/2 chains and explain why an XX chain coupled in this way to a single heat bath relaxes to thermodynamic-equilibrium while and XY chain does not. Additionally, we show that an XX chain coupled to a left and a right heat baths behaves as a quantum engine, a heater or refrigerator depending on the parameters, with efficiencies bounded by Carnot efficiencies. PMID:26445899

  8. The thermodynamic cost of driving quantum systems by their boundaries

    E-print Network

    Felipe Barra

    2015-10-22

    The laws of thermodynamics put limits to the efficiencies of thermal machines. Analogues of these laws are now established for quantum engines weakly and passively coupled to the environment providing a framework to find improvements to their performance. Systems whose interaction with the environment is actively controlled do not fall in that framework. Here we consider systems actively and locally coupled to the environment, evolving with a so-called boundary-driven Lindblad equation. Starting from a unitary description of the system plus the environment we simultaneously obtain the Lindblad equation and the appropriate expressions for heat, work and entropy-production of the system extending the framework for the analysis of new, and some already proposed, quantum heat engines. We illustrate our findings in spin 1/2 chains and explain why an XX chain coupled in this way to a single heat bath relaxes to thermodynamic-equilibrium while and XY chain does not. Additionally, we show that an XX chain coupled to a left and a right heat baths behaves as a quantum engine, a heater or refrigerator depending on the parameters, with efficiencies bounded by Carnot efficiencies.

  9. 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

  10. 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

  11. QUANTUM MECHANICS AND REAL Department of Mathematics

    E-print Network

    Penrose, Oliver

    QUANTUM MECHANICS AND REAL EVENTS O.Penrose Department of Mathematics Heriot-Watt University into the evolution of a quantum-mechanical system, without altering the usual laws of quantum mechanics in any way Although quantum mechanics is wonderfully successful for predicting the results of experiments done

  12. From Quantum Mechanics to String Theory

    E-print Network

    From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics, 2009 #12;Quantum Mechanics: Measurement and Uncertainty Thursday, May 7, 2009 #12;Puzzle: The Stern it. Quantum mechanics understanding: the particle exists in a state without definite position

  13. The Universal Arrow of Time II: Quantum mechanics case

    E-print Network

    Oleg Kupervasser

    2013-05-23

    This paper is a natural continuation of our previous paper arXiv:1011.4173 . We illustrated earlier that in classical Hamilton mechanics, for overwhelming majority of real chaotic macroscopic systems, alignment of their thermodynamic time arrows occurs because of their low interaction. This fact and impossibility to observe entropy decrease at introspection explain the second law of thermodynamics. The situation in quantum mechanics is even a little bit easier: all closed systems of finite volume are periodic or nearly periodic. The proof in quantum mechanics is in many respects similar to the proof in classical Hamilton mechanics - it also uses small interaction between subsystems and impossibility to observe entropy decrease at introspection. However, there are special cases which were not found in the classical mechanics. In these cases one microstate corresponds to a set of possible macrostates (more precisely, their quantum superposition). Consideration of this property with use of decoherence theory and taking into account thermodynamic time arrows will introduce new outcomes in quantum mechanics. It allows to resolve basic paradoxes of quantum mechanics: (a) to explain the paradox of wave packet reduction at measurements when an observer is included in the system (introspection) (paradox of the Schrodinger cat); (b) to explain unobservability of superposition of macroscopic states by an external observer in real experiments (paradox of Wigner's friend); (c) to prove full equivalence of multi-world and Copenhagen interpretations of quantum mechanics; (d) to explain deviations from the exponential law at decay of particles and pass from one energy level to another (paradox of a kettle which will never begin to boil).

  14. Quantum relativistic fluid at global thermodynamic equilibrium in curved spacetime

    E-print Network

    Becattini, F

    2015-01-01

    We present a new approach to the problem of the thermodynamical equilibrium of a quantum relativistic fluid in a curved spacetime in the limit of small curvature. We calculate the mean value of local operators by expanding the four-temperature Killing vector field in Riemann normal coordinates about the same spacetime point and we derive corrections with respect to the flat spacetime expressions. Thereby, we clarify the origin of the terms proportional to Riemann and Ricci tensors introduced in general hydrodynamic expansion of the stress-energy tensor.

  15. Quantum relativistic fluid at global thermodynamic equilibrium in curved spacetime

    E-print Network

    F. Becattini; E. Grossi

    2015-11-17

    We present a new approach to the problem of the thermodynamical equilibrium of a quantum relativistic fluid in a curved spacetime in the limit of small curvature. We calculate the mean value of local operators by expanding the four-temperature Killing vector field in Riemann normal coordinates about the same spacetime point and we derive corrections with respect to the flat spacetime expressions. Thereby, we clarify the origin of the terms proportional to Riemann and Ricci tensors introduced in general hydrodynamic expansion of the stress-energy tensor.

  16. Quantum Mechanics and Reality

    ERIC Educational Resources Information Center

    DeWitt, Bryce S.

    1970-01-01

    Discusses the quantum theory of measurement and von Neumann's catastrophe of infinite regression." Examines three ways of escapint the von Neumann catastrophe, and suggests that the solution to the dilemma of inteterminism is a universe in which all possible outcomes of an experiment actually occur. Bibliography. (LC)

  17. Thermodynamics of the quantum spin-S XXZ chain

    NASA Astrophysics Data System (ADS)

    Rojas, O.; de Souza, S. M.; Corrêa Silva, E. V.; Thomaz, M. T.

    2005-08-01

    The thermodynamics of the spin-S anisotropic quantum XXZ chain with arbitrary value of S and unitary norm, in the high-temperature regime, is reported. The single-ion anisotropy term and the interaction with an external magnetic field in the z-direction are taken into account. We obtain, for arbitrary value of S, the ?-expansion of the Helmholtz free energy of the model up to order ?6 and show that it actually depends on 1/S(S+1). Its classical limit is obtained by simply taking S??. At h=0 and D=0, our high temperature expansion of the classical model coincides with Joyce’s exact solution [11]. We study, in the high temperature region, some thermodynamic quantities such as the specific heat and the magnetic susceptibility as functions of spin and verify for which values of S those thermodynamic functions behave classically. Their finite temperature behavior is inferred from interpolation of their high- and low-temperature behavior, and shown to be in good agreement with numerical results. The finite temperature behavior is shown for higher values of spin.

  18. What quantum computers may tell us about quantum mechanics

    E-print Network

    Monroe, Christopher

    17 What quantum computers may tell us about quantum mechanics Christopher R. Monroe University of Michigan, Ann Arbor Quantum mechanics occupies a unique position in the history of science. It has sur successes of quantum mechanics, its foundations are often questioned, owing to the glaring difficulties

  19. From Quantum Mechanics to String Theory

    E-print Network

    From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics with constant velocity with respect to each other (These are inertial reference frames) Newton's Laws (mechanics

  20. Statistical thermodynamics of quantum Brownian motion: Birth of perpetuum mobile of the second kind

    E-print Network

    Th. M. Nieuwenhuizen; A. E. Allahverdyan

    2001-11-22

    The Brownian motion of a quantum particle in a harmonic confining potential and coupled to a harmonic quantum thermal bath is exactly solvable. It is shown that at low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. In physical terms, this happens when the cloud of bath modes around the particle starts to play a non-trivial role. Indeed, equilibrium thermodynamics of the total system, particle plus bath, does not imply standard equilibrium thermodynamics for the particle itself at low $T$. Various formulations of the second law are found to be invalid at low $T$. First, the Clausius inequality can be violated, because heat can be extracted from the zero point energy of the cloud of bath modes. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the entropy production is partly negative. Third, for non-adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobile of the second kind, having one or several work extraction cycles, enter the realm of condensed matter physics. Fourth, it follows that the equivalence between different formulations of the second law (e.g. those by Clausius and Thomson) can be violated at low temperatures. These effects are the consequence of quantum entanglement in the presence of the slightly off-equilibrium nature of the thermal bath, and become important when the characteristic quantum time scale $\\hbar/k_BT$ is larger than or comparable to other timescale of the system. They show that there is no general consensus between standard thermodynamics and quantum mechanics.

  1. Entanglement and Disentanglement in Relativistic Quantum Mechanics

    E-print Network

    Johnson, Kent

    Entanglement and Disentanglement in Relativistic Quantum Mechanics Jeffrey A. Barrett March 31 the quantum measurement problem.1 1 Relativistic Quantum Mechanics and Entanglement Work on the conceptual quantum mechanics and of the entangled states of spacelike separated systems requires a concrete

  2. Quantum Mechanical Earth: Where Orbitals Become Orbits

    ERIC Educational Resources Information Center

    Keeports, David

    2012-01-01

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

  3. QUANTUM MECHANICS AND DUALISM JEFFREY A. BARRETT

    E-print Network

    Johnson, Kent

    QUANTUM MECHANICS AND DUALISM JEFFREY A. BARRETT Abstract. The quantum measurement problem has led, and in a no-collapse formulation of quantum mechanics, a strong variety of dualism provides a way to account with Eugene Wigner's understanding of the standard collapse formulation of quantum mechanics. Two years prior

  4. EK424 THERMODYNAMICS AND STATISTICAL MECHANICS (Spring 2015) Thermodynamics is the study of processes (e.g., expansion of a gas, boiling of water, or diffusion

    E-print Network

    Vajda, Sandor

    EK424 THERMODYNAMICS AND STATISTICAL MECHANICS (Spring 2015) 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

  5. Quantum Techniques for Stochastic Mechanics

    E-print Network

    John C. Baez; Jacob Biamonte

    2015-10-22

    Some ideas from quantum theory are just beginning to percolate back to classical probability theory. For example, there is a widely used and successful theory of "chemical reaction networks", which describes the interactions of molecules in a stochastic rather than quantum way. Computer science and population biology use the same ideas under a different name: "stochastic Petri nets". But if we look at these theories from the perspective of quantum theory, they turn out to involve creation and annihilation operators, coherent states and other well-known ideas - but in a context where probabilities replace amplitudes. We explain this connection as part of a detailed analogy between quantum mechanics and stochastic mechanics. We use this analogy to present new proofs of two major results in the theory of chemical reaction networks: the deficiency zero theorem and the Anderson-Craciun-Kurtz theorem. We also study the overlap of quantum mechanics and stochastic mechanics, which involves Hamiltonians that can generate either unitary or stochastic time evolution. These Hamiltonians are called "Dirichlet forms", and they arise naturally from electrical circuits made only of resistors.

  6. Non-thermal quantum channels as a thermodynamical resource

    E-print Network

    Miguel Navascués; Luis Pedro García-Pintos

    2015-06-15

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

  7. Kowalevski top in quantum mechanics

    SciTech Connect

    Matsuyama, A.

    2013-09-15

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

  8. QUANTUM MECHANICS. Quantum squeezing of motion in a mechanical resonator.

    PubMed

    Wollman, E E; Lei, C U; Weinstein, A J; Suh, J; Kronwald, A; Marquardt, F; Clerk, A A; Schwab, K C

    2015-08-28

    According to quantum mechanics, a harmonic oscillator can never be completely at rest. Even in the ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. Using microwave frequency radiation pressure, we have manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state. We also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. Our results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion. PMID:26315431

  9. On determining absolute entropy without quantum theory or the Third Law of thermodynamics

    E-print Network

    Steane, Andrew

    2015-01-01

    We employ classical thermodynamics to gain information about absolute entropy, without recourse to statistical methods, quantum mechanics or the Third Law of thermodynamics. The Gibbs-Duhem equation yields various simple methods to determine the absolute entropy of a fluid. We also study the entropy of an ideal gas and the ionization of a plasma in thermal equilibrium. A single measurement of the degree of ionization can be used to determine an unknown constant in the entropy equation, and thus determine the absolute entropy of a gas. It follows from all these examples that the value of entropy at absolute zero temperature does not need to be assigned by postulate, but can be deduced empirically.

  10. BOOK REVIEW: Relativistic Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Antoine, J.-P.

    2004-01-01

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

  11. Quantum Mechanics Course Number: C668 C668: Special topics in physical chemistry: Advanced Quantum Mechanics

    E-print Network

    Iyengar, Srinivasan S.

    Quantum Mechanics Course Number: C668 C668: Special topics in physical chemistry: Advanced Quantum@gmail.com Chemistry, Indiana University i c 2014, Srinivasan S. Iyengar (instructor) #12;Quantum Mechanics Course Mechanics by J. J. Sakurai · Quantum Mechanics in Chemistry by Schatz and Ratner · Introduction to Quantum

  12. Self-Referential Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Mitchell, Mark Kenneth

    1993-01-01

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

  13. From Quantum Mechanics to String Theory

    E-print Network

    From Quantum Mechanics to String Theory Relativity (why it makes sense) Quantum mechanics Mechanical Particle Physics General Relativistic Quantum Gravity increasing speed decreasing size increasing Extra Dimensions Strings and the Strong Force Thursday, June 4, 2009 #12;The Higgs Mechanism Summary

  14. Faster than Hermitian quantum mechanics.

    PubMed

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

    2007-01-26

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

  15. The Grammatical Universe and the Laws of Thermodynamics and Quantum Entanglement

    NASA Astrophysics Data System (ADS)

    Marcer, Peter J.; Rowlands, Peter

    2010-11-01

    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 (E2-p2m2) = 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).

  16. The Grammatical Universe and the Laws of Thermodynamics and Quantum Entanglement

    SciTech Connect

    Marcer, Peter J.; Rowlands, Peter

    2010-11-24

    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).

  17. Remarks on osmosis, quantum mechanics, and gravity

    E-print Network

    Robert Carroll

    2011-04-03

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

  18. Remarks on osmosis, quantum mechanics, and gravity

    E-print Network

    Carroll, Robert

    2011-01-01

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

  19. Creation mechanism of quantum accelerator modes

    E-print Network

    Summy, G. S.

    We investigate the creation mechanism of quantum accelerator modes which are attributed to the existence of the stability islands in an underlying pseudoclassical phase space of the quantum delta-kicked accelerator. Quantum ...

  20. QUICK QUANTUM MECHANICS ---Introduction ---

    E-print Network

    Jackson, Andrew D.

    of Classical Mechanics After Newton found his equations of motion, physicists knew they would have to wait are completely equivalent to Newton's laws. 2 A generalized coordinate can be, e.g., a Cartesian coordinate the behaviour of all of the generalized coordinates, q(t), subject to initial boundary conditions. Since Newton

  1. Hermeneutics, Underdetermination and Quantum Mechanics.

    ERIC Educational Resources Information Center

    Cushing, James T.

    1995-01-01

    States that the existence of an essential underdetermination in the interpretation of the formalism of quantum mechanics, in spite of the widespread belief that logic and empirical considerations alone demand an indeterministic world view in physics, legitimizes the analysis of hermeneutics in science education. (LZ)

  2. Renormalization group in quantum mechanics

    SciTech Connect

    Polony, J.

    1996-12-01

    The running coupling constants are introduced in quantum mechanics and their evolution is described with the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The Hamiltonian and the Lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models. Copyright {copyright} 1996 Academic Press, Inc.

  3. The quantum field theory interpretation of quantum mechanics

    E-print Network

    Alberto C. de la Torre

    2015-03-02

    It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.

  4. Thermodynamics of Maximum Transition Entropy for Quantum Assemblies

    E-print Network

    David M. Rogers

    2015-03-27

    This work presents a general unifying theoretical framework for quantum non-equilibrium systems. It is based on a re-statement of the dynamical problem as one of inferring the distribution of collision events that move a system toward thermal equilibrium from an arbitrary starting distribution. Using a form based on maximum entropy for this transition distribution leads to a statistical description of open quantum systems with strong parallels to the conventional, maximum-entropy, equilibrium thermostatics. A precise form of the second law of thermodynamics can be stated for this dynamics at every time-point in a trajectory. Numerical results are presented for low-dimensional systems interacting with cavity fields. The dynamics and stationary state are compared to a reference model of a weakly coupled oscillator plus cavity supersystem thermostatted by periodic partial measurements. Despite the absence of an explicit cavity in the present model of open quantum dynamics, both the relaxation rates and stationary state properties closely match the reference. Additionally, the time-course of energy exchange and entropy increase is given throughout an entire measurement process for a single spin system. The results show the process to be capable of initially absorbing heat when starting from a superposition state, but not from an isotropic distribution. Based on these results, it is argued that logical inference in the presence of environmental noise is sufficient to resolve the paradox of wavefunction collapse.

  5. Continuum mechanics beyond the second law of thermodynamics

    PubMed Central

    Ostoja-Starzewski, M.; Malyarenko, A.

