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Sample records for thermodynamics quantum mechanics

  1. Thermodynamic integration from classical to quantum mechanics.

    PubMed

    Habershon, Scott; Manolopoulos, David E

    2011-12-14

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

  2. 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.

  3. Quantum Statistical Mechanical Derivation of the Second Law of Thermodynamics: A Hybrid Setting Approach.

    PubMed

    Tasaki, Hal

    2016-04-29

    Based on quantum statistical mechanics and microscopic quantum dynamics, we prove Planck's and Kelvin's principles for macroscopic systems in a general and realistic setting. We consider a hybrid quantum system that consists of the thermodynamic system, which is initially in thermal equilibrium, and the "apparatus" which operates on the former, and assume that the whole system evolves autonomously. This provides a satisfactory derivation of the second law for macroscopic systems.

  4. Developing and assessing research-based tools for teaching quantum mechanics and thermodynamics

    NASA Astrophysics Data System (ADS)

    Brown, Benjamin R.

    Research-based tools to educate college students in physics courses from introductory level to graduate level are essential for helping students with a diverse set of goals and backgrounds learn physics. This thesis explores issues related to student common difficulties with some topics in undergraduate quantum mechanics and thermodynamics courses. Student difficulties in learning quantum mechanics and thermodynamics are investigated by administering written tests and surveys to many classes and conducting individual interviews with a subset of students outside the class to unpack the cognitive mechanisms of the difficulties. The quantum mechanics research also focuses on using the research on student difficulties for the development and evaluation of a Quantum Interactive Learning Tutorial (QuILT) to help students learn about the time-dependence of expectation values using the context of Larmor precession of spin and evaluating the role of asking students to self-diagnose their mistakes on midterm examination on their performance on subsequent problem solving. The QuILT on Larmor precession of spin has both paper-pencil activities and a simulation component to help students learn these foundational issues in quantum mechanics. Preliminary evaluations suggest that the QuILT, which strives to help students build a robust knowledge structure of time-dependence of expectation values in quantum mechanics using a guided approach, is successful in helping students learn these topics in the junior-senior level quantum mechanics courses. The technique to help upper-level students in quantum mechanics courses effectively engage in the process of learning from their mistakes is also found to be effective. In particular, research shows that the self-diagnosis activity in upper-level quantum mechanics significantly helps students who are struggling and this activity can reduce the gap between the high and low achieving students on subsequent problem solving. Finally, a survey

  5. Origin of microbial life: Nano- and molecular events, thermodynamics/entropy, quantum mechanisms and genetic instructions.

    PubMed

    Trevors, J T

    2011-03-01

    Currently, there are no agreed upon mechanisms and supporting evidence for the origin of the first microbial cells on the Earth. However, some hypotheses have been proposed with minimal supporting evidence and experimentation/observations. The approach taken in this article is that life originated at the nano- and molecular levels of biological organization, using quantum mechanic principles that became manifested as classical microbial cell(s), allowing the origin of microbial life on the Earth with a core or minimal, organic, genetic code containing the correct instructions for cell(s) for growth and division, in a micron dimension environment, with a local entropy range conducive to life (present about 4 billion years ago), and obeying the laws of thermodynamics. An integrated approach that explores all encompassing factors necessary for the origin of life, may bring forth plausible hypotheses (and mechanisms) with much needed supporting experimentation and observations for an origin of life theory.

  6. Non-hermitian quantum thermodynamics

    PubMed Central

    Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh

    2016-01-01

    Thermodynamics is the 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 leads to the Carnot bound which is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Furthermore, we propose two setups to test our predictions, namely with strongly interacting excitons and photons in a semiconductor microcavity and in the non-hermitian tight-binding model. PMID:27003686

  7. Non-hermitian quantum thermodynamics

    SciTech Connect

    Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh

    2016-03-22

    Thermodynamics is the 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 leads to the Carnot bound which is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Lastly, we propose two setups to test our predictions, namely with strongly interacting excitons and photons in a semiconductor microcavity and in the non-hermitian tight-binding model.

  8. Non-hermitian quantum thermodynamics

    DOE PAGES

    Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh

    2016-03-22

    Thermodynamics is the 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 leads to the Carnot bound which is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Lastly, we propose two setups to test our predictions,more » namely with strongly interacting excitons and photons in a semiconductor microcavity and in the non-hermitian tight-binding model.« less

  9. Autonomous quantum thermodynamic machines

    NASA Astrophysics Data System (ADS)

    Tonner, Friedemann; Mahler, Günter

    2005-12-01

    We investigate the dynamics of a quantum system consisting of a single spin coupled to an oscillator and sandwiched between two thermal baths at different temperatures. By means of an adequately designed Lindblad equation, it is shown that this device can function as a thermodynamic machine exhibiting Carnot-type cycles. For the present model, this means that when run as a heat engine, coherent motion of the oscillator is amplified. Contrary to the quantum computer, such a machine has a quantum as well as a classical limit. Away from the classical limit, it asymptotically approaches a stationary transport scenario.

  10. Coherence and measurement in quantum thermodynamics

    PubMed Central

    Kammerlander, P.; Anders, J.

    2016-01-01

    Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines to 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. Recent theoretical breakthroughs include the characterisation of the efficiency of quantum thermal engines, the extension of classical non-equilibrium fluctuation theorems to the quantum regime and a new thermodynamic resource theory has led to the discovery of a set of second laws for finite size systems. These results have substantially advanced our understanding of nanoscale thermodynamics, however putting a finger on what is genuinely quantum in quantum thermodynamics has remained a challenge. 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. Repercussions on quantum work fluctuation relations and thermodynamic single-shot approaches are also discussed. PMID:26916503

  11. Coherence and measurement in quantum thermodynamics.

    PubMed

    Kammerlander, P; Anders, J

    2016-02-26

    Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines to 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. Recent theoretical breakthroughs include the characterisation of the efficiency of quantum thermal engines, the extension of classical non-equilibrium fluctuation theorems to the quantum regime and a new thermodynamic resource theory has led to the discovery of a set of second laws for finite size systems. These results have substantially advanced our understanding of nanoscale thermodynamics, however putting a finger on what is genuinely quantum in quantum thermodynamics has remained a challenge. 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. Repercussions on quantum work fluctuation relations and thermodynamic single-shot approaches are also discussed.

  12. Coherence and measurement in quantum thermodynamics

    NASA Astrophysics Data System (ADS)

    Kammerlander, P.; Anders, J.

    2016-02-01

    Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines to 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. Recent theoretical breakthroughs include the characterisation of the efficiency of quantum thermal engines, the extension of classical non-equilibrium fluctuation theorems to the quantum regime and a new thermodynamic resource theory has led to the discovery of a set of second laws for finite size systems. These results have substantially advanced our understanding of nanoscale thermodynamics, however putting a finger on what is genuinely quantum in quantum thermodynamics has remained a challenge. 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. Repercussions on quantum work fluctuation relations and thermodynamic single-shot approaches are also discussed.

  13. Quantum mechanics based force field for carbon (QMFF-Cx) validated to reproduce the mechanical and thermodynamics properties of graphite.

    PubMed

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

    2010-10-07

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

  14. A hierarchical approach to accurate predictions of macroscopic thermodynamic behavior from quantum mechanics and molecular simulations

    NASA Astrophysics Data System (ADS)

    Garrison, Stephen L.

    2005-07-01

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

  15. 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.

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

    PubMed

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

    2005-04-15

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

  17. Mechanics, Waves and Thermodynamics

    NASA Astrophysics Data System (ADS)

    Ranjan Jain, Sudhir

    2016-05-01

    Figures; Preface; Acknowledgement; 1. Energy, mass, momentum; 2. Kinematics, Newton's laws of motion; 3. Circular motion; 4. The principle of least action; 5. Work and energy; 6. Mechanics of a system of particles; 7. Friction; 8. Impulse and collisions; 9. Central forces; 10. Dimensional analysis; 11. Oscillations; 12. Waves; 13. Sound of music; 14. Fluid mechanics; 15. Water waves; 16. The kinetic theory of gases; 17. Concepts and laws of thermodynamics; 18. Some applications of thermodynamics; 19. Basic ideas of statistical mechanics; Bibliography; Index.

  18. 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.

  19. 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.

  20. Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Commins, Eugene D.

    2014-10-01

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

  1. 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.

  2. Higher Derivative Corrections to Black Hole Thermodynamics from Supersymmetric Matrix Quantum Mechanics

    SciTech Connect

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

    2009-05-15

    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}{sup '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}{sup '} corrections. The coefficient of the subleading term extracted from the fit to the Monte Carlo data provides a prediction for the gravity side.

  3. Thermodynamics of discrete quantum processes

    NASA Astrophysics Data System (ADS)

    Anders, Janet; Giovannetti, Vittorio

    2013-03-01

    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.

  4. Quantum thermodynamics: a nonequilibrium Green's function approach.

    PubMed

    Esposito, Massimiliano; Ochoa, Maicol A; Galperin, Michael

    2015-02-27

    We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green's functions. The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit.

  5. 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.

  6. Thermodynamic universality of quantum Carnot engines

    SciTech Connect

    Gardas, Bartłomiej; 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.

  7. Thermodynamic universality of quantum Carnot engines

    DOE PAGES

    Gardas, Bartłomiej; 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

  8. Thermodynamic universality of quantum Carnot engines.

    PubMed

    Gardas, Bartłomiej; 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.

  9. Thermodynamics of projective quantum measurements

    NASA Astrophysics Data System (ADS)

    Erez, Noam

    2012-11-01

    Quantum measurement of a system can change its mean energy as well as entropy. A selective measurement (classical or quantum) can be used as a ‘Maxwell's demon’ to power a single-temperature heat engine by decreasing the entropy. Quantum mechanically, so can a non-selective measurement, despite increasing the entropy of a thermal state. The maximal amount of work extractable following the measurement is given by the change in free energy: W(non-)selmax = ΔEmeas - TBathΔS(non-)selmeas. This follows from the ‘generalized 2nd law for nonequilibrium initial state’ (Hasegawa et al 2010 Phys. Lett. A 374 1001-4), an elementary reduction of which to the standard law is given here. It is shown that Wselmax - Wnon-selmax is equal to the work required for resetting the memory of the measuring device and that no such resetting is needed in the non-selective case. Consequently, a single-bath engine powered by either kind of measurement works at a net loss of TBathΔSnon-selmeas per cycle. By replacing the measurement by a reversible ‘pre-measurement’ and allowing a work source to couple to the system and memory, the cycle can be rendered completely reversible.

  10. Quantum work and the thermodynamic cost of quantum measurements

    DOE PAGES

    Deffner, Sebastian; Paz, Juan Pablo; Zurek, Wojciech H.

    2016-07-07

    Quantum work is usually determined from two projective measurements of the energy at the beginning and at the end of a thermodynamic process. However, this paradigm cannot be considered thermodynamically consistent as it does not account for the thermodynamic cost of these measurements. To remedy this conceptual inconsistency we introduce a paradigm that relies only on the expected change of the average energy given the initial energy eigenbasis. In particular, we completely omit quantum measurements in the definition of quantum work, and hence quantum work is identified as a thermodynamic quantity of only the system. As main results we derivemore » a modified quantum Jarzynski equality and a sharpened maximum work theorem in terms of the information free energy. Lastly, a comparison of our results with the standard approach allows one to quantify the informational cost of projective measurements.« less

  11. Quantum work and the thermodynamic cost of quantum measurements

    SciTech Connect

    Deffner, Sebastian; Paz, Juan Pablo; Zurek, Wojciech H.

    2016-07-07

    Quantum work is usually determined from two projective measurements of the energy at the beginning and at the end of a thermodynamic process. However, this paradigm cannot be considered thermodynamically consistent as it does not account for the thermodynamic cost of these measurements. To remedy this conceptual inconsistency we introduce a paradigm that relies only on the expected change of the average energy given the initial energy eigenbasis. In particular, we completely omit quantum measurements in the definition of quantum work, and hence quantum work is identified as a thermodynamic quantity of only the system. As main results we derive a modified quantum Jarzynski equality and a sharpened maximum work theorem in terms of the information free energy. Lastly, a comparison of our results with the standard approach allows one to quantify the informational cost of projective measurements.

  12. Thermodynamics of Weakly Measured Quantum Systems

    NASA Astrophysics Data System (ADS)

    Alonso, Jose Joaquin; Lutz, Eric; Romito, Alessandro

    2016-02-01

    We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superposition 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.

  13. Thermodynamics of Weakly Measured Quantum Systems.

    PubMed

    Alonso, Jose Joaquin; Lutz, Eric; Romito, Alessandro

    2016-02-26

    We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superposition 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.

  14. On some neglected thermodynamic peculiarities of quantum non-locality

    NASA Astrophysics Data System (ADS)

    Elitzur, Avshalom C.

    1990-12-01

    The existence of non-local correlations has been discussed so far almost exclusively in the context of its apparent incompatibility with relativity theory. However, it also involves some intriguing thermodynamic problems. These problems are demonstrated by analyzing the EPR experiment. It is then shown that the “transactional” interpretation of quantum mechanics, originally devised to meet the relativistic problem associated with the EPR, provides an elegant solution for the thermodynamic problems as well.

  15. Copenhagen quantum mechanics

    NASA Astrophysics Data System (ADS)

    Hollowood, Timothy J.

    2016-07-01

    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 1950s 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 Schrödinger 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.

  16. Quantum stochastic thermodynamic on harmonic networks

    NASA Astrophysics Data System (ADS)

    Deffner, Sebastian

    2016-01-01

    Fluctuation theorems are symmetry relations for the probability to observe an amount of entropy production in a finite-time process. In a recent paper Pigeon et al (2016 New. J. Phys. 18 013009) derived fluctuation theorems for harmonic networks by means of the large deviation theory. Their novel approach is illustrated with various examples of experimentally relevant systems. As a main result, however, Pigeon et al provide new insight how to consistently formulate quantum stochastic thermodynamics, and provide new and robust tools for the study of the thermodynamics of quantum harmonic networks.

  17. Quantum mechanics of black holes.

    PubMed

    Witten, Edward

    2012-08-03

    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.

  18. 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...

  19. Black Holes, Thermodynamics, and Quantum Theory

    NASA Astrophysics Data System (ADS)

    Wald, Robert

    2017-01-01

    A black hole is a region of ``no escape'' that remains behind after a body has undergone complete gravitational collapse. It is truly remarkable that (i) black holes obey the ordinary laws of thermodynamics, (ii) the entropy of a black hole is given by a simple formula involving geometrical properties of its event horizon, and (iii) quantum theory plays an essential role in the thermodynamic properties of black holes. In this talk, I will review some of the key developments related to these properties of black holes, which fascinated me as a graduate student and continue to fascinate me now.

  20. Quantum thermodynamic processes: a control theory for machine cycles

    NASA Astrophysics Data System (ADS)

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

    2008-07-01

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

  1. Nonequilibrium critical scaling in quantum thermodynamics

    NASA Astrophysics Data System (ADS)

    Bayat, Abolfazl; Apollaro, Tony J. G.; Paganelli, Simone; De Chiara, Gabriele; Johannesson, Henrik; Bose, Sougato; Sodano, Pasquale

    2016-05-01

    The emerging field of quantum thermodynamics is contributing important results and insights into archetypal many-body problems, including quantum phase transitions. Still, the question whether out-of-equilibrium quantities, such as fluctuations of work, exhibit critical scaling after a sudden quench in a closed system has remained elusive. Here, we take a novel approach to the problem by studying a quench across an impurity quantum critical point. By performing density matrix renormalization group computations on the two-impurity Kondo model, we are able to establish that the irreversible work produced in a quench exhibits finite-size scaling at quantum criticality. This scaling faithfully predicts the equilibrium critical exponents for the crossover length and the order parameter of the model, and, moreover, implies an exponent for the rescaled irreversible work. By connecting the irreversible work to the two-impurity spin correlation function, our findings can be tested experimentally.

  2. The thermodynamic cost of quantum operations

    NASA Astrophysics Data System (ADS)

    Bedingham, D. J.; Maroney, O. J. E.

    2016-11-01

    The amount of heat generated by computers is rapidly becoming one of the main problems for developing new generations of information technology. The thermodynamics of computation sets the ultimate physical bounds on heat generation. A lower bound is set by the Landauer limit, at which computation becomes thermodynamically reversible. For classical computation there is no physical principle which prevents this limit being reached, and approaches to it are already being experimentally tested. In this paper we show that for quantum computation with a set of signal states satisfying given conditions, there is an unavoidable excess heat generation that renders it inherently thermodynamically irreversible. The Landauer limit cannot, in general, be reached by quantum computers. We show the existence of a lower bound to the heat generated by quantum computing that exceeds that given by the Landauer limit, give the special conditions where this excess cost may be avoided, and provide a protocol for achieving the limiting heat cost when these conditions are met. We also show how classical computing falls within the special conditions.

  3. Quantum mechanics and the second law of thermodynamics: an insight gleaned from magnetic hysteresis in the first order phase transition of an isolated mesoscopic-size type I superconductor

    NASA Astrophysics Data System (ADS)

    Keefe, Peter D.

    2012-11-01

    J Bardeen proposed that the adiabatic phase transition of mesoscopic-size type I superconductors must be accompanied by magnetic hysteresis in the critical magnetic field of sufficient magnitude to satisfy the second law of thermodynamics, herein referred to as ‘Bardeen Hysteresis’. Bardeen Hysteresis remains speculative in that it has not been reported in the literature. This paper investigates Bardeen Hysteresis as a possible accompaniment to the adiabatic phase transition of isolated mesoscopic-size type I superconductors and its implications with respect to the second law of thermodynamics. A causal mechanism for Bardeen Hysteresis is discussed which contrasts with the long accepted causal mechanism of magnetic hysteresis, as first summarized by Pippard, herein referred to as ‘Pippard Hysteresis’. The paper offers guidance for an experimental verification and comments on how the existence of Bardeen Hysteresis has relation to a quantum mechanical basis for the second law of thermodynamics.

  4. Testing Nonassociative Quantum Mechanics.

    PubMed

    Bojowald, Martin; Brahma, Suddhasattwa; Büyükçam, Umut

    2015-11-27

    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.

  5. Small quantum networks operating as quantum thermodynamic machines

    NASA Astrophysics Data System (ADS)

    Henrich, M. J.; Michel, M.; Mahler, G.

    2006-12-01

    We show that a 3-qubit system as studied for quantum information purposes can alternatively be used as a thermodynamic machine when externally driven in finite time and interfaced between two split baths. The spins are arranged in a chain where the working spin in the middle exercises Carnot cycles the area of which defines the exchanged work. The cycle orientation (sign of the exchanged work) flips as the difference of bath temperatures goes through a critical value.

  6. Periodic thermodynamics of open quantum systems.

    PubMed

    Brandner, Kay; Seifert, Udo

    2016-06-01

    The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to an additional constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.

  7. Periodic thermodynamics of open quantum systems

    NASA Astrophysics Data System (ADS)

    Brandner, Kay; Seifert, Udo

    2016-06-01

    The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to an additional constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.

  8. 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.

  9. 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…

  10. Thermodynamics of Maximum Transition Entropy for Quantum Assemblies

    NASA Astrophysics Data System (ADS)

    Rogers, David

    2015-03-01

    We present one possible unifying framework for the statistics of driven quantum systems in terms of a stochastic propagator for the density matrix. Its classical limit [Rogers, Beck and Rempe, J. Stat. Phys 145:385, 2011] takes the form of a Langevin equation with an associated large-deviation functional intimately related to the partition function of statistical mechanics. Surprising results of this quantum theory are that work is a measurable quantity, and that a precise form of the second law of thermodynamics can be stated for dynamical systems. Numerical results are presented for the time-course of work and heat production for trapped 1D particles. Properties of the large deviation functional are discussed in the context of the quantum measurement problem.

  11. Thermodynamics of quantum-jump-conditioned feedback control.

    PubMed

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

    2013-12-01

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

  12. Maximum entropy production rate in quantum thermodynamics

    NASA Astrophysics Data System (ADS)

    Beretta, Gian Paolo

    2010-06-01

    In the framework of the recent quest for well-behaved nonlinear extensions of the traditional Schrödinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the microscopic level, a recent paper [Gheorghiu-Svirschevski 2001 Phys. Rev. A 63 054102] reproposes the nonlinear equation of motion proposed by the present author [see Beretta G P 1987 Found. Phys. 17 365 and references therein] for quantum (thermo)dynamics of a single isolated indivisible constituent system, such as a single particle, qubit, qudit, spin or atomic system, or a Bose-Einstein or Fermi-Dirac field. As already proved, such nonlinear dynamics entails a fundamental unifying microscopic proof and extension of Onsager's reciprocity and Callen's fluctuation-dissipation relations to all nonequilibrium states, close and far from thermodynamic equilibrium. In this paper we propose a brief but self-contained review of the main results already proved, including the explicit geometrical construction of the equation of motion from the steepest-entropy-ascent ansatz and its exact mathematical and conceptual equivalence with the maximal-entropy-generation variational-principle formulation presented in Gheorghiu-Svirschevski S 2001 Phys. Rev. A 63 022105. Moreover, we show how it can be extended to the case of a composite system to obtain the general form of the equation of motion, consistent with the demanding requirements of strong separability and of compatibility with general thermodynamics principles. The irreversible term in the equation of motion describes the spontaneous attraction of the state operator in the direction of steepest entropy ascent, thus implementing the maximum entropy production principle in quantum theory. The time rate at which the path of steepest entropy ascent is followed has so far been left unspecified. As a step towards the identification of such rate, here we propose a possible, well

  13. 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…

  14. 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.

  15. Quantum approach to classical statistical mechanics.

    PubMed

    Somma, R D; Batista, C D; Ortiz, G

    2007-07-20

    We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.

  16. 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.

  17. Relativity and Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Brändas, Erkki J.

    2007-12-01

    The old dilemma of quantum mechanics versus the theory of relativity is reconsidered via a first principles relativistically invariant theory. By analytic extension of quantum mechanics into the complex plane one may (i) include dynamical features such as time- and length-scales and (ii) examine the possibility and flexibility of so-called general Jordan block formations. The present viewpoint asks for a new perspective on the age-old problem of quantum mechanics versus the theory of relativity. To bring these ideas together, we will establish the relation with the Klein-Gordon-Dirac relativistic theory and confirm some dynamical features of both the special and the general relativity theory.

  18. 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)

  19. Correlations in quantum thermodynamics: Heat, work, and entropy production

    NASA Astrophysics Data System (ADS)

    Alipour, S.; Benatti, F.; Bakhshinezhad, F.; Afsary, M.; Marcantoni, S.; Rezakhani, A. T.

    2016-10-01

    We provide a characterization of energy in the form of exchanged heat and work between two interacting constituents of a closed, bipartite, correlated quantum system. By defining a binding energy we derive a consistent quantum formulation of the first law of thermodynamics, in which the role of correlations becomes evident, and this formulation reduces to the standard classical picture in relevant systems. We next discuss the emergence of the second law of thermodynamics under certain—but fairly general—conditions such as the Markovian assumption. We illustrate the role of correlations and interactions in thermodynamics through two examples.

  20. Correlations in quantum thermodynamics: Heat, work, and entropy production.

    PubMed

    Alipour, S; Benatti, F; Bakhshinezhad, F; Afsary, M; Marcantoni, S; Rezakhani, A T

    2016-10-21

    We provide a characterization of energy in the form of exchanged heat and work between two interacting constituents of a closed, bipartite, correlated quantum system. By defining a binding energy we derive a consistent quantum formulation of the first law of thermodynamics, in which the role of correlations becomes evident, and this formulation reduces to the standard classical picture in relevant systems. We next discuss the emergence of the second law of thermodynamics under certain-but fairly general-conditions such as the Markovian assumption. We illustrate the role of correlations and interactions in thermodynamics through two examples.

  1. Correlations in quantum thermodynamics: Heat, work, and entropy production

    PubMed Central

    Alipour, S.; Benatti, F.; Bakhshinezhad, F.; Afsary, M.; Marcantoni, S.; Rezakhani, A. T.

    2016-01-01

    We provide a characterization of energy in the form of exchanged heat and work between two interacting constituents of a closed, bipartite, correlated quantum system. By defining a binding energy we derive a consistent quantum formulation of the first law of thermodynamics, in which the role of correlations becomes evident, and this formulation reduces to the standard classical picture in relevant systems. We next discuss the emergence of the second law of thermodynamics under certain—but fairly general—conditions such as the Markovian assumption. We illustrate the role of correlations and interactions in thermodynamics through two examples. PMID:27767124

  2. 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)

  3. 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 α 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.

  4. Quantum Rényi relative entropies affirm universality of thermodynamics.

    PubMed

    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 α 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.

  5. Grassmann matrix quantum mechanics

    DOE PAGES

    Anninos, Dionysios; Denef, Frederik; Monten, Ruben

    2016-04-21

    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 Kähler 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.more » In conclusion, we discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.« less

  6. Grassmann matrix quantum mechanics

    SciTech Connect

    Anninos, Dionysios; Denef, Frederik; Monten, Ruben

    2016-04-21

    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 Kähler 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. In conclusion, we discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.

  7. 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.

  8. 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.

  9. Quantum Chemical Approach to Estimating the Thermodynamics of Metabolic Reactions

    PubMed Central

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

    2014-01-01

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

  10. Quantum chemical approach to estimating the thermodynamics of metabolic reactions.

    PubMed

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

    2014-11-12

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

  11. 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.

  12. Introduction to Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Griffiths, David J.

    2016-09-01

    Part I. Theory: 1. The wave function; 2. Time-independent Schrödinger equation; 3. Formalism; 4. Quantum mechanics in three dimensions; 5. Identical particles; Part II. Applications: 6. Time-independent perturbation theory; 7. The variational principle; 8. The WKB approximation; 9. Time-dependent perturbation theory; 10. The adiabatic approximation; 11. Scattering; 12. Afterword; Appendix. Linear algebra.

  13. A thermodynamical formalism describing mechanical interactions

    NASA Astrophysics Data System (ADS)

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

    2014-10-01

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

  14. Thermodynamics of a statistically interacting quantum gas in D dimensions.

    PubMed

    Potter, Geoffrey G; Müller, Gerhard; Karbach, Michael

    2007-12-01

    We present the exact thermodynamics (isochores, isotherms, isobars, response functions) of a statistically interacting quantum gas in D dimensions. The results in D=1 are those of the thermodynamic Bethe ansatz for the nonlinear Schrödinger model, a gas with repulsive two-body contact potential. In all dimensions the ideal boson and fermion gases are recovered in the weak-coupling and strong-coupling limits, respectively. For all nonzero couplings ideal fermion gas behavior emerges for D>1 and, in the limit D-->infinity , a phase transition occurs at T>0 . Significant deviations from ideal quantum gas behavior are found for intermediate coupling and finite D .

  15. Thermodynamical properties of Strunz’s quantum dissipative models

    SciTech Connect

    Zen, Freddy P.; Sulaiman, A.

    2015-09-30

    The existence of the negative of specific heat from quantum dissipative theory is investigated. Strunz’s quantum dissipative model will be used in this studies. The thermodynamical properties will be studied starts out from the thermo-dynamic partition function of the dissipative system. The path integral technique is used to calculate the partition function under consideration. The results shows that the specific heat can be negative if the damping parameter more than a half the oscillator frequency and also occur at low temperatures. For damping factor greater than the frequency of harmonic oscillator then specific heat will oscillate at low temperatures and approaching normal conditions at a high temperature.

  16. 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.

  17. The second laws of quantum thermodynamics.

    PubMed

    Brandão, Fernando; Horodecki, Michał; 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.

  18. Thermodynamic constraints on the amplitude of quantum oscillations

    NASA Astrophysics Data System (ADS)

    Shekhter, Arkady; Modic, K. A.; McDonald, R. D.; Ramshaw, B. J.

    2017-03-01

    Magneto-quantum oscillation experiments in high-temperature superconductors show a strong thermally induced suppression of the oscillation amplitude approaching the critical dopings [B. J. Ramshaw et al., Science 348, 317 (2014), 10.1126/science.aaa4990; H. Shishido et al., Phys. Rev. Lett. 104, 057008 (2010), 10.1103/PhysRevLett.104.057008; P. Walmsley et al., Phys. Rev. Lett. 110, 257002 (2013), 10.1103/PhysRevLett.110.257002]—in support of a quantum-critical origin of their phase diagrams. We suggest that, in addition to a thermodynamic mass enhancement, these experiments may directly indicate the increasing role of quantum fluctuations that suppress the quantum oscillation amplitude through inelastic scattering. We show that the traditional theoretical approaches beyond Lifshitz-Kosevich to calculate the oscillation amplitude in correlated metals result in a contradiction with the third law of thermodynamics and suggest a way to rectify this problem.

  19. Epigenetics: Biology's Quantum Mechanics.

    PubMed

    Jorgensen, Richard A

    2011-01-01

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

  20. Existence of the thermodynamic limit for disordered quantum Coulomb systems

    NASA Astrophysics Data System (ADS)

    Blanc, Xavier; Lewin, Mathieu

    2012-09-01

    Following a recent method introduced by Hainzl, Solovej, and Lewin, we prove the existence of the thermodynamic limit for a system made of quantum electrons, and classical nuclei whose positions and charges are randomly perturbed in an ergodic fashion. All the particles interact through Coulomb forces.

  1. Quantum mechanics and quantum information theory

    NASA Astrophysics Data System (ADS)

    van Camp, Wesley William

    The principle aim of this dissertation is to investigate the philosophical application of quantum information theory to interpretational issues regarding the theory of quantum mechanics. Recently, quantum information theory has emerged as a potential source for such an interpretation. The main question with which this dissertation will be concerned is whether or not an information-theoretic interpretation can serve as a conceptually acceptable interpretation of quantum mechanics. It will be argued that some of the more obvious approaches -- that quantum information theory shows us that ultimately the world is made of information, and quantum Bayesianism -- fail as philosophical interpretations of quantum mechanics. However, the information-theoretic approach of Clifton, Bub, and Halvorson introduces Einstein's distinction between principle theories and constructive theories, arguing that quantum mechanics is best understood as an information-theoretic principle theory. While I argue that this particular approach fails, it does offer a viable new philosophical role for information theory. Specifically, an investigation of interpretationally successful principle theories such as Newtonian mechanics, special relativity, and general relativity, shows that the particular principles employed are necessary as constitutive elements of a framework which partially defines the basic explanatory concepts of space, time, and motion. Without such constitutive principles as preconditions for empirical meaning, scientific progress is hampered. It is argued that the philosophical issues in quantum mechanics stem from an analogous conceptual crisis. On the basis of this comparison, the best strategy for resolving these problems is to apply a similar sort of conceptual analysis to quantum mechanics so as to provide an appropriate set of constitutive principles clarifying the conceptual issues at stake. It is further argued that quantum information theory is ideally placed as a novel

  2. Statistical mechanics and thermodynamics: A Maxwellian view

    NASA Astrophysics Data System (ADS)

    Myrvold, Wayne C.

    One finds, in Maxwell's writings on thermodynamics and statistical physics, a conception of the nature of these subjects that differs in interesting ways from the way they are usually conceived. In particular, though-in agreement with the currently accepted view-Maxwell maintains that the second law of thermodynamics, as originally conceived, cannot be strictly true, the replacement he proposes is different from the version accepted by most physicists today. The modification of the second law accepted by most physicists is a probabilistic one: although statistical fluctuations will result in occasional spontaneous differences in temperature or pressure, there is no way to predictably and reliably harness these to produce large violations of the original version of the second law. Maxwell advocates a version of the second law that is strictly weaker; the validity of even this probabilistic version is of limited scope, limited to situations in which we are dealing with large numbers of molecules en masse and have no ability to manipulate individual molecules. Connected with this is his conception of the thermodynamic concepts of heat, work, and entropy; on the Maxwellian view, these are concept that must be relativized to the means we have available for gathering information about and manipulating physical systems. The Maxwellian view is one that deserves serious consideration in discussions of the foundation of statistical mechanics. It has relevance for the project of recovering thermodynamics from statistical mechanics because, in such a project, it matters which version of the second law we are trying to recover.

  3. Quantum Mechanics, Volume 1

    NASA Astrophysics Data System (ADS)

    Cohen-Tannoudji, Claude; Diu, Bernard; Laloe, Frank

    1986-06-01

    Beginning students of quantum mechanics frequently experience difficulties separating essential underlying principles from the specific examples to which these principles have been historically applied. Nobel-Prize-winner Claude Cohen-Tannoudji and his colleagues have written this book to eliminate precisely these difficulties. Fourteen chapters provide a clarity of organization, careful attention to pedagogical details, and a wealth of topics and examples which make this work a textbook as well as a timeless reference, allowing to tailor courses to meet students' specific needs. Each chapter starts with a clear exposition of the problem which is then treated, and logically develops the physical and mathematical concept. These chapters emphasize the underlying principles of the material, undiluted by extensive references to applications and practical examples which are put into complementary sections. The book begins with a qualitative introduction to quantum mechanical ideas using simple optical analogies and continues with a systematic and thorough presentation of the mathematical tools and postulates of quantum mechanics as well as a discussion of their physical content. Applications follow, starting with the simplest ones like e.g. the harmonic oscillator, and becoming gradually more complicated (the hydrogen atom, approximation methods, etc.). The complementary sections each expand this basic knowledge, supplying a wide range of applications and related topics as well as detailed expositions of a large number of special problems and more advanced topics, integrated as an essential portion of the text.

  4. Second Law of Thermodynamics with Discrete Quantum Feedback Control

    NASA Astrophysics Data System (ADS)

    Sagawa, Takahiro; Ueda, Masahito

    2008-02-01

    A new thermodynamic inequality is derived which leads to the maximum work that can be extracted from multi-heat-baths with the assistance of discrete quantum feedback control. The maximum work is determined by the free-energy difference and a generalized mutual information content between the thermodynamic system and the feedback controller. This maximum work can exceed that in conventional thermodynamics and, in the case of a heat cycle with two heat baths, the heat efficiency can be greater than that of the Carnot cycle. The consistency of our results with the second law of thermodynamics is ensured by the fact that work is needed for information processing of the feedback controller.

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

    SciTech Connect

    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 Schroedinger dynamics. On the other hand the study of the probability distributions of some functions, such as the entropy or the equilibrium state of a subsystem, in statistical ensembles of pure states reveals the crucial role of typicality as the bridge between macroscopic thermodynamics and microscopic quantum dynamics. We shall consider two particular ensembles: the random pure state ensemble and the fixed expectation energy ensemble. The relation between the introduced ensembles, the properties of a given isolated system, and the standard quantum statistical description are discussed throughout the presentation. Finally we point out the conditions which should be satisfied by an ensemble in order to get meaningful thermodynamical characterization of an isolated quantum system.

  6. Hamiltonian and Thermodynamic Modeling of Quantum Turbulence

    NASA Astrophysics Data System (ADS)

    Grmela, Miroslav

    2010-10-01

    The state variables in the novel model introduced in this paper are the fields playing this role in the classical Landau-Tisza model and additional fields of mass, entropy (or temperature), superfluid velocity, and gradient of the superfluid velocity, all depending on the position vector and another tree dimensional vector labeling the scale, describing the small-scale structure developed in 4He superfluid experiencing turbulent motion. The fluxes of mass, momentum, energy, and entropy in the position space as well as the fluxes of energy and entropy in scales, appear in the time evolution equations as explicit functions of the state variables and of their conjugates. The fundamental thermodynamic relation relating the fields to their conjugates is left in this paper undetermined. The GENERIC structure of the equations serves two purposes: (i) it guarantees that solutions to the governing equations, independently of the choice of the fundamental thermodynamic relation, agree with the observed compatibility with thermodynamics, and (ii) it is used as a guide in the construction of the novel model.

  7. Dynamical and thermodynamical control of open quantum Brownian motion

    NASA Astrophysics Data System (ADS)

    Petruccione, Francesco; Sinayskiy, Ilya

    Open quantum Brownian motion was introduced as a new type of quantum Brownian motion for Brownian particles with internal quantum degrees of freedom. Recently, an example of the microscopic derivation of open quantum Brownian motion has been presented [I. Sinayskiy and F. Petruccione, Phys. Scr. T165, 014017 (2015)]. The microscopic derivation allows to relate the dynamical properties of open Quantum Brownian motion and the thermodynamical properties of the environment. In the present work, we study the possibility of control of the external degrees of freedom of the ''walker'' (position) by manipulating the internal one, e.g. spin, polarization, occupation numbers. In the particular example of the known microscopic derivation the connection between dynamics of the ''walker'' and thermodynamical parameters of the system is established. For the system of open Brownian walkers coupled to the same environment controllable creation of quantum correlations is investigated. This work is based upon research supported by the South African Research Chair Initiative of the Department of Science and Technology and National Research Foundation.

  8. Supersymmetric Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    David, J.; Fernández, C.

    2010-10-01

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

  9. Statistical Mechanics and Thermodynamics of Viral Evolution

    NASA Astrophysics Data System (ADS)

    Jones, Barbara; Kaufman, James

    Using methods drawn from physics we study the life cycle of viruses. We analyze a model of viral infection and evolution using the ``grand canonical ensemble'' and formalisms from statistical mechanics and thermodynamics. Using this approach we determine possible genetic states of a model virus and host as a function of two independent pressures-immune response and system temperature. We show 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. 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.

  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. Quantum Mechanics and Quantum Field Theory

    NASA Astrophysics Data System (ADS)

    Dimock, Jonathan

    2011-02-01

    Introduction; Part I. Non-relativistic: 1. Mathematical prelude; 2. Classical mechanics; 3. Quantum mechanics; 4. Single particle; 5. Many particles; 6. Statistical mechanics; Part II. Relativistic: 7. Relativity; 8. Scalar particles and fields; 9. Electrons and photons; 10. Field theory on a manifold; Part III. Probabilistic Methods: 11. Path integrals; 12. Fields as random variables; 13. A nonlinear field theory; Appendices; References; Index.

  12. Comparison between thermodynamic work and heat in autonomous quantum systems.

    PubMed

    Xu, Y Y

    2016-12-01

    One of the most important problems in quantum thermodynamics is how to distinguish work and heat in autonomous quantum systems. In this paper, work and heat are defined through the following criterion, i.e., work is the energy that cannot change the entropy of the energy resource, and satisfies the Jarzynski equality, while heat does not. Two kinds of definitions satisfying the two corresponding requirements are proposed and demonstrated, and the consistency condition of the two kinds is given. Through the first definition, the problem of entropy production is investigated. A model study is also presented to verify the proposal.

  13. Comparison between thermodynamic work and heat in autonomous quantum systems

    NASA Astrophysics Data System (ADS)

    Xu, Y. Y.

    2016-12-01

    One of the most important problems in quantum thermodynamics is how to distinguish work and heat in autonomous quantum systems. In this paper, work and heat are defined through the following criterion, i.e., work is the energy that cannot change the entropy of the energy resource, and satisfies the Jarzynski equality, while heat does not. Two kinds of definitions satisfying the two corresponding requirements are proposed and demonstrated, and the consistency condition of the two kinds is given. Through the first definition, the problem of entropy production is investigated. A model study is also presented to verify the proposal.

  14. Quantum gravity effects on charged microblack holes thermodynamics

    NASA Astrophysics Data System (ADS)

    Abbasvandi, Niloofar; Soleimani, M. J.; Radiman, Shahidan; Wan Abdullah, W. A. T.

    2016-08-01

    The charged black hole thermodynamics is corrected in terms of the quantum gravity effects. Most of the quantum gravity theories support the idea that near the Planck scale, the standard Heisenberg uncertainty principle should be reformulated by the so-called Generalized Uncertainty Principle (GUP) which provides a perturbation framework to perform required modifications of the black hole quantities. In this paper, we consider the effects of the minimal length and maximal momentum as GUP type I and the minimal length, minimal momentum and maximal momentum as GUP type II on thermo dynamics of the charged TeV-scale black holes. We also generalized our study to the universe with the extra dimensions based on the ADD model. In this framework, the effect of the electrical charge on thermodynamics of the black hole and existence of the charged black hole remnants as a potential candidate for the dark matter particles are discussed.

  15. Bell's theorem and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Rosen, Nathan

    1994-02-01

    Bell showed that assuming locality leads to a disagreement with quantum mechanics. Here the nature of the nonlocality that follows from quantum mechanics is investigated. Note by the Editor—Readers will recognize Professor Rosen, author of this paper, as one of the co-authors of the famous EPR paper, Albert Einstein, Boris Podolsky, and Nathan Rosen, ``Can Quantum-Mechanical Description of Physical Reality be considered Complete?'', Phys. Rev. 47, 770-780 (1935). Robert H. Romer, Editor

  16. Diagrammatic quantum mechanics

    NASA Astrophysics Data System (ADS)

    Kauffman, Louis H.; Lomonaco, Samuel J.

    2015-05-01

    This paper explores how diagrams of quantum processes can be used for modeling and for quantum epistemology. The paper is a continuation of the discussion where we began this formulation. Here we give examples of quantum networks that represent unitary transformations by dint of coherence conditions that constitute a new form of non-locality. Local quantum devices interconnected in space can form a global quantum system when appropriate coherence conditions are maintained.

  17. Klein's programme and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Clemente-Gallardo, Jesús; Marmo, Giuseppe

    2015-04-01

    We review the geometrical formulation of quantum mechanics to identify, according to Klein's programme, the corresponding group of transformations. For closed systems, it is the unitary group. For open quantum systems, the semigroup of Kraus maps contains, as a maximal subgroup, the general linear group. The same group emerges as the exponentiation of the C*-algebra associated with the quantum system, when thought of as a Lie algebra. Thus, open quantum systems seem to identify the general linear group as associated with quantum mechanics and moreover suggest to extend the Klein programme also to groupoids. The usual unitary group emerges as a maximal compact subgroup of the general linear group.

  18. 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.

  19. 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.

  20. Dynamics and Thermodynamics of Linear Quantum Open Systems

    NASA Astrophysics Data System (ADS)

    Martinez, Esteban A.; Paz, Juan Pablo

    2013-03-01

    We analyze the evolution of the quantum state of networks of quantum oscillators coupled with arbitrary external environments. We show that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime demonstrating two main results: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (thus, nonlinearity is an essential resource for such refrigerators recently studied by Levy and Kosloff [Phys. Rev. Lett. 108, 070604 (2012)] and Levy et al. [Phys. Rev. B 85, 061126 (2012)]). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities.

  1. Dynamics and thermodynamics of linear quantum open systems.

    PubMed

    Martinez, Esteban A; Paz, Juan Pablo

    2013-03-29

    We analyze the evolution of the quantum state of networks of quantum oscillators coupled with arbitrary external environments. We show that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime demonstrating two main results: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (thus, nonlinearity is an essential resource for such refrigerators recently studied by Levy and Kosloff [Phys. Rev. Lett. 108, 070604 (2012)] and Levy et al. [Phys. Rev. B 85, 061126 (2012)]). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities.

  2. Expected behavior of quantum thermodynamic machines with prior information.

    PubMed

    Thomas, George; Johal, Ramandeep S

    2012-04-01

    We estimate the expected behavior of the quantum model of a heat engine when we have incomplete information about external macroscopic parameters such as the magnetic field controlling the intrinsic energy scales of the working medium. We explicitly derive the prior probability distribution for these unknown parameters ai (i=1,2). Based on a few simple assumptions, the prior probability distribution is found to be of the form Π(ai)∝1/ai. By calculating the expected values of various physical quantities related to this engine, we find that the expected behavior of the quantum model exhibits thermodynamiclike features. This leads us to a surprising proposal that incomplete information quantified as an appropriate prior distribution can lead us to expect classical thermodynamic behavior in quantum models.

  3. Principles of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Landé, Alfred

    2013-10-01

    ödinger'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.

  4. 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.

  5. Dissipation effects in mechanics and thermodynamics

    NASA Astrophysics Data System (ADS)

    Güémez, J.; Fiolhais, M.

    2016-07-01

    With the discussion of three examples, we aim at clarifying the concept of energy transfer associated with dissipation in mechanics and in thermodynamics. The dissipation effects due to dissipative forces, such as the friction force between solids or the drag force in motions in fluids, lead to an internal energy increase of the system and/or to heat transfer to the surroundings. This heat flow is consistent with the second law, which states that the entropy of the universe should increase when those forces are present because of the irreversibility always associated with their actions. As far as mechanics is concerned, the effects of the dissipative forces are included in Newton’s equations as impulses and pseudo-works.

  6. Thermodynamics of CaMgSi2O6-KAlSi2O6 clinopyroxene solid solution: Quantum mechanical and static lattice energy calculations

    NASA Astrophysics Data System (ADS)

    Vinograd, V. L.; Safonov, O. G.; Wilson, D. J.; Gale, J. D.; Perchuk, L. L.; Winkler, B.

    2007-12-01

    K-enriched clinopyroxenes are often found in mineral assemblages formed at high and ultrahigh pressures, such as inclusions in diamonds, eclogitic and peridotitic xenoliths in kimberlites and lamproites. Thermodynamic properties of the solid solution between diopside and potassium jadeite cannot be studied experimentally due to impossibility to synthesize crystals with more than 25% of KAlSi2O6. Here we show that the missing thermodynamic information can be obtained with the aid of computer simulations. A set of empirical interatomic potentials has been used for calculation of static lattice energies of 800 different structures in a 2x2x4 supercell of C2/c pyroxene with compositions intermediate between diopside (Di) and K-jadeite (KJd), as well as with different ordering states of the exchangeable K/Ca and Mg/Al cations. Excess static energies of these structures were cluster expanded in a basis set of 37 pair-interaction parameters. These parameters were used to constrain Monte Carlo simulations of temperature-dependent properties in the range of 273-2023 K and to calculate a T-X phase diagram for the solid solution. The simulations predicted the formation of stable intermediate compounds at 1/3, 5/12, 1/2, 7/12 and 2/3 of the KJd mole fraction. The compound at 1/2 with a space group P2/b is analogous to omphacite in the diopside - jadeite system. However, the cation distribution in this phase is inverted: K and Ca in K-omphacite occupy positions which would be Ca-rich and Na-rich, respectively, in Na-omphacite. The standard enthalpies and volumes of KJd and K-omphacite were estimated from first principles calculations, while the standard entropies, thermal expansion coefficients and bulk moduli were predicted on the basis of the force field lattice dynamics. The activity-composition relations in the disordered C2/c phase were approximated with respect to Di and KJd end-members with a Redlich-Kister polynomial. Using these results and thermodynamic data available

  7. Dissipative Forces and Quantum Mechanics

    ERIC Educational Resources Information Center

    Eck, John S.; Thompson, W. J.

    1977-01-01

    Shows how to include the dissipative forces of classical mechanics in quantum mechanics by the use of non-Hermetian Hamiltonians. The Ehrenfest theorem for such Hamiltonians is derived, and simple examples which show the classical correspondences are given. (MLH)

  8. Thermodynamic Consistency of Mechanical Granular Theories

    NASA Astrophysics Data System (ADS)

    Hutter, K.

    Constitutive Theories of the mechanical behaviour of soils are often derived without resort to thermodynamic considerations. The form of the closure conditions, however, needs to be in conformity with the second law of thermodynamics and depends on it, even on the particular form which the second law is postulated to take. We outline two common forms of the entropy principle, (i) due to Clausius-Duhem and exploited according to Coleman-Noll and (ii) due to I. Müller and exploited ac- cording to Liu. We subject them to certain classes of material behaviour of saturated and unsaturated soil and show that not only the dynamic behaviour depends on the satisfaction of the second law, but equally also that in equilibrium. Examples illus- trating this will be given for (i) a dry soil with voids and exhibiting plastic internal frictional behaviour, (ii) a saturated granular fluid mixture able to model ground water soil interactions as well as (iii) a mixture of a finite number of grains with different diameters that is capable to describe inverse grading of a soil with a broad grain size distribution. In postulating constitutive relations for continuous granular mixtures, the rule of equipresence is often replaced by the rule of phase separation to simplify the com- putations. It is made plausible that, when constituents are strongly interacting, this principle is not likely to yield satisfactory formulations for the intended phenomena.

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

    PubMed

    Barra, Felipe

    2015-10-08

    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.

  10. 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

  11. Thermodynamics of information exchange between two coupled quantum dots

    NASA Astrophysics Data System (ADS)

    Kutvonen, Aki; Sagawa, Takahiro; Ala-Nissila, Tapio

    2016-03-01

    We propose a setup based on two coupled quantum dots where thermodynamics of a measurement can be quantitatively characterized. The information obtained in the measurement can be utilized by performing feedback in a manner apparently breaking the second law of thermodynamics. In this way the setup can be operated as a Maxwell's demon, where both the measurement and feedback are performed separately by controlling an external parameter. This is analogous to the case of the original Szilard engine. Since the setup contains both the microscopic demon and the engine itself, the operation of the whole measurement-feedback cycle can be explained in detail at the level of single realizations. In addition, we derive integral fluctuation relations for both the bare and coarse-grained entropy productions in the setup.

  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. Thermodynamics of quantum systems with multiple conserved quantities

    PubMed Central

    Guryanova, Yelena; Popescu, Sandu; Short, Anthony J.; Silva, Ralph; Skrzypczyk, Paul

    2016-01-01

    Recently, there has been much progress in understanding the thermodynamics of quantum systems, even for small individual systems. Most of this work has focused on the standard case where energy is the only conserved quantity. Here we consider a generalization of this work to deal with multiple conserved quantities. Each conserved quantity, which, importantly, need not commute with the rest, can be extracted and stored in its own battery. Unlike the standard case, in which the amount of extractable energy is constrained, here there is no limit on how much of any individual conserved quantity can be extracted. However, other conserved quantities must be supplied, and the second law constrains the combination of extractable quantities and the trade-offs between them. We present explicit protocols that allow us to perform arbitrarily good trade-offs and extract arbitrarily good combinations of conserved quantities from individual quantum systems. PMID:27384384

  14. Thermodynamical cost of some interpretations of quantum theory

    NASA Astrophysics Data System (ADS)

    Cabello, Adán; Gu, Mile; Gühne, Otfried; Larsson, Jan-Åke; Wiesner, Karoline

    2016-11-01

    The interpretation of quantum theory is one of the longest-standing debates in physics. Type I interpretations see quantum probabilities as determined by intrinsic properties of the observed system. Type II see them as relational experiences between an observer and the system. It is usually believed that a decision between these two options cannot be made simply on purely physical grounds but requires an act of metaphysical judgment. Here we show that, under some assumptions, the problem is decidable using thermodynamics. We prove that type I interpretations are incompatible with the following assumptions: (i) The choice of which measurement is performed can be made randomly and independently of the system under observation, (ii) the system has limited memory, and (iii) Landauer's erasure principle holds.

  15. 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).

  16. 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.

  17. An Introduction to Thermodynamics and Statistical Mechanics - 2nd Edition

    NASA Astrophysics Data System (ADS)

    Stowe, Keith

    2003-03-01

    This introductory textbook for standard undergraduate courses in thermodynamics has been completely rewritten. Starting with an overview of important quantum behaviours, the book teaches students how to calculate probabilities, in order to provide a firm foundation for later chapters. It introduces the ideas of classical thermodynamics and explores them both in general and as they are applied to specific processes and interactions. The remainder of the book deals with statistical mechanics - the study of small systems interacting with huge reservoirs. The changes to this second edition have been made after more than 10 years classroom testing and student feedback. Each topic ends with a boxed summary of ideas and results, and every chapter contains numerous homework problems, covering a broad range of difficulties. Answers are given to odd numbered problems, and solutions to even problems are available to instructors at www.cambridge.org/9780521865579. The entire book has been re-written and now covers more topics It has a greater number of homework problems which range in difficulty from warm-ups to challenges It is concise and has an easy reading style

  18. 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)

  19. Physical analogy between continuum thermodynamics and classical mechanics.

    PubMed

    Umantsev, Alex

    2004-01-01

    The main focus of this paper is the profound physical analogy between a continuum thermodynamical system, which evolves with relaxation under (possibly) nonisothermal conditions, and a classical mechanical system of a few interacting particles moving with dissipation in (possibly), time-dependent nonconservative fields. This analogy is applied to the problem of phase transitions in a one-dimensional thermodynamic system. The thermomechanical analogy stems from the validity of variational methods in mechanics and thermodynamics and allows for a different interpretation of the dynamical selection principle in the theory of pattern formation. This physical analogy is very helpful for understanding different nonlinear thermodynamic phenomena and for developing intuition in numerical simulations.

  20. Non-Hermitian quantum mechanics

    NASA Astrophysics Data System (ADS)

    Jones-Smith, Katherine

    The basic structure of quantum mechanics was delineated in the early days of the theory and has not been modified since. One of the fundamental assumptions used in formulating the theory is that operators are represented by Hermitian matrices. In recent years it has been shown that quantum mechanics can be formulated consistently without making this assumption, using instead a combination of the parity (P) and time-reversal (T) operators and a number of other requirements related to P and T. Only the case of even T has been analyzed in the literature; here we generalize the principles to include odd time-reversal. We use this generalization to construct a non-Hermitian version of the Dirac equation, and in doing so discover a new type of particle not allowed within the (Hermitian) Standard Model. Finally we present a potential application of the ideas of non-Hermitian quantum mechanics to the unsolved problems of quantum magnetism and high temperature superconductivity.

  1. 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.

  2. Quantum Mechanics and Narratability

    NASA Astrophysics Data System (ADS)

    Myrvold, Wayne C.

    2016-07-01

    As has been noted by several authors, in a relativistic context, there is an interesting difference between classical and quantum state evolution. For a classical system, a state history of a quantum system given along one foliation uniquely determines, without any consideration of the system's dynamics, a state history along any other foliation. This is not true for quantum state evolution; there are cases in which a state history along one foliation is compatible with multiple distinct state histories along some other, a phenomenon that David Albert has dubbed "non-narratability." In this article, we address the question of whether non-narratability is restricted to the sorts of special states that so far have been used to illustrate it. The results of the investigation suggest that there has been a misplaced emphasis on underdetermination of state histories; though this is generic for the special cases that have up until now been considered, involving bipartite systems in pure entangled states, it fails generically in cases in which more component systems are taken into account, and for bipartite systems that have some entanglement with their environment. For such cases, if we impose relativistic causality constraints on the evolution, then, except for very special states, a state history along one foliation uniquely determines a state history along any other. But this in itself is a marked difference between classical and quantum state evolution, because, in a classical setting, no considerations of dynamics at all are needed to go from a state history along one foliation to a state history along another.

  3. Thermodynamics of trajectories of open quantum systems, step by step

    NASA Astrophysics Data System (ADS)

    Pigeon, Simon; Xuereb, André

    2016-06-01

    Thermodynamics of trajectories promises to make possible the thorough analysis of the dynamical properties of an open quantum system, a sought-after goal in modern physics. Unfortunately, calculation of the relevant quantities presents severe challenges. Determining the large-deviation function that gives access to the full counting statistics associated with a dynamical order parameter is challenging, if not impossible, even for systems evolving in a restricted Liouville space. Acting on the realisation that the salient features of most dynamical systems are encoded in the first few moments of the counting statistics, in this article we present a method that gives sequential access to these moments. Our method allows for obtaining analytical result in several cases, as we illustrate, and allows using large deviation theory to reinterpret certain well-known results.

  4. Driven spin systems as quantum thermodynamic machines: Fundamental limits

    NASA Astrophysics Data System (ADS)

    Henrich, Markus J.; Mahler, Günter; Michel, Mathias

    2007-05-01

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

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

    PubMed

    Rigol, Marcos

    2014-09-01

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

  6. The quantum and thermodynamical characteristics of fission taking into account adiabatic and nonadiabatic modes of motion

    SciTech Connect

    Kadmensky, S. G.

    2007-09-15

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

  7. Classical, quantum, and thermodynamics of a lattice model exhibiting structural negative thermal expansion

    NASA Astrophysics Data System (ADS)

    Occhialini, Connor A.; Handunkanda, Sahan U.; Curry, Erin B.; Hancock, Jason N.

    2017-03-01

    We consider in detail a simple model supporting a single floppy mode that is often used to heuristically describe instances of negative thermal expansion. A key result is that the translational kinetic energy of the dilating bond network scales extensively with system size and results in dynamical properties which differ qualitatively from considerations built upon harmonic models. We develop an analogy between the dynamics of this model and a modified mechanical pendulum to elucidate the connection between the new results and the familiar harmonic limit. We then propose an appropriate Schrödinger equation for this system and study numerically the quantum mechanical solutions. Marked differences from conventional phonon dynamics and thermodynamics are seen in both classical and quantum limits, in particular a strong twofold enhancement of the (negative) coefficient of thermal expansion. We contextualize the results against real material parameters and discuss related empirical observations.

  8. Thermodynamic meaning of local temperature of nonequilibrium open quantum systems

    NASA Astrophysics Data System (ADS)

    Ye, LvZhou; Zheng, Xiao; Yan, YiJing; Di Ventra, Massimiliano

    2016-12-01

    Measuring the local temperature of nanoscale systems out of equilibrium has emerged as a new tool to study local heating effects and other local thermal properties of systems driven by external fields. Although various experimental protocols and theoretical definitions have been proposed to determine the local temperature, the thermodynamic meaning of the measured or defined quantities remains unclear. By performing analytical and numerical analysis of bias-driven quantum dot systems both in the noninteracting and strongly-correlated regimes, we elucidate the underlying physical meaning of local temperature as determined by two definitions: the zero-current condition that is widely used but not measurable and the minimal-perturbation condition that is experimentally realizable. We show that, unlike the zero-current condition, the local temperature determined by the minimal-perturbation protocol establishes a quantitative correspondence between the nonequilibrium system of interest and a reference equilibrium system, provided the probed system observable and the related electronic excitations are fully local. The quantitative correspondence thus allows the well-established thermodynamic concept to be extended to nonequilibrium situations.

  9. The effects of quantum gravity on some thermodynamical quantities

    NASA Astrophysics Data System (ADS)

    Kamali, A. D.; Shababi, H.; Nozari, K.

    2016-10-01

    In this paper, using a deformed algebra [X,P] = iℏ/(1 - α2P2) which is originated from various theories of gravity, we study thermodynamical properties of the classical and extreme relativistic gases in canonical ensembles. In this regards, we exactly calculate the modified partition function, Helmholtz free energy, internal energy, entropy, heat capacity and the thermal pressure which conclude to the familiar form of the equation of state for the ideal gas. The advantage of applying this algebra is not only considering all natural cutoffs but also its structure is similar to the other effective quantum gravity models such as polymer, Snyder and noncommutative space-time frameworks. Moreover, after obtaining some thermodynamical quantities including internal energy and entropy, we conclude at high temperature limits due to the decreasing of the number of microstates, these quantities reach to maximal bounds which do not exist in standard cases and it concludes that at the presence of gravity for both micro-canonic and canonic ensembles, the internal energy and the entropy tend to these upper bounds.