    2014-01-01

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

  6. Continuum mechanics beyond the second law of thermodynamics.

    PubMed

    Ostoja-Starzewski, M; Malyarenko, A

    2014-11-01

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

  7. Quantum Mechanics Of Consciousness

    E-print Network

    Rajat Kumar Pradhan

    2009-07-29

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

  8. Algorithmic Information Theoretic Issues in Quantum Mechanics

    E-print Network

    Algorithmic Information Theoretic Issues in Quantum Mechanics Gavriel Segre - PHD thesis October 20 of qubits one has to give up the Hilbert- Space Axiomatization of Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 III The road for quantum algorithmic randomness 104 5 The irreducibility of quantum probability

  9. Probable Inference and Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Grandy, W. T.

    2009-12-01

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

  10. Thermodynamics properties of the dark energy in loop quantum cosmology

    E-print Network

    Kui Xiao; Jian-Yang Zhu

    2010-06-28

    Considering an arbitrary, varying equation of the state parameter, the thermodynamic properties of the dark energy fluid in a semiclassical loop quantum cosmology scenario, which we consider the inverse volume modification, is studied. The equation of the state parameters are corrected as a semiclassical one during considering the effective behavior. Assuming that the apparent horizon has Hawking temperature, the modified entropy-area relation is obtained, we find that this relation is different from the one which is obtained by considering the holonomy correction. Considering the dark energy is a thermal equilibrium fluid, we get the expressions for modified temperature, chemical potential and entropy. The temperature, chemical potential and entropy are well-defined in the semiclassical regions.

  11. Irreversible Work and Inner Friction in Quantum Thermodynamic Processes

    NASA Astrophysics Data System (ADS)

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

    2014-12-01

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

  12. Star Products for Relativistic Quantum Mechanics

    E-print Network

    P. Henselder

    2007-05-24

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

  13. Violation of the second law of thermodynamics in the quantum microworld

    NASA Astrophysics Data System (ADS)

    ?ápek, V.; Bok, J.

    2001-02-01

    One of the previously reported linear models of open quantum systems (interacting with a single thermal bath but otherwise not aided from outside) endowed with the faculty of spontaneous self-organization challenging standard thermodynamics is reconstructed here. It is then able to produce, in a cyclic manner, a useful (this time mechanical) work at the cost of just thermal energy in the bath whose quanta get properly in-phased. This means perpetuum mobile of the second kind explicitly violating the second law in its Thomson formulation. No approximations can be made responsible for the effect as a special scaling procedure is used that makes the chosen kinetic theory exact. The effect is purely quantum and disappears in the classical limit.

  14. Statistical thermodynamics of quantum Brownian motion: Construction of perpetuum mobile of the second kind

    NASA Astrophysics Data System (ADS)

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

    2002-09-01

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

  15. Statistical thermodynamics of quantum Brownian motion: construction of perpetuum mobile of the second kind.

    PubMed

    Nieuwenhuizen, Th M; Allahverdyan, A E

    2002-09-01

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

  16. Thermodynamics and mechanism of cutinase stabilization by trehalose.

    PubMed

    Baptista, Ricardo P; Pedersen, Shona; Cabrita, Gonçalo J M; Otzen, Daniel E; Cabral, Joaquim M S; Melo, Eduardo P

    2008-06-01

    Trehalose has been widely used to stabilize cellular structures such as membranes and proteins. The effect of trehalose on the stability of the enzyme cutinase was studied. Thermal unfolding of cutinase reveals that trehalose delays thermal unfolding, thus increasing the temperature at the midpoint of unfolding by 7.2 degrees . Despite this stabilizing effect, trehalose also favors pathways that lead to irreversible denaturation. Stopped-flow kinetics of cutinase folding and unfolding was measured and temperature was introduced as experimental variable to assess the mechanism and thermodynamics of protein stabilization by trehalose. The main stabilizing effect of trehalose was to delay the rate constant of the unfolding of an intermediate. A full thermodynamic analysis of this step has revealed that trehalose induces the phenomenon of entropy-enthalpy compensation, but the enthalpic contribution increases more significantly leading to a net stabilizing effect that slows down unfolding of the intermediate. Regarding the molecular mechanism of stabilization, trehalose increases the compactness of the unfolded state. The conformational space accessible to the unfolded state decreases in the presence of trehalose when the unfolded state acquires residual native interactions that channel the folding of the protein. This residual structure results into less hydrophobic groups being newly exposed upon unfolding, as less water molecules are immobilized upon unfolding. PMID:18213692

  17. Lecture Notes in Quantum Mechanics Doron Cohen

    E-print Network

    Cohen, Doron

    Lecture Notes in Quantum Mechanics Doron Cohen Department of Physics, Ben-Gurion University, Beer-Sheva 84105, Israel These are the lecture notes of quantum mechanics courses that are given by DC at Ben · Spherical geometry, phase shifts · Cross section, optical theorem, resonances Quantum mechanics in practice

  18. Lecture Notes in Quantum Mechanics Doron Cohen

    E-print Network

    Cohen, Doron

    Lecture Notes in Quantum Mechanics Doron Cohen Department of Physics, Ben-Gurion University, Beer-Sheva 84105, Israel (arXiv:quant-ph/0605180) These are the lecture notes of quantum mechanics courses · Spherical geometry, phase shifts · Cross section, optical theorem, resonances Quantum mechanics in practice

  19. Quantum Mechanics Dung-Hai Lee

    E-print Network

    Murayama, Hitoshi

    Quantum Mechanics Dung-Hai Lee Summer 2000 #12;Contents 1 A brief reminder of linear Algebra 3 1 classical to quantum mechanics . . . . . . . . . . . 47 3.14.1 Route I . . . . . . . . . . . . . . . . . . . . . 53 4 Symmetry in quantum mechanics 57 4.1 General discussions

  20. 221B Lecture Notes Relativistic Quantum Mechanics

    E-print Network

    Murayama, Hitoshi

    221B Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics We the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We's equation of motion in mechanics. The initial condtions to solve the Newton's equation of motion

  1. Causal Structure in Categorical Quantum Mechanics

    E-print Network

    Murawski, Andrzej

    Causal Structure in Categorical Quantum Mechanics Raymond Lal Christ Church University of Oxford mechanics is a way of formalising the structural features of quantum theory using category theory. It uses. In particular, categorical quantum mechanics provides a graphical calculus that exposes the information flow

  2. 129 Lecture Notes Relativistic Quantum Mechanics

    E-print Network

    Murayama, Hitoshi

    129 Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We's equation of motion in mechanics. The initial condtions to solve the Newton's equation of motion

  3. Visualizing quantum mechanics in phase space

    E-print Network

    Heiko Bauke; Noya Ruth Itzhak

    2011-01-11

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

  4. 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

  5. 221B Lecture Notes Relativistic Quantum Mechanics

    E-print Network

    Murayama, Hitoshi

    221B Lecture Notes Relativistic Quantum Mechanics 1 Need for Relativistic Quantum Mechanics We the single-particle Schr¨odinger wave equation, but obtained only by going to quantum field theory. We, similarly to the Newton's equation of motion in mechanics. The initial condtions to solve the Newton

  6. Quantum Mechanics: Structures, Axioms and Paradoxes

    E-print Network

    Aerts, Diederik

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

  7. Improving student understanding of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Singh, Chandralekha

    2015-04-01

    Learning quantum mechanics is challenging for many students. We are investigating the difficulties that upper-level students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) and tools for peer-instruction. Many of the QuILTs employ computer simulations to help students visualize and develop better intuition about quantum phenomena. We will discuss the common students' difficulties and research-based tools we are developing to bridge the gap between quantitative and conceptual aspects of quantum mechanics and help students develop a solid grasp of quantum concepts. Support from the National Science Foundation is gratefully acknowledged.

  8. Paradoxical Reflection in Quantum Mechanics

    E-print Network

    Pedro L. Garrido; Sheldon Goldstein; Jani Lukkarinen; Roderich Tumulka

    2011-05-03

    This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast, classical particles get reflected only at upward steps. The conditions for this effect are that the wave length is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. This phenomenon is suggested by non-normalizable solutions to the time-independent Schroedinger equation, and we present evidence, numerical and mathematical, that it is also indeed predicted by the time-dependent Schroedinger equation. Furthermore, this paradoxical reflection effect suggests, and we confirm mathematically, that a quantum particle can be trapped for a long time (though not forever) in a region surrounded by downward potential steps, that is, on a plateau.

  9. Conceptual Development of Quantum Mechanics: Experiences with the Visual Quantum Mechanics Materials*

    E-print Network

    Larkin, Teresa L.

    Conceptual Development of Quantum Mechanics: Experiences with the Visual Quantum Mechanics using a portion of the materials developed by the Visual Quantum Mechanics (VQM) project1 as part of our recent efforts to investigate student understanding of basic quantum mechanics concepts. The VQM

  10. Pragmatic Information in Quantum Mechanics

    E-print Network

    Juan G. Roederer

    2015-12-16

    An objective definition of pragmatic information and the consideration of recent results about information processing in the human brain can help overcome some traditional difficulties with the interpretation of quantum mechanics. Rather than attempting to define information ab initio, I introduce the concept of interaction between material bodies as a primary concept. Two distinct categories can be identified: 1) Interactions which can always be reduced to a superposition of physical interactions (forces) between elementary constituents; 2) Interactions between complex bodies which cannot be reduced to a superposition of interactions between parts, and in which patterns and forms (in space and/or time) play the determining role. Pragmatic information is then defined as the correspondence between a given pattern and the ensuing pattern-specific change. I will show that pragmatic information is a biological concept that plays no active role in the purely physical domain; it only does so when a living organism intervenes. The consequences for the foundations of both classical and quantum physics are important and will be discussed in detail. Since by its very definition pragmatic information (the one our brain uses to represent, think about and react to the outside world)cannot operate in the quantum domain, it is advisable to refrain from using it in our mental representation of what is happening 'inside' a quantum system. Although the theoretical framework developed for quantum mechanics handles mathematical entities specifically attributed to a quantum system, the only truly pragmatic information it can provide relates to macroscopic effects on the environment (natural, or artificial as in a measurement instrument) with which the system interacts.

  11. Quantum mechanics and the psyche

    NASA Astrophysics Data System (ADS)

    Galli Carminati, G.; Martin, F.

    2008-07-01

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

  12. Jarzynski equality in PT-symmetric quantum mechanics

    SciTech Connect

    Deffner, Sebastian; Saxena, Avadh

    2015-04-13

    We show that the quantum Jarzynski equality generalizes to PT -symmetric quantum mechanics with unbroken PT -symmetry. In the regime of broken PT -symmetry the Jarzynski equality does not hold as also the CPT -norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system – two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken PT -symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.

  13. Quantum mechanics without statistical postulates

    E-print Network

    H. Geiger; G. Obermair; Ch. Helm

    1999-05-21

    The Bohmian formulation of quantum mechanics is used in order to describe the measurement process in an intuitive way without a reduction postulate in the framework of a deterministic single system theory. Thereby the motion of the hidden classical particle is chaotic during almost all nontrivial measurement processes. For the correct reproduction of experimental results, it is further essential that the distribution function $P(x)$ of the results of a position measurement is identical with $|\\Psi|^2$ of the wavefunction $\\Psi$ of the single system under consideration. It is shown that this feature is not an additional assumption, but can be derived strictly from the chaotic motion of a single system during a sequence of measurements, providing a completely deterministic picture of the statistical features of quantum mechanics.

  14. The Transactional Interpretation of Quantum Mechanics and Quantum Nonlocality

    E-print Network

    John G. Cramer

    2015-02-28

    Quantum nonlocality is discussed as an aspect of the quantum formalism that is seriously in need of interpretation. The Transactional Interpretation of quantum mechanics, which describes quantum processes as transactional "handshakes" between retarded $\\psi$ waves and advanced $\\psi*$ waves, is discussed. Examples of the use of the Transactional Interpretation in resolving quantum paradoxes and in understanding the counter-intuitive aspects of the formalism, particularly quantum nonlocality, are provided.

  15. Supersymmetric Quantum Mechanics with Reflections

    E-print Network

    S. Post; L. Vinet; A. Zhedanov

    2011-08-09

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

  16. Description of quantum coherence in thermodynamic processes requires constraints beyond free energy

    E-print Network

    Matteo Lostaglio; David Jennings; Terry Rudolph

    2015-03-16

    Recent studies have developed fundamental limitations on nanoscale thermodynamics, in terms of a set of independent free energy relations. Here we show that free energy relations cannot properly describe quantum coherence in thermodynamic processes. By casting time-asymmetry as a quantifiable, fundamental resource of a quantum state we arrive at an additional, independent set of thermodynamic constraints that naturally extend the existing ones. These asymmetry relations reveal that the traditional Szilard engine argument does not extend automatically to quantum coherences, but instead only relational coherences in a multipartite scenario can contribute to thermodynamic work. We find that coherence transformations are always irreversible. Our results also reveal additional structural parallels between thermodynamics and the theory of entanglement.

  17. Description of quantum coherence in thermodynamic processes requires constraints beyond free energy

    PubMed Central

    Lostaglio, Matteo; Jennings, David; Rudolph, Terry

    2015-01-01

    Recent studies have developed fundamental limitations on nanoscale thermodynamics, in terms of a set of independent free energy relations. Here we show that free energy relations cannot properly describe quantum coherence in thermodynamic processes. By casting time-asymmetry as a quantifiable, fundamental resource of a quantum state, we arrive at an additional, independent set of thermodynamic constraints that naturally extend the existing ones. These asymmetry relations reveal that the traditional Szilárd engine argument does not extend automatically to quantum coherences, but instead only relational coherences in a multipartite scenario can contribute to thermodynamic work. We find that coherence transformations are always irreversible. Our results also reveal additional structural parallels between thermodynamics and the theory of entanglement. PMID:25754774

  18. On reconciling quantum mechanics and local realism

    E-print Network

    Donald A. Graft

    2013-09-04

    A necessary and natural change in our application of quantum mechanics to separated systems is shown to reconcile quantum mechanics and local realism. An analysis of separation and localization justifies the proposed change in application of quantum mechanics. An important EPRB experiment is reconsidered and it is seen that when it is correctly interpreted it supports local realism. This reconciliation of quantum mechanics with local realism allows the axiom sets of quantum mechanics, probability, and special relativity to be joined in a consistent global axiom set for physics.

  19. Quantum mechanics and the direction of time

    SciTech Connect

    Hasegawa, H.; Petrosky, T. ); Prigogine, I. International Solvay Inst. for Physics and Chemistry, Brussels ); Tasaki, S. )

    1991-03-01

    In recent papers the authors have discussed the dynamical properties of large Poincare systems (LPS), that is, nonintegrable systems with a continuous spectrum (both classical and quantum). An interesting example of LPS is given by the Friedrichs model of field theory. As is well known, perturbation methods analytic in the coupling constant diverge because of resonant denominators. They show that this Poincare catastrophe can be eliminated by a natural time ordering of the dynamical states. They obtain then a dynamical theory which incorporates a privileged direction of time (and therefore the second law of thermodynamics). However, it is only in very simple situations that his time ordering can be performed in an extended Hilbert space. In general, they need to go to the Liouville space (superspace) and introduce a time ordering of dynamical states according to the number of particles involved in correlations. This leads then to a generalization of quantum mechanics in which the usual Heisenberg's eigenvalue problem is replaced by a complex eigenvalue problem in the Liouville space.

  20. Effective equations for the quantum pendulum from momentous quantum mechanics

    SciTech Connect

    Hernandez, Hector H.; Chacon-Acosta, Guillermo

    2012-08-24

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

  1. Game Theory in Categorical Quantum Mechanics

    E-print Network

    Ali Nabi Duman

    2014-05-17

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

  2. Faster than Hermitian Quantum Mechanics

    SciTech Connect

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

    2007-01-26

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

  3. Teaching Quantum Mechanics on an Introductory Level.

    ERIC Educational Resources Information Center

    Muller, Rainer; Wiesner, Hartmut

    2002-01-01

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

  4. Quantum Mechanical Observers and Time Reparametrization Symmetry

    E-print Network

    Eiji Konishi

    2012-12-20

    We propose that the degree of freedom of measurement by quantum mechanical observers originates in the Goldstone mode of the spontaneously broken time reparametrization symmetry. Based on the classification of quantum states by their non-unitary temporal behavior as seen in the measurement processes, we describe the concepts of the quantum mechanical observers via the time reparametrization symmetry.

  5. Quantum mechanical effects from deformation theory

    SciTech Connect

    Much, A.

    2014-02-15

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

  6. BOOK REVIEWS: Quantum Mechanics: Fundamentals

    NASA Astrophysics Data System (ADS)

    Whitaker, A.

    2004-02-01

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

  7. Quantum Mechanics Joachim Burgdorfer and Stefan Rotter

    E-print Network

    Rotter, Stefan

    1 1 Quantum Mechanics Joachim Burgd¨orfer and Stefan Rotter 1.1 Introduction 3 1.2 Particle and Quantization 8 1.5 Angular Momentum in Quantum Mechanics 9 1.6 Formalism of Quantum Mechanics 12 1.7 Solution 29 1.8.3 Resonances 30 1.9 Semiclassical Mechanics 31 1.9.1 The WKB Approximation 31 1.9.2 The EBK

  8. Non-relativistic Quantum Mechanics versus Quantum Field Theories

    E-print Network

    Antonio Pineda

    2007-05-29

    We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.

  9. Quantum Mechanics: Myths and Facts

    NASA Astrophysics Data System (ADS)

    Nikoli?, Hrvoje

    2007-11-01

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

  10. Treating Time Travel Quantum Mechanically

    E-print Network

    John-Mark A. Allen

    2014-10-10

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

  11. Treating time travel quantum mechanically

    NASA Astrophysics Data System (ADS)

    Allen, John-Mark A.

    2014-10-01

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

  12. The irreversible quantum

    NASA Astrophysics Data System (ADS)

    Fernández de Córdoba, P.; Isidro, J. M.; Perea, Milton H.; Vazquez Molina, J.