  10. 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

  11. 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

  12. 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…

  13. Energy conservation in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Prentis, Jeffrey J.; Fedak, William A.

    2004-05-01

    In the classical mechanics of conservative systems, the position and momentum evolve deterministically such that the sum of the kinetic energy and potential energy remains constant in time. This canonical trademark of energy conservation is absent in the standard presentations of quantum mechanics based on the Schrödinger picture. We present a purely canonical proof of energy conservation that focuses exclusively on the time-dependent position x(t) and momentum p(t) operators. This treatment of energy conservation serves as an introduction to the Heisenberg picture and illuminates the classical-quantum connection. We derive a quantum-mechanical work-energy theorem and show explicitly how the time dependence of x and p and the noncommutivity of x and p conspire to bring about a perfect temporal balance between the evolving kinetic and potential parts of the total energy operator.

  14. 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.

  15. On determining absolute entropy without quantum theory or the third law of thermodynamics

    NASA Astrophysics Data System (ADS)

    Steane, Andrew M.

    2016-04-01

    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.

  16. Intrusion Detection With Quantum Mechanics: A Photonic Quantum Fence

    DTIC Science & Technology

    2008-12-01

    computing and quantum key distribution (QKD). Some of the most remarkable examples include quantum teleportation for the non-local transfer of...1 INTRUSION DETECTION WITH QUANTUM MECHANICS: A PHOTONIC QUANTUM FENCE T. S. Humble*, R. S. Bennink, and W. P. Grice Oak Ridge National...use of quantum -mechanically entangled photons for sensing intrusions across a physical perimeter. Our approach to intrusion detection uses the no

  17. An analysis of the quantum effect on the thermodynamic and transport properties of cryogenic hydrogen using molecular dynamics method

    NASA Astrophysics Data System (ADS)

    Nagashima, Hiroki; Tsuda, Shin-ichi; Tsuboi, Nobuyuki; Koshi, Mitsuo; Hayashi, A. Koichi; Tokumasu, Takashi

    2014-03-01

    In this paper, we have analysed an effect of quantum nature of the hydrogen molecule on its thermodynamic and transport properties using molecular dynamics (MD) method based on the path integral method. We performed NVE constant MD simulation and the quantum effect on the molecular mechanism was analysed. The simulation results were compared with experimental data. As a result, we clarified that the quantum nature makes the virial pressure larger than in classical mechanics and taking account the quantum nature makes smaller intermolecular interaction energy and larger repulsive force than classical representation. Besides, we have confirmed that the path-integral-based MD method well reproduces the thermal conductivity and quantum effect on the transport properties is also large.

  18. On Heat in a Quantum Mechanical Process

    NASA Astrophysics Data System (ADS)

    Deesuwan, Tanapat; Anders, Janet

    2013-05-01

    Heat is the portion of energy exchange between systems in thermodynamic process which, unlike work, is always associated with the change of the entropies of the systems. In the context of quantum thermodynamics, heat process is described by an incoherent generalised quantum evolution, which is a map between two quantum states that does not preserve the entropy. Based on an information-theoretic reasoning, we propose that heat involving in a general quantum thermodynamic process can be separated into two types: one that is due to the unital subclass of the evolutions and another one that is due to the others. According to these categories, we show how the former type of heat can be incorporated into Jarzynski equality, resulting in a generalised version of the equality. We also derive a Jarzynski inequality which incorporates all heat into the picture and show that this situation is just equivalent to the presence of Maxwell's demon.

  19. 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.

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

    PubMed

    Nieuwenhuizen, Th M; Allahverdyan, A E

    2002-09-01

    (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.

  1. Sharpening the second law of thermodynamics with the quantum Bayes theorem

    NASA Astrophysics Data System (ADS)

    Gharibyan, Hrant; Tegmark, Max

    2014-09-01

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

  2. Sharpening the second law of thermodynamics with the quantum Bayes theorem.

    PubMed

    Gharibyan, Hrant; Tegmark, Max

    2014-09-01

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

  3. 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

  4. Thermodynamical analysis of a quantum heat engine based on harmonic oscillators.

    PubMed

    Insinga, Andrea; Andresen, Bjarne; Salamon, Peter

    2016-07-01

    Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.

  5. Thermodynamical analysis of a quantum heat engine based on harmonic oscillators

    NASA Astrophysics Data System (ADS)

    Insinga, Andrea; Andresen, Bjarne; Salamon, Peter

    2016-07-01

    Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.

  6. An Introduction to Thermodynamics and Statistical Mechanics

    NASA Astrophysics Data System (ADS)

    Stowe, Keith

    2013-10-01

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

  7. An Introduction to Thermodynamics and Statistical Mechanics

    NASA Astrophysics Data System (ADS)

    Stowe, Keith

    2007-05-01

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

  8. 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.

  9. Atomistic-level non-equilibrium model for chemically reactive systems based on steepest-entropy-ascent quantum thermodynamics

    NASA Astrophysics Data System (ADS)

    Li, Guanchen; Al-Abbasi, Omar; von Spakovsky, Michael R.

    2014-10-01

    This paper outlines an atomistic-level framework for modeling the non-equilibrium behavior of chemically reactive systems. The framework called steepest- entropy-ascent quantum thermodynamics (SEA-QT) is based on the paradigm of intrinsic quantum thermodynamic (IQT), which is a theory that unifies quantum mechanics and thermodynamics into a single discipline with wide applications to the study of non-equilibrium phenomena at the atomistic level. SEA-QT is a novel approach for describing the state of chemically reactive systems as well as the kinetic and dynamic features of the reaction process without any assumptions of near-equilibrium states or weak-interactions with a reservoir or bath. Entropy generation is the basis of the dissipation which takes place internal to the system and is, thus, the driving force of the chemical reaction(s). The SEA-QT non-equilibrium model is able to provide detailed information during the reaction process, providing a picture of the changes occurring in key thermodynamic properties (e.g., the instantaneous species concentrations, entropy and entropy generation, reaction coordinate, chemical affinities, reaction rate, etc). As an illustration, the SEA-QT framework is applied to an atomistic-level chemically reactive system governed by the reaction mechanism F + H2 leftrightarrow FH + H.

  10. From First Principles: The Application of Quantum Mechanics to Complex Molecules and Solvated Systems

    SciTech Connect

    Freitag, Mark A.

    2001-12-31

    The major title of this dissertation, 'From first principles,' is a phase often heard in the study of thermodynamics and quantum mechanics. These words embody a powerful idea in the physical sciences; namely, that it is possible to distill the complexities of nature into a set of simple, well defined mathematical laws from which specific relations can then be derived . In thermodynamics, these fundamental laws are immediately familiar to the physical scientist by their numerical order: the First, Second and Third Laws. However, the subject of the present volume is quantum mechanics-specifically, non-relativistic quantum mechanics, which is appropriate for most systems of chemical interest.

  11. 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.

  12. 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.

  13. Quantum communication between remote mechanical resonators

    NASA Astrophysics Data System (ADS)

    Felicetti, S.; Fedortchenko, S.; Rossi, R.; Ducci, S.; Favero, I.; Coudreau, T.; Milman, P.

    2017-02-01

    Mechanical resonators represent one of the most promising candidates to mediate the interaction between different quantum technologies, bridging the gap between efficient quantum computation and long-distance quantum communication. Here, we introduce an interferometric scheme where the interaction of a mechanical resonator with input-output quantum pulses is controlled by an independent classical drive. We design protocols for state teleportation and direct quantum state transfer, between distant mechanical resonators. The proposed device, feasible with state-of-the-art technology, can serve as a building block for the implementation of long-distance quantum networks of mechanical resonators.

  14. Geometrical Phases in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Christian, Joy Julius

    In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a

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

    NASA Astrophysics Data System (ADS)

    Barnes, George L.; Kellman, Michael E.

    2013-12-01

    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.

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

    PubMed

    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.

  18. Facets of contextual realism in quantum mechanics

    SciTech Connect

    Pan, Alok Kumar; Home, Dipankar

    2011-09-23

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

  19. Sampling Molecular Conformers in Solution with Quantum Mechanical Accuracy at a Nearly Molecular-Mechanics Cost.

    PubMed

    Rosa, Marta; Micciarelli, Marco; Laio, Alessandro; Baroni, Stefano

    2016-09-13

    We introduce a method to evaluate the relative populations of different conformers of molecular species in solution, aiming at quantum mechanical accuracy, while keeping the computational cost at a nearly molecular-mechanics level. This goal is achieved by combining long classical molecular-dynamics simulations to sample the free-energy landscape of the system, advanced clustering techniques to identify the most relevant conformers, and thermodynamic perturbation theory to correct the resulting populations, using quantum-mechanical energies from density functional theory. A quantitative criterion for assessing the accuracy thus achieved is proposed. The resulting methodology is demonstrated in the specific case of cyanin (cyanidin-3-glucoside) in water solution.

  20. Jarzynski equality in PT-symmetric quantum mechanics

    DOE PAGES

    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.

  1. Jarzynski Equality in PT-Symmetric Quantum Mechanics.

    PubMed

    Deffner, Sebastian; Saxena, Avadh

    2015-04-17

    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.

  2. 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.

  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. Deformation of noncommutative quantum mechanics

    NASA Astrophysics Data System (ADS)

    Jiang, Jian-Jian; Chowdhury, S. Hasibul Hassan

    2016-09-01

    In this paper, the Lie group GNC α , β , γ , of which the kinematical symmetry group GNC of noncommutative quantum mechanics (NCQM) is a special case due to fixed nonzero α, β, and γ, is three-parameter deformation quantized using the method suggested by Ballesteros and Musso [J. Phys. A: Math. Theor. 46, 195203 (2013)]. A certain family of QUE algebras, corresponding to GNC α , β , γ with two of the deformation parameters approaching zero, is found to be in agreement with the existing results of the literature on quantum Heisenberg group. Finally, we dualize the underlying QUE algebra to obtain an expression for the underlying star-product between smooth functions on GNC α , β , γ .

  5. Quantum Mechanics: Myths and Facts

    NASA Astrophysics Data System (ADS)

    Nikolić, 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.

  6. Matrix quantum mechanics from qubits

    NASA Astrophysics Data System (ADS)

    Hartnoll, Sean A.; Huijse, Liza; Mazenc, Edward A.

    2017-01-01

    We introduce a transverse field Ising model with order N 2 spins interacting via a nonlocal quartic interaction. The model has an O( N, ℤ), hyperoctahedral, symmetry. We show that the large N partition function admits a saddle point in which the symmetry is enhanced to O( N). We further demonstrate that this `matrix saddle' correctly computes large N observables at weak and strong coupling. The matrix saddle undergoes a continuous quantum phase transition at intermediate couplings. At the transition the matrix eigenvalue distribution becomes disconnected. The critical excitations are described by large N matrix quantum mechanics. At the critical point, the low energy excitations are waves propagating in an emergent 1 + 1 dimensional spacetime.

  7. Quantum-mechanical twin paradox

    NASA Astrophysics Data System (ADS)

    Franson, J. D.

    2016-10-01

    In the twin paradox of special relativity, an observer that travels along an accelerated trajectory at a high velocity will experience a smaller amount of elapsed time than an observer that remains at rest. This illustrates the fact that time is relative unlike the situation in classical physics where time is absolute. In a recent paper, Bushev et al (2016 New J. Phys. 18 093050) showed that the twin paradox can also be demonstrated using a single electron that functions as a quantum-mechanical clock. The wave function of the electron can travel along two different paths simultaneously, which allows a measurement of the difference in proper times along the two trajectories using a single particle. Quantum interference effects show that time cannot be thought of as a classical parameter even when associated with a single clock or observer.

  8. The Second Law of Thermodynamics in a Quantum Heat Engine Model

    NASA Astrophysics Data System (ADS)

    Zhang, Ting; Cai, Li-Feng; Chen, Ping-Xing; Li, Cheng-Zu

    2006-03-01

    The second law of thermodynamics has been proven by many facts in classical world. Is there any new property of it in quantum world? In this paper, we calculate the change of entropy in T.D. Kieu's model for quantum heat engine (QHE) and prove the broad validity of the second law of thermodynamics. It is shown that the entropy of the quantum heat engine neither decreases in a whole cycle, nor decreases in either stage of the cycle. The second law of thermodynamics still holds in this QHE model. Moreover, although the modified quantum heat engine is capable of extracting more work, its efficiency does not improve at all. It is neither beyond the efficiency of T.D. Kieu's initial model, nor greater than the reversible Carnot efficiency.

  9. Mechanism for quantum speedup in open quantum systems

    NASA Astrophysics Data System (ADS)

    Liu, Hai-Bin; Yang, W. L.; An, Jun-Hong; Xu, Zhen-Yu

    2016-02-01

    The quantum speed limit (QSL) time for open system characterizes the most efficient response of the system to the environmental influences. Previous results showed that the non-Markovianity governs the quantum speedup. Via studying the dynamics of a dissipative two-level system, we reveal that the non-Markovian effect is only the dynamical way of the quantum speedup, while the formation of the system-environment bound states is the essential reason for the quantum speedup. Our attribution of the quantum speedup to the energy-spectrum character can supply another vital path for experiments when the quantum speedup shows up without any dynamical calculations. The potential experimental observation of our quantum speedup mechanism in the circuit QED system is discussed. Our results may be of both theoretical and experimental interest in exploring the ultimate QSL in realistic environments, and may open new perspectives for devising active quantum speedup devices.

  10. Quantum localization of classical mechanics

    NASA Astrophysics Data System (ADS)

    Batalin, Igor A.; Lavrov, Peter M.

    2016-07-01

    Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.

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

    SciTech Connect

    Kadmensky, S.G.

    2005-12-01

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

  12. 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)

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

    PubMed

    Ćwikliński, Piotr; Studziński, Michał; Horodecki, Michał; 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.

  14. 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

  15. Propagators in polymer quantum mechanics

    NASA Astrophysics Data System (ADS)

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

    2013-09-01

    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 μ0, the length scale introduced in the polymer dynamics and which plays a role analog of that of Planck length in Quantum Gravity.

  16. Bridging classical and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Haddad, D.; Seifert, F.; Chao, L. S.; Li, S.; Newell, D. B.; Pratt, J. R.; Williams, C.; Schlamminger, S.

    2016-10-01

    Using a watt balance and a frequency comb, a mass-energy equivalence is derived. The watt balance compares mechanical power measured in terms of the meter, the second, and the kilogram to electrical power measured in terms of the volt and the ohm. A direct link between mechanical action and the Planck constant is established by the practical realization of the electrical units derived from the Josephson and the quantum Hall effects. By using frequency combs to measure velocities and acceleration of gravity, the unit of mass can be realized from a set of three defining constants: the Planck constant h, the speed of light c, and the hyperfine splitting frequency of 133Cs.

  17. Quantum mechanical light harvesting mechanisms in photosynthesis

    NASA Astrophysics Data System (ADS)

    Scholes, Gregory

    2012-02-01

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

  18. Heisenberg and the Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Camilleri, Kristian

    2009-02-01

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

  19. Heisenberg and the Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Camilleri, Kristian

    2011-09-01

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

  20. The quantum-chemical determination of group contributions to the thermodynamic properties of organophosphorus compounds

    NASA Astrophysics Data System (ADS)

    Dorofeeva, O. V.; Ryzhova, O. N.; Moiseeva, N. F.

    2008-06-01

    The enthalpies of formation, entropies, and heat capacities of 95 organophosphorus derivatives calculated by nonempirical quantum-chemical methods were used to develop the additive method for estimating the thermodynamic properties of these compounds. 86 group contribution values were obtained for estimating the thermodynamic properties of diverse organic derivatives of phosphorus in the oxidation states 3 and 5 (three-and four-coordinate phosphorus atoms).

  1. Speakable and Unspeakable in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Bell, J. S.; Aspect, Introduction by Alain

    2004-06-01

    List of papers on quantum philosophy by J. S. Bell; Preface; Acknowledgements; Introduction by Alain Aspect; 1. On the problem of hidden variables in quantum mechanics; 2. On the Einstein-Rosen-Podolsky paradox; 3. The moral aspects of quantum mechanics; 4. Introduction to the hidden-variable question; 5. Subject and object; 6. On wave packet reduction in the Coleman-Hepp model; 7. The theory of local beables; 8. Locality in quantum mechanics: reply to critics; 9. How to teach special relativity; 10. Einstein-Podolsky-Rosen experiments; 11. The measurement theory of Everett and de Broglie's pilot wave; 12. Free variables and local causality; 13. Atomic-cascade photons and quantum-mechanical nonlocality; 14. de Broglie-Bohm delayed choice double-slit experiments and density matrix; 15. Quantum mechanics for cosmologists; 16. Bertlmann's socks and the nature of reality; 17. On the impossible pilot wave; 18. Speakable and unspeakable in quantum mechanics; 19. Beables for quantum field theory; 20. Six possible worlds of quantum mechanics; 21. EPR correlations and EPR distributions; 22. Are there quantum jumps?; 23. Against 'measurement'; 24. La Nouvelle cuisine.

  2. Towards a Constructive Foundation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Smilga, Walter

    2016-11-01

    I describe a constructive foundation for quantum mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of quantum mechanics. The quantum mechanical description is identified as a mathematical tool that allows describing objects, whose degree of freedom in space-time has a discrete spectrum, relative to classical observers in space-time. This description is covariant with respect to (continuous) coordinate transformations and meets the requirement that the spectrum is the same in every inertial system. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of quantum mechanics.

  3. Towards a Constructive Foundation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Smilga, Walter

    2017-01-01

    I describe a constructive foundation for quantum mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of quantum mechanics. The quantum mechanical description is identified as a mathematical tool that allows describing objects, whose degree of freedom in space-time has a discrete spectrum, relative to classical observers in space-time. This description is covariant with respect to (continuous) coordinate transformations and meets the requirement that the spectrum is the same in every inertial system. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of quantum mechanics.

  4. Bohmian mechanics and quantum field theory.

    PubMed

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

    2004-08-27

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

  5. 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.

  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

  7. Quantum mechanics without potential function

    SciTech Connect

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

    2015-07-15

    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.

  8. Quantum mechanics of Proca fields

    NASA Astrophysics Data System (ADS)

    Zamani, Farhad; Mostafazadeh, Ali

    2009-05-01

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

  9. Does the Third Law of Thermodynamics Hold in the Quantum Regime?

    NASA Astrophysics Data System (ADS)

    O'Connell, R. F.

    2006-07-01

    The first in a long series of papers by John T. Lewis, in collaboration with G. W. Ford and the present author, considered the problem of the most general coupling of a quantum particle to a linear passive heat bath, in the course of which they derived an exact formula for the free energy of an oscillator coupled to a heat bath in thermal equilibrium at temperature T. This formula, and its later extension to three dimensions to incorporate a magnetic field, has proved to be invaluable in analyzing problems in quantum thermodynamics. Here, we address the question raised in our title viz. Nernst's third law of thermodynamics.

  10. 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.

  11. Quantum mechanics, relativity and time

    NASA Astrophysics Data System (ADS)

    Basini, Giuseppe; Capozziello, Salvatore

    2005-01-01

    A discussion on quantum mechanics, general relativity and their relations is introduced. The assumption of the absolute validity of conservation laws and the extension to a 5D-space lead to reconsider several shortcomings and paradoxes of modern physics under a new light without the necessity to take into account symmetry breakings. In this picture, starting from first principles, and after a reduction procedure from 5D to 4D, dynamics leads to the natural emergence of two time arrows and ofa scalar-tensor theory of gravity. In this framework, phenomena like entanglement of systems and topology changes can be naturally accounted and, furthermore, several experimental evidences as gamma ray bursts, sizes of astrophysical structures and the observed values of cosmological parameters can be explained. The identification, thanks to conservation laws, of a covariant symplectic structure as a general feature also for gravity can be seen as a deep link common to all the interactions.

  12. Quantum mechanics/molecular mechanics restrained electrostatic potential fitting.

    PubMed

    Burger, Steven K; Schofield, Jeremy; Ayers, Paul W

    2013-12-05

    We present a quantum mechanics/molecular mechanics (QM/MM) method to evaluate the partial charges of amino acid residues for use in MM potentials based on their protein environment. For each residue of interest, the nearby residues are included in the QM system while the rest of the protein is treated at the MM level of theory. After a short structural optimization, the partial charges of the central residue are fit to the electrostatic potential using the restrained electrostatic potential (RESP) method. The resulting charges and electrostatic potential account for the individual environment of the residue, although they lack the transferable nature of library partial charges. To evaluate the quality of the QM/MM RESP charges, thermodynamic integration is used to measure the pKa shift of the aspartic acid residues in three different proteins, turkey egg lysozyme, beta-cryptogein, and Thioredoxin. Compared to the AMBER ff99SB library values, the QM/MM RESP charges show better agreement between the calculated and experimental pK(a) values for almost all of the residues considered.

  13. 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.

  14. Quantum Mechanics and physical calculations

    NASA Astrophysics Data System (ADS)

    Karayan, H. S.

    2014-03-01

    We suggest to realize the computer simulation and calculation by the algebraic structure built on the basis of the logic inherent to processes in physical systems (called physical computing). We suggest a principle for the construction of quantum algorithms of neuroinformatics of quantum neural networks. The role of academician Sahakyan is emphasized in the development of quantum physics in Armenia.

  15. Einstein's equivalence principle in quantum mechanics revisited

    NASA Astrophysics Data System (ADS)

    Nauenberg, Michael

    2016-11-01

    The gravitational equivalence principle in quantum mechanics is of considerable importance, but it is generally not included in physics textbooks. In this note, we present a precise quantum formulation of this principle and comment on its verification in a neutron diffraction experiment. The solution of the time dependent Schrödinger equation for this problem also gives the wave function for the motion of a charged particle in a homogeneous electric field, which is also usually ignored in textbooks on quantum mechanics.

  16. 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…

  17. Dynamical Casimir effect and minimal temperature in quantum thermodynamics

    NASA Astrophysics Data System (ADS)

    Benenti, Giuliano; Strini, Giuliano

    2015-02-01

    We study the fundamental limitations of cooling to absolute zero for a qubit, interacting with a single mode of the electromagnetic field. Our results show that the dynamical Casimir effect, which is unavoidable in any finite-time thermodynamic cycle, forbids the attainability of the absolute zero of temperature, even in the limit of an infinite number of cycles.

  18. Improving students' understanding of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Zhu, Guangtian

    2011-12-01

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

  19. Symmetry and the thermodynamics of currents in open quantum systems

    NASA Astrophysics Data System (ADS)

    Manzano, Daniel; Hurtado, Pablo I.

    2014-09-01

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

  20. Quantum Mechanical Models Of The Fermi Shuttle

    SciTech Connect

    Sternberg, James

    2011-06-01

    The Fermi shuttle is a mechanism in which high energy electrons are produced in an atomic collision by multiple collisions with a target and a projectile atom. It is normally explained purely classically in terms of the electron's orbits prescribed in the collision. Common calculations to predict the Fermi shuttle use semi-classical methods, but these methods still rely on classical orbits. In reality such collisions belong to the realm of quantum mechanics, however. In this paper we discuss several purely quantum mechanical calculations which can produce the Fermi shuttle. Being quantum mechanical in nature, these calculations produce these features by wave interference, rather than by classical orbits.

  1. Experiments on cloaking in optics, thermodynamics and mechanics.

    PubMed

    Kadic, Muamer; Bückmann, Tiemo; Schittny, Robert; Wegener, Martin

    2015-08-28

    Spatial coordinate transformations can be used to transform boundaries, material parameters or discrete lattices. We discuss fundamental constraints in regard to cloaking and review our corresponding experiments in optics, thermodynamics and mechanics. For example, we emphasize three-dimensional broadband visible-frequency carpet cloaking, transient thermal cloaking, three-dimensional omnidirectional macroscopic broadband cloaking for diffuse light throughout the entire visible range, cloaking for flexural waves in thin plates and three-dimensional elasto-static core-shell cloaking using pentamode mechanical metamaterials.

  2. Thermodynamic Mechanism Analysis of Calcification Roasting Process of Bastnaesite Concentrates

    NASA Astrophysics Data System (ADS)

    Cen, Peng; Wu, Wenyuan; Bian, Xue

    2017-03-01

    A novel calcification roasting decomposition method for bastnaesite concentrates has been proposed previously. In this work, the thermodynamic mechanism was investigated via simultaneous measurements of thermogravimetry and differential thermal analyses, combined with X-ray diffraction analyses. Rare earth oxides and calcium fluorides were generated after bastnaesite and calcium hydroxide broke down, respectively. The generation and decomposition of calcium carbonate occurred at the same time. Considering the difficulties in obtaining pure substances, theoretical calculations were applied to determine the standard enthalpy of formation (Δf H 298), Gibbs free energies of formation (Δf G 298), and heat capacities at constant pressure (C p) of some rare earth minerals (CeFCO3 and CeOF). Based on these results, the standard Gibbs energy of reaction at different temperatures (Δr G T) was ascertained, and the major reactions were verified to be thermodynamically reasonable.

  3. Thermodynamic signatures of an underlying quantum phase transition: A grand canonical approach

    NASA Astrophysics Data System (ADS)

    Jimenez, Kevin; Reslen, Jose

    2016-08-01

    The grand canonical formalism is employed to study the thermodynamic structure of a model displaying a quantum phase transition when studied with respect to the canonical formalism. A numerical survey shows that the grand partition function diverges following a power law when the interaction parameter approaches a limiting constant. The power-law exponent takes a distinctive value when such limiting constant coincides with the critical point of the subjacent quantum phase transition. An approximated expression for the grand partition function is derived analytically implementing a mean field scheme and a number of thermodynamic observables are obtained. The system observables show signatures that can be used to track the critical point of the underlying transition. This result provides a simple fact that can be exploited to verify the existence of a quantum phase transition avoiding the zero temperature regime.

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

    NASA Astrophysics Data System (ADS)

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

    2013-06-01

    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.

  5. 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.

  6. 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.

  7. Principles and Dynamics of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Efthimiades, Spyros

    2009-05-01

    Quantum mechanics can be founded on three principles: particle waves, concurrent states and averaged energy relations. The Schrodinger, time-evolution and Dirac equations are derived to be the conditions the wavefunction must satisfy in order to fulfill the corresponding averaged energy relations. Adopting a particle and wave balanced approach we attain a clear, consistent and justified quantum theory.

  8. Dynamical and thermodynamical control of Open Quantum Walks

    NASA Astrophysics Data System (ADS)

    Petruccione, Francesco; Sinayskiy, Ilya

    2014-03-01

    Over the last few years dynamical properties and limit distributions of Open Quantum Walks (OQWs), quantum walks driven by dissipation, have been intensely studied [S. Attal et. al. J. Stat. Phys. 147, Issue 4, 832 (2012)]. For some particular cases of OQWs central limit theorems have been proven [S. Attal, N. Guillotin, C. Sabot, ``Central Limit Theorems for Open Quantum Random Walks,'' to appear in Annales Henri Poincaré]. However, only recently the connection between the rich dynamical behavior of OQWs and the corresponding microscopic system-environment models has been established. The microscopic derivation of an OQW as a reduced system dynamics on a 2-nodes graph [I. Sinayskiy, F. Petruccione, Open Syst. Inf. Dyn. 20, 1340007 (2013)] and its generalization to arbitrary graphs allow to explain the dependance of the dynamical behavior of the OQW on the temperature and coupling to the environment. For thermal environments we observe Gaussian behaviour, whereas at zero temperature population trapping and ``soliton''-like behaviour are possible. Physical realizations of OQWs in quantum optical setups will be also presented. This work is based on research supported by the South African Research Chair Initiative of the Department of Science and Technology and National Research Foundation.

  9. Dynamics of nonrelativistic quantum mechanics

    NASA Astrophysics Data System (ADS)

    Efthimiades, Spyros

    2017-01-01

    We show that the wavefunction of an electron interacting with an electric potential is accurately represented by the superposition of plane waves that fulfills the total energy relation. As a result, we explicitly derive the Schrödinger, Pauli, Klein-Gordon, and Dirac equations. While the traditional nonrelativistic quantum dynamics is based on postulates, the dynamics we introduce is theoretically justified, in agreement with experimental measurements, and consistent with the fundamental theory of quantum electrodynamics.

  10. 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.

  11. 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)

  12. 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.

  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. Continuum mechanics beyond the second law of thermodynamics.

    PubMed

    Ostoja-Starzewski, M; Malyarenko, A

    2014-11-08

    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.

  15. Uncertainty in quantum mechanics: faith or fantasy?

    PubMed

    Penrose, Roger

    2011-12-13

    The word 'uncertainty', in the context of quantum mechanics, usually evokes an impression of an essential unknowability of what might actually be going on at the quantum level of activity, as is made explicit in Heisenberg's uncertainty principle, and in the fact that the theory normally provides only probabilities for the results of quantum measurement. These issues limit our ultimate understanding of the behaviour of things, if we take quantum mechanics to represent an absolute truth. But they do not cause us to put that very 'truth' into question. This article addresses the issue of quantum 'uncertainty' from a different perspective, raising the question of whether this term might be applied to the theory itself, despite its unrefuted huge success over an enormously diverse range of observed phenomena. There are, indeed, seeming internal contradictions in the theory that lead us to infer that a total faith in it at all levels of scale leads us to almost fantastical implications.

  16. On the geometrization of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Tavernelli, Ivano

    2016-08-01

    Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave-particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie-Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space-time, as it is the case for gravitation in the general relativity.

  17. 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.

  18. Geometric Hamiltonian quantum mechanics and applications

    NASA Astrophysics Data System (ADS)

    Pastorello, Davide

    2016-08-01

    Adopting a geometric point of view on Quantum Mechanics is an intriguing idea since, we know that geometric methods are very powerful in Classical Mechanics then, we can try to use them to study quantum systems. In this paper, we summarize the construction of a general prescription to set up a well-defined and self-consistent geometric Hamiltonian formulation of finite-dimensional quantum theories, where phase space is given by the Hilbert projective space (as Kähler manifold), in the spirit of celebrated works of Kibble, Ashtekar and others. Within geometric Hamiltonian formulation quantum observables are represented by phase space functions, quantum states are described by Liouville densities (phase space probability densities), and Schrödinger dynamics is induced by a Hamiltonian flow on the projective space. We construct the star-product of this phase space formulation and some applications of geometric picture are discussed.

  19. On the geometrization of quantum mechanics

    SciTech Connect

    Tavernelli, Ivano

    2016-08-15

    Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave–particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie–Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space–time, as it is the case for gravitation in the general relativity.

  20. Self-consistent mean field theory studies of the thermodynamics and quantum spin dynamics of magnetic Skyrmions.

    PubMed

    Wieser, R

    2017-05-04

    A self-consistent mean field theory is introduced and used to investigate the thermodynamics and spin dynamics of an S  =  1 quantum spin system with a magnetic Skyrmion. The temperature dependence of the Skyrmion profile as well as the phase diagram are calculated. In addition, the spin dynamics of a magnetic Skyrmion is described by solving the time dependent Schrödinger equation with additional damping term. The Skyrmion annihilation process driven by an electric field is used to compare the trajectories of the quantum mechanical simulation with a semi-classical description for the spin expectation values using a differential equation similar to the classical Landau-Lifshitz-Gilbert equation.

  1. Antonio Gramsci's Reflection on Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Tassani, Isabella

    2006-06-01

    As the first step of a wider historical reconstruction of the reception of quantum mechanics in the nineteenth-century philosophy, we are going to consider Antonio Gramsci's philosophy. He asks himself about the nature of quantum objects, if their existence depends on the act of measuring by the experimenter and if this kind of relationship can be interpreted as an argument in favour of an immaterialistic philosophy. We will remark how an idealistic interpretation of quantum mechanics found a fertile field in the Italian culture, characterized by an antiscientific attitude and at the same time needing to find in science a term of comparison.

  2. Quantum mechanics near closed timelike lines

    NASA Astrophysics Data System (ADS)

    Deutsch, David

    1991-11-01

    The methods of the quantum theory of computation are used to analyze the physics of closed timelike lines. This is dominated, even at the macroscopic level, by quantum mechanics. In classical physics the existence of such lines in a spacetime imposes ``paradoxical'' constraints on the state of matter in their past and also provides means for knowledge to be created in ways that conflict with the principles of the philosophy of science. In quantum mechanics the first of these pathologies does not occur. The second is mitigated, and may be avoidable without such spacetimes being ruled out. Several novel and distinctive (but nonparadoxical) quantum-mechanical effects occur on and near closed timelike lines, including violations of the correspondence principle and of unitarity. It becomes possible to ``clone'' quantum systems and to measure the state of a quantum system. A new experimental test of the Everett interpretation against all others becomes possible. Consideration of these and other effects sheds light on the nature of quantum mechanics.

  3. Reprint of : Thermodynamic properties of a quantum Hall anti-dot interferometer

    NASA Astrophysics Data System (ADS)

    Levy Schreier, Sarah; Stern, Ady; Rosenow, Bernd; Halperin, Bertrand I.

    2016-08-01

    We study quantum Hall interferometers in which the interference loop encircles a quantum anti-dot. We base our study on thermodynamic considerations, which we believe reflect the essential aspects of interference transport phenomena. We find that similar to the more conventional Fabry-Perot quantum Hall interferometers, in which the interference loop forms a quantum dot, the anti-dot interferometer is affected by the electro-static Coulomb interaction between the edge modes defining the loop. We show that in the Aharonov-Bohm regime, in which effects of fractional statistics should be visible, is easier to access in interferometers based on anti-dots than in those based on dots. We discuss the relevance of our results to recent measurements on anti-dots interferometers.

  4. Thermodynamic mechanism for the evasion of antibody neutralization in flaviviruses.

    PubMed

    Maillard, Rodrigo A; Liu, Tong; Beasley, David W C; Barrett, Alan D T; Hilser, Vincent J; Lee, J Ching

    2014-07-23

    Mutations in the epitopes of antigenic proteins can confer viral resistance to antibody-mediated neutralization. However, the fundamental properties that characterize epitope residues and how mutations affect antibody binding to alter virus susceptibility to neutralization remain largely unknown. To address these questions, we used an ensemble-based algorithm to characterize the effects of mutations on the thermodynamics of protein conformational fluctuations. We applied this method to the envelope protein domain III (ED3) of two medically important flaviviruses: West Nile and dengue 2. We determined an intimate relationship between the susceptibility of a residue to thermodynamic perturbations and epitope location. This relationship allows the successful identification of the primary epitopes in each ED3, despite their high sequence and structural similarity. Mutations that allow the ED3 to evade detection by the antibody either increase or decrease conformational fluctuations of the epitopes through local effects or long-range interactions. Spatially distant interactions originate in the redistribution of conformations of the ED3 ensembles, not through a mechanically connected array of contiguous amino acids. These results reconcile previous observations of evasion of neutralization by mutations at a distance from the epitopes. Finally, we established a quantitative correlation between subtle changes in the conformational fluctuations of the epitope and large defects in antibody binding affinity. This correlation suggests that mutations that allow viral growth, while reducing neutralization, do not generate significant structural changes and underscores the importance of protein fluctuations and long-range interactions in the mechanism of antibody-mediated neutralization resistance.

  5. 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…

  6. Nonrelativistic Quantum Mechanics with Fundamental Environment

    NASA Astrophysics Data System (ADS)

    Gevorkyan, Ashot S.

    2011-03-01

    Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations ( fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantum system (QS) + FE" is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ⊗ R { ξ}, where R 3 and R { ξ} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.

  7. 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.

  8. 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.

  9. Measurements and mathematical formalism of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Slavnov, D. A.

    2007-03-01

    A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantum mechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.

  10. Photon Quantum Mechanics in the Undergraduate Curriculum

    NASA Astrophysics Data System (ADS)

    Pearson, Brett; Carson, Zack; Jackson, David

    2011-05-01

    Although it has been discussed for centuries, the true nature of light is still being debated. In fact, the quantum mechanical aspects of light have only been observed within the past 30 years. Recent advances in technology have decreased the complexity of such tests, and the Department of Physics and Astronomy at Dickinson College has worked to infuse various quantum optics experiments throughout our curriculum. We describe a set of experiments that includes the existence of photons, single-photon interference, the quantum eraser, and tests of Bell's theorem. A primary motivation is bringing undergraduate students face to face with some of the fascinating and subtle aspects of quantum mechanics in a hands-on setting. Supported by Dickinson College and NSF DUE-0737230.

  11. 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 Ψ(t,x), a solution to the Schrödinger equation; meanwhile, the closed-loop guidance system forms a complex state–space dynamics for Ψ(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 Ψ{sup ∗}Ψ. -- 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.

  12. Computations in quantum mechanics made easy

    NASA Astrophysics Data System (ADS)

    Korsch, H. J.; Rapedius, K.

    2016-09-01

    Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of spectral and dynamical properties for one-dimensional and two-dimensional single-particle systems as well as bosonic many-particle and open quantum systems. Due to their technical simplicity these methods are well suited as a tool for teaching quantum mechanics to undergraduates and graduates. Explicit implementations of the presented numerical methods in Matlab are given.

  13. Emergent quantum mechanics of finances

    NASA Astrophysics Data System (ADS)

    Nastasiuk, Vadim A.

    2014-06-01

    This paper is an attempt at understanding the quantum-like dynamics of financial markets in terms of non-differentiable price-time continuum having fractal properties. The main steps of this development are the statistical scaling, the non-differentiability hypothesis, and the equations of motion entailed by this hypothesis. From perspective of the proposed theory the dynamics of S&P500 index are analyzed.

  14. 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.

  15. Operational approach to fluctuations of thermodynamic variables in finite quantum systems.

    PubMed

    Jahnke, T; Lanéry, S; Mahler, G

    2011-01-01

    In this paper we present a quantum approach to the old problem of temperature fluctuations. We start by observing that according to quantum thermodynamics, fluctuations of intensive parameters like temperature cannot exist. Furthermore, such parameters are not observables, so their estimation has to be done indirectly. The respective temperature estimate based on quantum measurements of the energy is shown to fluctuate according to the well-known formula ΔT(2)=k(B)T(2)/C, but only within a certain temperature range and if the system is not too small. We also calculate the fourth-order correction term, becoming important at higher temperatures. Finally we illustrate our results with a concrete model of n spins.

  16. Quantum and statistical mechanics in open systems: theory and examples

    NASA Astrophysics Data System (ADS)

    Zueco, David

    2009-08-01

    Using the system-bath model Hamiltonian this thesis covers the equilibrium and out of equilibrium properties of quantum open systems. Topics included are the calculation of thermodynamical quantities of open systems, derivation of quantum master equations, phase space and numerical methods and Linear and non Linear Response Theory. Applications are the transport in periodic potentials and the dynamics of spins.

  17. 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.

  18. Statistical Mechanics of Confined Quantum Particles

    NASA Astrophysics Data System (ADS)

    Bannur, Vishnu M.; Udayanandan, K. M.

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

  19. An Axiomatic Basis for Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Cassinelli, Gianni; Lahti, Pekka

    2016-10-01

    In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in this derivation are the co-ordinatization of generalized geometries and a theorem of Solér which characterizes Hilbert spaces among the orthomodular spaces. A generalized Wigner theorem is applied to reduce some of the assumptions of Solér's theorem to the theory of symmetry in quantum mechanics. Since this reduction is only partial we also point out the remaining open questions.

  20. 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.

  1. Two basic Uncertainty Relations in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Angelow, Andrey

    2011-04-01

    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 Schrödinger 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.

  2. 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.

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

    PubMed

    Yu, Xiaohua; Zhan, Zhaolin

    2014-01-01

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

  4. Quantum Mechanical Aspects of Free Electron Lasers.

    NASA Astrophysics Data System (ADS)

    Saritepe, Selcuk

    Scope of study. A 2-D quantum theory of the Free Electron Laser (FEL) has been developed based on the solutions of Dirac equation for the motion of electrons moving in various wiggler geometries, uniform, tapered and enhanced by an axial guide field. It is shown that these solutions can be written in terms of Mathieu functions of fractional order. Using these solutions a perturbational analysis is carried out to calculate the frequencies and the gain of the FEL in each magnet configuration. Finally, an optical model for the FEL interaction is developed to explain the saturation behaviour and the short-pulse effects such as Laser Lethargy. Findings and conclusions. It is found that the quantum mechanical effects due to transverse momentum correction were gamma (Lorentz factor) times larger than the quantum recoil and spin effects and therefore important for the short wavelength FELs. These quantum mechanical effects cause a broadening in the spontaneous emission lineshape, a decrease in gain and an increase in the rate of harmonic frequency generation. In the presence of an axial field, gain is increased, harmonic frequency rate is reduced and Dirac solutions exhibit instability. The optical model developed in this thesis correctly predicts the oscillator rise time and uses a simpler algorithm to calculate the nonlinear saturation behaviour. Optical model also incorporates inhomogeneous broadening and quantum mechanical effects and explains the Laser Lethargy effect as an optical pulse compression phenomenon.

  5. 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.

  6. Quantum Mechanics in the Light of Quantum Cosmology

    NASA Astrophysics Data System (ADS)

    Gell-Mann, Murray; Hartle, James B.

    We sketch a quantum-mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the "quasiclassical domain" of familiar experience and for characterizing the process of measurement. Predictions in quantum mechanics are made from probabilities for sets of alternative histories. Probabilities (approximately obeying the rules of probability theory) can be assigned only to sets of histories that approximately decohere. Decoherence is defined and the mechanism of decoherence is reviewed. Decoherence requires a sufficiently coarse-grained description of alternative histories of the universe. A quasiclassical domain consists of a branching set of alternative decohering histories, described by a coarse graining that is, in an appropriate sense, maximally refined consistent with decoherence, with individual branches that exhibit a high level of classical correlation in time. We pose the problem of making these notions precise and quantitative. A quasiclassical domain is emergent in the universe as a consequence of the initial condition and the action function of the elementary particles. It is an important question whether all the quasiclassical domains are roughly equivalent or whether there are various essentially inequivalent ones. A measurement is a correlation with variables in a quasiclassical domain. An "observer" (or information gathering and utilizing system) is a complex adaptive system that has evolved to exploit the relative predictability of a quasiclassical domain, or rather a set of such domains among which it cannot discriminate because of its own very coarse graining. We suggest that resolution of many of the problems of interpretation presented by quantum mechanics is to be accomplished, not by further scrutiny of the subject as it applies to reproducible laboratory situations, but rather by an examination of alternative histories of the universe, stemming from its

  7. Quantum statistics and anharmonicity in the thermodynamics of spin waves in ferromagnetic metals.

    PubMed

    Wen, Haohua; Woo, C H

    2016-09-01

    The average energy needed to create a magnon is high in ferromagnetic metals due to the high-strength spin stiffness, which results in strong quantization effects that could be important even at thousands of degrees. To take into account quantum statistics at such high temperatures, the associated effects of anharmonicity of the spin vibrations must be taken into account. In addition to the complex nature of such effects, anharmonicity also affects the occupation of the density of state of the vibration states in the context of quantum statistics. Thus, an unoccupied vibration state might become occupied when its spring stiffness is substantially reduced with anharmonicity. Combined effects of quantum statistics and anharmonicity are expected. In this regard, the thermodynamics of ferromagnetic metals are investigated in this paper through the example of bcc iron between 10 and 1400 K. Theoretical analysis and spin-lattice dynamic simulations are performed, through which the physics behind the complex and dramatic temperature dependence of the thermodynamic functions of bcc iron is understood.

  8. Quantum statistics and anharmonicity in the thermodynamics of spin waves in ferromagnetic metals

    NASA Astrophysics Data System (ADS)

    Wen, Haohua; Woo, C. H.

    2016-09-01

    The average energy needed to create a magnon is high in ferromagnetic metals due to the high-strength spin stiffness, which results in strong quantization effects that could be important even at thousands of degrees. To take into account quantum statistics at such high temperatures, the associated effects of anharmonicity of the spin vibrations must be taken into account. In addition to the complex nature of such effects, anharmonicity also affects the occupation of the density of state of the vibration states in the context of quantum statistics. Thus, an unoccupied vibration state might become occupied when its spring stiffness is substantially reduced with anharmonicity. Combined effects of quantum statistics and anharmonicity are expected. In this regard, the thermodynamics of ferromagnetic metals are investigated in this paper through the example of bcc iron between 10 and 1400 K. Theoretical analysis and spin-lattice dynamic simulations are performed, through which the physics behind the complex and dramatic temperature dependence of the thermodynamic functions of bcc iron is understood.

  9. Quantum-Gravity Thermodynamics, Incorporating the Theory of Exactly Soluble Active Stochastic Processes, with Applications

    NASA Astrophysics Data System (ADS)

    Daley, K.

    2009-08-01

    A re-visitation of QFT is first cited, deriving the Feynman integral from the theory of active stochastic processes (Glueck and Hueffler, Phys. Lett. B. 659(1-2):447-451, 2008; Hueffel and Kelnhofer, Phys. Lett. B 588(1-2):145-150, 2004). We factor the lie group “generator” of the inverse wavefunction over an entropy-maximizing basis. Performing term-by-term Ito-integration leads us to an analytical, evaluable trajectory for a charged particle in an arbitrary field given a Maximum-Entropy distribution. We generalize this formula to many-body electrodynamics. In theory, it is capable of predicting plasma’s thermodynamic properties from ionic spectral data and thermodynamic and optical distributions. Blessed with the absence of certain limitations (e.g., renormalization) strongly present in competing formalisms and the incorporation of research related to many different phenomena, we outline a candidate quantum gravity theory based on these developments.

  10. Consistent interpretations of quantum mechanics

    SciTech Connect

    Omnes, R. )

    1992-04-01

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

  11. Emerging interpretations of quantum mechanics and recent progress in quantum measurement

    NASA Astrophysics Data System (ADS)

    Clarke, M. L.

    2014-01-01

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

  12. 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)

  13. The geometric semantics of algebraic quantum mechanics.

    PubMed

    Cruz Morales, John Alexander; Zilber, Boris

    2015-08-06

    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.

  14. Quantum mechanics is compatible with realism

    SciTech Connect

    Burgos, M.E.

    1987-08-01

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

  15. Holism, physical theories and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Seevinck, M. P.

    Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these resources include at least all local operations and classical communication. This approach is contrasted with the well-known approaches to holism in terms of supervenience. The criterion for holism proposed here involves a shift in emphasis from ontology to epistemology. I apply this epistemological criterion to classical physics and Bohmian mechanics as represented on a phase and configuration space respectively, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum operations as completely positive trace non-increasing maps. Furthermore, I provide an interesting example from which one can conclude that quantum mechanics is holistic in the above mentioned sense, although, perhaps surprisingly, no entanglement is needed.

  16. 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.

  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 in classical and in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Elçi, A.

    2010-07-01

    This paper presents an analysis of the time concept in classical mechanics from the perspective of the invariants of a motion. The analysis shows that there is a conceptual gap concerning time in the Dirac-Heisenberg-von Neumann formalism and that Bohr's complementarity principle does not fill the gap. In the Dirac-Heisenberg-von Neumann formalism, a particle's properties are represented by Heisenberg matrices. This axiom is the source of the time problem in quantum mechanics.

  19. 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.

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

    NASA Astrophysics Data System (ADS)

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

    1981-11-01

    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.

  1. 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.

  2. Quantum mechanics of 4-derivative theories.

    PubMed

    Salvio, Alberto; Strumia, Alessandro

    2016-01-01

    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 quantization. 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, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm.

  3. A Primer on Resonances in Quantum Mechanics

    SciTech Connect

    Rosas-Ortiz, Oscar; Fernandez-Garcia, Nicolas; Cruz y Cruz, Sara

    2008-11-13

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

  4. 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.

  5. Global and local horizon quantum mechanics

    NASA Astrophysics Data System (ADS)

    Casadio, Roberto; Giugno, Andrea; Giusti, Andrea

    2017-02-01

    Horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum mechanical matter state by lifting the classical "Hamiltonian" constraint that relates the gravitational radius to the ADM mass, thus giving rise to a "horizon wave-function". This minisuperspace-like formalism is shown here to be able to consistently describe also the local gravitational radius related to the Misner-Sharp mass function of the quantum source, provided its energy spectrum is determined by spatially localised modes.

  6. 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.

  7. 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.

  8. Initial and apparent temperatures of finite nuclear systems - a quantum statistical thermodynamics study.

    NASA Astrophysics Data System (ADS)

    Majka; Staszel, P.; Natowitz, J. B.; Cibor, J.; Hagel, K.; Li, J.; Mdeiwayeh, N.; Wada, R.; Zhao, Y.

    1996-10-01

    Quantum statistical thermodynamics has been used to calculate the number of available states and their occupation for fermions and bosons at temperature, T_in, of finite nuclear sytems. An apparent temperature of these systems, T_app, has been calculated from double yield ratios of two isotope pairs. The importance of employing the quantum statistics when high densities and/or low temperatures are involved is shown. However, at high temperatures and low densities, the system behaves as a Maxwell-Boltzmann gas. Sequental decays of fragments from excited states influence the double yield ratio observable, causing problems with the temperature extraction. The model has been applied to study the high temperature branch of the "caloric curve".

  9. ``the Human BRAIN & Fractal quantum mechanics''

    NASA Astrophysics Data System (ADS)

    Rosary-Oyong, Se, Glory

    In mtDNA ever retrieved from Iman Tuassoly, et.al:Multifractal analysis of chaos game representation images of mtDNA''.Enhances the price & valuetales of HE. Prof. Dr-Ing. B.J. HABIBIE's N-219, in J. Bacteriology, Nov 1973 sought:'' 219 exist as separate plasmidDNA species in E.coli & Salmonella panama'' related to ``the brain 2 distinct molecular forms of the (Na,K)-ATPase..'' & ``neuron maintains different concentration of ions(charged atoms'' thorough Rabi & Heisenber Hamiltonian. Further, after ``fractal space time are geometric analogue of relativistic quantum mechanics''[Ord], sought L.Marek Crnjac: ``Chaotic fractals at the root of relativistic quantum physics''& from famous Nottale: ``Scale relativity & fractal space-time:''Application to Quantum Physics , Cosmology & Chaotic systems'',1995. Acknowledgements to HE. Mr. H. TUK SETYOHADI, Jl. Sriwijaya Raya 3, South-Jakarta, INDONESIA.

  10. Thermodynamic behaviour of Rashba quantum dot in the presence of magnetic field

    NASA Astrophysics Data System (ADS)

    Sukirti, Gumber; Manoj, Kumar; Pradip, Kumar Jha; Man, Mohan

    2016-05-01

    The thermodynamic properties of an InSb quantum dot have been investigated in the presence of Rashba spin-orbit interaction and a static magnetic field. The energy spectrum and wave-functions for the system are obtained by solving the Schrodinger wave-equation analytically. These energy levels are employed to calculate the specific heat, entropy, magnetization and susceptibility of the quantum dot system using canonical formalism. It is observed that the system is susceptible to maximum heat absorption at a particular value of magnetic field which depends on the Rashba coupling parameter as well as the temperature. The variation of specific heat shows a Schottky-like anomaly in the low temperature limit and rapidly converges to the value of 2k B with the further increase in temperature. The entropy of the quantum dot is found to be inversely proportional to the magnetic field but has a direct variation with temperature. The substantial effect of Rashba spin-orbit interaction on the magnetic properties of quantum dot is observed at low values of magnetic field and temperature. Project support by the University Grants Commission, India, the Department of Science and Technology, and the University Grants Commission-Basic Science Research (UGC-BSR).

  11. Dummett vs Bell on quantum mechanics

    NASA Astrophysics Data System (ADS)

    Ben-Menahem, Yemima

    The purpose of this paper is to cast doubt on the common allegation that quantum mechanics (QM) is incompatible with realism. I argue that the results usually considered inimical to realism, notably the violation of Bells inequality, in fact play the opposite role-they support realism. The argument is not intended, however, to demonstrate realism or refute its alternatives as general metaphysical positions. It is directed specifically at the view that QM differs from classical mechanics in that, unlike classical mechanics, it is not amenable to a realist interpretation.

  12. 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

  13. Quantum statistical mechanics in arithmetic topology

    NASA Astrophysics Data System (ADS)

    Marcolli, Matilde; Xu, Yujie

    2017-04-01

    This paper provides a construction of a quantum statistical mechanical system associated to knots in the 3-sphere and cyclic branched coverings of the 3-sphere, which is an analog, in the sense of arithmetic topology, of the Bost-Connes system, with knots replacing primes, and cyclic branched coverings of the 3-sphere replacing abelian extensions of the field of rational numbers. The operator algebraic properties of this system differ significantly from the Bost-Connes case, due to the properties of the action of the semigroup of knots on a direct limit of knot groups. The resulting algebra of observables is a noncommutative Bernoulli product. We describe the main properties of the associated quantum statistical mechanical system and of the relevant partition functions, which are obtained from simple knot invariants like genus and crossing number.

  14. Quantum-Mechanical Prediction of Nanoscale Photovoltaics.

    PubMed

    Zhang, Yu; Meng, LingYi; Yam, ChiYung; Chen, GuanHua

    2014-04-03

    Previous simulations of photovoltaic devices are based on classical models, which neglect the atomistic details and quantum-mechanical effects besides the dependence on many empirical parameters. Here, within the nonequilibrium Green's function formalism, we present a quantum-mechanical study of the performance of inorganic nanowire-based photovoltaic devices. On the basis of density-functional tight-binding theory, the method allows simulation of current-voltage characteristics and optical properties of photovoltaic devices without relying on empirical parameters. Numerical studies of silicon nanowire-based devices of realistic sizes with 10 000 atoms are performed, and the results indicate that atomistic details and nonequilibrium conditions have a clear impact on the photoresponse of the devices.

  15. Applications of computational quantum mechanics

    NASA Astrophysics Data System (ADS)

    Temel, Burcin

    This original research dissertation is composed of a new numerical technique based on Chebyshev polynomials that is applied on scattering problems, a phenomenological kinetics study for CO oxidation on RuO2 surface, and an experimental study on methanol coupling with doped metal oxide catalysts. Minimum Error Method (MEM), a least-squares minimization method, provides an efficient and accurate alternative to solve systems of ordinary differential equations. Existing methods usually utilize matrix methods which are computationally costful. MEM, which is based on the Chebyshev polynomials as a basis set, uses the recursion relationships and fast Chebyshev transforms which scale as O(N). For large basis set calculations this provides an enormous computational efficiency in the calculations. Chebyshev polynomials are also able to represent non-periodic problems very accurately. We applied MEM on elastic and inelastic scattering problems: it is more efficient and accurate than traditionally used Kohn variational principle, and it also provides the wave function in the interaction region. Phenomenological kinetics (PK) is widely used in industry to predict the optimum conditions for a chemical reaction. PK neglects the fluctuations, assumes no lateral interactions, and considers an ideal mix of reactants. The rate equations are tested by fitting the rate constants to the results of the experiments. Unfortunately, there are numerous examples where a fitted mechanism was later shown to be erroneous. We have undertaken a thorough comparison between the phenomenological equations and the results of kinetic Monte Carlo (KMC) simulations performed on the same system. The PK equations are qualitatively consistent with the KMC results but are quantitatively erroneous as a result of interplays between the adsorption and desorption events. The experimental study on methanol coupling with doped metal oxide catalysts demonstrates the doped metal oxides as a new class of catalysts

  16. Probing pores using elementary quantum mechanics.

    PubMed

    Ryu, S

    2001-01-01

    The relaxation of polarized spins in a porous medium has been utilized as a probe of its structure. We note that the governing diffusion problem has a close parallel to that of a particle in a box, an elementary Quantum mechanics toy model. Following the spirits of "free electron" model, we use generic properties of the eigen spectrum to understand features common to a wide variety of pore geometry, consistent with large scale numerical simulations and experimental data.

  17. 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.

  18. 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.

  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. The Foundations of Quantum Mechanics: Historical Analysis and Open Questions -- Cesena, 2004

    NASA Astrophysics Data System (ADS)

    Garola, Claudio; Rossi, Arcangelo; Sozzo, Sandro

    Introduction / C. Garola, A. Rossi and S. Sozzo -- If Bertlmann had three feet / A. Afriat -- Macroscopic interpretability of quantum component systems / R. Ascoli -- Premeasurement versus measurement: a basic form of complementarity / G. Auletta and G. Tarozzi -- Remarks on conditioning / E. G. Beltrametti -- Entangled state preparation in experiments on quantum non-locality / V. Berardi and A. Garuccio -- The first steps of quantum electrodynamics: what is it that's being quantized? / S. Bergia -- On the meaning of element in the science of italic tradition, the question of physical objectivity (and/or physical meaning) and quantum mechanics / G. Boscarino -- Mathematics and epistemology in Planck's theoretical work (1898-1915) / P. Campogalliani -- On the free motion with noise / B. Carazza and R. Tedeschi -- Field quantization and wave/particle duality / M. Cini -- Parastatistics in econophysics? / D. Costantini and U. Garibaldi -- Theory-laden instruments and quantum mechanics / S. D'Agostino -- Quantum non-locality and the mathematical representation of experience / V. Fano -- On the notion of proposition in classical and quantum mechanics / C. Garola and S. Sozzo -- The electromagnetic conception of nature and the origins of quantum physics / E. A. Giannetto -- What we talk about when we talk about universe computability / S. Guccione -- Bohm and Bohmian mechanics / G. Introzzi and M. Rossetti -- An objective background for quantum theory relying on thermodynamic concepts / L. Lanz and B. Vacchini -- The entrance of quantum mechanics in Italy: from Garbasso to Fermi / M. Leone and N. Robotti -- The measure of momentum in quantum mechanics / F. Logiurato and C. Tarsitani -- On the two-slit interference experiment: a statistical discussion / M. Minozzo -- Why the reactivity of the elements is a relational property, and why it matters / V. Mosini -- Detecting non compatible properties in double-slit experiment without erasure / G. Nisticò -- If you can

  1. 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}.

  2. Classical and quantum-mechanical state reconstruction

    NASA Astrophysics Data System (ADS)

    Khanna, F. C.; Mello, P. A.; Revzen, M.

    2012-07-01

    The aim of this paper is to present the subject of state reconstruction in classical and in quantum physics, a subject that deals with the experimentally acquired information that allows the determination of the physical state of a system. Our first purpose is to explain a method for retrieving a classical state in phase space, similar to that used in medical imaging known as computer-aided tomography. It is remarkable that this method can be taken over to quantum mechanics, where it leads to a description of the quantum state in terms of the Wigner function which, although it may take on negative values, plays the role of the probability density in phase space in classical physics. We then present another approach to quantum state reconstruction based on the notion of mutually unbiased bases—a notion of current research interest, for which we give explanatory remarks—and indicate the relation between these two approaches. Since the subject of state reconstruction is rarely considered at the level of textbooks, the presentation in this paper is aimed at graduate-level readers.

  3. The definition of the thermodynamic entropy in statistical mechanics

    NASA Astrophysics Data System (ADS)

    Swendsen, Robert H.