    2015-11-01

    We elaborate on the existing notion that quantum mechanics is an emergent phenomenon, by presenting a thermodynamical theory that is dual to quantum mechanics. This dual theory is that of classical irreversible thermodynamics. The linear regime of irreversibility considered here corresponds to the semiclassical approximation in quantum mechanics. An important issue we address is how the irreversibility of time evolution in thermodynamics is mapped onto the quantum-mechanical side of the correspondence.

  13. Molecular thermodynamics of metabolism: quantum thermochemical calculations for key metabolites.

    PubMed

    Hadadi, N; Ataman, M; Hatzimanikatis, V; Panayiotou, C

    2015-04-28

    The present work is the first of a series of papers aiming at a coherent and unified development of the thermodynamics of metabolism and the rationalization of feasibility analysis of metabolic pathways. The focus in this part is on high-level quantum chemical calculations of the thermochemical quantities of relatively heavy metabolites such as amino acids/oligopeptides, nucleosides, saccharides and their derivatives in the ideal gas state. The results of this study will be combined with the corresponding hydration/solvation results in subsequent parts of this work in order to derive the desired thermochemical quantities in aqueous solutions. The above metabolites exist in a vast conformational/isomerization space including rotational conformers, tautomers or anomers exhibiting often multiple or cooperative intramolecular hydrogen bonding. We examine the challenges posed by these features for the reliable estimation of thermochemical quantities. We discuss conformer search, conformer distribution and averaging processes. We further consider neutral metabolites as well as protonated and deprotonated metabolites. In addition to the traditional presentation of gas-phase acidities, basicities and proton affinities, we also examine heats and free energies of ionic species. We obtain simple linear relations between the thermochemical quantities of ions and the formation quantities of their neutral counterparts. Furthermore, we compare our calculations with reliable experimental measurements and predictive calculations from the literature, when available. Finally, we discuss the next steps and perspectives for this work. PMID:25799954

  14. Errors and paradoxes in quantum mechanics

    E-print Network

    D. Rohrlich

    2007-08-28

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

  15. Propagators in polymer quantum mechanics

    SciTech Connect

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

    2013-09-15

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

  16. A continuum thermodynamics formulation for micro-magneto-mechanics with applications to ferromagnetic shape memory alloys

    E-print Network

    A continuum thermodynamics formulation for micro-magneto- mechanics with applications Article history: Received 2 October 2007 Received in revised form 22 April 2008 Accepted 26 May 2008 and actuators a b s t r a c t A continuum thermodynamics formulation for micromagnetics coupled with mechanics

  17. The Konigsberg Interpretation Of Quantum Mechanics?

    E-print Network

    Horner, Jack K.

    THE KÖNIGSBERG INTERPRETATION OF QUANTUM MECHANICS? Jack K. Horner It is surely a truism that the science and philos­ ophy of an age influence one another; and this century has been no exception: the rise of quantum theory in particular profoundly threatened... against this criterion to show that the rejoinder must, if cogent, assume B. 1. The EPR argument. The object of the EPR argu­ ment Ts to show that the quantum theory fails to describe "completely" certain quantum-mechanical events. Provided...

  18. An extended phase space for Quantum Mechanics

    E-print Network

    C. Lopez

    2015-09-23

    The standard formulation of Quantum Mechanics violates locality of interactions and the action reaction principle. An alternative formulation in an extended phase space could preserve both principles, but Bell's theorems show that a distribution of probability in a space of local variables can not reproduce the quantum correlations. An extended phase space is defined in an alternative formulation of Quantum Mechanics. Quantum states are represented by a complex va\\-lued distribution of amplitude, so that Bell's theorems do not apply.

  19. Diffusion-based DNA target colocalization by thermodynamic mechanisms

    E-print Network

    Antonio Scialdone; Mario Nicodemi

    2011-05-04

    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.

  20. Propagators in Polymer Quantum Mechanics

    E-print Network

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

    2013-02-07

    Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has been used to represent some aspects of the loop quantization in a simpler context, and, on the other, it has been applied to each of the infinite mechanical modes of other systems. Indeed, this polymer approach was recently implemented for the free scalar field propagator. In this work we compute the polymer propagators of the free particle and a particle in a box; amusingly, just as in the non polymeric case, the one of the particle in a box may be computed also from that of the free particle using the method of images. We verify the propagators hereby obtained satisfy standard properties such as: consistency with initial conditions, composition and Green's function character. Furthermore they are also shown to reduce to the usual Schr\\"odinger propagators in the limit of small parameter $\\mu_0$, the length scale introduced in the polymer dynamics and which plays a role analog of that of Planck length in Quantum Gravity.

  1. Bohmian particle trajectories contradict quantum mechanics

    E-print Network

    Michael Zirpel

    2009-03-23

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

  2. Quantum Mechanics and Closed Timelike Curves

    E-print Network

    Florin Moldoveanu

    2007-04-23

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

  3. Quantum Mechanics and Closed Timelike Curves

    E-print Network

    Moldoveanu, Florin

    2007-01-01

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

  4. Quantum-mechanical Brayton engine working with a particle in a one-dimensional harmonic trap

    NASA Astrophysics Data System (ADS)

    Wang, H.

    2013-05-01

    Based on the quantum version of thermodynamic processes, a quantum-mechanical Brayton engine model has been established. Expressions for the power output and efficiency of the engine are derived. Some fundamental optimal relations and general performance characteristic curves of the cycle are obtained. Furthermore, we note that it is possible to resist the reduction in efficiency, caused by compression of the adiabatic process, by decreasing the amount of energy levels of the quantum system. The results obtained here will provide theoretical guidance for the design of some new quantum-mechanical engines.

  5. Algebraic quantum mechanics Algebraic quantum mechanics is an abstraction and generalization of the Hilbert space formulation

    E-print Network

    Landsman, N.P. "Klaas"

    (H), for some Hilbert space H. Another key example is A = C0(X), the space of all continuous complex- valuedAlgebraic quantum mechanics Algebraic quantum mechanics is an abstraction and generalization of the Hilbert space formulation of quantum mechanics due to von Neumann [5]. In fact, von Neumann himself played

  6. Electronic, mechanical, and thermodynamic properties of americium dioxide

    NASA Astrophysics Data System (ADS)

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

    2013-10-01

    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.

  7. A Bit of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Oss, Stefano; Rosi, Tommaso

    2015-04-01

    We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many reasons why quantum mechanical systems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called "common sense" based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.

  8. Bohmian Mechanics and the Quantum Revolution

    E-print Network

    Sheldon Goldstein

    1995-12-26

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

  9. Quantum mechanics without potential function

    NASA Astrophysics Data System (ADS)

    Alhaidari, A. D.; Ismail, M. E. H.

    2015-07-01

    In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schrödinger equation, which is solved for the wavefunction, bound states energy spectrum, and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which is written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states, and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and three-parameter systems.

  10. Quantum mechanics without potential function

    E-print Network

    A. D. Alhaidari; M. E. H. Ismail

    2015-06-26

    In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\\"odinger equation, which is solved for the wave function, bound states energy spectrum and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which is written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and there-parameter systems.

  11. Negative Observations in Quantum Mechanics

    E-print Network

    D. M. Snyder

    1999-12-06

    In quantum mechanics, it is possible to make observations that affect physical entities without there being a physical interaction between the observer and the physical entity measured. Epstein (1945) and Renninger (1960) discussed this situation, and Renninger called this type of observation a "negative observation." Empirical research on electron shelving supports the possibility of negative observations (Bergquist, Hulet, Itano, and Wineland, 1986; Nagourney, Sandberg, and Dehmelt, 1986; Sauter, Neuhauser, Blatt, and Toschek, 1986). Two scenarios are presented that emphasize the role of human observation in negative observations. The first is modeled after the two hole gedankenexperiments of Feynman, Leighton, and Sands (1965) and portrays negative observations in a non-technical manner. The second scenario allows for quantifying the affect on physical entities of negative observations in a simple fashion. In addition, various issues related to negative observation are discussed, including an objection that might be raised. The Schrodinger cat gedankenexperiment is discussed briefly as well.

  12. Kindergarten Quantum Mechanics: Lecture Notes

    SciTech Connect

    Coecke, Bob

    2006-01-04

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

  13. Pragmatic Information in Quantum Mechanics

    E-print Network

    Roederer, Juan G

    2015-01-01

    An objective definition of pragmatic information and the consideration of recent results about information processing in the human brain can help overcome some traditional difficulties with the interpretation of quantum mechanics. Rather than attempting to define information ab initio, I introduce the concept of interaction between material bodies as a primary concept. Two distinct categories can be identified: 1) Interactions which can always be reduced to a superposition of physical interactions (forces) between elementary constituents; 2) Interactions between complex bodies which cannot be reduced to a superposition of interactions between parts, and in which patterns and forms (in space and/or time) play the determining role. Pragmatic information is then defined as the correspondence between a given pattern and the ensuing pattern-specific change. I will show that pragmatic information is a biological concept that plays no active role in the purely physical domain; it only does so when a living organism ...

  14. Statistical mechanical studies on the information processing with quantum fluctuation

    NASA Astrophysics Data System (ADS)

    Otsubo, Yosuke; Inoue, Jun-Ichi; Nagata, Kenji; Okada, Masato

    2014-03-01

    Quantum fluctuation induces the tunneling between states in a system and then can be used in combinatorial optimization problems. Such an algorithm is called quantum adiabatic computing. In this work, we investigate the quality of an information processing based on Bayes inference with the quantum fluctuation through the statistical mechanical approach. We then focus on the error correcting codes and CDMA multiuser demodulation which are described by conventional solvable spin glass models and can be analyzed by replica method in the thermodynamic limit. Introducing the quantum fluctuation into the decoding process of each problem, which is called quantum maximizer of the posteriori probability (QMPM) estimate, we analyze the decoding quality and then compare the results with those by the conventional MPM estimate which corresponds to finite temperature decoding From our limited results, the MPM based on the quantum fluctuation seems to achieve the same decoding quality as the thermal MPM does. We clarify the relationship between the optimal amplitude of transverse field and temperature for the mixture of quantum and classical MPMs. This work is supported by JSPS KAKENHI Grant Numbers 12J06501, 25330283, 25120009.

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

    SciTech Connect

    Barnes, George L.; Kellman, Michael E.

    2013-12-07

    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.

  16. Testing non-associative quantum mechanics

    E-print Network

    Bojowald, Martin; Buyukcam, Umut

    2015-01-01

    The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to non-associative algebras. Their quantum physics has remained obscure. This letter presents the first derivation of potentially testable physical results in non-associative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.

  17. Testing non-associative quantum mechanics

    E-print Network

    Martin Bojowald; Suddhasattwa Brahma; Umut Buyukcam

    2015-10-26

    The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to non-associative algebras. Their quantum physics has remained obscure. This letter presents the first derivation of potentially testable physical results in non-associative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.

  18. 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

  19. 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

  20. Pseudospectra in non-Hermitian quantum mechanics

    NASA Astrophysics Data System (ADS)

    Krej?i?ík, D.; Siegl, P.; Tater, M.; Viola, J.

    2015-10-01

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

  1. Quantum Mechanics with a Little Less Mystery

    ERIC Educational Resources Information Center

    Cropper, William H.

    1969-01-01

    Suggests the "route of the inquiring mind in presenting the esoteric quantum mechanical postulates and concepts in an understandable form. Explains that the quantum mechanical postulates are but useful mathematical forms to express thebroader principles of superposition and correspondence. Briefly describes some of the features which makes the…

  2. Quaternionic Formulation of Supersymmetric Quantum Mechanics

    E-print Network

    Seema Rawat; O. P. S. Negi

    2007-03-18

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

  3. An analysis of quantum effects on the thermodynamic properties of cryogenic hydrogen using the path integral method

    SciTech Connect

    Nagashima, H.; Tsuda, S.; Tsuboi, N.; Koshi, M.; Hayashi, K. A.; Tokumasu, T.

    2014-04-07

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

  4. Random Matrix theory approach to Quantum mechanics

    E-print Network

    K. V. S. Shiv Chaitanya

    2015-01-27

    In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of random matrix theory. This study helps in identify the potential appear in the joint probability distribution function in the random matrix theory as a super potential. This approach allows to extend the random matrix theory to the newly discovered exceptional polynomials.

  5. Quantum mechanics in complex systems

    NASA Astrophysics Data System (ADS)

    Hoehn, Ross Douglas

    This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown. These nodes are spaced far enough from each other to minimized the electronic repulsion of the electrons, while still providing adequate enough attraction so as to bind the excess elections into orbitals. We have found that even with relativistic considerations these species are stably bound within the field. It was also found that performing the dimensional scaling calculations for systems within the confines of laser fields to be a much simpler and more cost-effective method than the supporting D=3 SCF method. The dimensional scaling method is general and can be extended to include relativistic corrections to describe the stability of simple molecular systems in super-intense laser fields. Chapter 3, we delineate the model, and aspects therein, of inelastic electron tunneling and map this model to the protein environment. G protein-coupled receptors (GPCRs) constitute a large family of receptors that sense molecules outside of a cell and activate signal transduction pathways inside the cell. Modeling how an agonist activates such a receptor is important for understanding a wide variety of physiological processes and it is of tremendous value for pharmacology and drug design. Inelastic electron tunneling spectroscopy (IETS) has been proposed as the mechanism by which olfactory GPCRs are activated by an encapsulated agonist. In this note we apply this notion to GPCRs within the mammalian nervous system using ab initio quantum chemical modeling. We found that non-endogenous agonists of the serotonin receptor share a singular IET spectral aspect both amongst each other and with the serotonin molecule: a peak that scales in intensity with the known agonist activities. We propose an experiential validation of this model by utilizing lysergic acid dimethylamide (DAM-57), an ergot derivative, and its isotopologues in which hydrogen atoms are replaced by deuterium. If validated our theory may provide new avenues for guided drug design and better in silico prediction of efficacies. Our final chapter, explores methods which may be explored to assist in the early instructio

  6. Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels

    E-print Network

    Suo, Zhigang

    Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels and Technology, Harvard University, Cambridge, MA 02138, USA a r t i c l e i n f o Article history: Received 12 a c t This paper uses the thermodynamic data of aqueous solutions of uncrosslinked poly- (N

  7. Mechanical and Industrial Engineering 230 Thermodynamics Course Syllabus

    E-print Network

    Rothstein, Jonathan

    /20/2009 Second Law of Thermodynamics Heat engines and refrigerators Carnot cycle Entropy Process efficiencies cycles Refrigeration and heat pump systems Final Exam (Date and time TBA) Suggested Reading Chapter 1

  8. Polymer Quantum Mechanics and its Continuum Limit

    E-print Network

    Alejandro Corichi; Tatjana Vukasinac; Jose A. Zapata

    2007-08-22

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

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

    E-print Network

    Aalok Pandya

    2008-09-08

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

  10. Limitations on the Evolution of Quantum Coherences: Towards Fully Quantum Second Laws of Thermodynamics.

    PubMed

    ?wikli?ski, Piotr; Studzi?ski, Micha?; Horodecki, Micha?; Oppenheim, Jonathan

    2015-11-20

    The second law of thermodynamics places a limitation into which states a system can evolve into. For systems in contact with a heat bath, it can be combined with the law of energy conservation, and it says that a system can only evolve into another if the free energy goes down. Recently, it's been shown that there are actually many second laws, and that it is only for large macroscopic systems that they all become equivalent to the ordinary one. These additional second laws also hold for quantum systems, and are, in fact, often more relevant in this regime. They place a restriction on how the probabilities of energy levels can evolve. Here, we consider additional restrictions on how the coherences between energy levels can evolve. Coherences can only go down, and we provide a set of restrictions which limit the extent to which they can be maintained. We find that coherences over energy levels must decay at rates that are suitably adapted to the transition rates between energy levels. We show that the limitations are matched in the case of a single qubit, in which case we obtain the full characterization of state-to-state transformations. For higher dimensions, we conjecture that more severe constraints exist. We also introduce a new class of thermodynamical operations which allow for greater manipulation of coherences and study its power with respect to a class of operations known as thermal operations. PMID:26636834

  11. Limitations on the Evolution of Quantum Coherences: Towards Fully Quantum Second Laws of Thermodynamics

    NASA Astrophysics Data System (ADS)

    ?wikli?ski, Piotr; Studzi?ski, Micha?; Horodecki, Micha?; Oppenheim, Jonathan

    2015-11-01

    The second law of thermodynamics places a limitation into which states a system can evolve into. For systems in contact with a heat bath, it can be combined with the law of energy conservation, and it says that a system can only evolve into another if the free energy goes down. Recently, it's been shown that there are actually many second laws, and that it is only for large macroscopic systems that they all become equivalent to the ordinary one. These additional second laws also hold for quantum systems, and are, in fact, often more relevant in this regime. They place a restriction on how the probabilities of energy levels can evolve. Here, we consider additional restrictions on how the coherences between energy levels can evolve. Coherences can only go down, and we provide a set of restrictions which limit the extent to which they can be maintained. We find that coherences over energy levels must decay at rates that are suitably adapted to the transition rates between energy levels. We show that the limitations are matched in the case of a single qubit, in which case we obtain the full characterization of state-to-state transformations. For higher dimensions, we conjecture that more severe constraints exist. We also introduce a new class of thermodynamical operations which allow for greater manipulation of coherences and study its power with respect to a class of operations known as thermal operations.

  12. Quantum Mechanics in Noncommutative space

    E-print Network

    Veronika Gáliková; Samuel Ková?ik; Peter Prešnajder

    2015-12-09

    This paper provides an examination of how are prediction of standard quantum mechanic (QM) affected by introducing a noncommutative (NC) structure into the configuration space of the considered system (electron in the Coulomb potential in the present case). The parameter controlling the extent of modification is denoted as {\\lambda}. The coordinates in the NC space are realized via creation and annihilation operators acting in an auxiliary Fock space, this one being chosen in such a way that the rotational invariance of the system remains intact also in NCQM. Analog of Schr\\"odinger equation for hydrogen atom is found and analytically solved, both for bound states and scattering. The exact formulas for NC corrections are given. None of the NC predictions contradicts experimentally verified QM results, since in the correspondence limit {\\lambda} -> 0 both QM and NCQM coincide. Highly surprising feature of the NC version is the existence of bound states for repulsive potential at ultra-high energies. However, these disappear from the Hilbert space in the mentioned limit. The whole problem is solved also using a method analogous to that of Pauli. Besides rotational invariance, the dynamical symmetry related to the conservation of NC analog of Laplace-Runge-Lenz vector is being used and the results obtained this way are in the full agreement with those given by "Schr\\"odinger-like" approach. The presented NC deformation of QM preserves all those mysterious properties of the Coulomb system that made it a distinguished key-stone of the modern physics.

  13. Quantum Mechanics in Noncommutative space

    E-print Network

    Veronika Gáliková; Samuel Ková?ik; Peter Prešnajder

    2015-10-15

    This paper provides an examination of how are prediction of standard quantum mechanic (QM) affected by introducing a noncommutative (NC) structure into the configuration space of the considered system (electron in the Coulomb potential in the present case). The parameter controlling the extent of modification is denoted as {\\lambda}. The coordinates in the NC space are realized via creation and annihilation operators acting in an auxiliary Fock space, this one being chosen in such a way that the rotational invariance of the system remains intact also in NCQM. Analog of Schr\\"odinger equation for hydrogen atom is found and analytically solved, both for bound states and scattering. The exact formulas for NC corrections are given. None of the NC predictions contradicts experimentally verified QM results, since in the correspondence limit {\\lambda} -> 0 both QM and NCQM coincide. Highly surprising feature of the NC version is the existence of bound states for repulsive potential at ultra-high energies. However, these disappear from the Hilbert space in the mentioned limit. The whole problem is solved also using a method analogous to that of Pauli. Besides rotational invariance, the dynamical symmetry related to the conservation of NC analog of Laplace-Runge-Lenz vector is being used and the results obtained this way are in the full agreement with those given by "Schr\\"odinger-like" approach. The presented NC deformation of QM preserves all those mysterious properties of the Coulomb system that made it a distinguished key-stone of the modern physics.

  14. Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology

    E-print Network

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

    1993-01-01

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

  15. Four-dimensional understanding of quantum mechanics

    E-print Network

    Jarek Duda

    2009-10-14

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

  16. Liquid Thermodynamics and Liquid Shear Turbulence Derived from Discontinuum Mechanics

    NASA Astrophysics Data System (ADS)

    Stout, Ray B.

    2002-03-01

    A liquid turbulence theory is formulated that is based on dense sets of inter-atomic discontinuities described by the motion and kinetics of dislocations. The derivation is a mechanistic, descriptive theory of liquid fluidity and thermodynamics at an atomic spacing length scale. In this formulation a liquid has a weak elasticity response, and a small value of a thermodynamic chemical potential for dislocation kinetics relative to a classical solid. The primary mechanistic explanation of turbulent initiation and turbulence in liquid shear flows is developed as a discontinuum momentum transport tensor and it is an explicit dislocation dependent functional. The classical ``Reynolds momentum stress" closure problem becomes a bogus concept. Also, the use of the dimensionless Reynolds Number as a demarcation index for turbulence initiation is replaced by a stochastic metric given by a dislocation thermodynamic chemical potential.

  17. Irreversibility and Measurement in Quantum Mechanics

    E-print Network

    D. M. Snyder

    2000-02-28

    Irreversibility is often considered to characterize measurements in quantum mechanics. Fundamental problems with this characterization are addressed. First, whether a measurement is made in quantum mechanics is an arbitrary decision on the part of the experimenter concerning how the experimental circumstances are structured. Second, how is irreversibility that occurs in making a measurement explained in terms of a neurophysiological mechanism where a macroscopic measuring instrument is not required in principle to make the measurement, as in macroscopic quantum tunneling? Third, how does irreversibility characterize a negative observation where there is no physical interaction in the measurement process?

  18. A Quantum Mechanical Travelling Salesman

    E-print Network

    Ravindra N. Rao

    2011-08-23

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

  19. Playing Games with Quantum Mechanics

    E-print Network

    Simon J. D. Phoenix; Faisal Shah Khan

    2012-02-22

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

  20. Strange Bedfellows: Quantum Mechanics and Data Mining

    SciTech Connect

    Weinstein, Marvin; /SLAC

    2009-12-16

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

  1. Strange Bedfellows: Quantum Mechanics and Data Mining

    E-print Network

    Marvin Weinstein

    2009-11-03

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

  2. Thermodynamics of the fully frustrated quantum Josephson-junction array: A hybrid Monte Carlo study

    SciTech Connect

    Mikalopas, J.; Jarrell, M.; Pinski, F.J.; Chung, W. ); Novotny, M.A. )

    1994-07-01

    We use a hybrid Monte Carlo algorithm to simulate the thermodynamic properties of a two-dimensional periodic array of fully frustrated quantum Josephson junctions. We find a variety of metastable configurations that correspond to spatial domain boundaries that are also present in classical arrays. In previous work, due to long temporal correlations between configurations in diffusive Monte Carlo algorithms, such metastable states were interpreted as evidence for a quantum-induced low-temperature first-order transition.

  3. Quantum mechanics and the generalized uncertainty principle

    SciTech Connect

    Bang, Jang Young; Berger, Micheal S.

    2006-12-15

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

  4. Quantum Mechanics and Multiply Connected Spaces

    E-print Network

    B. G. Sidharth

    2006-05-16

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

  5. Local quantum mechanics with finite Planck mass

    E-print Network

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

    2007-04-20

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

  6. Tensor Fields in Relativistic Quantum Mechanics

    E-print Network

    Valeriy V. Dvoeglazov

    2015-11-21

    We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We discuss corresponding massless limits. We analize the quantum field theory taking into account the mass dimensions of the notoph and the photon. Next, we deduced the gravitational field equations from relativistic quantum mechanics.

  7. Quantum Mechanics and the Generalized Uncertainty Principle

    E-print Network

    Jang Young Bang; Micheal S. Berger

    2006-11-30

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

  8. Tensor Fields in Relativistic Quantum Mechanics

    E-print Network

    Dvoeglazov, Valeriy V

    2015-01-01

    We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We discuss corresponding massless limits. We analize the quantum field theory taking into account the mass dimensions of the notoph and the photon. Next, we deduced the gravitational field equations from relativistic quantum mechanics.

  9. On the Birth of Quantum Mechanics.

    ERIC Educational Resources Information Center

    Singh, C. P.

    1991-01-01

    An event that created a revolution in physics, the birth of quantum mechanics, is discussed. The rich, complex, dramatic as well as touching story of fights and contradictions between two groups of great scientists is described. (Author)

  10. Quantum mechanical streamlines. I - Square potential barrier

    NASA Technical Reports Server (NTRS)

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

    1974-01-01

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

  11. Beyond Quantum Mechanics and General Relativity

    E-print Network

    Andrea Gregori

    2010-02-24

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

  12. Student Difficulties in Learning Quantum Mechanics.

    ERIC Educational Resources Information Center

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

    1998-01-01

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

  13. Quantum mechanical stabilization of Minkowski signature wormholes

    SciTech Connect

    Visser, M.

    1989-05-19

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

  14. Supersymmetric q-deformed quantum mechanics

    SciTech Connect

    Traikia, M. H.; Mebarki, N.

    2012-06-27

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

  15. Fundamental Quantum Mechanics--A Graphic Presentation

    ERIC Educational Resources Information Center

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

    1977-01-01

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

  16. Is quantum field theory a generalization of quantum mechanics?

    E-print Network

    A. V. Stoyanovsky

    2009-09-10

    We construct a mathematical model analogous to quantum field theory, but without the notion of vacuum and without measurable physical quantities. This model is a direct mathematical generalization of scattering theory in quantum mechanics to path integrals with multidimensional trajectories (whose mathematical interpretation has been given in a previous paper). In this model the normal ordering of operators in the Fock space is replaced by the Weyl-Moyal algebra. This model shows to be useful in proof of various results in quantum field theory: one first proves these results in the mathematical model and then "translates" them into the usual language of quantum field theory by more or less "ugly" procedures.

  17. 2T Physics and Quantum Mechanics

    E-print Network

    W. Chagas-Filho

    2008-02-20

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

  18. Quantum mechanics in de Sitter space

    E-print Network

    Subir Ghosh; Salvatore Mignemi

    2011-01-25

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

  19. Quantum mechanical effects on the shock Hugoniot

    SciTech Connect

    Bennett, B.I. ); Liberman, D.A. )

    1991-01-01

    Calculations of the locus of shock Hugoniot states of aluminum, using two equations of state that either omit or include a quantum mechanical treatment for the material's electronic excitations, will be presented. The difference between the loci will be analyzed in the context of a comparison between an ab initio quantum mechanical model and a semiclassical treatment of the electronic states. The theoretical results are compared with high pressure (4--300 Mbars) data. 5 refs., 2 figs.

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

    E-print Network

    Aalok Pandya

    2009-01-19

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

  1. 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

  2. On a New Form of Quantum Mechanics (II)

    E-print Network

    N. Gorobey; A. Lukyanenko; I. Lukyanenko

    2009-12-16

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

  3. Uniqueness results by covariance in covariant quantum mechanics

    E-print Network

    JanyÂ?ka, Josef

    Uniqueness results by covariance in covariant quantum mechanics Josef JanyŸska 1 , Marco Modugno 2 is the covariant quantum mechanics of a scalar quantum particle in a curved spacetime which is fibred over absolute beginning of quantum mechanics the quantum operators associated with classical quantisable functions

  4. Linear Logic for Generalized Quantum Mechanics Vaughan Pratt

    E-print Network

    Pratt, Vaughan

    Linear Logic for Generalized Quantum Mechanics Vaughan Pratt Dept. of Computer Science Stanford connection to quantum mechanics. 1 Motivation VLSI designers will eventually need to reckon with quantum with a deduction theorem or currying principle. Quantum logic as a faithful abstraction of quantum mechanics must

  5. Mechanical equivalent of quantum heat engines

    NASA Astrophysics Data System (ADS)

    Arnaud, Jacques; Chusseau, Laurent; Philippe, Fabrice

    2008-06-01

    Quantum heat engines employ as working agents multilevel systems instead of classical gases. We show that under some conditions quantum heat engines are equivalent to a series of reservoirs at different altitudes containing balls of various weights. A cycle consists of picking up at random a ball from one reservoir and carrying it to the next, thereby performing or absorbing some work. In particular, quantum heat engines, employing two-level atoms as working agents, are modeled by reservoirs containing balls of weight 0 or 1. The mechanical model helps us prove that the maximum efficiency of quantum heat engines is the Carnot efficiency. Heat pumps and negative temperatures are considered.

  6. Quantum Information Theory and the Foundations of Quantum Mechanics

    E-print Network

    Christopher Gordon Timpson

    2004-12-08

    This thesis is a contribution to the debate on the implications of quantum information theory for the foundations of quantum mechanics. In Part 1, the logical and conceptual status of various notions of information is assessed. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; however it is maintained that in both settings `information' functions as an abstract noun, hence does not refer to a particular or substance (the worth of this point is illustrated in application to quantum teleportation). The claim that `Information is Physical' is assessed and argued to face a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. The reflections of Bruckner and Zeilinger (2001) and Deutsch and Hayden (2000) on the nature of information in quantum mechanics are critically assessed and some results presented on the characterization of entanglement in the Deutsch-Hayden formalism. Some philosophical aspects of quantum computation are discussed and general morals drawn concerning the nature of quantum information theory. In Part II, following some preliminary remarks, two particular information-theoretic approaches to the foundations of quantum mechanics are assessed in detail. It is argued that Zeilinger's (1999) Foundational Principle is unsuccessful as a foundational principle for quantum mechanics. The information-theoretic characterization theorem of Clifton, Bub and Halvorson (2003) is assessed more favourably, but the generality of the approach is questioned and it is argued that the implications of the theorem for the traditional foundational problems in quantum mechanics remains obscure.

  7. The information entropy of quantum mechanical states

    E-print Network

    Alexander Stotland; Andrei A. Pomeransky; Eitan Bachmat; Doron Cohen

    2004-05-24

    It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the latter is problematic from quantum information point of view. Consequently we introduce a new definition of entropy that reflects the inherent uncertainty of quantum mechanical states. We derive for it an explicit expression, and discuss some of its general properties. We distinguish between the minimum uncertainty entropy of pure states, and the excess statistical entropy of mixtures.

  8. Interpretations of Quantum Mechanics: a critical survey

    E-print Network

    Michele Caponigro

    2008-11-24

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

  9. Testing foundations of quantum mechanics with photons

    E-print Network

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

    2015-01-15

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

  10. Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit

    E-print Network

    Bernardini, Alex E

    2013-01-01

    In this work we examine the effect of phase-space noncommutativity on some typically quantum properties such as quantum beating, quantum information, and decoherence. To exemplify these issues we consider the two-dimensional noncommutative quantum harmonic oscillator whose components behavior we monitor in time. This procedure allows to determine how the noncommutative parameters are related to the missing information quantified by the linear quantum entropy and by the mutual information between the relevant Hilbert space coordinates. Particular issues concerning the thermodynamic limit of some relevant properties are also discussed in order to evince the effects of noncommutativity. Finally, through an analogy with the Zeeman effect, we identify how some aspects of the axial symmetry of the problem suggest the possibility of decoupling the noncommutative quantum perturbations from unperturbed commutative well-known solutions.

  11. Macroscopic quantum mechanics in a classical spacetime.

    PubMed

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

    2013-04-26

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

  12. Relativistic mechanical–thermodynamical formalism—description of inelastic collisions

    NASA Astrophysics Data System (ADS)

    Güémez, J.; Fiolhais, M.; Fernández, L. A.

    2016-01-01

    We present a relativistic formalism inspired by the Minkowski four-vectors that also includes conservation laws such as the first law of thermodynamics. It remains close to the relativistic four-vector formalism developed for a single particle, but is also related to the classical treatment of problems that require both Newton's second law and the energy conservation law. We apply the developed formalism to inelastic collisions to better show how it works.

  13. Chaotic Evolution in Quantum Mechanics

    E-print Network

    Asher Peres

    1995-08-11

    A quantum system is described, whose wave function has a complexity which increases exponentially with time. Namely, for any fixed orthonormal basis, the number of components required for an accurate representation of the wave function increases exponentially.

  14. Quantum Field Theory for Mathematicians Hamiltonian Mechanics and Symplectic Geometry

    E-print Network

    Woit, Peter

    Quantum Field Theory for Mathematicians · Hamiltonian Mechanics and Symplectic Geometry Integral Quantization ­ Supersymmetric Quantum Mechanics ­ Introduction to Scattering Theory · Classical Field Theory · Relativistic Fields, Poincar´e Group and Wigner Classification · Free Quantum Fields

  15. Avoiding Negative Probabilities in Quantum Mechanics

    E-print Network

    Nyambuya, Golden Gadzirayi

    2013-01-01

    As currently understood since its discovery, the bare Klein-Gordon theory consists of negative quantum probabilities which are considered to be physically meaningless if not outright obsolete. Despite this annoying setback, these negative probabilities are what led the great Paul Dirac in 1928 to the esoteric discovery of the Dirac Equation. The Dirac Equation led to one of the greatest advances in our understanding of the physical world. In this reading, we ask the seemingly senseless question, "Do negative probabilities exist in quantum mechanics?" In an effort to answer this question, we arrive at the conclusion that depending on the choice one makes of the quantum probability current, one will obtain negative probabilities. We thus propose a new quantum probability current of the Klein-Gordon theory. This quantum probability current leads directly to positive definite quantum probabilities. Because these negative probabilities are in the bare Klein-Gordon theory, intrinsically a result of negative energie...

  16. Cryptographic Distinguishability Measures for Quantum Mechanical States

    E-print Network

    Christopher A. Fuchs; Jeroen van de Graaf

    1998-04-03

    This paper, mostly expository in nature, surveys four measures of distinguishability for quantum-mechanical states. This is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography. Each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions: namely, the probability of an identification error, the Kolmogorov distance, the Bhattacharyya coefficient, and the Shannon distinguishability (as defined through mutual information). These measures have a long history of use in statistical pattern recognition and classical cryptography. We obtain several inequalities that relate the quantum distinguishability measures to each other, one of which may be crucial for proving the security of quantum cryptographic key distribution. In another vein, these measures and their connecting inequalities are used to define a single notion of cryptographic exponential indistinguishability for two families of quantum states. This is a tool that may prove useful in the analysis of various quantum cryptographic protocols.