    2017-02-01

    A definition of the thermodynamic entropy based on the time-dependent probability distribution of the macroscopic variables is developed. When a constraint in a composite system is released, the probability distribution for the new equilibrium values goes to a narrow peak. Defining the entropy by the logarithm of the probability distribution automatically makes it a maximum at the equilibrium values, so it satisfies the Second Law. It also satisfies the postulates of thermodynamics. Objections to this definition by Dieks and Peters are discussed and resolved.

  4. Quantum four-stroke heat engine: thermodynamic observables in a model with intrinsic friction.

    PubMed

    Feldmann, Tova; Kosloff, Ronnie

    2003-07-01

    The fundamentals of a quantum heat engine are derived from first principles. The study is based on the equation of motion of a minimum set of operators, which is then used to define the state of the system. The relation between the quantum framework and the thermodynamical observables is examined. A four-stroke heat engine model with a coupled two-level system as a working fluid is used to explore the fundamental relations. In the model used, the internal Hamiltonian does not commute with the external control field, which defines the two adiabatic branches. Heat is transferred to the working fluid by coupling to hot and cold reservoirs under constant field values. Explicit quantum equations of motion for the relevant observables are derived on all branches. The dynamics on the heat transfer constant field branches is solved in closed form. On the adiabats, a general numerical solution is used and compared with a particular analytic solution. These solutions are combined to construct the cycle of operation. The engine is then analyzed in terms of the frequency-entropy and entropy-temperature graphs. The irreversible nature of the engine is the result of finite heat transfer rates and frictionlike behavior due to noncommutability of the internal and external Hamiltonians.

  5. 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 ηmp≤η+≡ηC2/[ηC-(1 -ηC) ln(1 -ηC) ] with ηC=1 -Tc/Th as the Carnot efficiency. This expression ηmp possesses the same universality of the CA efficiency ηCA=1 -√{1 -ηC } at small relative temperature difference. Within the context of irreversible thermodynamics, we calculate the Onsager coefficients and show that the value of ηCA is indeed the upper bound of EMP for an Otto engine working in the linear-response regime.

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

    PubMed

    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 T(h) and T(c) (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 η(mp)≤η(+)≡η(C)(2)/[η(C)-(1-η(C))ln(1-η(C))] with η(C)=1-T(c)/T(h) as the Carnot efficiency. This expression η(mp) possesses the same universality of the CA efficiency η(CA)=1-√(1-η(C)) at small relative temperature difference. Within the context of irreversible thermodynamics, we calculate the Onsager coefficients and show that the value of η(CA) is indeed the upper bound of EMP for an Otto engine working in the linear-response regime.

  7. Classical and quantum many-body effects on the critical properties and thermodynamic regularities of silicon

    NASA Astrophysics Data System (ADS)

    Desgranges, C.; Anderson, P. W.; Delhommelle, J.

    2017-02-01

    Using molecular simulation, we determine the critical properties of Si as well as the loci for several remarkable thermodynamic contours spanning the supercritical region of the phase diagram. We consider a classical three-body potential as well as a quantum (tight-binding) many-body model, and determine the loci for the ideality contours, including the Zeno line and the H line of ideal enthalpy. The two strategies (classical or quantum) lead to strongly asymmetric binodals and to critical properties in good agreement with each other. The Zeno and H lines are found to remain linear over a wide temperature interval, despite the changes in electronic structure undergone by the fluid along these contours. We also show that the classical and quantum model yield markedly different results for the parameters defining the H line, the exponents for the power-laws underlying the line of minima for the isothermal enthalpy and for the density required to achieve ideal behavior, most notably for the enthalpy.

  8. On Quantum Collapse as a Basis for the Second Law of Thermodynamics

    NASA Astrophysics Data System (ADS)

    Kastner, Ruth

    2017-03-01

    It was first suggested by David Z. Albert that the existence of a real, physical non-unitary process (i.e., "collapse") at the quantum level would yield a complete explanation for the Second Law of Thermodynamics (i.e., the increase in entropy over time). The contribution of such a process would be to provide a physical basis for the ontological indeterminacy needed to derive the irreversible Second Law against a backdrop of otherwise reversible, deterministic physical laws. An alternative understanding of the source of this possible quantum "collapse" or non-unitarity is presented herein, in terms of the Transactional Interpretation (TI). The present model provides a specific physical justification for Boltzmann's often-criticized assumption of molecular randomness (Stosszahlansatz), thereby changing its status from an ad hoc postulate to a theoretically grounded result, without requiring any change to the basic quantum theory. In addition, it is argued that TI provides an elegant way of reconciling, via indeterministic collapse, the time-reversible Liouville evolution with the time-irreversible evolution inherent in so-called "master equations" that specify the changes in occupation of the various possible states in terms of the transition rates between them. The present model is contrasted with the Ghirardi-Rimini-Weber (GRW) "spontaneous collapse" theory previously suggested for this purpose by Albert.

  9. Classical and quantum many-body effects on the critical properties and thermodynamic regularities of silicon.

    PubMed

    Desgranges, C; Anderson, P W; Delhommelle, J

    2017-02-01

    Using molecular simulation, we determine the critical properties of Si as well as the loci for several remarkable thermodynamic contours spanning the supercritical region of the phase diagram. We consider a classical three-body potential as well as a quantum (tight-binding) many-body model, and determine the loci for the ideality contours, including the Zeno line and the H line of ideal enthalpy. The two strategies (classical or quantum) lead to strongly asymmetric binodals and to critical properties in good agreement with each other. The Zeno and H lines are found to remain linear over a wide temperature interval, despite the changes in electronic structure undergone by the fluid along these contours. We also show that the classical and quantum model yield markedly different results for the parameters defining the H line, the exponents for the power-laws underlying the line of minima for the isothermal enthalpy and for the density required to achieve ideal behavior, most notably for the enthalpy.

  10. Conversion of heat to light using Townes' maser-laser engine: Quantum optics and thermodynamic analysis

    SciTech Connect

    Ooi, C. H. Raymond

    2011-04-15

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

  11. Quantum mechanics with coordinate dependent noncommutativity

    NASA Astrophysics Data System (ADS)

    Kupriyanov, V. G.

    2013-11-01

    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.

  12. An approach to nonstandard quantum mechanics

    NASA Astrophysics Data System (ADS)

    Raab, A.

    2004-12-01

    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 nonrelativistic 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 Mo/ller wave operators and the S-matrix.

  13. Bohmian Mechanics In A Macroscopic Quantum System

    NASA Astrophysics Data System (ADS)

    Haven, Emmanuel

    2006-01-01

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

  14. Indirect Acquisition of Information in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Ballesteros, M.; Fraas, M.; Fröhlich, J.; Schubnel, B.

    2016-02-01

    Long sequences of successive direct (projective) measurements or observations of just a few "uninteresting" physical quantities pertaining to a quantum system, such as clicks of some detectors, may reveal indirect, but precise and unambiguous information on the values of some very "interesting" observables of the system. In this paper, the mathematics underlying this claim is developed; i.e., we attempt to contribute to a mathematical theory of indirect and, in particular, non-demolition observations and measurements in quantum mechanics. Our attempt leads us to make some novel uses of classical notions and results of probability theory, such as the "algebra of functions measurable at infinity", the Central Limit Theorem, results concerning relative entropy and its role in the theory of large deviations, etc.

  15. Quantum mechanical hamiltonian models of turing machines

    NASA Astrophysics Data System (ADS)

    Benioff, Paul

    1982-11-01

    Quantum mechanical Hamiltonian models, which represent an aribtrary but finite number of steps of any Turing machine computation, are constructed here on a finite lattice of spin-1/2 systems. Different regions of the lattice correspond to different components of the Turing machine (plus recording system). Successive states of any machine computation are represented in the model by spin configuration states. Both time-independent and time-dependent Hamiltonian models are constructed here. The time-independent models do not dissipate energy or degrade the system state as they evolve. They operate close to the quantum limit in that the total system energy uncertainty/computation speed is close to the limit given by the time-energy uncertainty relation. However, the model evolution is time global and the Hamiltonian is more complex. The time-dependent models do not degrade the system state. Also they are time local and the Hamiltonian is less complex.

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

    NASA Astrophysics Data System (ADS)

    Vershynina, Anna

    This dissertation discusses the properties of two open quantum systems with a general class of irreversible quantum dynamics. First we study Lieb-Robinson bounds in a quantum lattice systems. This bound gives an estimate for the speed of growth of the support of an evolved local observable up to an exponentially small error. In a second model we study the properties of a leaking cavity pumped by a random atomic beam. We begin by describing quantum systems on an infinite lattice with associated finite or infinite dimensional Hilbert space. The generator of the dynamics of this system is of the Lindblad-Kossakowski type and consists of two parts: the Hamiltonian interactions and the dissipative terms. We allow both of them to be time-dependent. This generator satisfies some suitable decay condition in space. We show that the dynamics with a such generator on a finite system is a well-defined quantum dynamics in a sense of a norm-continuous cocycle of unit preserving completely positive maps. Lieb-Robinson bounds for irreversible dynamics were first considered in the classical context and in for a class of quantum lattice systems with finite-range interactions. We extend those results by proving a Lieb-Robinson bound for lattice models with a more general class of quantum dynamics. Then we use Lieb-Robinson bounds for a finite lattice systems to prove the existence of the thermodynamic limit of the dynamics. We show that in a strong limit there exits a strongly continuous cocycle of unit preserving completely positive maps. Which means that the dynamics exists in an infinite system, where Lieb-Robinson bounds also holds. In the second part of the dissertation we consider a system that consists of a beam of two-level atoms that pass one by one through the microwave cavity. The atoms are randomly excited and there is exactly one atom present in the cavity at any given moment. We consider both the ideal and leaky cavity and study the time asymptotic behavior of the state

  17. Unstable trajectories and the quantum mechanical uncertainty

    SciTech Connect

    Moser, Hans R.

    2008-08-15

    There is still an ongoing discussion about various seemingly contradictory aspects of classical particle motion and its quantum mechanical counterpart. One of the best accepted viewpoints that intend to bridge the gap is the so-called Copenhagen Interpretation. A major issue there is to regard wave functions as probability amplitudes (usually for the position of a particle). However, the literature also reports on approaches that claim a trajectory for any quantum mechanical particle, Bohmian mechanics probably being the most prominent one among these ideas. We introduce a way to calculate trajectories as well, but our crucial ingredient is their well controlled local (thus also momentaneous) degree of instability. By construction, at every moment their unpredictability, i.e., their local separation rates of neighboring trajectories, is governed by the local value of the given modulus square of a wave function. We present extensive numerical simulations of the H and He atom, and for some velocity-related quantities, namely angular momentum and total energy, we inspect their agreement with the values appearing in wave mechanics. Further, we interpret the archetypal double slit interference experiment in the spirit of our findings. We also discuss many-particle problems far beyond He, which guides us to a variety of possible applications.

  18. Quantum mechanics. Mechanically detecting and avoiding the quantum fluctuations of a microwave field.

    PubMed

    Suh, J; Weinstein, A J; Lei, C U; Wollman, E E; Steinke, S K; Meystre, P; Clerk, A A; Schwab, K C

    2014-06-13

    Quantum fluctuations of the light field used for continuous position detection produce stochastic back-action forces and ultimately limit the sensitivity. To overcome this limit, the back-action forces can be avoided by giving up complete knowledge of the motion, and these types of measurements are called "back-action evading" or "quantum nondemolition" detection. We present continuous two-tone back-action evading measurements with a superconducting electromechanical device, realizing three long-standing goals: detection of back-action forces due to the quantum noise of a microwave field, reduction of this quantum back-action noise by 8.5 ± 0.4 decibels (dB), and measurement imprecision of a single quadrature of motion 2.4 ± 0.7 dB below the mechanical zero-point fluctuations. Measurements of this type will find utility in ultrasensitive measurements of weak forces and nonclassical states of motion.

  19. Variational Average-Atom in Quantum Plasmas (VAAQP) - A check of thermodynamic consistency

    NASA Astrophysics Data System (ADS)

    Piron, R.; Blenski, T.; Cichocki, B.

    2009-12-01

    A new code called VAAQP (Variational Average-Atom in Quantum Plasmas) is presented. The conceptual model on which the code is based, as well as the important results of previous studies are briefly discussed. The code is based on a new fully variational model of equilibrium dense plasmas employing a quantal treatment of all electrons. VAAQP can calculate the Average-Atom structure and the mean ionization from the variational equations satisfying the virial theorem and without imposing the neutrality of the Wigner-Seitz sphere. The formula obtained for the electron pressure is simple and does not require any numerical differentiation. A description of the principal features of the code is given. The thermodynamic consistency of the results obtained with VAAQP is shown by a comparison with another approach for the aluminium 2 eV isotherm. An initial comparison to an INFERNO-type model is also presented.

  20. Thermodynamics of ideal quantum gas with fractional statistics in D dimensions.

    PubMed

    Potter, Geoffrey G; Müller, Gerhard; Karbach, Michael

    2007-06-01

    We present exact and explicit results for the thermodynamic properties (isochores, isotherms, isobars, response functions, velocity of sound) of a quantum gas in dimensions D > or = 1 and with fractional exclusion statistics 0 < or = g < or =1 connecting bosons (g=0) and fermions (g=1) . In D=1 the results are equivalent to those of the Calogero-Sutherland model. Emphasis is given to the crossover between bosonlike and fermionlike features, caused by aspects of the statistical interaction that mimic long-range attraction and short-range repulsion. A phase transition along the isobar occurs at a nonzero temperature in all dimensions. The T dependence of the velocity of sound is in simple relation to isochores and isobars. The effects of soft container walls are accounted for rigorously for the case of a pure power-law potential.

  1. Quantum Monte Carlo Simulation of Nanoscale MgH2 Cluster Thermodynamics

    NASA Astrophysics Data System (ADS)

    Wu, Zhigang; Allendorf, Mark; Grossman, Jeffrey

    2010-03-01

    We calculated the desorption energy of MgH2 clusters using the quantum Monte Carlo (QMC) approach, which can provide desorption energies with chemical accuracy (within 1 kcal/mol) and therefore a valuable benchmark for such hydrogen-storage simulations. Compared with these QMC results, the widely used density-functional-theory (DFT) computations cannot reach a consistent and suitable level of accuracy across the thermodynamically tunable range for MgH2 clusters, for a wide range of exchange-correlation functionals. Furthermore, our QMC calculations show that the DFT error depends substantially on cluster size. These results suggest that in simulating metal-hydride systems it is crucial to apply accurate methods that go beyond traditional mean-field approaches as a benchmark of their performance for a given material, and QMC is an appealing method for such a benchmark due to its high level of accuracy and favorable scaling (N^3) with number of electrons.

  2. Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamical resource

    NASA Astrophysics Data System (ADS)

    Silva, Ralph; Manzano, Gonzalo; Skrzypczyk, Paul; Brunner, Nicolas

    2016-09-01

    Multilevel autonomous quantum thermal machines are discussed. In particular, we explore the relationship between the size of the machine (captured by Hilbert space dimension) and the performance of the machine. Using the concepts of virtual qubits and virtual temperatures, we show that higher dimensional machines can outperform smaller ones. For instance, by considering refrigerators with more levels, lower temperatures can be achieved, as well as higher power. We discuss the optimal design for refrigerators of a given dimension. As a consequence we obtain a statement of the third law in terms of Hilbert space dimension: Reaching absolute zero temperature requires infinite dimension. These results demonstrate that Hilbert space dimension should be considered a thermodynamic resource.

  3. The metaphysics of quantum mechanics: Modal interpretations

    NASA Astrophysics Data System (ADS)

    Gluck, Stuart Murray

    2004-11-01

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

  4. The Simpson's paradox in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Selvitella, Alessandro

    2017-03-01

    In probability and statistics, the Simpson's paradox is a paradox in which a trend that appears in different groups of data disappears when these groups are combined, while the reverse trend appears for the aggregate data. In this paper, we give some results about the occurrence of the Simpson's paradox in quantum mechanics. In particular, we prove that the Simpson's paradox occurs for solutions of the quantum harmonic oscillator both in the stationary case and in the non-stationary case. In the non-stationary case, the Simpson's paradox is persistent: if it occurs at any time t =t ˜ , then it occurs at any time t ≠t ˜ . Moreover, we prove that the Simpson's paradox is not an isolated phenomenon, namely, that, close to initial data for which it occurs, there are lots of initial data (a open neighborhood), for which it still occurs. Differently from the case of the quantum harmonic oscillator, we also prove that the paradox appears (asymptotically) in the context of the nonlinear Schrödinger equation but at intermittent times.

  5. BiHermitian supersymmetric quantum mechanics

    NASA Astrophysics Data System (ADS)

    Zucchini, Roberto

    2007-04-01

    BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2, 2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kähler manifolds recently developed by Gualtieri in [33]. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li in [9].

  6. Quantum Mechanical Studies of Molecular Hyperpolarizabilities.

    DTIC Science & Technology

    1980-04-30

    exponent , reflects the screening of an electron in a given orbital by the interior electrons in the atom or molecule. In practice, when studying...Basis sets have evolved over the years in molecular quantum mechanics until sets of orbital exponents for the different atoms composing the molecule have...and R. P. Hurst , J. Chem. Phys. 46, 2356 (1967); S. P. LickmannI and J. W. Moskowitz, J. Chem. Phys. 54, 3622 7T971). 26. T. H. Dunning, J. Chem. Phys

  7. 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.

  8. Thermodynamics and renormalized quasiparticles in the vicinity of the dilute Bose gas quantum critical point in two dimensions

    NASA Astrophysics Data System (ADS)

    Krieg, Jan; Strassel, Dominik; Streib, Simon; Eggert, Sebastian; Kopietz, Peter

    2017-01-01

    We use the functional renormalization group (FRG) to derive analytical expressions for thermodynamic observables (density, pressure, entropy, and compressibility) as well as for single-particle properties (wave-function renormalization and effective mass) of interacting bosons in two dimensions as a function of temperature T and chemical potential μ . We focus on the quantum disordered and the quantum critical regime close to the dilute Bose gas quantum critical point. Our approach is based on a truncated vertex expansion of the hierarchy of FRG flow equations and the decoupling of the two-body contact interaction in the particle-particle channel using a suitable Hubbard-Stratonovich transformation. Our analytic FRG results extend previous analytical renormalization-group calculations for thermodynamic observables at μ =0 to finite values of μ . To confirm the validity of our FRG approach, we have also performed quantum Monte Carlo simulations to obtain the magnetization, susceptibility, and correlation length of the two-dimensional spin-1 /2 quantum X Y model with coupling J in a regime where its quantum critical behavior is controlled by the dilute Bose gas quantum critical point. We find that our analytical results describe the Monte Carlo data for μ ≤0 rather accurately up to relatively high temperatures T ≲0.1 J .

  9. Thermodynamics of liquid metal

    SciTech Connect

    Kushnirenko, A.N.

    1988-01-01

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

  10. Nonequilibrium quantum mechanics: A "hot quantum soup" of paramagnons

    NASA Astrophysics Data System (ADS)

    Scammell, H. D.; Sushkov, O. P.

    2017-01-01

    Motivated by recent measurements of the lifetime (decay width) of paramagnons in quantum antiferromagnet TlCuCl3, we investigate paramagnon decay in a heat bath and formulate an appropriate quantum theory. Our formulation can be split into two regimes: (i) a nonperturbative, "hot quantum soup" regime where the paramagnon width is comparable to its energy; (ii) a usual perturbative regime where the paramagnon width is significantly lower than its energy. Close to the Neel temperature, the paramagnon width becomes comparable to its energy and falls into the hot quantum soup regime. To describe this regime, we develop a new finite frequency, finite temperature technique for a nonlinear quantum field theory; the "golden rule of quantum kinetics." The formulation is generic and applicable to any three-dimensional quantum antiferromagnet in the vicinity of a quantum critical point. Specifically, we apply our results to TlCuCl3 and find agreement with experimental data. Additionally, we show that logarithmic running of the coupling constant in the upper critical dimension changes the commonly accepted picture of the quantum disordered and quantum critical regimes.

  11. The formal path integral and quantum mechanics

    SciTech Connect

    Johnson-Freyd, Theo

    2010-11-15

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

  12. Quantum Mechanical Study of Nanoscale MOSFET

    NASA Technical Reports Server (NTRS)

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

    2001-01-01

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

  13. Mathematical model I. Electron and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Gadre, Nitin Ramchandra

    2011-03-01

    The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is `difficult' to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.

  14. Differentiability of correlations in realistic quantum mechanics

    SciTech Connect

    Cabrera, Alejandro; Faria, Edson de; Pujals, Enrique; Tresser, Charles

    2015-09-15

    We prove a version of Bell’s theorem in which the locality assumption is weakened. We start by assuming theoretical quantum mechanics and weak forms of relativistic causality and of realism (essentially the fact that observable values are well defined independently of whether or not they are measured). Under these hypotheses, we show that only one of the correlation functions that can be formulated in the framework of the usual Bell theorem is unknown. We prove that this unknown function must be differentiable at certain angular configuration points that include the origin. We also prove that, if this correlation is assumed to be twice differentiable at the origin, then we arrive at a version of Bell’s theorem. On the one hand, we are showing that any realistic theory of quantum mechanics which incorporates the kinematic aspects of relativity must lead to this type of rough correlation function that is once but not twice differentiable. On the other hand, this study brings us a single degree of differentiability away from a relativistic von Neumann no hidden variables theorem.

  15. Quantum mechanical wavefunction: visualization at undergraduate level

    NASA Astrophysics Data System (ADS)

    Chhabra, Mahima; Das, Ritwick

    2017-01-01

    Quantum mechanics (QM) forms the most crucial ingredient of modern-era physical science curricula at undergraduate level. The abstract ideas involved in QM related concepts pose a challenge towards appropriate visualization as a consequence of their counter-intuitive nature and lack of experiment-assisted visualization tools. At the heart of the quantum mechanical formulation lies the concept of ‘wavefunction’, which forms the basis for understanding the behavior of physical systems. At undergraduate level, the concept of ‘wavefunction’ is introduced in an abstract framework using mathematical tools and therefore opens up an enormous scope for alternative conceptions and erroneous visualization. The present work is an attempt towards exploring the visualization models constructed by undergraduate students for appreciating the concept of ‘wavefunction’. We present a qualitative analysis of the data obtained from administering a questionnaire containing four visualization based questions on the topic of ‘wavefunction’ to a group of ten undergraduate-level students at an institute in India which excels in teaching and research of basic sciences. Based on the written responses, all ten students were interviewed in detail to unravel the exact areas of difficulty in visualization of ‘wavefunction’. The outcome of present study not only reveals the gray areas in students’ conceptualization, but also provides a plausible route to address the issues at the pedagogical level within the classroom.

  16. Molecular model with quantum mechanical bonding information.

    PubMed

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

    2011-11-17

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

  17. Student Understanding of Time Dependence in Quantum Mechanics

    ERIC Educational Resources Information Center

    Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.

    2015-01-01

    The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…

  18. Anyons in quantum mechanics with a minimal length

    NASA Astrophysics Data System (ADS)

    Buisseret, Fabien

    2017-02-01

    The existence of anyons, i.e. quantum states with an arbitrary spin, is a generic feature of standard quantum mechanics in (2 + 1) -dimensional Minkowski spacetime. Here it is shown that relativistic anyons may exist also in quantum theories where a minimal length is present. The interplay between minimal length and arbitrary spin effects are discussed.

  19. Thermodynamic framework for the ground state of a simple quantum system

    NASA Astrophysics Data System (ADS)

    Souza, Andre M. C.; Nobre, Fernando D.

    2017-01-01

    The ground state of a two-level system (associated with probabilities p and 1 -p , respectively) defined by a general Hamiltonian H ̂=Ĥ0+λ V ̂ is studied. The simple case characterized by λ =0 , whose Hamiltonian Ĥ0 is represented by a diagonal matrix, is well established and solvable within Boltzmann-Gibbs statistical mechanics; in particular, it follows the third law of thermodynamics, presenting zero entropy (SBG=0 ) at zero temperature (T =0 ). Herein it is shown that the introduction of a perturbation λ V ̂ (λ >0 ) in the Hamiltonian may lead to a nontrivial ground state, characterized by an entropy S [p ] (with S [p ] ≠SBG[p ] ), if the Hermitian operator V ̂ is represented by a 2 ×2 matrix, defined by nonzero off-diagonal elements V12=V21=-z , where z is a real positive number. Hence, this new term in the Hamiltonian, presenting V12≠0 , may produce physically significant changes in the ground state, and especially, it allows for the introduction of an effective temperature θ (θ ∝λ z ), which is shown to be a parameter conjugated to the entropy S . Based on this, one introduces an infinitesimal heatlike quantity, δ Q =θ d S , leading to a consistent thermodynamic framework, and by proposing an infinitesimal form for the first law, a Carnot cycle and thermodynamic potentials are obtained. All results found are very similar to those of usual thermodynamics, through the identification T ↔θ , and particularly the form for the efficiency of the proposed Carnot Cycle. Moreover, S also follows a behavior typical of a third law, i.e., S →0 , when θ →0 .

  20. Thermodynamic framework for the ground state of a simple quantum system.

    PubMed

    Souza, Andre M C; Nobre, Fernando D

    2017-01-01

    The ground state of a two-level system (associated with probabilities p and 1-p, respectively) defined by a general Hamiltonian H[over ̂]=H[over ̂]_{0}+λV[over ̂] is studied. The simple case characterized by λ=0, whose Hamiltonian H[over ̂]_{0} is represented by a diagonal matrix, is well established and solvable within Boltzmann-Gibbs statistical mechanics; in particular, it follows the third law of thermodynamics, presenting zero entropy (S_{BG}=0) at zero temperature (T=0). Herein it is shown that the introduction of a perturbation λV[over ̂] (λ>0) in the Hamiltonian may lead to a nontrivial ground state, characterized by an entropy S[p] (with S[p]≠S_{BG}[p]), if the Hermitian operator V[over ̂] is represented by a 2×2 matrix, defined by nonzero off-diagonal elements V_{12}=V_{21}=-z, where z is a real positive number. Hence, this new term in the Hamiltonian, presenting V_{12}≠0, may produce physically significant changes in the ground state, and especially, it allows for the introduction of an effective temperature θ (θ∝λz), which is shown to be a parameter conjugated to the entropy S. Based on this, one introduces an infinitesimal heatlike quantity, δQ=θdS, leading to a consistent thermodynamic framework, and by proposing an infinitesimal form for the first law, a Carnot cycle and thermodynamic potentials are obtained. All results found are very similar to those of usual thermodynamics, through the identification T↔θ, and particularly the form for the efficiency of the proposed Carnot Cycle. Moreover, S also follows a behavior typical of a third law, i.e., S→0, when θ→0.

  1. Surveying Instructors' Attitudes and Approaches to Teaching Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Siddiqui, Shabnam; Singh, Chandralekha

    2010-10-01

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

  2. Tampering detection system using quantum-mechanical systems

    DOEpatents

    Humble, Travis S [Knoxville, TN; Bennink, Ryan S [Knoxville, TN; Grice, Warren P [Oak Ridge, TN

    2011-12-13

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

  3. Exact and Optimal Quantum Mechanics/Molecular Mechanics Boundaries.

    PubMed

    Sun, Qiming; Chan, Garnet Kin-Lic

    2014-09-09

    Motivated by recent work in density matrix embedding theory, we define exact link orbitals that capture all quantum mechanical (QM) effects across arbitrary quantum mechanics/molecular mechanics (QM/MM) boundaries. Exact link orbitals are rigorously defined from the full QM solution, and their number is equal to the number of orbitals in the primary QM region. Truncating the exact set yields a smaller set of link orbitals optimal with respect to reproducing the primary region density matrix. We use the optimal link orbitals to obtain insight into the limits of QM/MM boundary treatments. We further analyze the popular general hybrid orbital (GHO) QM/MM boundary across a test suite of molecules. We find that GHOs are often good proxies for the most important optimal link orbital, although there is little detailed correlation between the detailed GHO composition and optimal link orbital valence weights. The optimal theory shows that anions and cations cannot be described by a single link orbital. However, expanding to include the second most important optimal link orbital in the boundary recovers an accurate description. The second optimal link orbital takes the chemically intuitive form of a donor or acceptor orbital for charge redistribution, suggesting that optimal link orbitals can be used as interpretative tools for electron transfer. We further find that two optimal link orbitals are also sufficient for boundaries that cut across double bonds. Finally, we suggest how to construct "approximately" optimal link orbitals for practical QM/MM calculations.

  4. Statistical origin of classical mechanics and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Chu, Shu-Yuan

    1993-11-01

    The classical action for interacting strings, obtained by generalizing the time-symmetric electrodynamics of Wheeler and Feynman, is exactly additive. The additivity of the string action suggests a connection between the area of the string world sheets and entropy. We find that the action principle of classical mechanics is the condition that the total entropy of the strings be at an extremum, and the path-integral representation of the quantum density matrix element is an approximation to the partition function of the string theory.

  5. Testing quantum mechanics using third-order correlations

    NASA Astrophysics Data System (ADS)

    Kinsler, Paul

    1996-04-01

    Semiclassical theories similar to stochastic electrodynamics are widely used in optics. The distinguishing feature of such theories is that the quantum uncertainty is represented by random statistical fluctuations. They can successfully predict some quantum-mechanical phenomena; for example, the squeezing of the quantum uncertainty in the parametric oscillator. However, since such theories are not equivalent to quantum mechanics, they will not always be useful. Complex number representations can be used to exactly model the quantum uncertainty, but care has to be taken that approximations do not reduce the description to a hidden variable one. This paper helps show the limitations of ``semiclassical theories,'' and helps show where a true quantum-mechanical treatment needs to be used. Third-order correlations are a test that provides a clear distinction between quantum and hidden variable theories in a way analogous to that provided by the ``all or nothing'' Greenberger-Horne-Zeilinger test of local hidden variable theories.