  17. Quantum mechanically enhanced performance of simple heat machines

    NASA Astrophysics Data System (ADS)

    Gelbwaser-Klimovsky, D.; Kurizki, G.

    2015-10-01

    We revisit the thermodynamic bounds of work extraction in simple quantum heat machines subject to control by frequent modulations that do not comply with adiabatic assumptions. The laws of thermodynamics are obeyed, yet anomalous deviations from the known bounds are revealed.

  18. The Möbius symmetry of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Faraggi, Alon E.; Matone, Marco

    2015-07-01

    The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under D-dimensional Mobius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global Mobius transformations implies that spatial space is compact. Furthermore, it implies energy quantisation and undefinability of quantum trajectories without assuming any prior interpretation of the wave function. The approach may be viewed as conventional quantum mechanics with the caveat that spatial space is compact, as dictated by the Möbius symmetry, with the classical limit corresponding to the decompactification limit. Correspondingly, there exists a finite length scale in the formalism and consequently an intrinsic regularisation scheme. Evidence for the compactness of space may exist in the cosmic microwave background radiation.

  19. The Möbius Symmetry of Quantum Mechanics

    E-print Network

    Alon E. Faraggi; Marco Matone

    2015-02-16

    The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under $D$--dimensional M\\"obius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global M\\"obius transformations implies that spatial space is compact. Furthermore, it implies energy quantisation and undefinability of quantum trajectories without assuming any prior interpretation of the wave function. The approach may be viewed as conventional quantum mechanics with the caveat that spatial space is compact, as dictated by the M\\"obius symmetry, with the classical limit corresponding to the decompactification limit. Correspondingly, there exists a finite length scale in the formalism and consequently an intrinsic regularisation scheme. Evidence for the compactness of space may exist in the cosmic microwave background radiation.

  20. Classical explanations of results of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Giese, Albrecht

    2015-09-01

    We present a particle model which was developed to explain special relativity by classical means. This model is also able to account for physical processes that are normally attributed to quantum mechanics. The model is able to describe several well-known QM processes by means of classical calculations, making them accessible to the imagination. An essential difference compared with the Standard Model of present-day particle physics is the fact that, in the model presented, particles are viewed as being extended rather than point-like. In addition, the strong force is shown to be the universal force operating in all particles. Also, the photon, which quantum mechanics views as being nothing but a quantum of energy, can be understood to have an internal structure. The model presented here is not merely a different way of explaining physics with similar results; in contrast to quantum mechanics, it has the ability to provide deeper insights into physical processes.

  1. e measure of all things: quantum mechanics and the soul

    E-print Network

    Halvorson, Hans

    e measure of all things: quantum mechanics and the soul Hans Halvorson Introduction e twentieth and our place in the universe). e introduction of quantum mechanics may be the greatest scienti c around quantum mechanics. For example, some claim that quantum mechanics proves that the universe

  2. Quantum Mechanics Summary/Review Spring 2009 Compton Lecture Series

    E-print Network

    Quantum Mechanics Summary/Review Spring 2009 Compton Lecture Series: From Quantum Mechanics one component at a time. · Planck's constant determines the scale at which quantum mechanical effects could get rid of quantum mechanical effects ­ The "wavelength" of particles given by h mv would all

  3. Chem 7940 Quantum Mechanics II Spring 2013 Chemistry 7940

    E-print Network

    Chem 7940 Quantum Mechanics II Spring 2013 Chemistry 7940 Quantum Mechanics II Spring 2013. (Confucius) We shall refer to a variety of sources. You should have a standard quantum mechanics text investigation of foundational issues in quantum mechanics. See also the article by Zeilinger [31

  4. Chem 7940 Quantum Mechanics II Spring 2013 Chemistry 7940

    E-print Network

    Chem 7940 Quantum Mechanics II Spring 2013 Chemistry 7940 Quantum Mechanics II Spring 2013 Course with classical mechanics. · Relaxation and decoherence. · Generalized measurements, quantum information theory of the path integral. · Path integral formulation of quantum statistical mechanics: polymer beads, and all

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

    E-print Network

    Hiromi Kaneko; Akihiro Tohsaki; Atsushi Hosaka

    2012-06-29

    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.

  6. Effects of quantum gravity on the inflationary parameters and thermodynamics of the early universe

    E-print Network

    A. Tawfik; H. Magdy; A. Farag Ali

    2013-03-23

    The effects of generalized uncertainty principle (GUP) on the inflationary dynamics and the thermodynamics of the early universe are studied. Using the GUP approach, the tensorial and scalar density fluctuations in the inflation era are evaluated and compared with the standard case. We find a good agreement with the Wilkinson Microwave Anisotropy Probe data. Assuming that a quantum gas of scalar particles is confined within a thin layer near the apparent horizon of the Friedmann-Lemaitre-Robertson-Walker universe which satisfies the boundary condition, the number and entropy densities and the free energy arising form the quantum states are calculated using the GUP approach. A qualitative estimation for effects of the quantum gravity on all these thermodynamic quantities is introduced.

  7. Quantum Mechanics and the Principle of Least Radix Economy

    NASA Astrophysics Data System (ADS)

    Garcia-Morales, Vladimir

    2015-03-01

    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 Schrödinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new (pre-geometrical) foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann's principle of classical statistical thermodynamics. A new expression for a general (path-dependent) nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics.

  8. Quantum mechanics: last stop for reductionism

    E-print Network

    Gabriele Carcassi

    2012-03-16

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

  9. PHYSICAL REVIEW B 85, 224106 (2012) Thermodynamics of coherent interfaces under mechanical stresses. I. Theory

    E-print Network

    Mishin, Yuri

    2012-01-01

    PHYSICAL REVIEW B 85, 224106 (2012) Thermodynamics of coherent interfaces under mechanical stresses. I. Theory T. Frolov* and Y. Mishin Department of Physics and Astronomy, MSN 3F3, George Mason to nonhydrostatic mechanical stresses. The interstitial and substitutional chemical components are treated

  10. 7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics

    E-print Network

    Abdou, Mohamed

    i #12;ExHFT-7 7th World Conference on Experimental Heat Transfer, Fluid Mechanics Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 28 June ­ 03 July 2009, Krakow FOR HUMANITY M. A. Abdou Center for Energy Science and Technology Advanced Research (CESTAR), Los Angeles, USA

  11. Quantum mechanics as applied mathematical statistics

    SciTech Connect

    Skala, L.; Cizek, J.; Kapsa, V.

    2011-05-15

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

  12. Bibliographic guide to the foundations of quantum mechanics and quantum information

    E-print Network

    Adan Cabello

    2004-11-15

    This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, web sites, etc.), sorted alphabetically and (some of them) classified by subject, on foundations of quantum mechanics and quantum information. Specifically, it covers hidden variables (``no-go'' theorems, experiments), interpretations of quantum mechanics, entanglement, quantum effects (quantum Zeno effect, quantum erasure, ``interaction-free'' measurements, quantum ``non-demolition'' measurements), quantum information (cryptography, cloning, dense coding, teleportation), and quantum computation.

  13. A quantum model for bending vibrations and thermodynamic properties of C3.

    NASA Technical Reports Server (NTRS)

    Hansen, C. F.; Pearson, W. E.

    1973-01-01

    The investigation reported was conducted to clarify the thermodynamic properties of C3 by further developing the limit to the partition function suggested by Strauss and Thiele (1967). A quantum solution for the energy levels of a quadratically perturbed square well potential is presented and the consistency of this limit with observed energy levels is established. In the process a more complete physical picture of the bending C3 molecules emerges. The values of entropy deduced from various measurements of graphite pressure are compared with this limit, and the thermodynamic properties predicted for the limiting case are evaluated.

  14. Information and entropy in quantum Brownian motion: Thermodynamic entropy versus von Neumann entropy

    E-print Network

    Christian Hoerhammer; Helmut Buettner

    2007-11-14

    We compare the thermodynamic entropy of a quantum Brownian oscillator derived from the partition function of the subsystem with the von Neumann entropy of its reduced density matrix. At low temperatures we find deviations between these two entropies which are due to the fact that the Brownian particle and its environment are entangled. We give an explanation for these findings and point out that these deviations become important in cases where statements about the information capacity of the subsystem are associated with thermodynamic properties, as it is the case for the Landauer principle.

  15. Quantum Mechanics, Spacetime Locality, and Gravity

    NASA Astrophysics Data System (ADS)

    Nomura, Yasunori

    2013-08-01

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

  16. How to teach Quantum Mechanics

    E-print Network

    Oliver Passon

    2004-04-22

    In the spirit and style of John S. Bell's well known paper on How to Teach Special Relativity it is argued, that a ``Bohmian pedagogy''provides a very useful tool to illustrate the relation between classical and quantum physics and illuminates the peculiar features of the latter.

  17. Quantum mechanism of Biological Search

    E-print Network

    Younghun Kwon

    2006-05-09

    We wish to suggest an algorithm for biological search including DNA search. Our argument supposes that biological search be performed by quantum search.If we assume this, we can naturally answer the following long lasting puzzles such that "Why does DNA use the helix structure?" and "How can the evolution in biological system occur?".

  18. A "Bit" of Quantum Mechanics

    ERIC Educational Resources Information Center

    Oss, Stefano; Rosi, Tommaso

    2015-01-01

    We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many…

  19. Integrating Computational Chemistry into a Course in Classical Thermodynamics

    ERIC Educational Resources Information Center

    Martini, Sheridan R.; Hartzell, Cynthia J.

    2015-01-01

    Computational chemistry is commonly addressed in the quantum mechanics course of undergraduate physical chemistry curricula. Since quantum mechanics traditionally follows the thermodynamics course, there is a lack of curricula relating computational chemistry to thermodynamics. A method integrating molecular modeling software into a semester long…

  20. Canonical Relational Quantum Mechanics from Information Theory

    E-print Network

    Joakim Munkhammar

    2011-01-07

    In this paper we construct a theory of quantum mechanics based on Shannon information theory. We define a few principles regarding information-based frames of reference, including explicitly the concept of information covariance, and show how an ensemble of all possible physical states can be setup on the basis of the accessible information in the local frame of reference. In the next step the Bayesian principle of maximum entropy is utilized in order to constrain the dynamics. We then show, with the aid of Lisi's universal action reservoir approach, that the dynamics is equivalent to that of quantum mechanics. Thereby we show that quantum mechanics emerges when classical physics is subject to incomplete information. We also show that the proposed theory is relational and that it in fact is a path integral version of Rovelli's relational quantum mechanics. Furthermore we give a discussion on the relation between the proposed theory and quantum mechanics, in particular the role of observation and correspondence to classical physics is addressed. In addition to this we derive a general form of entropy associated with the information covariance of the local reference frame. Finally we give a discussion and some open problems.

  1. Geometry of Quantum Observables and Thermodynamics of Small Systems

    NASA Astrophysics Data System (ADS)

    Olshanii, Maxim

    2015-02-01

    We show that for classical and quantum observables, the integrability-to-ergodicity transition leaves constant the sum of (a) the ensemble variance of the temporal average and (b) the ensemble average of temporal variance. The induced Frobenius (Hilbert-Schmidt) geometry of quantum observables encodes how eigenstate thermalization appears, the inverse participation ratio decreases, and the integrals of motion disappear during the transition. We use it to optimize the set of conserved quantities entering the generalized Gibbs ensemble for integrable, near-integrable, or mesoscopic systems.

  2. Efficiency at Maximum Power Output of a Quantum-Mechanical Brayton Cycle

    NASA Astrophysics Data System (ADS)

    Yuan, Yuan; He, Ji-Zhou; Gao, Yong; Wang, Jian-Hui

    2014-03-01

    The performance in finite time of a quantum-mechanical Brayton engine cycle is discussed, without introduction of temperature. The engine model consists of two quantum isoenergetic and two quantum isobaric processes, and works with a single particle in a harmonic trap. Directly employing the finite-time thermodynamics, the efficiency at maximum power output is determined. Extending the harmonic trap to a power-law trap, we find that the efficiency at maximum power is independent of any parameter involved in the model, but depends on the confinement of the trapping potential.

  3. Standard Quantum Limit for Probing Mechanical Energy Quantization

    E-print Network

    Corbitt, Thomas R.

    We derive a standard quantum limit for probing mechanical energy quantization in a class of systems with mechanical modes parametrically coupled to external degrees of freedom. To resolve a single mechanical quantum, it ...

  4. Coherent states in noncommutative quantum mechanics

    SciTech Connect

    Ben Geloun, J.; Scholtz, F. G.

    2009-04-15

    Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position uncertainty relation, obey a Poisson distribution, and possess a flat geometry. Using the natural isometry between the quantum Hilbert space of Hilbert-Schmidt operators and the tensor product of the classical configuration space and its dual, we reveal the inherent vector feature of these states.

  5. Epistemology of quantum mechanics: the Växjö viewpoint

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei

    2011-09-01

    This paper summarizes the experience of the Växjö series of conferences - the longest series of conferences on foundations of quantum mechanics. One of the main lessons of this series is that the present state of development of quantum theory does not exclude a possibility to elaborate a local realistic interpretation. One of such interpretations, the Växjö interpretation, combines realism and contextuality. And it became recognized worldwide.

  6. Failure of Standard Quantum Mechanics for the Description of Compound Quantum Entities

    E-print Network

    Aerts, Diederik

    Failure of Standard Quantum Mechanics for the Description of Compound Quantum Entities Diederik that proves that two separated quantum entities cannot be described by means of standard quantum mechanics of this result indicates a failure of standard quantum mechanics, and not just some peculiar shortcoming due

  7. The Linearity of Quantum Mechanics at Stake: The Description of Separated Quantum Entities

    E-print Network

    Aerts, Diederik

    The Linearity of Quantum Mechanics at Stake: The Description of Separated Quantum Entities Diederik entity cannot be described by standard quantum mechanics. More precisely, it was shown that two with the superposition principle, which means that sep- arated quantum entities put the linearity of quantum mechanics

  8. Philosophy of Quantum Mechanics Quantum theory is arguably the most accurate scientific theory ever

    E-print Network

    Callender, Craig

    1 PHIL 245: Philosophy of Quantum Mechanics Quantum theory is arguably the most accurate scientific: yes, but youll have to learn some simple quantum mechanics. A good test is whether youre able to get through the chapter on the quantum formalism in #12;2 Alberts Quantum Mechanics and Experience. Well go

  9. On Time. 6b: Quantum Mechanical Time

    E-print Network

    C. K. Raju

    2008-08-09

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

  10. Optimal guidance law in quantum mechanics

    SciTech Connect

    Yang, Ciann-Dong Cheng, Lieh-Lieh

    2013-11-15

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

  11. Local thermodynamical equilibrium and the beta frame for a quantum relativistic fluid

    E-print Network

    F. Becattini; L. Bucciantini; E. Grossi; L. Tinti

    2015-04-28

    We discuss the concept of local thermodynamical equilibrium in relativistic hydrodynamics in flat spacetime in a quantum statistical framework without an underlying kinetic description, suitable for strongly interacting fluids. We show that the appropriate definition of local equilibrium naturally leads to the introduction of a relativistic hydrodynamical frame in which the four-velocity vector is the one of a relativistic thermometer at equilibrium with the fluid, parallel to the inverse temperature four-vector \\beta, which then becomes a primary quantity. We show that this frame is the most appropriate for the expansion of stress-energy tensor from local thermodynamical equilibrium and that therein the local laws of thermodynamics take on their simplest form. We discuss the difference between the \\beta frame and Landau frame and present an instance where they differ.

  12. Realism and Objectivism in Quantum Mechanics

    E-print Network

    Vassilios Karakostas

    2012-03-01

    The present study attempts to provide a consistent and coherent account of what the world could be like, given the conceptual framework and results of contemporary quantum theory. It is suggested that standard quantum mechanics can, and indeed should, be understood as a realist theory within its domain of application. It is pointed out, however, that a viable realist interpretation of quantum theory requires the abandonment or radical revision of the classical conception of physical reality and its traditional philosophical presuppositions. It is argued, in this direction, that the conceptualization of the nature of reality, as arising out of our most basic physical theory, calls for a kind of contextual realism. Within the domain of quantum mechanics, knowledge of 'reality in itself', 'the real such as it truly is' independent of the way it is contextualized, is impossible in principle. In this connection, the meaning of objectivity in quantum mechanics is analyzed, whilst the important question concerning the nature of quantum objects is explored.

  13. Presenting Nonreflexive Quantum Mechanics: Formalism and Metaphysics

    E-print Network

    Krause, Decio

    2015-01-01

    Nonreflexive quantum mechanics is a formulation of quantum theory based on a non-classical logic termed \\ita{nonreflexive logic} (a.k.a. `non-reflexive'). In these logics, the standard notion of identity, as encapsulated in classical logic and set theories, does not hold in full. The basic aim of this kind of approach to quantum mechanics is to take seriously the claim made by some authors according to whom quantum particles are \\ita{non-individuals} in some sense, and also to take into account the fact that they may be absolutely indistinguishable (or indiscernible). The nonreflexive formulation of quantum theory assumes these features of the objects already at the level of the underlying logic, so that no use is required of symmetrization postulates or other mathematical devices that serve to pretend that the objects are indiscernible (when they are not: all objects that obey classical logic are \\ita{individuals} in a sense). Here, we present the ideas of the development of nonreflexive quantum mechanics an...

  14. 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 mechanics 1 This paper, to be presented to the Nordic Symposium on Basic Problems in Quantum Physics, June

  15. Green's Functions and Their Applications to Quantum Mechanics

    E-print Network

    Morrow, James A.

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

  16. Multichannel framework for singular quantum mechanics

    SciTech Connect

    Camblong, Horacio E.; Epele, Luis N.; Fanchiotti, Huner; García Canal, Carlos A.; Ordóñez, Carlos R.

    2014-01-15

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

  17. Quantum mechanics and consciousness: fact and fiction

    E-print Network

    Ulrich Mohrhoff

    2014-08-03

    This article was written in response to a request from an editor of American Vedantist. It is shown that the idea that consciousness is essential to understanding quantum mechanics arises from logical fallacies. This may be welcome news to those who share the author's annoyance at consciousness being dragged into discussions of physics, but beware: The same fallacies may underlie the reader's own way of making sense of quantum mechanics. The article ends up embracing a Vedantic world view, for two reasons. For one, such a world view seems to the author to be the most sensible alternative to a materialistic one. For another, quantum mechanics is inconsistent with a materialistic world view but makes perfect sense within a Vedantic framework of thought.

  18. The Central Mystery of Quantum Mechanics

    E-print Network

    Partha Ghose

    2009-06-04

    A critical re-examination of the double-slit experiment and its variants is presented to clarify the nature of what Feynmann called the ``central mystery'' and the ``only mystery'' of quantum mechanics, leading to an interpretation of complementarity in which a `wave {\\em and} particle' description rather than a `wave {\\em or} particle' description is valid for the {\\em same} experimental set up, with the wave culminating in the particle sequentially in time. This interpretation is different from Bohr's but is consistent with the von Neumann formulation as well as some more recent interpretations of quantum mechanics.

  19. Two basic Uncertainty Relations in Quantum Mechanics

    SciTech Connect

    Angelow, Andrey

    2011-04-07

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

  20. Quantum mechanics is a relativity theory

    E-print Network

    Léon Brenig

    2006-08-02

    Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the Heisenberg inequalities invariant and form a group. They are related to dilatations of space variables provided the quantum potential is added to the classical Hamiltonian functional. The Schr\\"odinger equation appears to have a nonunitary and nonlinear companion acting in another time variable. Evolution in this time seems related to the state vector reduction.

  1. Mossbauer neutrinos in quantum mechanics and quantum field theory

    E-print Network

    Joachim Kopp

    2009-06-12

    We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence, and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detection cross section, including localization and Lamb-Mossbauer terms, cannot be predicted in quantum mechanics and have to be put in by hand.

  2. Space and time from quantum mechanics

    NASA Astrophysics Data System (ADS)

    Chew, G. F.

    1992-09-01

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

  3. Space and time from quantum mechanics

    SciTech Connect

    Chew, G.F.

    1992-09-16

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

  4. Quantum and classical areas of black hole thermodynamics

    NASA Astrophysics Data System (ADS)

    Ghosh, A.; Mitra, P.

    2015-08-01

    Most calculations of black hole entropy in loop quantum gravity indicate a term proportional to the area eigenvalue A with a correction involving the logarithm of A. This violates the additivity of the entropy. An entropy proportional to A, with a correction term involving the logarithm of the classical area k, which is consistent with the additivity of entropy, is derived in both U(1) and SU(2) formulations.

  5. Scattering Relativity in Quantum Mechanics

    E-print Network

    Richard Shurtleff

    2015-07-06

    By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the particle field translated along one displacement, particle states are translated along a possibly different displacement. Arbitrary phase results. And particle momentum, a spin (1/2,1/2) quantity, is allowed to change when field and states are translated. It is shown that a path of extreme phase obeys a semiclassical equation for force with derived terms that can describe electromagnetism and gravitation.

  6. Thermodynamics of trajectories and local fluctuation theorems for harmonic quantum networks

    E-print Network

    Simon Pigeon; Lorenzo Fusco; André Xuereb; Gabriele De Chiara; Mauro Paternostro

    2015-10-07

    We present a general method to undertake a thorough analysis of the thermodynamics of the quantum jump trajectories followed by an arbitrary quantum harmonic network undergoing linear and bilinear dynamics. The approach is based on the phase-space representation of the state of a harmonic network. The large deviation function associated with this system encodes the full counting statistics of exchange and also allows one to deduce for fluctuation theorems obeyed by the dynamics. We illustrate the method showing the validity of a local fluctuation theorem about the exchange of excitations between a restricted part of the environment (i.e., a local bath) and a harmonic network coupled with different schemes.

  7. Quantum mechanical studies of carbon structures

    SciTech Connect

    Bartelt, Norman Charles; Ward, Donald; Zhou, Xiaowang; Foster, Michael E.; Schultz, Peter A.; Wang, Bryan M.; McCarty, Kevin F.

    2015-10-01

    Carbon nanostructures, such as nanotubes and graphene, are of considerable interest due to their unique mechanical and electrical properties. The materials exhibit extremely high strength and conductivity when defects created during synthesis are minimized. Atomistic modeling is one technique for high resolution studies of defect formation and mitigation. To enable simulations of the mechanical behavior and growth mechanisms of C nanostructures, a high- fidelity analytical bond-order potential for the C is needed. To generate inputs for developing such a potential, we performed quantum mechanical calculations of various C structures.

  8. Horizon Quantum Mechanics: a hitchhiker's guide to quantum black holes

    E-print Network

    R. Casadio; A. Giugno; O. Micu

    2015-12-13

    It is congruous with the quantum nature of the world to view the space-time geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the space-time manifold as a purely theoretical arena, where quantum states are defined, with the additional freedom of changing coordinates like any other symmetry. Observables, including positions and distances, should then be described by suitable operators acting on such quantum states. In principle, the top-down (canonical) quantisation of Einstein-Hilbert gravity falls right into this picture, but is notoriously very involved. The complication stems from allowing all the classical canonical variables that appear in the (presumably) fundamental action to become quantum observables acting on the "superspace" of all metrics, regardless of whether they play any role in the description of a specific physical system. On can instead revisit the more humble "minisuperspace" approach and choose the gravitational observables not simply by imposing some symmetry, but motivated by their proven relevance in the (classical) description of a given system. In particular, this review focuses on compact, spherically symmetric, quantum mechanical sources, in order to determine the probability they are black holes rather than regular particles. The gravitational radius is therefore lifted to the status of a quantum mechanical operator acting on the "horizon wave-function", the latter being determined by the quantum state of the source. This formalism is then applied to several sources with a mass around the fundamental scale, which are viewed as natural candidates of quantum black holes.

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

    PubMed

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

    2014-06-01

    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

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

    NASA Technical Reports Server (NTRS)

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

    1981-01-01

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

  11. A new introductory quantum mechanics curriculum

    NASA Astrophysics Data System (ADS)

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

    2014-01-01

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

  12. Macroscopic Quantum Mechanics in a Classical Spacetime

    E-print Network

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

    2013-04-23

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

  13. Can quantum mechanics fool the cosmic censor?

    NASA Astrophysics Data System (ADS)

    Matsas, G. E. A.; Richartz, M.; Saa, A.; da Silva, A. R. R.; Vanzella, D. A. T.

    2009-05-01

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

  14. Quantum statistical mechanics, L-series, Anabelian Geometry

    E-print Network

    Marcolli, Matilde

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

  15. Mechanism of the quantum speed-up

    E-print Network

    Giuseppe Castagnoli

    2011-05-23

    We explain the mechanism of the quantum speed-up - quantum algorithms requiring fewer computation steps than their classical equivalent - for a family of algorithms. Bob chooses a function and gives to Alice the black box that computes it. Alice, without knowing Bob's choice, should find a character of the function (e. g. its period) by computing its value for different arguments. There is naturally correlation between Bob's choice and the solution found by Alice. We show that, in quantum algorithms, this correlation becomes quantum. This highlights an overlooked measurement problem: sharing between two measurements the determination of correlated (thus redundant) measurement outcomes. Solving this problem explains the speed-up. All is like Alice, by reading the solution at the end of the algorithm, contributed to the initial choice of Bob, for half of it in quantum superposition for all the possible ways of taking this half. This contribution, back evolved to before running the algorithm, where Bob's choice is located, becomes Alice knowing in advance half of this choice. The quantum algorithm is the quantum superposition of all the possible ways of taking half of Bob's choice and, given the advanced knowledge of it, classically computing the missing half. This yields a speed-up with respect to the classical case where, initially, Bob's choice is completely unknown to Alice.

  16. Quantum mechanics and the time travel paradox

    E-print Network

    Pegg, D T

    2005-01-01

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

  17. Quantum mechanics and the time travel paradox

    E-print Network

    David T. Pegg

    2005-06-17

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

  18. CPT and Quantum Mechanics Tests with Kaons

    E-print Network

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

    2006-07-28

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

  19. A Euclidean formulation of relativistic quantum mechanics

    E-print Network

    Philip Kopp; Wayne Polyzou

    2011-06-21

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

  20. Differentiable-path integrals in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Koch, Benjamin; Reyes, Ignacio

    2015-06-01

    A method is presented which restricts the space of paths entering the path integral of quantum mechanics to subspaces of C?, by only allowing paths which possess at least ? derivatives. The method introduces two external parameters, and induces the appearance of a particular time scale ?D such that for time intervals longer than ?D the model behaves as usual quantum mechanics. However, for time scales smaller than ?D, modifications to standard formulation of quantum theory occur. This restriction renders convergent some quantities which are usually divergent in the time-continuum limit ? ? 0. We illustrate the model by computing several meaningful physical quantities such as the mean square velocity , the canonical commutator, the Schrödinger equation and the energy levels of the harmonic oscillator. It is shown that an adequate choice of the parameters introduced makes the evolution unitary.

  1. Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics

    NASA Astrophysics Data System (ADS)

    Grössing, Gerhard

    2015-10-01

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

  2. Quantum mechanics of time travel through post-selected teleportation

    E-print Network

    Maccone, Lorenzo

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

  3. The geometric semantics of algebraic quantum mechanics

    E-print Network

    John Alex Cruz Morales; Boris Zilber

    2014-10-27

    In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.

  4. Quantum mechanics of the damped harmonic oscillator

    E-print Network

    Blasone, Massimo

    645 Quantum mechanics of the damped harmonic oscillator Massimo Blasone and Petr Jizba Abstract: We quantize the system of a damped harmonic oscillator coupled to its time- reversed image, known as Bateman of the simplest dissipative system -- the damped harmonic oscillator (DHO) -- is not an easy task [1], and indeed

  5. quantum mechanics position and momentum Pigment Molecules

    E-print Network

    quantum mechanics position and momentum Pigment Molecules A typical pigment molecule has a photon of wavelength at the pigment molecule. What is the largest value of such that the photon can be absorbed by an electron in the pigment molecule? When the photon is absorbed, the electron must be able

  6. Comparison of Classical and Quantum Mechanical Uncertainties.

    ERIC Educational Resources Information Center

    Peslak, John, Jr.

    1979-01-01

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

  7. Quantum Mechanics Studies of Cellobiose Conformations

    Technology Transfer Automated Retrieval System (TEKTRAN)

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

  8. The inside observer in quantum mechanics

    SciTech Connect

    Mould, R.

    1995-11-01

    The {open_quotes}observer{close_quotes} in physics has always referred to someone who stands on the outside of a system looking in. In this paper an {open_quotes}inside observer{close_quotes} is defined, and an experiment is proposed that tests a given formulation of the problem of measurement in quantum mechanics.

  9. Quantum Mechanical Effects in Gravitational Collapse

    E-print Network

    Eric Greenwood

    2010-01-12

    In this thesis we investigate quantum mechanical effects to various aspects of gravitational collapse. These quantum mechanical effects are implemented in the context of the Functional Schr\\"odinger formalism. The Functional Schr\\"odinger formalism allows us to investigate the time-dependent evolutions of the quantum mechanical effects, which is beyond the scope of the usual methods used to investigate the quantum mechanical corrections of gravitational collapse. Utilizing the time-dependent nature of the Functional Schr\\"odinger formalism, we study the quantization of a spherically symmetric domain wall from the view point of an asymptotic and infalling observer, in the absence of radiation. To build a more realistic picture, we then study the time-dependent nature of the induced radiation during the collapse using a semi-classical approach. Using the domain wall and the induced radiation, we then study the time-dependent evolution of the entropy of the domain wall. Finally we make some remarks about the possible inclusion of backreaction into the system.

  10. Is Quantum Mechanics needed to explain consciousness ?

    E-print Network

    Knud Thomsen

    2007-11-13

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

  11. Conventions in relativity theory and quantum mechanics

    E-print Network

    Karl Svozil

    2001-10-09

    The conventionalistic aspects of physical world perception are reviewed with an emphasis on the constancy of the speed of light in relativity theory and the irreversibility of measurements in quantum mechanics. An appendix contains a complete proof of Alexandrov's theorem using mainly methods of affine geometry.

  12. The geometric semantics of algebraic quantum mechanics.

    PubMed

    Cruz Morales, John Alexander; Zilber, Boris

    2015-08-01

    In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. PMID:26124252

  13. Molecular Mechanisms, Thermodynamics, and Dissociation Kinetics of Knob-Hole Interactions in Fibrin*S

    E-print Network

    Barsegov, Valeri

    Molecular Mechanisms, Thermodynamics, and Dissociation Kinetics of Knob-Hole Interactions in Fibrin*S-hole interactions underlie formation and properties of fibrin polymer, the scaffold of blood clots and thrombi into fibrin polymerization. Polymerization of fibrin, the primary structural protein of blood clots

  14. Black hole thermodynamics

    NASA Astrophysics Data System (ADS)

    Carlip, S.

    2014-10-01

    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.

  15. Spin Glass: A Bridge between quantum computation and statistical mechanics

    E-print Network

    Masayuki Ohzeki

    2012-04-24

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

  16. Applications of density matrix in the fractional quantum mechanics

    E-print Network

    Jianping Dong

    2010-12-22

    The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, and obtain the quantum pressure of the free electron gas. We also show the validity of the Hohenberg-Kohn theory in the space fractional quantum mechanics and generalize the density functional theory to the fractional quantum mechanics.

  17. The Compton effect: Transition to quantum mechanics

    NASA Astrophysics Data System (ADS)

    Stuewer, R. H.

    2000-11-01

    The discovery of the Compton effect at the end of 1922 was a decisive event in the transition to the new quantum mechanics of 1925-1926 because it stimulated physicists to examine anew the fundamental problem of the interaction between radiation and matter. I first discuss Albert Einstein's light-quantum hypothesis of 1905 and why physicists greeted it with extreme skepticism, despite Robert A. Millikan's confirmation of Einstein's equation of the photoelectric effect in 1915. I then follow in some detail the experimental and theoretical research program that Arthur Holly Compton pursued between 1916 and 1922 at the University of Minnesota, the Westinghouse Lamp Company, the Cavendish Laboratory, and Washington University that culminated in his discovery of the Compton effect. Surprisingly, Compton was not influenced directly by Einstein's light-quantum hypothesis, in contrast to Peter Debye and H.A. Kramers, who discovered the quantum theory of scattering independently. I close by discussing the most significant response to that discovery, the Bohr-Kramers-Slater theory of 1924, its experimental refutation, and its influence on the emerging new quantum mechanics.

  18. Time and the foundations of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Pashby, Thomas

    Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain kinds of `time observables' to find a representation within quantum theory, including clock operators (which provide the means to measure the passage of time) and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on re ection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantum mechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack.

  19. Comparison of Quantum Mechanics and Molecular Mechanics Dimerization Energy Landscapes for Pairs of Ring-Containing Amino Acids in Proteins

    E-print Network

    Morozov, Alexandre V.

    Comparison of Quantum Mechanics and Molecular Mechanics Dimerization Energy Landscapes for Pairs, quantum mechanical calculations on small molecule models, and molecular mechanics potential decomposition find reasonable qualitative agreement between molecular mechanics and quantum chemistry calculations

  20. Quantum statistical mechanics, L-series, Anabelian Geometry

    E-print Network

    Marcolli, Matilde

    Quantum statistical mechanics, L-series, Anabelian Geometry Matilde Marcolli Colloquium, Harvard University, March 24, 2011 Matilde Marcolli Quantum statistical mechanics, L-series, Anabelian Geometry #12;joint work with Gunther Cornelissen General philosophy: Zeta functions are counting devices: spectra

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

    E-print Network

    Koch, Christof

    1 The relation between quantum mechanics and higher brain functions: Lessons from quantum should be addressed. Email koch@klab.caltech.edu The relationship between quantum mechanics and higher-founded understanding of these issues is desirable. The role of quantum mechanics for the photons received by the eye

  2. Probability and Quantum Symmetries. II. The Theorem of Noether in quantum mechanics

    E-print Network

    Zambrini, Jean-Claude

    Probability and Quantum Symmetries. II. The Theorem of Noether in quantum mechanics S. Albeverio, a new rigorous, but not probabilistic, Lagrangian version of nonrelativistic quantum mechanics is given in Schrödinger's Euclidean quantum mechanics."1 There, a proba- bilistic i.e., "Euclidean" generalization

  3. Limits to the Universality of Quantum Mechanics

    E-print Network

    Brian D. Josephson

    2011-10-08

    Niels Bohr's arguments indicating the non-applicability of quantum methodology to the study of the ultimate details of life given in his book "Atomic physics and human knowledge" conflict with the commonly held opposite view. The bases for the usual beliefs are examined and shown to have little validity. Significant differences do exist between the living organism and the type of system studied successfully in the physics laboratory. Dealing with living organisms in quantum-mechanical terms with the same degree of rigour as is normal for non-living systems would seem not to be possible without considering also questions of the origins of life and of the universe.