  6. Structural, mechanical and thermodynamic properties of ZrO2 polymorphs by first-principles calculation

    NASA Astrophysics Data System (ADS)

    Liang, Zuozhong; Wang, Wei; Zhang, Min; Wu, Fei; Chen, Jian-Feng; Xue, Chunyu; Zhao, Hong

    2017-04-01

    The structural, mechanical and thermodynamic properties of ZrO2 polymorphs (namely, monoclinic (P21/c), tetragonal (P42/nmc), cubic (Fm 3 bar m), and orthorhombic (Pbca and Pnma)) are investigated systematically by employing DFT functionals (LDA, PBE and PW91). It is found that the structural parameters of ZrO2 polymorphs calculated by PBE and PW91 functionals are highly consistent with previous experiments with low absolute relative error (ARE). Moreover, all considered structures are mechanically stable according to the Born-Huang criterion and the PBE and PW91 functionals are more accurate than the LDA functional in predicting mechanical and thermodynamic properties. Significantly, we described mechanical and thermodynamic properties of ZrO2 polymorphs by introducing the charge density difference of related surfaces, which provides a better understanding of different behaviors of elastic constants (Cij) in various crystal structures of ZrO2.

  7. Harmonizing General Relativity with Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Alfonso-Faus, Antonio

    2007-04-01

    Gravitation is the common underlying texture between General Relativity and Quantum Mechanics. We take gravitation as the link that can make possible the marriage between these two sciences. We use here the duality of Nature for gravitation: A continuous warped space, wave-like, and a discrete quantum gas, particle-like, both coexistent and producing an equilibrium state in the Universe. The result is a static, non expanding, spherical, unlimited and finite Universe, with no cosmological constant and no dark energy. Macht's Principle is reproduced here by the convergence of the two cosmological equations of Einstein. From this a Mass Boom concept is born given by M = t, M the mass of the Universe and t its age. Also a decreasing speed of light is the consequence of the Mass Boom, c = 1/t, which explains the Supernovae Type Ia observations without the need of expansion (nor, of course, accelerated expansion). Our Mass Boom model completely wipes out the problems and paradoxes built in the Big Bang model, like the horizon, monopole, entropy, flatness, fine tuning, etc. It also eliminates the need for inflation.

  8. Dynamical phase transitions in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Rotter, Ingrid

    2012-02-01

    The nucleus is described as an open many-body quantum system with a non-Hermitian Hamilton operator the eigenvalues of which are complex, in general. The eigenvalues may cross in the complex plane (exceptional points), the phases of the eigenfunctions are not rigid in approaching the crossing points and the widths bifurcate. By varying only one parameter, the eigenvalue trajectories usually avoid crossing and width bifurcation occurs at the critical value of avoided crossing. An analog spectroscopic redistribution takes place for discrete states below the particle decay threshold. By this means, a dynamical phase transition occurs in the many-level system starting at a critical value of the level density. Hence the properties of the low-lying nuclear states (described well by the shell model) and those of highly excited nuclear states (described by random ensembles) differ fundamentally from one another. The statement of Niels Bohr on the collective features of compound nucleus states at high level density is therefore not in contradiction to the shell-model description of nuclear (and atomic) states at low level density. Dynamical phase transitions are observed experimentally in different quantum mechanical systems by varying one or two parameters.

  9. Causal localizations in relativistic quantum mechanics

    SciTech Connect

    Castrigiano, Domenico P. L. Leiseifer, Andreas D.

    2015-07-15

    Causal localizations describe the position of quantum systems moving not faster than light. They are constructed for the systems with finite spinor dimension. At the center of interest are the massive relativistic systems. For every positive mass, there is the sequence of Dirac tensor-localizations, which provides a complete set of inequivalent irreducible causal localizations. They obey the principle of special relativity and are fully Poincaré covariant. The boosters are determined by the causal position operator and the other Poincaré generators. The localization with minimal spinor dimension is the Dirac localization. Thus, the Dirac equation is derived here as a mere consequence of the principle of causality. Moreover, the higher tensor-localizations, not known so far, follow from Dirac’s localization by a simple construction. The probability of localization for positive energy states results to be described by causal positive operator valued (PO-) localizations, which are the traces of the causal localizations on the subspaces of positive energy. These causal Poincaré covariant PO-localizations for every irreducible massive relativistic system were, all the more, not known before. They are shown to be separated. Hence, the positive energy systems can be localized within every open region by a suitable preparation as accurately as desired. Finally, the attempt is made to provide an interpretation of the PO-localization operators within the frame of conventional quantum mechanics attributing an important role to the negative energy states.

  10. Causal localizations in relativistic quantum mechanics

    NASA Astrophysics Data System (ADS)

    Castrigiano, Domenico P. L.; Leiseifer, Andreas D.

    2015-07-01

    Causal localizations describe the position of quantum systems moving not faster than light. They are constructed for the systems with finite spinor dimension. At the center of interest are the massive relativistic systems. For every positive mass, there is the sequence of Dirac tensor-localizations, which provides a complete set of inequivalent irreducible causal localizations. They obey the principle of special relativity and are fully Poincaré covariant. The boosters are determined by the causal position operator and the other Poincaré generators. The localization with minimal spinor dimension is the Dirac localization. Thus, the Dirac equation is derived here as a mere consequence of the principle of causality. Moreover, the higher tensor-localizations, not known so far, follow from Dirac's localization by a simple construction. The probability of localization for positive energy states results to be described by causal positive operator valued (PO-) localizations, which are the traces of the causal localizations on the subspaces of positive energy. These causal Poincaré covariant PO-localizations for every irreducible massive relativistic system were, all the more, not known before. They are shown to be separated. Hence, the positive energy systems can be localized within every open region by a suitable preparation as accurately as desired. Finally, the attempt is made to provide an interpretation of the PO-localization operators within the frame of conventional quantum mechanics attributing an important role to the negative energy states.

  11. Extending quantum mechanics entails extending special relativity

    NASA Astrophysics Data System (ADS)

    Aravinda, S.; Srikanth, R.

    2016-05-01

    The complementarity between signaling and randomness in any communicated resource that can simulate singlet statistics is generalized by relaxing the assumption of free will in the choice of measurement settings. We show how to construct an ontological extension for quantum mechanics (QMs) through the oblivious embedding of a sound simulation protocol in a Newtonian spacetime. Minkowski or other intermediate spacetimes are ruled out as the locus of the embedding by virtue of hidden influence inequalities. The complementarity transferred from a simulation to the extension unifies a number of results about quantum non-locality, and implies that special relativity has a different significance for the ontological model and for the operational theory it reproduces. Only the latter, being experimentally accessible, is required to be Lorentz covariant. There may be certain Lorentz non-covariant elements at the ontological level, but they will be inaccessible at the operational level in a valid extension. Certain arguments against the extendability of QM, due to Conway and Kochen (2009) and Colbeck and Renner (2012), are attributed to their assumption that the spacetime at the ontological level has Minkowski causal structure.

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

    NASA Astrophysics Data System (ADS)

    Plotnitsky, Arkady

    2014-12-01

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

  13. Quantum mechanics of a generalised rigid body

    NASA Astrophysics Data System (ADS)

    Gripaios, Ben; Sutherland, Dave

    2016-05-01

    We consider the quantum version of Arnold’s generalisation of a rigid body in classical mechanics. Thus, we quantise the motion on an arbitrary Lie group manifold of a particle whose classical trajectories correspond to the geodesics of any one-sided-invariant metric. We show how the derivation of the spectrum of energy eigenstates can be simplified by making use of automorphisms of the Lie algebra and (for groups of type I) by methods of harmonic analysis. We show how the method can be extended to cosets, generalising the linear rigid rotor. As examples, we consider all connected and simply connected Lie groups up to dimension 3. This includes the universal cover of the archetypical rigid body, along with a number of new exactly solvable models. We also discuss a possible application to the topical problem of quantising a perfect fluid.

  14. Gauge invariance and reciprocity in quantum mechanics

    SciTech Connect

    Leung, P. T.; Young, K.

    2010-03-15

    Reciprocity in wave propagation usually refers to the symmetry of the Green's function under the interchange of the source and the observer coordinates, but this condition is not gauge invariant in quantum mechanics, a problem that is particularly significant in the presence of a vector potential. Several possible alternative criteria are given and analyzed with reference to different examples with nonzero magnetic fields and/or vector potentials, including the case of a multiply connected spatial domain. It is shown that the appropriate reciprocity criterion allows for specific phase factors separable into functions of the source and observer coordinates and that this condition is robust with respect to the addition of any scalar potential. In the Aharonov-Bohm effect, reciprocity beyond monoenergetic experiments holds only because of subsidiary conditions satisfied in actual experiments: the test charge is in units of e and the flux is produced by a condensate of particles with charge 2e.

  15. Waveform information from quantum mechanical entropy

    NASA Astrophysics Data System (ADS)

    Funkhouser, Scott; Suski, William; Winn, Andrew

    2016-06-01

    Although the entropy of a given signal-type waveform is technically zero, it is nonetheless desirable to use entropic measures to quantify the associated information. Several such prescriptions have been advanced in the literature but none are generally successful. Here, we report that the Fourier-conjugated `total entropy' associated with quantum-mechanical probabilistic amplitude functions (PAFs) is a meaningful measure of information in non-probabilistic real waveforms, with either the waveform itself or its (normalized) analytic representation acting in the role of the PAF. Detailed numerical calculations are presented for both adaptations, showing the expected informatic behaviours in a variety of rudimentary scenarios. Particularly noteworthy are the sensitivity to the degree of randomness in a sequence of pulses and potential for detection of weak signals.

  16. Quantum mechanical calculations to chemical accuracy

    NASA Technical Reports Server (NTRS)

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

    1991-01-01

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

  17. On some hydrodynamical aspects of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Spera, Mauro

    2010-02-01

    In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the complex polynomial ( i.e. Borel-Weil) realization of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dimensional geometric quantum mechanics, the Schrödinger velocity field on projective Hilbert space is divergence-free (being Killing with respect to the Fubini-Study metric) and fulfils the stationary Euler equation, with pressure proportional to the Hamiltonian uncertainty (squared). We explicitly determine the critical points of the pressure of this “Schrödinger fluid”, together with its vorticity, which turns out to depend on the spacings of the energy levels. These results follow from hydrodynamical properties of Killing vector fields valid in any (finite dimensional) Riemannian manifold, of possible independent interest.

  18. On some hydrodynamical aspects of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Spera, Mauro

    2010-02-01

    In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the complex polynomial (i.e. Borel-Weil) realization of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dimensional geometric quantum mechanics, the Schrödinger velocity field on projective Hilbert space is divergence-free (being Killing with respect to the Fubini-Study metric) and fulfils the stationary Euler equation, with pressure proportional to the Hamiltonian uncertainty (squared). We explicitly determine the critical points of the pressure of this "Schrödinger fluid", together with its vorticity, which turns out to depend on the spacings of the energy levels. These results follow from hydrodynamical properties of Killing vector fields valid in any (finite dimensional) Riemannian manifold, of possible independent interest.

  19. New methods for quantum mechanical reaction dynamics

    SciTech Connect

    Thompson, Ward Hugh

    1996-12-01

    Quantum mechanical methods are developed to describe the dynamics of bimolecular chemical reactions. We focus on developing approaches for directly calculating the desired quantity of interest. Methods for the calculation of single matrix elements of the scattering matrix (S-matrix) and initial state-selected reaction probabilities are presented. This is accomplished by the use of absorbing boundary conditions (ABC) to obtain a localized (L2) representation of the outgoing wave scattering Green`s function. This approach enables the efficient calculation of only a single column of the S-matrix with a proportionate savings in effort over the calculation of the entire S-matrix. Applying this method to the calculation of the initial (or final) state-selected reaction probability, a more averaged quantity, requires even less effort than the state-to-state S-matrix elements. It is shown how the same representation of the Green`s function can be effectively applied to the calculation of negative ion photodetachment intensities. Photodetachment spectroscopy of the anion ABC- can be a very useful method for obtaining detailed information about the neutral ABC potential energy surface, particularly if the ABC- geometry is similar to the transition state of the neutral ABC. Total and arrangement-selected photodetachment spectra are calculated for the H3O- system, providing information about the potential energy surface for the OH + H2 reaction when compared with experimental results. Finally, we present methods for the direct calculation of the thermal rate constant from the flux-position and flux-flux correlation functions. The spirit of transition state theory is invoked by concentrating on the short time dynamics in the area around the transition state that determine reactivity. These methods are made efficient by evaluating the required quantum mechanical trace in the basis of eigenstates of the

  20. Categorical quantum mechanics II: Classical-quantum interaction

    NASA Astrophysics Data System (ADS)

    Coecke, Bob; Kissinger, Aleks

    2016-08-01

    This is the second part of a three-part overview, in which we derive the category-theoretic backbone of quantum theory from a process ontology, treating quantum theory as a theory of systems, processes and their interactions. In this part, we focus on classical-quantum interaction. Classical and quantum systems are treated as distinct types, of which the respective behavioral properties are specified in terms of processes and their compositions. In particular, classicality is witnessed by ‘spiders’ which fuse together whenever they connect. We define mixedness and show that pure processes are extremal in the space of all processes, and we define entanglement and show that quantum theory indeed exhibits entanglement. We discuss the classification of tripartite qubit entanglement and show that both the GHZ-state and the W-state come from spider-like families of processes, which differ only in how they behave when they are connected by two or more wires. We define measurements and provide fully comprehensive descriptions of several quantum protocols involving classical data flow. Finally, we give a notion of ‘genuine quantumness’, from which special processes called ‘phase spiders’ arise, and get a first glimpse of quantum nonlocality.

  1. Reverse Causation and the Transactional Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Cramer, John G.

    2006-10-01

    In the first part of the paper we present the transactional interpretation of quantum mechanics, a method of viewing the formalism of quantum mechanics that provides a way of visualizing quantum events and experiments. In the second part, we present an EPR gedankenexperiment that appears to lead to observer-level reverse causation. A transactional analysis of the experiment is presented. It easily accounts for the reported observations but does not reveal any barriers to its modification for reverse causation.

  2. Categorization of Quantum Mechanics Problems by Professors and Students

    ERIC Educational Resources Information Center

    Lin, Shih-Yin; Singh, Chandralekha

    2010-01-01

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

  3. Developing and Evaluating Animations for Teaching Quantum Mechanics Concepts

    ERIC Educational Resources Information Center

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

    2010-01-01

    In this paper, we describe animations and animated visualizations for introductory and intermediate-level quantum mechanics instruction developed at the University of St Andrews. The animations aim to help students build mental representations of quantum mechanics concepts. They focus on known areas of student difficulty and misconceptions by…

  4. Do Free Quantum-Mechanical Wave Packets Always Spread?

    ERIC Educational Resources Information Center

    Klein, James R.

    1980-01-01

    The spreading or shrinking of free three-dimensional quantum-mechanical wave packets is addressed. A seeming paradox concerning the time evolution operator and nonspreading wave packets is discussed, and the necessity of taking into account the appropriate mathematical structure of quantum mechanics is emphasized. Teaching implications are given.…

  5. Design and Validation of the Quantum Mechanics Conceptual Survey

    ERIC Educational Resources Information Center

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

    2010-01-01

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

  6. In Defense of a Heuristic Interpretation of Quantum Mechanics

    ERIC Educational Resources Information Center

    Healy, Eamonn F.

    2010-01-01

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

  7. Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems

    ERIC Educational Resources Information Center

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

    2009-01-01

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

  8. Quantum Mechanics from Periodic Dynamics: the bosonic case

    SciTech Connect

    Dolce, Donatello

    2010-05-04

    Enforcing the periodicity hypothesis of the 'old' formulation of Quantum Mechanics we show the possibility for a new scenario where Special Relativity and Quantum Mechanics are unified in a deterministic field theory. A novel interpretation of the AdS/CFT conjecture is discussed.

  9. A snapshot of foundational attitudes toward quantum mechanics

    NASA Astrophysics Data System (ADS)

    Schlosshauer, Maximilian; Kofler, Johannes; Zeilinger, Anton

    2013-08-01

    Foundational investigations in quantum mechanics, both experimental and theoretical, gave birth to the field of quantum information science. Nevertheless, the foundations of quantum mechanics themselves remain hotly debated in the scientific community, and no consensus on essential questions has been reached. Here, we present the results of a poll carried out among 33 participants of a conference on the foundations of quantum mechanics. The participants completed a questionnaire containing 16 multiple-choice questions probing opinions on quantum-foundational issues. Participants included physicists, philosophers, and mathematicians. We describe our findings, identify commonly held views, and determine strong, medium, and weak correlations between the answers. Our study provides a unique snapshot of current views in the field of quantum foundations, as well as an analysis of the relationships between these views.

  10. Mechanics and thermodynamics of propulsion (2nd revised and enlarged edition)

    NASA Astrophysics Data System (ADS)

    Hill, Philip G.; Peterson, Carl R.

    The present volume proceeds under the principle that a few fundamental physical principles can with suitable application furnish students of mechanical and aeronautical engineering with an understanding of all aspects of aircraft and spacecraft propulsion. This methodology can further yield usefully quantitative assessments of performance, and indicate prospects for further improvement. Attention is given to the jet propulsion principle, the mechanics and thermodynamics of fluid flow, the thermodynamics of aircraft gas turbine engines, axial compressors and turbines, centrifugal compressors, chemical propellant rocket engine operation and performance, turbomachinery for liquid propellant rockets, and electrical rocket propulsion.

  11. Chirality, quantum mechanics, and biological determinism

    NASA Astrophysics Data System (ADS)

    Davies, P. C. W.

    2006-08-01

    life with biochemical make-up resembling that of known life. Whilst the experimental search for a second sample of life - possibly by detecting a chiral "anomaly" - continues, some theoretical investigations may be pursued to narrow down the options. Chiral determinism would be an intrinsically quantum process. There are hints that quantum mechanics plays a key role in biology, but the claim remains contentious. Here I review some of the evidence for quantum aspects of biology. I also summarize some proposals for testing biological determinism by seeking evidence for a multiple genesis events on Earth, and for identifying extant "alien microbes" - micro-organisms descended from an independent origin from familiar life.

  12. Quantum Chemical Insight into the Interactions and Thermodynamics Present in Choline Chloride Based Deep Eutectic Solvents.

    PubMed

    Wagle, Durgesh V; Deakyne, Carol A; Baker, Gary A

    2016-07-14

    We report quantum chemical calculations performed on three popular deep eutectic solvents (DESs) in order to elucidate the molecular interactions, charge transfer interactions, and thermodynamics associated with these systems. The DESs studied comprise 1:2 choline chloride/urea (reline), 1:2 choline chloride/ethylene glycol (ethaline), and 1:1 choline chloride/malonic acid (maloline). The excellent correlation between calculated and experimental vibrational spectra allowed for identification of dominant interactions in the DES systems. The DESs were found to be stabilized by both conventional hydrogen bonds and C-H···O/C-H···π interactions between the components. The hydrogen-bonding network established in the DES is clearly distinct from that which exists within the neat hydrogen-bond donor dimer. Charge decomposition analysis indicates significant charge transfer from choline and chloride to the hydrogen-bond donor with a higher contribution from the cation, and a density of states analysis confirms the direction of the charge transfer. Consequently, the sum of the bond orders of the choline-Cl(-) interactions in the DESs correlates directly with the melting temperatures of the DESs, a correlation that offers insight into the effect of the tuning of the choline-Cl(-) interactions by the hydrogen-bond donors on the physical properties of the DESs. Finally, the differences in the vibrational entropy changes upon DES formation are consistent with the trend in the overall entropy changes upon DES formation.

  13. Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics

    NASA Astrophysics Data System (ADS)

    Ohzeki, Masayuki

    2013-09-01

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

  14. Statistical mechanics of quantum-classical systems with holonomic constraints.

    PubMed

    Sergi, Alessandro

    2006-01-14

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

  15. High-efficiency quantum state transfer and quantum memory using a mechanical oscillator

    NASA Astrophysics Data System (ADS)

    Sete, Eyob A.; Eleuch, H.

    2015-03-01

    We analyze an optomechanical system that can be used to efficiently transfer a quantum state between an optical cavity and a distant mechanical oscillator coupled to a second optical cavity. We show that for a moderate mechanical Q factor it is possible to achieve a transfer efficiency of 99.4 % by using adjustable cavity damping rates and destructive interference. We also show that the quantum mechanical oscillator can be used as a quantum memory device with an efficiency of 96 % employing a pulsed optomechanical coupling. Although the mechanical dissipation slightly decreases the efficiency, its effect can be significantly reduced by designing a high-Q mechanical oscillator.

  16. Quantum mechanics/molecular mechanics study of oxygen binding in hemocyanin.

    PubMed

    Saito, Toru; Thiel, Walter

    2014-05-15

    We report a combined quantum mechanics/molecular mechanics (QM/MM) study on the mechanism of reversible dioxygen binding in the active site of hemocyanin (Hc). The QM region is treated by broken-symmetry density functional theory (DFT) with spin projection corrections. The X-ray structures of deoxygenated (deoxyHc) and oxygenated (oxyHc) hemocyanin are well reproduced by QM/MM geometry optimizations. The computed relative energies strongly depend on the chosen density functional. They are consistent with the available thermodynamic data for oxygen binding in hemocyanin and in synthetic model complexes when the BH&HLYP hybrid functional with 50% Hartree-Fock exchange is used. According to the QM(BH&HLYP)/MM results, the reaction proceeds stepwise with two sequential electron transfer (ET) processes in the triplet state followed by an intersystem crossing to the singlet product. The first ET step leads to a nonbridged superoxo CuB(II)-O2(•-) intermediate via a low-barrier transition state. The second ET step is even more facile and yields a side-on oxyHc complex with the characteristic Cu2O2 butterfly core, accompanied by triplet-singlet intersystem crossing. The computed barriers are very small so that the two ET processes are expected to very rapid and nearly simultaneous.

  17. Water properties from first principles: Simulations by a general-purpose quantum mechanical polarizable force field

    PubMed Central

    Donchev, A. G.; Galkin, N. G.; Illarionov, A. A.; Khoruzhii, O. V.; Olevanov, M. A.; Ozrin, V. D.; Subbotin, M. V.; Tarasov, V. I.

    2006-01-01

    We have recently introduced a quantum mechanical polarizable force field (QMPFF) fitted solely to high-level quantum mechanical data for simulations of biomolecular systems. Here, we present an improved form of the force field, QMPFF2, and apply it to simulations of liquid water. The results of the simulations show excellent agreement with a variety of experimental thermodynamic and structural data, as good or better than that provided by specialized water potentials. In particular, QMPFF2 is the only ab initio force field to accurately reproduce the anomalous temperature dependence of water density to our knowledge. The ability of the same force field to successfully simulate the properties of both organic molecules and water suggests it will be useful for simulations of proteins and protein–ligand interactions in the aqueous environment. PMID:16723394

  18. Calendar effects in quantum mechanics in view of interactive holography

    NASA Astrophysics Data System (ADS)

    Berkovich, Simon

    2013-04-01

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

  19. Thermodynamic and relativistic uncertainty relations

    NASA Astrophysics Data System (ADS)

    Artamonov, A. A.; Plotnikov, E. M.

    2017-01-01

    Thermodynamic uncertainty relation (UR) was verified experimentally. The experiments have shown the validity of the quantum analogue of the zeroth law of stochastic thermodynamics in the form of the saturated Schrödinger UR. We have also proposed a new type of UR for the relativistic mechanics. These relations allow us to consider macroscopic phenomena within the limits of the ratio of the uncertainty relations for different physical quantities.

  20. Review of student difficulties in upper-level quantum mechanics

    NASA Astrophysics Data System (ADS)

    Singh, Chandralekha; Marshman, Emily

    2015-12-01

    [This paper is part of the Focused Collection on Upper Division Physics Courses.] Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical mechanics and quantum mechanics are very different. Here, we review research on student reasoning difficulties in learning upper-level quantum mechanics and research on students' problem-solving and metacognitive skills in these courses. Some of these studies were multiuniversity investigations. The investigations suggest that there is large diversity in student performance in upper-level quantum mechanics regardless of the university, textbook, or instructor, and many students in these courses have not acquired a functional understanding of the fundamental concepts. The nature of reasoning difficulties in learning quantum mechanics is analogous to reasoning difficulties found via research in introductory physics courses. The reasoning difficulties were often due to overgeneralizations of concepts learned in one context to another context where they are not directly applicable. Reasoning difficulties in distinguishing between closely related concepts and in making sense of the formalism of quantum mechanics were common. We conclude with a brief summary of the research-based approaches that take advantage of research on student difficulties in order to improve teaching and learning of quantum mechanics.

  1. Thermodynamics and nonlinear mechanics of materials with photoresponsive microstructure

    NASA Astrophysics Data System (ADS)

    Oates, William S.; Bin, Jonghoon

    2014-03-01

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

  2. Observation and superselection in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Landsman, N. P.

    We attempt to clarify the main conceptual issues in approaches to 'objectification' or 'measurement' in quantum mechanics which are based on superselection rules. Such approaches venture to derive the emergence of classical 'reality' relative to a class of observers; those believing that the classical world exists intrinsically and absolutely are advised against reading this paper. The prototype approach (K. Hepp, Helv. Phys. Acta 45 (1972), 237-248) where superselection sectors are assumed in the state space of the apparatus is shown to be untenable. Instead, one should couple system and apparatus to an environment, and postulate superselection rules for the latter. These are motivated by the locality of any observer or other (actual or virtual) monitoring system. In this way 'environmental' solutions to the measurement problem (H.D. Zeh, Found. Phys. 1 (1970), 69-76; W. H. Zurek, Phys. Rev. D26 (1982), 1862-1880 and Progr. Theor. Phys. 89 (1993), 281-312) become consistent and acceptable, too. Points of contact with the modal interpretation are briefly discussed. We propose a minimal value attribution to observables in theories with superselection rules, in which only central observables have properties. In particular, the eigenvector-eigenvalue link is dropped. This is mainly motivated by Ockham's razor.

  3. "Mysticism" in Quantum Mechanics: The Forgotten Controversy

    ERIC Educational Resources Information Center

    Marin, Juan Miguel

    2009-01-01

    This paper argues that a European controversy over a "mystical" hypothesis, one assigning the mind a role to play at the material level of reality, shaped much of the debate over the interpretation of the quantum equations. It traces back the controversy to the past two decades, beginning in the late 1920s--birth of quantum theory--and concluding…

  4. Ab initio atomistic thermodynamics study on the oxidation mechanism of binary and ternary alloy surfaces

    SciTech Connect

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

    2015-02-14

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

  5. The physical principles of quantum mechanics. A critical review

    NASA Astrophysics Data System (ADS)

    Strocchi, F.

    2012-01-01

    The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more physically motivated formulation is discussed. The existence of non commuting observables, which characterizes quantum mechanics with respect to classical mechanics, is related to operationally testable complementarity relations, rather than to uncertainty relations. The drawbacks of Dirac argument for canonical quantization are avoided by a more geometrical approach.

  6. Quantum Hamilton mechanics: Hamilton equations of quantum motion, origin of quantum operators, and proof of quantization axiom

    SciTech Connect

    Yang, C.-D. . E-mail: cdyang@mail.ncku.edu.tw

    2006-12-15

    This paper gives a thorough investigation on formulating and solving quantum problems by extended analytical mechanics that extends canonical variables to complex domain. With this complex extension, we show that quantum mechanics becomes a part of analytical mechanics and hence can be treated integrally with classical mechanics. Complex canonical variables are governed by Hamilton equations of motion, which can be derived naturally from Schroedinger equation. Using complex canonical variables, a formal proof of the quantization axiom p {sup {yields}} p = -ih{nabla}, which is the kernel in constructing quantum-mechanical systems, becomes a one-line corollary of Hamilton mechanics. The derivation of quantum operators from Hamilton mechanics is coordinate independent and thus allows us to derive quantum operators directly under any coordinate system without transforming back to Cartesian coordinates. Besides deriving quantum operators, we also show that the various prominent quantum effects, such as quantization, tunneling, atomic shell structure, Aharonov-Bohm effect, and spin, all have the root in Hamilton mechanics and can be described entirely by Hamilton equations of motion.

  7. Ruling out multi-order interference in quantum mechanics.

    PubMed

    Sinha, Urbasi; Couteau, Christophe; Jennewein, Thomas; Laflamme, Raymond; Weihs, Gregor

    2010-07-23

    Quantum mechanics and gravitation are two pillars of modern physics. Despite their success in describing the physical world around us, they seem to be incompatible theories. There are suggestions that one of these theories must be generalized to achieve unification. For example, Born's rule--one of the axioms of quantum mechanics--could be violated. Born's rule predicts that quantum interference, as shown by a double-slit diffraction experiment, occurs from pairs of paths. A generalized version of quantum mechanics might allow multipath (i.e., higher-order) interference, thus leading to a deviation from the theory. We performed a three-slit experiment with photons and bounded the magnitude of three-path interference to less than 10(-2) of the expected two-path interference, thus ruling out third- and higher-order interference and providing a bound on the accuracy of Born's rule. Our experiment is consistent with the postulate both in semiclassical and quantum regimes.