  4. Models of Damped Oscillators in Quantum Mechanics

    E-print Network

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

    2009-06-04

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

  5. Quantum mechanical coherence, resonance, and mind

    SciTech Connect

    Stapp, H.P.

    1995-03-26

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

  6. Quantum mechanics of 4-derivative theories

    E-print Network

    Salvio, Alberto

    2015-01-01

    A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantisation. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalisable wave functions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm.

  7. Thermodynamics of trajectories of a quantum harmonic oscillator coupled to N baths

    NASA Astrophysics Data System (ADS)

    Pigeon, Simon; Fusco, Lorenzo; Xuereb, André; De Chiara, Gabriele; Paternostro, Mauro

    2015-07-01

    We undertake a thorough analysis of the thermodynamics of the trajectories followed by a quantum harmonic oscillator coupled to N dissipative baths by using an approach to large-deviation theory inspired by phase-space quantum optics. As an illustrative example, we study the archetypal case of a harmonic oscillator coupled to two thermal baths, allowing for a comparison with the analogous classical result. In the low-temperature limit, we find a significant quantum suppression in the rate of work exchanged between the system and each bath. We further show how the presented method is capable of giving analytical results even for the case of a driven harmonic oscillator. Based on that result, we analyze the laser cooling of the motion of a trapped ion or optomechanical system, illustrating how the emission statistics can be controllably altered by the driving force.

  8. Efficiency at maximum power of a quantum Otto cycle within finite-time or irreversible thermodynamics

    NASA Astrophysics Data System (ADS)

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

    2014-12-01

    We consider the efficiency at maximum power of a quantum Otto engine, which uses a spin or a harmonic system as its working substance and works between two heat reservoirs at constant temperatures Th and Tc (quantum statistics, the efficiencies at maximum power based on these two different kinds of quantum systems are bounded from the upper side by the same expression ?mp??+??C2/[?C-(1 -?C) ln(1 -?C) ] with ?C=1 -Tc/Th as the Carnot efficiency. This expression ?mp possesses the same universality of the CA efficiency ?CA=1 -?{1 -?C } at small relative temperature difference. Within the context of irreversible thermodynamics, we calculate the Onsager coefficients and show that the value of ?CA is indeed the upper bound of EMP for an Otto engine working in the linear-response regime.

  9. Emergence of quantum mechanics from a sub-quantum statistical mechanics

    NASA Astrophysics Data System (ADS)

    Grössing, Gerhard

    2014-07-01

    A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level. It is further demonstrated both analytically and with the aid of computer simulations that our model provides explanations for various quantum effects such as double-slit or n-slit interference. We show the averaged trajectories emerging from our model to be identical to Bohmian trajectories, albeit without the need to invoke complex wavefunctions or any other quantum mechanical tool. Finally, the model provides new insights into the origins of entanglement, and, in particular, into the phenomenon of a "systemic" non-locality.

  10. Thermodynamic limits to the conversion of blackbody radiation by quantum systems. [with application to solar energy conversion devices

    NASA Technical Reports Server (NTRS)

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

    1982-01-01

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

  11. Macroscopic test of quantum mechanics versus stochastic electrodynamics S. Chaturvedi

    E-print Network

    Queensland, University of

    Macroscopic test of quantum mechanics versus stochastic electrodynamics S. Chaturvedi School with quantum mechanics at the microscopic level, from the Bell inequalities 1 . Experimental tests at this level have decided in favor of quantum mechanics 2 , although there are still some experimental problems

  12. Putnam looks at quantum mechanics (again and again) Christian Wthrich

    E-print Network

    Wüthrich, Christian

    1 Putnam looks at quantum mechanics (again and again) Christian Wüthrich University of California Hilary Putnam (1965, 2005) has argued that from a realist perspective, quantum mechanics stands in need that quantum mechanics needs no interpretation and thus stands in tension with his claim of three years later

  13. Outline of Quantum Mechanics William G. Faris 1

    E-print Network

    Ueltschi, Daniel

    Contents Outline of Quantum Mechanics William G. Faris 1 Inequalities for Schr¨odinger Operators is the goal of the present lecture notes. They include an excellent introduction to quantum mechanics been de- veloped over the years for, and because of, quantum mechanics. These are the subject of two

  14. How to Teach the Postulates of Quantum Mechanics without Enigma.

    ERIC Educational Resources Information Center

    Teixeira-Dias, Jose J. C.

    1983-01-01

    Shows how a statistical approach can help students accept postulates of quantum mechanics. The approach, which also makes students aware of the philosophical/humanistic implications of quantum mechanics, involves the following sequence: (1) important experiments in quantum mechanics; (2) conventional statistical interpretation; (3) mathematical…

  15. Quantum Mechanics as a Science -Religion Bridge By Stanley Klein

    E-print Network

    Klein, Stanley

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

  16. Bicomplex Quantum Mechanics: I. The Generalized Schrodinger Equation

    E-print Network

    Rochon, Dominic

    Bicomplex Quantum Mechanics: I. The Generalized Schr¨odinger Equation D. Rochon1 and S. Tremblay2 D) #12;232 Bicomplex Quantum Mechanics: I. The Generalized ... D. Rochon & S. Tremblay · i0 i1 i2 j i0 i0 are commutative with some non-invertible elements situated on the "null cone". The extension of quantum mechanics

  17. MSE 157: Quantum Mechanics of Nanoscale Materials Course Information

    E-print Network

    MSE 157: Quantum Mechanics of Nanoscale Materials Course Information Basic info Prof. Aaron to Quantum Mechanics by David Griffiths but we will make many diversions from this. This book is on reserve at the Engineering Library. Other recommended books for outside reading: Applied Quantum Mechanics by David Levi

  18. 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

  19. A Factor-Graph Representation of Probabilities in Quantum Mechanics

    E-print Network

    Loeliger, Hans-Andrea

    A Factor-Graph Representation of Probabilities in Quantum Mechanics Hans-Andrea Loeliger ETH Zurich for statistical inference. So far, however, quantum mechanics (e.g., [8], [9]) has been standing apart. Despite categories. Indeed, it has often been emphasized that quantum mechanics is a generalization of probability

  20. A NOTE ON RELATION BETWEEN QUANTUM MECHANICS AND ALGEBRAIC INVARIANTS

    E-print Network

    A NOTE ON RELATION BETWEEN QUANTUM MECHANICS AND ALGEBRAIC INVARIANTS Alex A. Samoletov Department appeared in the quantum mechanics at its early period [4],[5] and then took clear form in the work [6 representation of quantum mechanics and the group of affine canonical transformations of the phase space. 2

  1. Operational Axioms for Quantum Mechanics Giacomo Mauro D'Ariano

    E-print Network

    D'Ariano, Giacomo Mauro

    Operational Axioms for Quantum Mechanics Giacomo Mauro D'Ariano QUIT Group, Dipartimento di Fisica formulation of Quantum Mechanics in terms of complex Hilbert space is derived for finite dimensions, starting: 03.65.-w 1. INTRODUCTION Quantum Mechanics has been universally accepted as a general law of nature

  2. -ALGEBRAIC FORMALISM OF QUANTUM MECHANICS JONATHAN JAMES GLEASON

    E-print Network

    May, J. Peter

    THE C -ALGEBRAIC FORMALISM OF QUANTUM MECHANICS JONATHAN JAMES GLEASON Abstract. In this paper 7 6. Quantum Mechanics from the Ground Up 8 7. Closing Comments 17 8. Appendix: Definitions 18 of quantum mechan- ics (i.e., the states are elements of a separable Hilbert space and the observables self

  3. JEFFREY A. BARRETT A QUANTUM-MECHANICAL ARGUMENT

    E-print Network

    Johnson, Kent

    JEFFREY A. BARRETT A QUANTUM-MECHANICAL ARGUMENT FOR MIND­BODY DUALISM ABSTRACT. I argue that a strong mind­body dualism is required of any formu- lation of quantum mechanics that satisfies. From the earliest formulation of the theory, physicists have thought that quantum mechanics has

  4. Quantum interference between H + D2 quasiclassical reaction mechanisms

    E-print Network

    Quantum interference between H + D2 quasiclassical reaction mechanisms Pablo G. Jambrina1 , Diego the origin of that structure to the quantum interference between different quasiclassical mechanisms of the quasiclassical trajectory (QCT) method in which quantum mechanical (QM) binning is imposed on the results

  5. Hidden Variables and Commutativity in Quantum Mechanics Benjamin Feintzeig

    E-print Network

    Johnson, Kent

    Hidden Variables and Commutativity in Quantum Mechanics Benjamin Feintzeig Department of Logic takes up a suggestion that the reason we cannot find hidden variable theories for quantum mechanics theories for quantum mechanics, so the proposal for getting around Bell's Theorem fails. Contents 1

  6. The Liar-paradox in a Quantum Mechanical Perspective

    E-print Network

    Aerts, Diederik

    The Liar-paradox in a Quantum Mechanical Perspective Diederik Aerts, Jan Broekaert, Sonja Smets paradox in a quantum mechanical perspective", Foundations of Science, 4, 156. 1 #12;on the other side can be described in a meaningful way by the quantum mechanical formalism. The theories of chaos

  7. Np Incorporation into Uranyl Alteration Phases: A Quantum Mechanical Approach

    SciTech Connect

    L.C. Huller; R.C. Win; U.Ecker

    2006-09-05

    Neptunium is a major contributor to the long-term radioactivity in a geologic repository for spent nuclear fuel (SNF) due to its long half-life (2.1 million years). The mobility of Np may be decreased by incorporation into the U{sup 6+} phases that form during the corrosion of SNF. The ionic radii of Np (0.089nm) and U (0.087nm) are similar, as is their chemistry. Experimental studies have shown Np can be incorporated into uranyl phases at concentrations of {approx} 100 ppm. The low concentration of Np in the uranyl phases complicates experimental detection and presents a significant challenge for determining the incorporation mechanism. Therefore, we have used quantum mechanical calculations to investigate incorporation mechanisms and evaluate the energetics of Np substituting for U. CASTEP, a density functional theory based code that uses plane waves and pseudo-potentials, was used to calculate optimal H positions, relaxed geometry, and energy of different uranyl phases. The incorporation energy for Np in uranyl alteration phases was calculated for studtite, [(UO{sub 2})O{sub 2}(H{sub 2}O){sub 2}](H{sub 2}){sub 2}, and boltwoodite, HK(UO{sub 2})(SiO{sub 4})* 1.5(H{sub 2}O). Studtite is the rare case of a stable uranyl hydroxyl-peroxide mineral that forms in the presence of H{sub 2}O{sub 2} from the radiolysis of H{sub 2}O. For studtite, two incorporation mechanisms were evaluated: (1) charge-balanced substitution of Np{sup 5+} and H{sup +} for one U{sup 6+}, and (2) direct substitution of Np{sup 6+} for U{sup 6+}. For boltwoodite, the H atomic positions prior to Np incorporation were determined, as well as the Np incorporation mechanisms and the corresponding substitution energies. The preferential incorporation of Np into different structure types of U{sup 6+} minerals was also investigated. Quantum mechanical substitution energies have to be derived at Np concentrations higher than the ones found in experiments or expected in a repository. However, the quantum mechanical results are crucial for subsequent empirical force-field and Monte-Carlo simulations to determine the thermodynamically stable limit of Np incorporation into these uranyl phases.

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

    E-print Network

    Gerhard Groessing

    2008-08-01

    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.

  9. Measurement and Fundamental Processes in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Jaeger, Gregg

    2015-07-01

    In the standard mathematical formulation of quantum mechanics, measurement is an additional, exceptional fundamental process rather than an often complex, but ordinary process which happens also to serve a particular epistemic function: during a measurement of one of its properties which is not already determined by a preceding measurement, a measured system, even if closed, is taken to change its state discontinuously rather than continuously as is usual. Many, including Bell, have been concerned about the fundamental role thus given to measurement in the foundation of the theory. Others, including the early Bohr and Schwinger, have suggested that quantum mechanics naturally incorporates the unavoidable uncontrollable disturbance of physical state that accompanies any local measurement without the need for an exceptional fundamental process or a special measurement theory. Disturbance is unanalyzable for Bohr, but for Schwinger it is due to physical interactions' being borne by fundamental particles having discrete properties and behavior which is beyond physical control. Here, Schwinger's approach is distinguished from more well known treatments of measurement, with the conclusion that, unlike most, it does not suffer under Bell's critique of quantum measurement. Finally, Schwinger's critique of measurement theory is explicated as a call for a deeper investigation of measurement processes that requires the use of a theory of quantum fields.

  10. Does quantum mechanics require non-locality?

    E-print Network

    Ghenadie N. Mardari

    2014-10-29

    Non-commutative properties of single quanta must violate the limit of Bell's theorem, but not the boundary of Tsirelson's theorem. This is a consequence of three basic principles: superposition (every quantum is in many states at the same time), correspondence (only the net state of interference is real), and uncertainty (conjugate variables have inversely proportional spectra). The two conditions have only been verified with entangled pairs of quanta. It is not possible to perform incompatible measurements on the same entity. Hence, the principles of quantum mechanics cannot be verified directly. At least one of them could be wrong. Though, as shown by EPR, this can only be true if non-locality is at work. In light of the latest developments in quantum theory, even that assumption is insufficient. Non-local effects are either unable to cross Bell's limit, or forced to violate Tsirelson's bound. New layers of hidden variables are required to maintain belief in action-at-a-distance, but the three principles cannot be rejected in any case. Therefore, quantum mechanics is immune to this challenge. The hypothesis of non-locality is superfluous.

  11. Quantum mechanics on phase space and teleportation

    NASA Astrophysics Data System (ADS)

    Messamah, Juba; Schroeck, Franklin E.; Hachemane, Mahmoud; Smida, Abdallah; Hamici, Amel H.

    2015-03-01

    The formalism of quantum mechanics on phase space is used to describe the standard protocol of quantum teleportation with continuous variables in order to partially investigate the interplay between this formalism and quantum information. Instead of the Wigner quasi-probability distributions used in the standard protocol, we use positive definite true probability densities which account for unsharp measurements through a proper wave function representing a non-ideal quantum measuring device. This is based on a result of Schroeck and may be taken on any relativistic or nonrelativistic phase space. The obtained formula is similar to a known formula in quantum optics, but contains the effect of the measuring device. It has been applied in three cases. In the first case, the two measuring devices, corresponding to the two entangled parts shared by Alice and Bob, are not entangled and described by two identical Gaussian wave functions with respect to the Heisenberg group. They lead to a probability density identical to the function which is analyzed and compared with the Wigner formalism. A new expression of the teleportation fidelity for a coherent state in terms of the quadrature variances is obtained. In the second case, these two measuring devices are entangled in a two-mode squeezed vacuum state. In the third case, two Gaussian states are combined in an entangled squeezed state. The overall observation is that the state of the measuring devices shared by Alice and Bob influences the fidelity of teleportation through their unsharpness and entanglement.

  12. Quantum Mechanics, Gravity, and the Multiverse

    E-print Network

    Yasunori Nomura

    2012-07-30

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

  13. Beyond relativity and quantum mechanics: space physics

    NASA Astrophysics Data System (ADS)

    Lindner, Henry H.