  8. Bell operator and Gaussian squeezed states in noncommutative quantum mechanics

    NASA Astrophysics Data System (ADS)

    Bastos, Catarina; Bernardini, Alex E.; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno

    2016-05-01

    We examine putative corrections to the Bell operator due to the noncommutativity in the phase space. Starting from a Gaussian squeezed envelope whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics, respectively, we conclude that although the time-evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations, noncommutativity versions of quantum mechanics remain as nonlocal as quantum mechanics itself.

  9. Predicting crystal structure by merging data mining with quantum mechanics.

    PubMed

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

    2006-08-01

    Modern methods of quantum mechanics have proved to be effective tools to understand and even predict materials properties. An essential element of the materials design process, relevant to both new materials and the optimization of existing ones, is knowing which crystal structures will form in an alloy system. Crystal structure can only be predicted effectively with quantum mechanics if an algorithm to direct the search through the large space of possible structures is found. We present a new approach to the prediction of structure that rigorously mines correlations embodied within experimental data and uses them to direct quantum mechanical techniques efficiently towards the stable crystal structure of materials.

  10. The actual content of quantum theoretical kinematics and mechanics

    NASA Technical Reports Server (NTRS)

    Heisenberg, W.

    1983-01-01

    First, exact definitions are supplied for the terms: position, velocity, energy, etc. (of the electron, for instance), such that they are valid also in quantum mechanics. Canonically conjugated variables are determined simultaneously only with a characteristic uncertainty. This uncertainty is the intrinsic reason for the occurrence of statistical relations in quantum mechanics. Mathematical formulation is made possible by the Dirac-Jordan theory. Beginning from the basic principles thus obtained, macroscopic processes are understood from the viewpoint of quantum mechanics. Several imaginary experiments are discussed to elucidate the theory.

  11. Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation

    NASA Astrophysics Data System (ADS)

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

    2013-08-01

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

  12. Calculations of Solvation Free Energy through Energy Reweighting from Molecular Mechanics to Quantum Mechanics.

    PubMed

    Jia, Xiangyu; Wang, Meiting; Shao, Yihan; König, Gerhard; Brooks, Bernard R; Zhang, John Z H; Mei, Ye

    2016-02-09

    In this work, the solvation free energies of 20 organic molecules from the 4th Statistical Assessment of the Modeling of Proteins and Ligands (SAMPL4) have been calculated. The sampling of phase space is carried out at a molecular mechanical level, and the associated free energy changes are estimated using the Bennett Acceptance Ratio (BAR). Then the quantum mechanical (QM) corrections are computed through the indirect Non-Boltzmann Bennett's acceptance ratio (NBB) or the thermodynamics perturbation (TP) method. We show that BAR+TP gives a minimum analytic variance for the calculated solvation free energy at the Gaussian limit and performs slightly better than NBB in practice. Furthermore, the expense of the QM calculations in TP is only half of that in NBB. We also show that defining the biasing potential as the difference of the solute-solvent interaction energy, instead of the total energy, can converge the calculated solvation free energies much faster but possibly to different values. Based on the experimental solvation free energies which have been published before, it is discovered in this study that BLYP yields better results than MP2 and some other later functionals such as B3LYP, M06-2X, and ωB97X-D.

  13. New Potentials for Old: The Darboux Transformation in Quantum Mechanics

    ERIC Educational Resources Information Center

    Williams, Brian Wesley; Celius, Tevye C.

    2008-01-01

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

  14. Classical and quantum Reissner-Nordström black hole thermodynamics and first order phase transition

    NASA Astrophysics Data System (ADS)

    Ghaffarnejad, Hossein

    2016-01-01

    First we consider classical Reissner-Nordström black hole (CRNBH) metric which is obtained by solving Einstein-Maxwell metric equation for a point electric charge e inside of a spherical static body with mass M. It has 2 interior and exterior horizons. Using Bekenstein-Hawking entropy theorem we calculate interior and exterior entropy, temperature, Gibbs free energy and heat capacity at constant electric charge. We calculate first derivative of the Gibbs free energy with respect to temperature which become a singular function having a singularity at critical point Mc=2|e|/√{3} with corresponding temperature Tc=1/24π√{3|e|}. Hence we claim first order phase transition is happened there. Temperature same as Gibbs free energy takes absolutely positive (negative) values on the exterior (interior) horizon. The Gibbs free energy takes two different positive values synchronously for 0< T< Tc but not for negative values which means the system is made from two subsystem. For negative temperatures entropy reaches to zero value at Tto-∞ and so takes Bose-Einstein condensation single state. Entropy increases monotonically in case 0< T< Tc. Regarding results of the work presented at Wang and Huang (Phys. Rev. D 63:124014, 2001) we calculate again the mentioned thermodynamical variables for remnant stable final state of evaporating quantum Reissner-Nordström black hole (QRNBH) and obtained results same as one in case of the CRNBH. Finally, we solve mass loss equation of QRNBH against advance Eddington-Finkelstein time coordinate and derive luminosity function. We obtain switching off of QRNBH evaporation before than the mass completely vanishes. It reaches to a could Lukewarm type of RN black hole which its final remnant mass is m_{final}=|e| in geometrical units. Its temperature and luminosity vanish but not in Schwarzschild case of evaporation. Our calculations can be take some acceptable statements about information loss paradox (ILP).

  15. Third Law of Thermodynamics and The Shape of the Phase Diagram for Systems With a First-Order Quantum Phase Transition.

    PubMed

    Kirkpatrick, T R; Belitz, D

    2015-07-10

    The third law of thermodynamics constrains the phase diagram of systems with a first-order quantum phase transition. For a zero conjugate field, the coexistence curve has an infinite slope at T=0. If a tricritical point exists at T>0, then the associated tricritical wings are perpendicular to the T=0 plane, but not to the zero-field plane. These results are based on the third law and basic thermodynamics only, and are completely general. As an explicit example we consider the ferromagnetic quantum phase transition in clean metals, where a first-order quantum phase transition is commonly observed.

  16. Superradiant Quantum Heat Engine.

    PubMed

    Hardal, Ali Ü C; Müstecaplıoğlu, Özgür E

    2015-08-11

    Quantum physics revolutionized classical disciplines of mechanics, statistical physics, and electrodynamics. One branch of scientific knowledge however seems untouched: thermodynamics. Major motivation behind thermodynamics is to develop efficient heat engines. Technology has a trend to miniaturize engines, reaching to quantum regimes. Development of quantum heat engines (QHEs) requires emerging field of quantum thermodynamics. Studies of QHEs debate whether quantum coherence can be used as a resource. We explore an alternative where it can function as an effective catalyst. We propose a QHE which consists of a photon gas inside an optical cavity as the working fluid and quantum coherent atomic clusters as the fuel. Utilizing the superradiance, where a cluster can radiate quadratically faster than a single atom, we show that the work output becomes proportional to the square of the number of the atoms. In addition to practical value of cranking up QHE, our result is a fundamental difference of a quantum fuel from its classical counterpart.

  17. Superradiant Quantum Heat Engine

    PubMed Central

    Hardal, Ali Ü. C.; Müstecaplıoğlu, Özgür E.

    2015-01-01

    Quantum physics revolutionized classical disciplines of mechanics, statistical physics, and electrodynamics. One branch of scientific knowledge however seems untouched: thermodynamics. Major motivation behind thermodynamics is to develop efficient heat engines. Technology has a trend to miniaturize engines, reaching to quantum regimes. Development of quantum heat engines (QHEs) requires emerging field of quantum thermodynamics. Studies of QHEs debate whether quantum coherence can be used as a resource. We explore an alternative where it can function as an effective catalyst. We propose a QHE which consists of a photon gas inside an optical cavity as the working fluid and quantum coherent atomic clusters as the fuel. Utilizing the superradiance, where a cluster can radiate quadratically faster than a single atom, we show that the work output becomes proportional to the square of the number of the atoms. In addition to practical value of cranking up QHE, our result is a fundamental difference of a quantum fuel from its classical counterpart. PMID:26260797

  18. Multiscale Quantum Mechanics/Molecular Mechanics Simulations with Neural Networks.

    PubMed

    Shen, Lin; Wu, Jingheng; Yang, Weitao

    2016-10-11

    Molecular dynamics simulation with multiscale quantum mechanics/molecular mechanics (QM/MM) methods is a very powerful tool for understanding the mechanism of chemical and biological processes in solution or enzymes. However, its computational cost can be too high for many biochemical systems because of the large number of ab initio QM calculations. Semiempirical QM/MM simulations have much higher efficiency. Its accuracy can be improved with a correction to reach the ab initio QM/MM level. The computational cost on the ab initio calculation for the correction determines the efficiency. In this paper we developed a neural network method for QM/MM calculation as an extension of the neural-network representation reported by Behler and Parrinello. With this approach, the potential energy of any configuration along the reaction path for a given QM/MM system can be predicted at the ab initio QM/MM level based on the semiempirical QM/MM simulations. We further applied this method to three reactions in water to calculate the free energy changes. The free-energy profile obtained from the semiempirical QM/MM simulation is corrected to the ab initio QM/MM level with the potential energies predicted with the constructed neural network. The results are in excellent accordance with the reference data that are obtained from the ab initio QM/MM molecular dynamics simulation or corrected with direct ab initio QM/MM potential energies. Compared with the correction using direct ab initio QM/MM potential energies, our method shows a speed-up of 1 or 2 orders of magnitude. It demonstrates that the neural network method combined with the semiempirical QM/MM calculation can be an efficient and reliable strategy for chemical reaction simulations.

  19. The Statistical Interpretation of Classical Thermodynamic Heating and Expansion Processes

    ERIC Educational Resources Information Center

    Cartier, Stephen F.

    2011-01-01

    A statistical model has been developed and applied to interpret thermodynamic processes typically presented from the macroscopic, classical perspective. Through this model, students learn and apply the concepts of statistical mechanics, quantum mechanics, and classical thermodynamics in the analysis of the (i) constant volume heating, (ii)…

  20. Quantum Mechanics in Biology: Photoexcitations in DNA

    NASA Astrophysics Data System (ADS)

    Bittner, Eric R.; Czader, Arkadiusz

    We consider here the theoretical and quantum chemical description of the photoexcitated states in DNA duplexes. We discuss the motivation and limitations of an exciton model and use this as the starting point for more detailed excited state quantum chemical evaluations. In particular, we focus upon the role of interbase proton transfer between Watson/Crick pairs in localizing an excitation and then quenching it through intersystem crossing and charge transfer.

  1. Why are probabilistic laws governing quantum mechanics and neurobiology?

    NASA Astrophysics Data System (ADS)

    Kröger, Helmut

    2005-08-01

    We address the question: Why are dynamical laws governing in quantum mechanics and in neuroscience of probabilistic nature instead of being deterministic? We discuss some ideas showing that the probabilistic option offers advantages over the deterministic one.

  2. Generalized Weyl-Wigner map and Vey quantum mechanics

    NASA Astrophysics Data System (ADS)

    Dias, Nuno Costa; Prata, João Nuno

    2001-12-01

    The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics directly from the standard operator formulation. The covariant generalization of Moyal theory, also known as Vey quantum mechanics, was presented in the literature many years ago. However, a derivation of the formalism directly from standard operator quantum mechanics, clarifying the relation between the two formulations, is still missing. In this article we present a covariant generalization of the Weyl order prescription and of the Weyl-Wigner map and use them to derive Vey quantum mechanics directly from the standard operator formulation. The procedure displays some interesting features: it yields all the key ingredients and provides a more straightforward interpretation of the Vey theory including a direct implementation of unitary operator transformations as phase space coordinate transformations in the Vey idiom. These features are illustrated through a simple example.

  3. Probabilistic Approach to Teaching the Principles of Quantum Mechanics

    ERIC Educational Resources Information Center

    Santos, Emilio

    1976-01-01

    Approaches the representation of quantum mechanics through Hilbert space postulates. Demonstrates that if the representation is to be accurate, an evolution operator of the form of a Hamiltonian must be used. (CP)

  4. Particles, Waves, and the Interpretation of Quantum Mechanics

    ERIC Educational Resources Information Center

    Christoudouleas, N. D.

    1975-01-01

    Presents an explanation, without mathematical equations, of the basic principles of quantum mechanics. Includes wave-particle duality, the probability character of the wavefunction, and the uncertainty relations. (MLH)

  5. Macroscopic test of quantum mechanics versus stochastic electrodynamics

    NASA Astrophysics Data System (ADS)

    Chaturvedi, S.; Drummond, Peter D.

    1997-02-01

    We identify a test of quantum mechanics versus macroscopic local realism in the form of stochastic electrodynamics. The test uses the steady-state triple quadrature correlations of a parametric oscillator below threshold.

  6. A Simplified Quantum Mechanical Model of Diatomic Molecules

    ERIC Educational Resources Information Center

    Nielsen, Lars Drud

    1978-01-01

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

  7. Quantum mechanics of the inverted oscillator potential

    NASA Astrophysics Data System (ADS)

    Barton, G.

    1986-02-01

    The Hamiltonian ( 1/2m)p 2 - 1/2mω 2x 2 yields equations solvable in closed form; one is led to them by questions about the longest mean sojourn time T allowed by quantum mechanics to a system near unstable equilibrium. These equations are then studied further in their own right. After criticism of earlier arguments, one finds, by aid of the Green's function, that T ˜ ω -1log{ l/( {h̷}/{mω) 1/2}} for sojourn in the region | x| < l, where l is the resolving power of the detector. Without appeal to some parameter like l one would get nonsense estimates T ˜ ω-1 (e.g., from the nondecay probability familiar in the decay of metastable states). in this potential wavepackets Gaussian in position do not split on impact: their peaks are either transmitted or reflected, depending on the sign of the energy E ≷ 0; however, they spread so fast that not all the probability ends up on the same side of the origin as the peak. The energy eigenfunctions (parabolic cylinder functions) identify the transmission and reflection amplitudes as T = (1 + e -2πE) -1/2eiφ, R = -i(1 + e -2πE) -1/2 e -πE e iφ, where φ = arg Γ( 1/2 - iE) (in units where 2m = 1 = ω = h̷). The density of states for the interval | x| ≤ L is 2π -1 log L + π -1ϕ'( E). Wavepackets that are peaked sharply enough in energy travel without dispersion in the asymptotic region | x| > | E|, and do split on impact in the usual way. The travel times and time delays of these packets are determined. For both reflection and transmission, and for both E ≷ 0, the time delays are given by φ'( E), which is a symmetric function of E, with a positive maximum at E = 0. In particular, packets tunneling under the barrier reemerge sooner if their energy is more negative. This paradox (which occurs also in other tunneling problems) is elucidated as far as possible. Coherent states are constructed by analogy to those of the ordinary oscillator. Though not integrable, their probability distributions do have a

  8. Quantum Mechanics/Molecular Mechanics Study of the Sialyltransferase Reaction Mechanism.

    PubMed

    Hamada, Yojiro; Kanematsu, Yusuke; Tachikawa, Masanori

    2016-10-11

    The sialyltransferase is an enzyme that transfers the sialic acid moiety from cytidine 5'-monophospho-N-acetyl-neuraminic acid (CMP-NeuAc) to the terminal position of glycans. To elucidate the catalytic mechanism of sialyltransferase, we explored the potential energy surface along the sialic acid transfer reaction coordinates by the hybrid quantum mechanics/molecular mechanics method on the basis of the crystal structure of sialyltransferase CstII. Our calculation demonstrated that CstII employed an SN1-like reaction mechanism via the formation of a short-lived oxocarbenium ion intermediate. The computational barrier height was 19.5 kcal/mol, which reasonably corresponded with the experimental reaction rate. We also found that two tyrosine residues (Tyr156 and Tyr162) played a vital role in stabilizing the intermediate and the transition states by quantum mechanical interaction with CMP.

  9. Quantum mechanical theory of dynamic nuclear polarization in solid dielectrics

    PubMed Central

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

    2011-01-01

    Microwave driven dynamic nuclear polarization (DNP) is a process in which the large polarization present in an electron spin reservoir is transferred to nuclei, thereby enhancing NMR signal intensities. In solid dielectrics there are three mechanisms that mediate this transfer—the solid effect (SE), the cross effect (CE), and thermal mixing (TM). Historically these mechanisms have been discussed theoretically using thermodynamic parameters and average spin interactions. However, the SE and the CE can also be modeled quantum mechanically with a system consisting of a small number of spins and the results provide a foundation for the calculations involving TM. In the case of the SE, a single electron–nuclear spin pair is sufficient to explain the polarization mechanism, while the CE requires participation of two electrons and a nuclear spin, and can be used to understand the improved DNP enhancements observed using biradical polarizing agents. Calculations establish the relations among the electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) frequencies and the microwave irradiation frequency that must be satisfied for polarization transfer via the SE or the CE. In particular, if δ, Δ < ω0I, where δ and Δ are the homogeneous linewidth and inhomogeneous breadth of the EPR spectrum, respectively, we verify that the SE occurs when ωM = ω0S ± ω0I, where ωM, ω0S and ω0I are, respectively, the microwave, and the EPR and NMR frequencies. Alternatively, when Δ > ω0I > δ, the CE dominates the polarization transfer. This two-electron process is optimized when ω0S1−ω0S2=ω0I and ωM∼ω0S1 orω0S2, where ω0S1 and ω0S2 are the EPR Larmor frequencies of the two electrons. Using these matching conditions, we calculate the evolution of the density operator from electron Zeeman order to nuclear Zeeman order for both the SE and the CE. The results provide insights into the influence of the microwave irradiation field, the

  10. Contexts, Systems and Modalities: A New Ontology for Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Auffèves, Alexia; Grangier, Philippe

    2016-02-01

    In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules. Rather than elaborating on the quantum formalism itself, we propose a new quantum ontology, where physical properties are attributed jointly to the system, and to the context in which it is embedded. In combination with a quantization principle, this non-classical definition of physical reality sheds new light on counter-intuitive features of quantum mechanics such as the origin of probabilities, non-locality, and the quantum-classical boundary.

  11. Probability in the Many-Worlds Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Vaidman, Lev

    It is argued that, although in the Many-Worlds Interpretation of quantum mechanics there is no "probability" for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: (a) A "sleeping pill" gedanken experiment which makes correspondence between an illegitimate question: "What is the probability of an outcome of a quantum measurement?" with a legitimate question: "What is the probability that `I' am in the world corresponding to that outcome?"; (b) A gedanken experiment which splits the world into several worlds which are identical according to some symmetry condition; and (c) Relativistic causality, which together with (b) explain the Born rule of standard quantum mechanics. The Quantum Sleeping Beauty controversy and "caring measure" replacing probability measure are discussed.

  12. On the hypothesis that quantum mechanism manifests classical mechanics: Numerical approach to the correspondence in search of quantum chaos

    SciTech Connect

    Lee, Sang-Bong

    1993-09-01

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

  13. $\\cN$-FOLD SUPERSYMMETRY IN QUANTUM MECHANICAL MATRIX MODELS

    NASA Astrophysics Data System (ADS)

    Tanaka, Toshiaki

    2012-03-01

    We formulate Ņ-fold supersymmetry in quantum mechanical matrix models. As an example, we construct general two-by-two Hermitian matrix two-fold supersymmetric quantum mechanical systems. We find that there are two inequivalent such systems, both of which are characterized by two arbitrary scalar functions, and one of which does not reduce to the scalar system. The obtained systems are all weakly quasi-solvable.

  14. Geometrical description of algebraic structures: Applications to Quantum Mechanics

    SciTech Connect

    Carinena, J. F.; Ibort, A.; Marmo, G.; Morandi, G.

    2009-05-06

    Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to quantum mechanics. We will concentrate our attention into quantum theories and we will show how to use in a systematic way the transition from algebraic to geometrical structures to explore their geometry, mainly its Jordan-Lie structure.

  15. Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics

    SciTech Connect

    Goldfarb, Yair; Degani, Ilan; Tannor, David J.

    2006-12-21

    In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared--it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification - a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10{sup -7} calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.

  16. Bohmian mechanics with complex action: a new trajectory-based formulation of quantum mechanics.

    PubMed

    Goldfarb, Yair; Degani, Ilan; Tannor, David J

    2006-12-21

    In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10(-7) calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.

  17. Quantum mechanical effects in plasmonic structures with subnanometre gaps

    PubMed Central

    Zhu, Wenqi; Esteban, Ruben; Borisov, Andrei G.; Baumberg, Jeremy J.; Nordlander, Peter; Lezec, Henri J.; Aizpurua, Javier; Crozier, Kenneth B.

    2016-01-01

    Metallic structures with nanogap features have proven highly effective as building blocks for plasmonic systems, as they can provide a wide tuning range of operating frequencies and large near-field enhancements. Recent work has shown that quantum mechanical effects such as electron tunnelling and nonlocal screening become important as the gap distances approach the subnanometre length-scale. Such quantum effects challenge the classical picture of nanogap plasmons and have stimulated a number of theoretical and experimental studies. This review outlines the findings of many groups into quantum mechanical effects in nanogap plasmons, and discusses outstanding challenges and future directions. PMID:27255556

  18. Acoustic Analog to Quantum Mechanical Level-Splitting

    NASA Astrophysics Data System (ADS)

    Hilbert, Shawn

    2010-03-01

    One difficulty in teaching quantum mechanics is the lack of classroom demonstrations. To sidestep this issue, analogies can provide an enlightening alternative. Acoustics governance by the same time-independent wave equation as quantum mechanics supports it use in such analogies. This presentation examines one such analogy for an infinite potential well with a delta potential perturbation. The physical acoustic system consists of continuous sounds waves traveling in a pair of tubes which are separated by a variable diaphragm. The level-splitting nature of the quantum system can be mimicked in the acoustic system.

  19. Quantum mechanics simulation of protein dynamics on long timescale.

    PubMed

    Liu, H; Elstner, M; Kaxiras, E; Frauenheim, T; Hermans, J; Yang, W

    2001-09-01

    Protein structure and dynamics are the keys to a wide range of problems in biology. In principle, both can be fully understood by using quantum mechanics as the ultimate tool to unveil the molecular interactions involved. Indeed, quantum mechanics of atoms and molecules have come to play a central role in chemistry and physics. In practice, however, direct application of quantum mechanics to protein systems has been prohibited by the large molecular size of proteins. As a consequence, there is no general quantum mechanical treatment that not only exceeds the accuracy of state-of-the-art empirical models for proteins but also maintains the efficiency needed for extensive sampling in the conformational space, a requirement mandated by the complexity of protein systems. Here we show that, given recent developments in methods, a general quantum mechanical-based treatment can be constructed. We report a molecular dynamics simulation of a protein, crambin, in solution for 350 ps in which we combine a semiempirical quantum-mechanical description of the entire protein with a description of the surrounding solvent, and solvent-protein interactions based on a molecular mechanics force field. Comparison with a recent very high-resolution crystal structure of crambin (Jelsch et al., Proc Natl Acad Sci USA 2000;102:2246-2251) shows that geometrical detail is better reproduced in this simulation than when several alternate molecular mechanics force fields are used to describe the entire system of protein and solvent, even though the structure is no less flexible. Individual atomic charges deviate in both directions from "canonical" values, and some charge transfer is found between the N and C-termini. The capability of simulating protein dynamics on and beyond the few hundred ps timescale with a demonstrably accurate quantum mechanical model will bring new opportunities to extend our understanding of a range of basic processes in biology such as molecular recognition and enzyme

  20. Quantum epistemology from subquantum ontology: Quantum mechanics from theory of classical random fields

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei

    2017-02-01

    The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations.

  1. 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.

  2. Virtual Learning Environment for Interactive Engagement with Advanced Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Pedersen, Mads Kock; Skyum, Birk; Heck, Robert; Müller, Romain; Bason, Mark; Lieberoth, Andreas; Sherson, Jacob F.

    2016-06-01

    A virtual learning environment can engage university students in the learning process in ways that the traditional lectures and lab formats cannot. We present our virtual learning environment StudentResearcher, which incorporates simulations, multiple-choice quizzes, video lectures, and gamification into a learning path for quantum mechanics at the advanced university level. StudentResearcher is built upon the experiences gathered from workshops with the citizen science game Quantum Moves at the high-school and university level, where the games were used extensively to illustrate the basic concepts of quantum mechanics. The first test of this new virtual learning environment was a 2014 course in advanced quantum mechanics at Aarhus University with 47 enrolled students. We found increased learning for the students who were more active on the platform independent of their previous performances.

  3. Optimal state discrimination and unstructured search in nonlinear quantum mechanics

    NASA Astrophysics Data System (ADS)

    Childs, Andrew M.; Young, Joshua

    2016-02-01

    Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics.

  4. 'Mysticism' in quantum mechanics: the forgotten controversy

    NASA Astrophysics Data System (ADS)

    Marin, Juan Miguel

    2009-07-01

    This paper argues that a European controversy over a 'mystical' hypothesis, one assigning the mind a role to play at the material level of reality, shaped much of the debate over the interpretation of the quantum equations. It traces back the controversy to the past two decades, beginning in the late 1920s—birth of quantum theory—and concluding with Erwin Schrödinger's lectures published as 'Mind and Matter'. Becoming aware of the issues at stake can help us understand the historical, philosophical and cultural background from which today's physics emerged.

  5. Deformation quantization: Quantum mechanics lives and works in phase space

    NASA Astrophysics Data System (ADS)

    Zachos, Cosmas K.

    2014-09-01

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

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

    NASA Astrophysics Data System (ADS)

    Lehner, Christoph Albert

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

  7. Free energies of binding from large-scale first-principles quantum mechanical calculations: application to ligand hydration energies.

    PubMed

    Fox, Stephen J; Pittock, Chris; Tautermann, Christofer S; Fox, Thomas; Christ, Clara; Malcolm, N O J; Essex, Jonathan W; Skylaris, Chris-Kriton

    2013-08-15

    Schemes of increasing sophistication for obtaining free energies of binding have been developed over the years, where configurational sampling is used to include the all-important entropic contributions to the free energies. However, the quality of the results will also depend on the accuracy with which the intermolecular interactions are computed at each molecular configuration. In this context, the energy change associated with the rearrangement of electrons (electronic polarization and charge transfer) upon binding is a very important effect. Classical molecular mechanics force fields do not take this effect into account explicitly, and polarizable force fields and semiempirical quantum or hybrid quantum-classical (QM/MM) calculations are increasingly employed (at higher computational cost) to compute intermolecular interactions in free-energy schemes. In this work, we investigate the use of large-scale quantum mechanical calculations from first-principles as a way of fully taking into account electronic effects in free-energy calculations. We employ a one-step free-energy perturbation (FEP) scheme from a molecular mechanical (MM) potential to a quantum mechanical (QM) potential as a correction to thermodynamic integration calculations within the MM potential. We use this approach to calculate relative free energies of hydration of small aromatic molecules. Our quantum calculations are performed on multiple configurations from classical molecular dynamics simulations. The quantum energy of each configuration is obtained from density functional theory calculations with a near-complete psinc basis set on over 600 atoms using the ONETEP program.

  8. The Transactional Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Kastner, Ruth E.

    2012-10-01

    Preface; 1. Introduction: quantum peculiarities; 2. The map vs the territory; 3. The original TI: fundamentals; 4. The new possibilist TI: fundamentals; 5. Challenges, replies, and applications; 6. PTI and relativity; 7. The metaphysics of possibility; 8. PTI and 'spacetime'; 9. Epilogue: more than meets the eye; Appendixes; References; Index.

  9. Classical and Quantum-Mechanical State Reconstruction

    ERIC Educational Resources Information Center

    Khanna, F. C.; Mello, P. A.; Revzen, M.

    2012-01-01

    The aim of this paper is to present the subject of state reconstruction in classical and in quantum physics, a subject that deals with the experimentally acquired information that allows the determination of the physical state of a system. Our first purpose is to explain a method for retrieving a classical state in phase space, similar to that…

  10. Curl flux, coherence, and population landscape of molecular systems: nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics.

    PubMed

    Zhang, Zhedong; Wang, Jin; Zhang, Z D; Wang, J

    2014-06-28

    We established a theoretical framework in terms of the curl flux, population landscape, and coherence for non-equilibrium quantum systems at steady state, through exploring the energy and charge transport in molecular processes. The curl quantum flux plays the key role in determining transport properties and the system reaches equilibrium when flux vanishes. The novel curl quantum flux reflects the degree of non-equilibriumness and the time-irreversibility. We found an analytical expression for the quantum flux and its relationship to the environmental pumping (non-equilibriumness quantified by the voltage away from the equilibrium) and the quantum tunneling. Furthermore, we investigated another quantum signature, the coherence, quantitatively measured by the non-zero off diagonal element of the density matrix. Populations of states give the probabilities of individual states and therefore quantify the population landscape. Both curl flux and coherence depend on steady state population landscape. Besides the environment-assistance which can give dramatic enhancement of coherence and quantum flux with high voltage at a fixed tunneling strength, the quantum flux is promoted by the coherence in the regime of small tunneling while reduced by the coherence in the regime of large tunneling, due to the non-monotonic relationship between the coherence and tunneling. This is in contrast to the previously found linear relationship. For the systems coupled to bosonic (photonic and phononic) reservoirs the flux is significantly promoted at large voltage while for fermionic (electronic) reservoirs the flux reaches a saturation after a significant enhancement at large voltage due to the Pauli exclusion principle. In view of the system as a quantum heat engine, we studied the non-equilibrium thermodynamics and established the analytical connections of curl quantum flux to the transport quantities such as energy (charge) transfer efficiency, chemical reaction efficiency, energy

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

    NASA Astrophysics Data System (ADS)

    Lloyd, Seth; Maccone, Lorenzo; Garcia-Patron, Raul; Giovannetti, Vittorio; Shikano, Yutaka

    2011-07-01

    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 on post-selected teleportation (P-CTCs). We compare the theory of P-CTCs to previously proposed quantum theories of time travel: the theory is inequivalent to Deutsch’s theory of CTCs, but it is consistent with path-integral approaches (which are the best suited for analyzing quantum-field theory in curved space-time). We derive the dynamical equations that a chronology-respecting system interacting with a CTC will experience. We discuss the possibility of time travel in the absence of general-relativistic closed-timelike curves, and investigate the implications of P-CTCs for enhancing the power of computation.