    2011-09-01

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

  14. Hidden variables and nonlocality in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Hemmick, Douglas Lloyd

    1997-05-01

    Most physicists hold a skeptical attitude toward a 'hidden variables' interpretation of quantum theory, despite David Bohm's successful construction of such a theory and John S. Bell's strong arguments in favor of the idea. The first reason for doubt concerns certain mathematical theorems (von Neumann's, Gleason's, Kochen and Specker's, and Bell's) which can be applied to the hidden variables issue. These theorems are often credited with proving that hidden variables are indeed 'impossible', in the sense that they cannot replicate the predictions of quantum mechanics. Many who do not draw such a strong conclusion nevertheless accept that hidden variables have been shown to exhibit prohibitively complicated features. The second concern is that the most sophisticated example of a hidden variables theory-that of David Bohm-exhibits non-locality, i.e., consequences of events at one place can propagate to other places instantaneously. However, neither the mathematical theorems in question nor the attribute of nonlocality detract from the importance of a hidden variables interpretation of quantum theory. Nonlocality is present in quantum mechanics itself, and is a required characteristic of any theory that agrees with the quantum mechanical predictions. We first discuss the earliest analysis of hidden variables-that of von Neumann's theorem-and review John S. Bell's refutation of von Neumann's 'impossibility proof'. We recall and elaborate on Bell's arguments regarding the theorems of Gleason, and Kochen and Specker. According to Bell, these latter theorems do not imply that hidden variables interpretations are untenable, but instead that such theories must exhibit contextuality, i.e., they must allow for the dependence of measurement results on the characteristics of both measured system and measuring apparatus. We demonstrate a new way to understand the implications of both Gleason's theorem and Kochen and Specker's theorem by noting that they prove a result we call 'spectral incompatibility'. We develop further insight into the concepts involved in these two theorems by investigating a special quantum mechanical experiment first described by David Albert. We review the Einstein-Podolsky-Rosen paradox, Bell's theorem, and Bell's later argument that these imply that quantum mechanics is irreducibly nonlocal. The paradox of Einstein, Podolsky, and Rosen was generalized by Erwin Schrodinger in the same paper where his famous 'cat paradox' appeared. We show that Schrodinger's conclusions can be derived using a simpler argument-one which makes clear the relationship between the quantum state and the 'perfect correlations' exhibited by the system. We use Schrodinger's EPR analysis to derive a wide variety of new quantum nonlocality proofs. These proofs share two important features with that of Greenberger, Horne, and Zeilinger. First, they are of a deterministic character, i.e., they are 'nonlocality without inequalities' proofs. Second, the quantum nonlocality results we develop may be experimentally verified so that one need only observe the 'perfect correlations' between the appropriate observables. This latter feature serves to contrast these proofs with EPR/Bell nonlocality, the laboratory confirmation of which demands not only the observation of perfect correlations, but also the observations required to test whether 'Bell's inequality' is violated. The 'Schrodinger nonlocality' proofs we give differ from the GHZ proof in that they apply to two-component composite systems, while the latter involves a composite system of at least three-components. In addition, some of the Schrodinger proofs involve classes of observables larger than that addressed in the GHZ proof. (Abstract shortened by UMI.)

  15. A quantum mechanics glimpse to standard cosmology

    SciTech Connect

    Barbosa-Cendejas, N.; Reyes, M.

    2010-07-12

    In this work we present a connection between a standard cosmology model for inflation and quantum mechanics. We consider a time independent Schroedinger type equation derived from the equations of motion for a single scalar field in a flat space time with a FRW metric and a cosmological constant; the fact that the equation of motion is precisely a Schroedinger equation allows us to investigate on the algebraic relations between the two models and probe the consequences derived from this point of view.

  16. Nonlinear entangled state representation in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Fan, Hongyi; Cheng, Hailing

    2002-03-01

    We develop Dirac's representation theory in quantum mechanics by constructing the nonlinear entangled state | ?> nl and its non-Hermite conjugate state nl??| with continuum variable. By virtue of the technique of integration within an ordered product of operators we show that | ?> nl and nl??| make up an orthonormal and complete representation. From | ?> nl we also deduce another kind of entangled states. Application of | ?> nl in studying two-mode squeezed state is demonstrated.

  17. Chiral quantum mechanics (CQM) for antihydrogen systems

    E-print Network

    G. Van Hooydonk

    2005-12-03

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

  18. Supersymmetric Dissipative Quantum Mechanics from Superstrings

    E-print Network

    Luigi Cappiello; Giancarlo D'Ambrosio

    2004-05-31

    Following the approach of Callan and Thorlacius applied to the superstring, we derive a supersymmetric extension of the non-local dissipative action of Caldeira and Leggett. The dissipative term turns out to be invariant under a group of superconformal transformations. When added to the usual kinetic term, it provides an example of supersymmetric dissipative quantum mechanics. As a by-product of our analysis, an intriguing connection to the homeotic/hybrid fermion model, proposed for CPT violation in neutrinos, appears.

  19. Supersymmetric Dissipative Quantum Mechanics from Superstrings

    E-print Network

    Cappiello, L; Cappiello, Luigi; Ambrosio, Giancarlo D'

    2004-01-01

    Following the approach of Callan and Thorlacius applied to the superstring, we derive a supersymmetric extension of the non-local dissipative action of Caldeira and Leggett. The dissipative term turns out to be invariant under a group of superconformal transformations. When added to the usual kinetic term, it provides an example of supersymmetric dissipative quantum mechanics. As a by-product of our analysis, an intriguing connection to the homeotic/hybrid fermion model, proposed for CPT violation in neutrinos, appears.

  20. Using the Internet to teach Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Breinig, Marianne

    1997-04-01

    All instructional materials for a Quantum Mechanics course for graduate students in physics at the University of Tennessee are distributed over the Internet. Class notes, problems, and solutions are available in portable document format (PDF). A discussion forum allows students to post questions and to discuss class materials among themselves and with the instructor. Using an Internet connection to various computers in the classroom allows the introduction of numerical and visualization techniques in class.

  1. Quantum Mechanics and Motion: A Modern Perspective

    E-print Network

    Gerald E. Marsh

    2009-12-27

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

  2. Mona Lisa - ineffable smile of quantum mechanics

    E-print Network

    Slobodan Prvanovic

    2003-02-25

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

  3. Physical Interpretations of Nilpotent Quantum Mechanics

    E-print Network

    Peter Rowlands

    2010-04-09

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

  4. Grounding quantum probability in psychological mechanism.

    PubMed

    Love, Bradley C

    2013-06-01

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

  5. Hunting for Snarks in Quantum Mechanics

    SciTech Connect

    Hestenes, David

    2009-12-08

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

  6. ME346A Introduction to Statistical Mechanics Wei Cai Stanford University Win 2011 Handout 6. Thermodynamics

    E-print Network

    Cai, Wei

    . Thermodynamics January 26, 2011 Contents 1 Laws of thermodynamics 2 1.1 The zeroth law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2 Mathematics of thermodynamics 9 2.1 Equation of state.5 Thermodynamic potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3 Worked examples 21 3

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

    NASA Astrophysics Data System (ADS)

    Chai, Weisin

    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.

  8. Thermodynamic limits for solar energy conversion by a quantum-thermal hybrid system

    NASA Technical Reports Server (NTRS)

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

    1981-01-01

    The limits are presented fo air mass 1.5 conditions. A maximum conversion efficiency of 74 percent is thermodynamically achievable for the quantum device operating at 3500 K and the heat engine in contact with a reservoir at 0 K. The efficiency drops to 56 percent for a cold reservoir at approximately room temperature conditions. Hybrid system efficiencies exceed 50 percent over receiver temperatures ranging from 1400 K to 4000 K, suggesting little benefit is gained in operating the system above 1400 K. The results are applied to a system consisting of a photovoltaic solar cell in series with a heat engine.

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

    SciTech Connect

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

    2014-07-15

    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.

  10. Quantum mechanics in structure-based drug design.

    PubMed

    Peters, Martin B; Raha, Kaushik; Merz, Kenneth M

    2006-05-01

    In principle, quantum mechanics provides a more accurate representation of molecular systems than other modeling approaches. While this notion is not a matter of dispute, it has not yet been definitively demonstrated within the realm of structure-based drug design that the use of quantum mechanical methods over the use of classical modeling approaches is justified in consideration of the increase in expense associated with quantum mechanical methods. Demonstrating that quantum mechanics-based methods can be superior to simpler models, and resolving problems relating to estimating the effects of conformational entropy, will provide key areas of interest in the coming years for in silico structure-based drug design. Recent applications using quantum mechanical methods in structure-based drug design are reviewed herein, and applications ranging from scoring receptor-ligand interactions using quantum mechanics to the generation of quantitative structure-activity relationships using quantum mechanics-derived descriptors are discussed. PMID:16729734

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

    E-print Network

    H. Nikolic

    2006-10-12

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

  12. From Cbits to Qbits: Teaching computer scientists quantum mechanics

    E-print Network

    N. David Mermin

    2002-07-19

    A strategy is suggested for teaching mathematically literate students, with no background in physics, just enough quantum mechanics for them to understand and develop algorithms in quantum computation and quantum information theory. Although the article as a whole addresses teachers of physics, well versed in quantum mechanics, the central pedagogical development is addressed directly to computer scientists and mathematicians, with only occasional asides to their teacher. Physicists uninterested in quantum pedagogy may be amused (or irritated) by some of the views of standard quantum mechanics that arise naturally from this unorthodox perspective.

  13. A thermodynamic theory for characterizing thermo-mechanical response of polymers during crystallization

    SciTech Connect

    Negahban, M.

    1995-12-31

    A thermodynamic theory will be presented to capture the thermo-mechanical characteristics associated with crystallization of polymers. The basic characteristics associated with crystallization consists of (a) crystallization in polymers is considered a gradual transition from an amorphous polymer to a semi-crystalline polymer, (b) there is a volume reduction associated with crystallization as the material moves to the denser morphology of the crystal structure, (c) there is a substantial stiffening of the polymer, (d) there is stress relaxation associated with crystallization for polymers under a constant stretch, (e) there is creep associated with crystallization in polymers under a fixed load. These and other characteristics are modeled in a multi-dimensional thermodynamic theory. As a first example, the simplest possible constitutive assumptions are studied in relation to characterizing the behavior of natural rubber. Natural rubber is selected due to the abundance of information on its thermo-mechanical behavior. This work is an extension to non-isothermal thermodynamic processes of previous work on characterizing the mechanical effects of polymer crystallization under isothermal conditions.

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

    E-print Network

    O. Tapia

    2014-04-02

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

  15. Neutrino oscillations: Quantum mechanics vs. quantum field theory

    SciTech Connect

    Akhmedov, Evgeny Kh.; Kopp, Joachim; ,

    2010-01-01

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

  16. Neutrino oscillations: Quantum mechanics vs. quantum field theory

    E-print Network

    Evgeny Kh. Akhmedov; Joachim Kopp

    2012-11-20

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

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

    E-print Network

    Artur Szczepanski

    2010-02-08

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

  18. Mixing Quantum and Classical Mechanics Oleg V. Prezhdo \\Lambda

    E-print Network

    and a clearer picture of physical events. Applica­ tions of various quantum­classical approaches range fromMixing Quantum and Classical Mechanics Oleg V. Prezhdo \\Lambda Department of Chemistry quantum­classical system. The quantum­classical bracket entering the equation pre­ serves the Lie algebra

  19. An approach to nonstandard quantum mechanics

    E-print Network

    Andreas Raab

    2006-12-27

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

  20. Quantum mechanics with coordinate dependent noncommutativity

    SciTech Connect

    Kupriyanov, V. G.

    2013-11-15

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

  1. Thermodynamics and quantum cosmology -- Continuous topological evolution of topologically coherent defects

    E-print Network

    R. M. Kiehn

    2006-03-17

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

  2. Bohmian Mechanics and Quantum Field Theory Detlef Durr,1,

    E-print Network

    Goldstein, Sheldon

    in the quantum field theory, the theory describes explicit creation and annihilation events: the world linesBohmian Mechanics and Quantum Field Theory Detlef D¨urr,1, Sheldon Goldstein,2, Roderich Tumulka: July 1, 2004) We discuss a recently proposed extension of Bohmian mechanics to quantum field theory

  3. Faculty Disagreement about the Teaching of Quantum Mechanics

    E-print Network

    Colorado at Boulder, University of

    Faculty Disagreement about the Teaching of Quantum Mechanics Michael Dubson1 , Steve Goldhaber1-level QM. We surveyed 27 faculty about their approaches to teaching QM, and reviewed 20 quantum textbooks (matter wave vs. information wave vs. something else). Keywords: upper-division quantum mechanics

  4. Quantum mechanism helps agents combat with "bad" social choice rules

    E-print Network

    Wu, Haoyang

    2010-01-01

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

  5. Adaptive Perturbation Theory I: Quantum Mechanics

    SciTech Connect

    Weinstein, Marvin; /SLAC

    2005-10-19

    Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be treatable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, H, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. This paper introduces the method in the context of the pure anharmonic oscillator and then goes on to apply it to the case of tunneling between both symmetric and asymmetric minima. It concludes with an introduction to the extension of these methods to the discussion of a quantum field theory. A more complete discussion of this issue will be given in the second paper in this series, and it will show how to use the method of adaptive perturbation theory to non-perturbatively extract the structure of mass, wavefunction and coupling constant renormalization.

  6. Quantum Information Theory Quantum mechanics makes probabilistic predictions about experiments, and indeed it is a theory of

    E-print Network

    Burton, Geoffrey R.

    Quantum Information Theory Quantum mechanics makes probabilistic predictions about experiments algebra and probability. Previous experience with quantum mechanics is helpful, but not required. Instead lead to the development of a theory of quantum information that generalises previous notions

  7. 5.74 Introductory Quantum Mechanics II, Spring 2005

    E-print Network

    Tokmakoff, Andrei

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

  8. 5.74 Introductory Quantum Mechanics II, Spring 2003

    E-print Network

    Tokmakoff, Andrei

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

  9. Lecture Script: Introduction to Computational Quantum Mechanics

    E-print Network

    Roman Schmied

    2015-06-05

    This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013 and in the Spring semester of 2015. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding analytical as well as numerical solutions and their visualization. Most of these calculations are too complicated to be done by hand. Even relatively simple problems, such as two interacting particles in a one-dimensional trap, do not have analytic solutions and require the use of computers for their solution and visualization. More complex problems scale exponentially with the number of degrees of freedom, and make the use of large computer simulations unavoidable. The course is taught using the Mathematica programming language; however, the concepts presented are readily translated to any other programming language.

  10. The Multiverse Interpretation of Quantum Mechanics

    E-print Network

    Raphael Bousso; Leonard Susskind

    2011-07-22

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

  11. Relativity and quantum mechanics: Jorgensen revisited

    E-print Network

    Bernhard Rothenstein

    2007-03-25

    We first define the functions which ensure the transformation of momentum and energy of a tardyon, the transformation of the wave vector and the frequency of the associated wave. Having done this, we show that they ensure the relativistic invariance of the quotient between momentum and wave vector and between energy and frequency if the product between particle velocity u and phase velocity w is a relativistic invariant (uw=c^2), a condition which is a natural combination of special relativity theory and quantum mechanics.

  12. Non-representative Quantum Mechanical Weak Values

    NASA Astrophysics Data System (ADS)

    Svensson, B. E. Y.

    2015-09-01

    The operational definition of a weak value for a quantum mechanical system involves the limit of the weak measurement strength tending to zero. I study how this limit compares to the situation for the undisturbed (no weak measurement) system. Under certain conditions, which I investigate, this limit is discontinuous in the sense that it does not merge smoothly to the Hilbert space description of the undisturbed system. Hence, in these discontinuous cases, the weak value does not represent the undisturbed system. As a result, conclusions drawn from such weak values regarding the properties of the studied system cannot be upheld. Examples are given.

  13. A New Formulation of Quantum Mechanics

    E-print Network

    Arbab I. Arbab; Faisal A. Yassein

    2010-07-22

    A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and Schrodinger probability density while keeping the Klein -Gordon and Schrodinger current unaltered. We have found time and space transformations under which Dirac's equation is invariant. The invariance of Maxwell's equations under these transformations shows that the electric and magnetic fields of a moving charged particle are perpendicular to the velocity of the propagating particle. This formulation agrees with the quaternionic formulation recently developed by Arbab.

  14. Non-representative Quantum Mechanical Weak Values

    NASA Astrophysics Data System (ADS)

    Svensson, B. E. Y.

    2015-12-01

    The operational definition of a weak value for a quantum mechanical system involves the limit of the weak measurement strength tending to zero. I study how this limit compares to the situation for the undisturbed (no weak measurement) system. Under certain conditions, which I investigate, this limit is discontinuous in the sense that it does not merge smoothly to the Hilbert space description of the undisturbed system. Hence, in these discontinuous cases, the weak value does not represent the undisturbed system. As a result, conclusions drawn from such weak values regarding the properties of the studied system cannot be upheld. Examples are given.

  15. Supersymmetric quantum mechanics and its applications

    SciTech Connect

    Sukumar, C.V.

    2004-12-23

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

  16. Improved lattice actions for supersymmetric quantum mechanics

    E-print Network

    Sebastian Schierenberg; Falk Bruckmann

    2012-10-19

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

  17. Euclidean Quantum Mechanics and Universal Nonlinear Filtering

    E-print Network

    Bhashyam Balaji

    2008-09-25

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

  18. Wigner Measures in Noncommutative Quantum Mechanics

    E-print Network

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

    2009-07-25

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

  19. A Global Optimization Approach to Quantum Mechanics

    E-print Network

    Xiaofei Huang

    2006-05-25

    This paper presents a global optimization approach to quantum mechanics, which describes the most fundamental dynamics of the universe. It suggests that the wave-like behavior of (sub)atomic particles could be the critical characteristic of a global optimization method deployed by nature so that (sub)atomic systems can find their ground states corresponding to the global minimum of some energy function associated with the system. The classic time-independent Schrodinger equation is shown to be derivable from the global optimization method to support this argument.

  20. Landau problem in noncommutative quantum mechanics

    NASA Astrophysics Data System (ADS)

    Sayipjamal, Dulat; Li, Kang

    2008-02-01

    The Landau problem in non-commutative quantum mechanics (NCQM) is studied. First by solving the Schrödinger equations on noncommutative (NC) space we obtain the Landau energy levels and the energy correction that is caused by space-space noncommutativity. Then we discuss the noncommutative phase space case, namely, space-space and momentum-momentum non-commutative case, and we get the explicit expression of the Hamiltonian as well as the corresponding eigenfunctions and eigenvalues. Supported by National Natural Science Foundation of China (10465004, 10665001, 10575026) and Abdus Salam ICTP, Trieste, Italy