  12. 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.

  13. N=2 supersymmetric quantum mechanics of N Lieb-Liniger-Yang bosons on a line

    NASA Astrophysics Data System (ADS)

    Mateos Guilarte, J.; Moreno Mosquera, A.

    2017-02-01

    A supersymmetric generalization of the Lieb-Liniger-Yang dynamics governing N massive bosons moving on a line with delta interactions among them at coinciding points is developed. The analysis of the delicate balance between integrability and-supersymmetry, starting from the exactly solvable non-supersymmetric LLY system, is one of the paper main concerns. Two extreme regimes of the N parameter are explored: 1) For few bosons we fall in the realm of supersymmetric quantum mechanics with a short number of degrees of freedom, e.g., the SUSY Pösch-Teller potentials if N = 1 . 2) For large N we deal with supersymmetric extensions of many-body systems in the thermodynamic limit akin, e.g., to the supersymmetric Calogero-Sutherland systems. Emphasis will be put in the investigation of the ground-state structure of these quantum mechanical systems enjoying {N}=2 extended supersymmetry without spoiling integrability. The decision about wether or not supersymmetry is spontaneously broken, a central question in SUSY quantum mechanics determined from the ground-state structure, is another goal of the paper.

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

    NASA Astrophysics Data System (ADS)

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

    2006-05-01

    The STA model is extended to include calculations of thermodynamical quantities required for equation of state (EOS). For that purpose the plasma free electrons are now treated quantum mechanically accounting for shape resonances. The resulting gradual orbital ionization assures a regular behavior of all the thermodynamical quantities vs. density and temperature. The relativistic quantum mechanical framework that we have applied in a new code named EOSTA follows Liberman's Inferno model with several improvements that accomplish higher accuracy. These improvements include: a numerical technique to trace all the resonances and follow their detailed structure and application of the phase amplitude method that allows the inclusion of higher angular momenta partial waves and higher energies of the free orbitals. In addition we employ two complementary methods to treat the exchange potential in the calculation of orbital wave functions: (1) for EOS calculations Local Density Approximation is used and (2) for ionization lowering and orbital energies required in the opacity calculations we have found two satisfactory alternatives: (a) the optimized effective potential (OEP) and (b) first order corrected Local Density Approximation. In both alternatives the resulting orbitals are used to calculate the detailed exchange term that includes a proper reduction of the self energy. A new approach for calculating the electronic pressure is presented. The relativistic virial theorem expresses the pressure as a sum of the total energy and a local density term. This form allows consistent calibration of the correlation energy to comply with the periodic table zero pressure density points and higher density pressures. Results are presented describing the various thermodynamical quantities vs. density and temperature in comparison with other calculations and experiments.

  15. Analogies between optical and quantum mechanical angular momentum.

    PubMed

    Nienhuis, Gerard

    2017-02-28

    The insight that a beam of light can carry orbital angular momentum (AM) in its propagation direction came up in 1992 as a surprise. Nevertheless, the existence of momentum and AM of an electromagnetic field has been well known since the days of Maxwell. We compare the expressions for densities of AM in general three-dimensional modes and in paraxial modes. Despite their classical nature, these expressions have a suggestive quantum mechanical appearance, in terms of linear operators acting on mode functions. In addition, paraxial wave optics has several analogies with real quantum mechanics, both with the wave function of a free quantum particle and with a quantum harmonic oscillator. We discuss how these analogies can be applied.This article is part of the themed issue 'Optical orbital angular momentum'.

  16. A modified Lax-Phillips scattering theory for quantum mechanics

    SciTech Connect

    Strauss, Y.

    2015-07-15

    The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.

  17. Quantum mechanics on profinite groups and partial order

    NASA Astrophysics Data System (ADS)

    Vourdas, A.

    2013-02-01

    Inverse limits and profinite groups are used in a quantum mechanical context. Two cases are considered: a quantum system with positions in the profinite group { {Z}}_p and momenta in the group { {Q}}_p/{ {Z}}_p, and a quantum system with positions in the profinite group {\\widehat{ {Z}}} and momenta in the group { {Q}}/{ {Z}}. The corresponding Schwatz-Bruhat spaces of wavefunctions and the Heisenberg-Weyl groups are discussed. The sets of subsystems of these systems are studied from the point of view of partial order theory. It is shown that they are directed-complete partial orders. It is also shown that they are topological spaces with T0-topologies, and this is used to define continuity of various physical quantities. The physical meaning of profinite groups, non-Archimedean metrics, partial orders and T0-topologies, in a quantum mechanical context, is discussed.

  18. Analogies between optical and quantum mechanical angular momentum

    NASA Astrophysics Data System (ADS)

    Nienhuis, Gerard

    2017-02-01

    The insight that a beam of light can carry orbital angular momentum (AM) in its propagation direction came up in 1992 as a surprise. Nevertheless, the existence of momentum and AM of an electromagnetic field has been well known since the days of Maxwell. We compare the expressions for densities of AM in general three-dimensional modes and in paraxial modes. Despite their classical nature, these expressions have a suggestive quantum mechanical appearance, in terms of linear operators acting on mode functions. In addition, paraxial wave optics has several analogies with real quantum mechanics, both with the wave function of a free quantum particle and with a quantum harmonic oscillator. We discuss how these analogies can be applied. This article is part of the themed issue 'Optical orbital angular momentum'.

  19. A modified Lax-Phillips scattering theory for quantum mechanics

    NASA Astrophysics Data System (ADS)

    Strauss, Y.

    2015-07-01

    The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.

  20. Comment on 'Nonlocality, Counterfactuals and Quantum Mechanics'

    SciTech Connect

    Stapp, H.P.

    1999-04-14

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

  1. Dirac particle in gravitational quantum mechanics

    NASA Astrophysics Data System (ADS)

    Pedram, Pouria

    2011-08-01

    In this Letter, we consider the effects of the Generalized (Gravitational) Uncertainty Principle (GUP) on the eigenvalues and the eigenfunctions of the Dirac equation. This form of GUP is consistent with various candidates of quantum gravity such as string theory, loop quantum gravity, doubly special relativity and black hole physics and predicts both a minimum measurable length and a maximum measurable momentum. The modified Hamiltonian contains two additional terms proportional to a( and a( where αi are Dirac matrices and a∼1/MPlc is the GUP parameter. For the case of the Dirac free particle and the Dirac particle in a box, we solve the generalized Dirac equation and find the modified energy eigenvalues and eigenfunctions.

  2. Quantum Mechanics for Beginning Physics Students

    NASA Astrophysics Data System (ADS)

    Schneider, Mark B.

    2010-10-01

    The past two decades of attention to introductory physics education has emphasized enhanced development of conceptual understanding to accompany calculational ability. Given this, it is surprising that current texts continue to rely on the Bohr model to develop a flawed intuition, and introduce correct atomic physics on an ad hoc basis. For example, Halliday, Resnick, and Walker describe the origin of atomic quantum numbers as such: "The restrictions on the values of the quantum number for the hydrogen atom, as listed in Table 39-2, are not arbitrary but come out of the solution to Schrödinger's equation." They give no further justification, but do point out the values are in conflict with the predictions of the Bohr model.

  3. Breaking the Carnot limit without violating the second law: A thermodynamic analysis of off-resonant quantum light generation

    NASA Astrophysics Data System (ADS)

    Boukobza, E.; Ritsch, H.

    2013-06-01

    The Carnot limit, formulated in 1824, represents the maximal efficiency of a classical heat engine. In this work we present a thermodynamical analysis of a light amplifier based on a three-level atom coupled off-resonantly to a single quantized cavity mode and to two heat reservoirs with positive temperatures. Based on standard work and heat flow equilibrium, we show that for a cavity blue-detuned with respect to the atomic resonance, the system can surpass the Carnot limit. Nevertheless, the second law of thermodynamics is still obeyed, as the total entropy always increases. By analyzing a semiclassical version of the model, we derive a formula for the critical frequency for which the Carnot limit is broken and a formula for the amplifier efficiency which agrees with its quantum counterpart. In the semiclassical regime, however, the second law is not satisfied and hence it does not offer a physically acceptable description of the system. Finally, we show that breaking the Carnot limit occurs also in a blue-detuned quantum amplifier with output coupling, which represents a realistic model of a laser or maser.

  4. Use of mathematical logical concepts in quantum mechanics: an example

    NASA Astrophysics Data System (ADS)

    Benioff, Paul

    2002-07-01

    The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has meaning. A simple example of such a system, based on an example described by Smullyan, is studied here. Based on a path interpretation for some word states, definitions of truth, validity, consistency and completeness are given and their properties studied. It is also shown that the relation between the potential meaning, if any, of word states and the quantum algorithmic complexity of the process generating the word states must be quite complex or nonexistent.

  5. Mathematical foundations of quantum mechanics: An advanced short course

    NASA Astrophysics Data System (ADS)

    Moretti, Valter

    2016-08-01

    This paper collects and extends the lectures I gave at the “XXIV International Fall Workshop on Geometry and Physics” held in Zaragoza (Spain) during September 2015. Within these lectures I review the formulation of Quantum Mechanics, and quantum theories in general, from a mathematically advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions, discussing some fundamental ideas, mathematical tools and theorems also related to the representation of physical symmetries. The final step consists of an elementary introduction the so-called (C∗-) algebraic formulation of quantum theories.

  6. Cosmology and the pilot wave interpretation of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Tipler, Frank J.

    1984-07-01

    Bell has recently revived the pilot wave interpretation of de Broglie and Bohm as a possible scheme for interpreting wave functions in quantum cosmology. I argue that the pilot wave interpretation cannot be applied consistently to systems whose wave functions split into macroscopically distinguishable states. At some stage the pilot wave interpretation must either tacitly invoke wave function reduction in the same manner as the Copenhagen interpretation, or else abandon locality by requiring physical particles to move faster than light. Consequently, the many-worlds interpretation is the only known realist interpretation of the quantum mechanical formalism which can be extended to quantum cosmology.

  7. Models on the boundary between classical and quantum mechanics.

    PubMed

    Hooft, Gerard 't

    2015-08-06

    Arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there cannot be physical laws that require 'conspiracy'. It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In this report, several such counterexamples are shown. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. So now the question is asked: how can such a model feature 'conspiracy', and how bad is that? Is there conspiracy in the vacuum fluctuations? Arguments concerning Bell's theorem are further sharpened.

  8. Quantum mechanics from an equivalence principle

    SciTech Connect

    Faraggi, A.E.; Matone, M.

    1997-05-15

    The authors show that requiring diffeomorphic equivalence for one-dimensional stationary states implies that the reduced action S{sub 0} satisfies the quantum Hamilton-Jacobi equation with the Planck constant playing the role of a covariantizing parameter. The construction shows the existence of a fundamental initial condition which is strictly related to the Moebius symmetry of the Legendre transform and to its involutive character. The universal nature of the initial condition implies the Schroedinger equation in any dimension.

  9. Randomness in quantum mechanics - nature's ultimate cryptogram?

    NASA Astrophysics Data System (ADS)

    Erber, T.; Putterman, S.

    1985-11-01

    The possibility that a single atom irradiated by coherent light will be equivalent to an infinite computer with regard to its ability to generate random numbers is addressed. A search for unexpected patterns of order by crypt analysis of the telegraph signal generated by the on/off time of the atom's fluorescence is described. The results will provide new experimental tests of the fundamental principles of quantum theory.

  10. Quantum mechanical models with strictly ergodic disorder

    NASA Astrophysics Data System (ADS)

    Mavi, Rajinder

    We study quantum Hamiltonians with potentials defined by strictly ergodic dynamical systems. Our interest here are models where physical properties are understood in some regimes of disorder and the extent to which they vary in alternate regimes of disorder. For Schrodinger operators we show properties known to hold in the case of analytic potentials on the torus hold even for rough potentials only required to be Holder continuous. Specifically in this case we show, assuming a positive Lyapunov exponent, dynamical localization properties hold; as well as continuity of the measure of the spectrum for all rotations. For the quantum Ising model we show for phase structure that occur in the random regime, there are similar conditions for existence under the assumption of strictly ergodic dynamics. That is, moment conditions for random disorder are paralleled by conditions on the sampling functions in deterministic disorder. We obtain conditions for existence of phase transitions given any strictly egodically defined disorder. In addition, a new multiscale analysis method is developed to show the existence of stretched exponential decay in the random cluster model generalization of the quantum Ising model where only slower decay was obainable by previous methods.

  11. Photon physics: from wave mechanics to quantum electrodynamics

    NASA Astrophysics Data System (ADS)

    Keller, Ole

    2009-05-01

    When rewritten in an appropriate manner, the microscopic Maxwell-Lorentz equations appear as a wave-mechanical theory for photons, and their quantum physical interaction with matter. A natural extension leads from photon wave mechanics to quantum electrodynamics (QED). In its modern formulation photon wave mechanics has given us valuable new insight in subjects such as spatial photon localization, near-field photon dynamics, transverse photon mass, photon eikonal theory, photon tunneling, and rim-zone electrodynamics. The present review is based on my plenary lecture at the SPIE-Europe 2009 Optics and Optoelectronics International Symposium in Prague.

  12. The conceptual and the anecdotal history of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Beller, Mara

    1996-04-01

    The aim of this paper is to combine the intellectual and the psychosocial aspects. blurring the distinction between the conceptual and the anecdotal history of quantum mechanics. The full realization of the importance of such “anecdotal” factors leads to the revision of our understanding of the conceptual development itself. The paper concludes with the suggestion that a major part of numerous inconsistencies in the Copenhagen interpretation of quantum physics are of a psychosocial origin.

  13. Preparing a mechanical oscillator in non-gaussian quantum states.

    PubMed

    Khalili, Farid; Danilishin, Stefan; Miao, Haixing; Müller-Ebhardt, Helge; Yang, Huan; Chen, Yanbei

    2010-08-13

    We propose a protocol for coherently transferring non-Gaussian quantum states from an optical field to a mechanical oscillator. We demonstrate its experimental feasibility in future gravitational-wave detectors and tabletop optomechanical devices. This work not only outlines a feasible way to investigate nonclassicality in macroscopic optomechanical systems, but also presents a new and elegant approach for solving non-Markovian open quantum dynamics in general linear systems.

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

    NASA Astrophysics Data System (ADS)

    Leong, Max Kangchien

    A method of combined quantum mechanics/molecular mechanics has been developed to model larger organometallic and metallobiochemical systems where neither quantum mechanics nor molecular mechanics, applied separately, can solve the problem. An electronically transparent interface, which allows charge transfers between the quantum and classical fragments, is devised and realized by employing a special iterative procedure of double (intrafragment and interfragment) self-consistent calculations. The combined QM/MM scheme was successfully applied to model iron picket-fence porphyrin, vitamin B12, aquocobalamin, and vitamin B12 coenzyme molecules.

  15. Investigations of fundamental phenomena in quantum mechanics with neutrons

    NASA Astrophysics Data System (ADS)

    Hasegawa, Yuji

    2014-04-01

    Neutron interferometer and polarimeter are used for the experimental investigations of quantum mechanical phenomena. Interferometry exhibits clear evidence of quantum-contextuality and polarimetry demonstrates conflicts of a contextual model of quantum mechanics á la Leggett. In these experiments, entanglements are achieved between degrees of freedom in a single-particle: spin, path and energy degrees of freedom are manipulated coherently and entangled. Both experiments manifest the fact that quantum contextuality is valid for phenomena with matter waves with high precision. In addition, another experiment is described which deals with error-disturbance uncertainty relation: we have experimentally tested error-disturbance uncertainty relations, one is derived by Heisenberg and the other by Ozawa. Experimental results confirm the fact that the Heisenberg's uncertainty relation is often violated and that the new relation by Ozawa is always larger than the limit. At last, as an example of a counterfactual phenomenon of quantum mechanics, observation of so-called quantum Cheshire Cat is carried out by using neutron interferometer. Experimental results suggest that pre- and post-selected neutrons travel through one of the arms of the interferometer while their magnetic moment is located in the other arm.

  16. Two-time Green's functions and spectral density method in nonextensive quantum statistical mechanics.

    PubMed

    Cavallo, A; Cosenza, F; De Cesare, L

    2008-05-01

    We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multiplier representation, the q -spectral properties and the methods for a direct calculation of the two-time q Green's functions and the related q -spectral density ( q measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive (q=1) counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the q -induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the q -induced nonextensivity close to the extensive regime are explicitly calculated in the low-temperature regime by overcoming the calculation of the q grand-partition function.

  17. Mechanical, electronic and thermodynamic properties of full Heusler compounds Fe2VX(X = Al, Ga)

    NASA Astrophysics Data System (ADS)

    Khalfa, M.; Khachai, H.; Chiker, F.; Baki, N.; Bougherara, K.; Yakoubi, A.; Murtaza, G.; Harmel, M.; Abu-Jafar, M. S.; Omran, S. Bin; Khenata, R.

    2015-11-01

    The electronic structure, mechanical and thermodynamic properties of Fe2VX, (with X = Al and Ga), have been studied self consistently by employing state-of-the-art full-potential linearized approach of augmented plane wave plus local orbitals (FP-LAPW + lo) method. The exchange-correlation potential is treated with the local density and generalized gradient approximations (LDA and GGA). Our predicted ground state properties such as lattice constants, bulk modulus and elastic constants appear more accurate when we employed the GGA rather than the LDA, and these results are in very good agreement with the available experimental and theoretical data. Further, thermodynamic properties of Fe2VAl and Fe2VGa are predicted with pressure and temperature in the ranges of 0-40 GPa and 0-1500 K using the quasi-harmonic Debye model. We have obtained successfully the variations of the heat capacities, primitive cell volume and volume expansion coefficient.

  18. Density functional theory and quantum mechanics/molecular mechanics study of cysteine protease inhibition by nitrile-based inhibitors.

    NASA Astrophysics Data System (ADS)

    De Visser, Sam; Quesne, Matthew; Ward, Richard

    2013-12-01

    Cysteine protease enzymes are important for human physiology and catalyze key protein degradation pathways. These enzymes react via a nucleophilic reaction mechanism that involves a cysteine residue and the proton of a proximal histidine. Particularly efficient inhibitors of these enzymes are nitrile-based, however, the details of the catalytic reaction mechanism currently are poorly understood. To gain further insight into the inhibition of these molecules, we have performed a combined density functional theory and quantum mechanics/molecular mechanics study on the reaction of a nitrile-based inhibitor with the enzyme active site amino acids. We show here that small perturbations to the inhibitor structure can have dramatic effects on the catalysis and inhibition processes. Thus, we investigated a range of inhibitor templates and show that specific structural changes reduce the inhibitory efficiency by several orders of magnitude. Moreover, as the reaction takes place on a polar surface, we find strong differences between the DFT and QM/MM calculated energetics. In particular, the DFT model led to dramatic distortions from the starting structure and the convergence to a structure that would not fit the enzyme active site. In the subsequent QM/MM study we investigated the use of mechanical versus electronic embedding on the kinetics, thermodynamics and geometries along the reaction mechanism. We find minor effects on the kinetics of the reaction but large geometric and thermodynamics differences as a result of inclusion of electronic embedding corrections. The work here highlights the importance of model choice in the investigation of this biochemical reaction mechanism.

  19. Estimates on Functional Integrals of Quantum Mechanics and Non-relativistic Quantum Field Theory

    NASA Astrophysics Data System (ADS)

    Bley, Gonzalo A.; Thomas, Lawrence E.

    2017-01-01

    We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form {E[{exp}(A_T)]} , the (effective) action {A_T} being a function of particle trajectories up to time T. The estimates in turn yield rigorous lower bounds for ground state energies, via the Feynman-Kac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is illustrated in familiar quantum mechanical settings: for the hydrogen atom, for a Schrödinger operator with {1/|x|^2} potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.

  20. Reality, Causality, and Probability, from Quantum Mechanics to Quantum Field Theory

    NASA Astrophysics Data System (ADS)

    Plotnitsky, Arkady

    2015-10-01

    These three lectures consider the questions of reality, causality, and probability in quantum theory, from quantum mechanics to quantum field theory. They do so in part by exploring the ideas of the key founding figures of the theory, such N. Bohr, W. Heisenberg, E. Schrödinger, or P. A. M. Dirac. However, while my discussion of these figures aims to be faithful to their thinking and writings, and while these lectures are motivated by my belief in the helpfulness of their thinking for understanding and advancing quantum theory, this project is not driven by loyalty to their ideas. In part for that reason, these lectures also present different and even conflicting ways of thinking in quantum theory, such as that of Bohr or Heisenberg vs. that of Schrödinger. The lectures, most especially the third one, also consider new physical, mathematical, and philosophical complexities brought in by quantum field theory vis-à-vis quantum mechanics. I close by briefly addressing some of the implications of the argument presented here for the current state of fundamental physics.

  1. Quantum mechanics, gravity and modified quantization relations.

    PubMed

    Calmet, Xavier

    2015-08-06

    In this paper, we investigate a possible energy scale dependence of the quantization rules and, in particular, from a phenomenological point of view, an energy scale dependence of an effective [Formula: see text] (reduced Planck's constant). We set a bound on the deviation of the value of [Formula: see text] at the muon scale from its usual value using measurements of the anomalous magnetic moment of the muon. Assuming that inflation has taken place, we can conclude that nature is described by a quantum theory at least up to an energy scale of about 10(16) GeV.

  2. Are nonlinear discrete cellular automata compatible with quantum mechanics?

    NASA Astrophysics Data System (ADS)

    Elze, Hans-Thomas

    2015-07-01

    We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises “Hamiltonian CA” with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The dynamics is linear, quite similar to unitary evolution described by the Schrödinger equation. This has been essential in our construction of an invertible map between such CA and continuous quantum mechanical models, which incorporate a fundamental discreteness scale. Based on Shannon's sampling theory, it leads, for example, to a one-to-one relation between quantum mechanical and CA conservation laws. The important issue of linearity of the theory is examined here by incorporating higher-order nonlinearities into the underlying action. These produce inconsistent nonlocal (in time) effects when trying to describe continuously such nonlinear CA. Therefore, in the present framework, only linear CA and local quantum mechanical dynamics are compatible.

  3. A deformation quantization theory for noncommutative quantum mechanics

    SciTech Connect

    Costa Dias, Nuno; Prata, Joao Nuno; Gosson, Maurice de; Luef, Franz

    2010-07-15

    We show that the deformation quantization of noncommutative quantum mechanics previously considered by Dias and Prata ['Weyl-Wigner formulation of noncommutative quantum mechanics', J. Math. Phys. 49, 072101 (2008)] and Bastos, Dias, and Prata ['Wigner measures in non-commutative quantum mechanics', e-print arXiv:math-ph/0907.4438v1; Commun. Math. Phys. (to appear)] can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef ['A new approach to the *-genvalue equation', Lett. Math. Phys. 85, 173-183 (2008)].

  4. Quantum-mechanical description of in-medium fragmentation

    NASA Astrophysics Data System (ADS)

    Kopeliovich, B. Z.; Pirner, H.-J.; Potashnikova, I. K.; Schmidt, Ivan; Tarasov, A. V.; Voskresenskaya, O. O.

    2008-11-01

    We present a quantum-mechanical description of quark-hadron fragmentation in a nuclear environment. It employs the path-integral formulation of quantum mechanics, which takes care of all phases and interferences and contains all relevant time scales, such as production, coherence, and formation. The cross section includes the probability of prehadron (colorless dipole) production both inside and outside the medium. Moreover, it also includes inside-outside production, which is a typical quantum-mechanical interference effect (like twin-slit electron propagation). We observe a substantial suppression caused by the medium, even if the prehadron is produced outside the medium and no energy loss is involved. This important source of suppression is missed in the usual energy-loss scenario interpreting the effect of jet quenching observed in heavy ion collisions. This may be one reason for the too large gluon density reported by such analyses.

  5. David Bohm's Hidden Variables Interpretation of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Hall, Ned; Feldman, Gary; Wulsin, Wells

    2001-04-01

    This talk presents the hidden variables interpretation of quantum mechanics as proposed by David Bohm in 1952. Using a pilot-wave, Bohm’s theory reproduces the standard predictions of quantum mechanics while at the same time postulating that particles at all times are localized at definite positions. By way of introduction, the foundational issue of the quantum mechanics measurement problem will be discussed. The talk will then focus on how Bohm’s formulation of a hidden variables theory stands up to philosophical examination. Traditional objections to the theory, such as the EPR paradox, will be addressed, as well as the deeper metaphysical implications it holds for our view of the universe.

  6. On testing for the stage of collapse in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Becker, Lon Stephen

    The question was considered whether it is possible to experimentally narrow down the time of collapse in the measurement process of quantum mechanics. A form of experiment was developed towards that end. The proof of John von Neumann that it is impossible to determine the time of collapse was analyzed, and its hidden assumptions were exploited in the design of the experiment. The reinterpretation of quantum mechanics by David Bohm was introduced to give an alternative way of looking at quantum mechanics. An objection to this view was discussed but rejected. Finally a pair of thought experiments were offered with the potential to be converted in the future into tests for whether collapse has occurred at various points in the measurement process.

  7. Quantum-mechanical transport equation for atomic systems.

    NASA Technical Reports Server (NTRS)

    Berman, P. R.

    1972-01-01

    A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

  8. Quantum mechanisms of density wave transport

    PubMed Central

    Miller, John H.; Wijesinghe, Asanga I.

    2012-01-01

    We report on new developments in the quantum picture of correlated electron transport in charge and spin density waves. The model treats the condensate as a quantum fluid in which charge soliton domain wall pairs nucleate above a Coulomb blockade threshold field. We employ a time-correlated soliton tunneling model, analogous to the theory of time-correlated single electron tunneling, to interpret the voltage oscillations and nonlinear current-voltage characteristics above threshold. An inverse scaling relationship between threshold field and dielectric response, originally proposed by Grüner, emerges naturally from the model. Flat dielectric and other ac responses below threshold in NbSe3 and TaS3, as well as small density wave phase displacements, indicate that the measured threshold is often much smaller than the classical depinning field. In some materials, the existence of two distinct threshold fields suggests that both soliton nucleation and classical depinning may occur. In our model, the ratio of electrostatic charging to pinning energy helps determine whether soliton nucleation or classical depinning dominates. PMID:22711979

  9. Reality in quantum mechanics, Extended Everett Concept, and consciousness

    NASA Astrophysics Data System (ADS)

    Mensky, M. B.

    2007-09-01

    Conceptual problems in quantum mechanics result from the specific quantum concept of reality and require, for their solution, including the observer’s consciousness into the quantum theory of measurements. Most naturally, this is achieved in the framework of Everett’s “many-world interpretation” of quantum mechanics. According to this interpretation, various classical alternatives are perceived by consciousness separately from each other. In the Extended Everett Concept (EEC) proposed by the present author, the separation of the alternatives is identified with the phenomenon of consciousness. This explains the classical character of the alternatives and unusual manifestations of consciousness arising “at the edge of consciousness” (i.e., in sleep or trance) when its access to “other alternative classical realities” (other Everett’s worlds) becomes feasible. Because of reversibility of quantum evolution in EEC, all time moments in the quantum world are equivalent, while the impression of flow of time appears only in consciousness. If it is assumed that consciousness may influence the probabilities of alternatives (which is consistent in case of infinitely many Everett’s worlds), EEC explains free will, “probabilistic miracles” (observing low-probability events), and decreasing entropy in the sphere of life.

  10. The Misapplication of Probability Theory in Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Racicot, Ronald

    2014-03-01

    This article is a revision of two papers submitted to the APS in the past two and a half years. In these papers, arguments and proofs are summarized for the following: (1) The wrong conclusion by EPR that Quantum Mechanics is incomplete, perhaps requiring the addition of ``hidden variables'' for completion. Theorems that assume such ``hidden variables,'' such as Bell's theorem, are also wrong. (2) Quantum entanglement is not a realizable physical phenomenon and is based entirely on assuming a probability superposition model for quantum spin. Such a model directly violates conservation of angular momentum. (3) Simultaneous multiple-paths followed by a quantum particle traveling through space also cannot possibly exist. Besides violating Noether's theorem, the multiple-paths theory is based solely on probability calculations. Probability calculations by themselves cannot possibly represent simultaneous physically real events. None of the reviews of the submitted papers actually refuted the arguments and evidence that was presented. These analyses should therefore be carefully evaluated since the conclusions reached have such important impact in quantum mechanics and quantum information theory.

  11. Exactly constructing model of quantum mechanics with random environment

    SciTech Connect

    Gevorkyan, A. S.

    2010-02-15

    Dissipation and decoherence, interaction with the random media, continuous measurements and many other complicated problems of open quantum systems are a result of interaction of quantum system with the random environment. These problems mathematically are described in terms of complex probabilistic processes (CPP). Note that CPP satisfies the stochastic differential equation (SDE) of Langevin-Schroedinger(L-Sch)type, and is defined on the extended space R{sup 1} - R{sub {l_brace}{gamma}{r_brace}}, where R{sup 1} and R{sub {l_brace}{gamma}{r_brace}} are the Euclidean and the functional spaces, correspondingly. For simplicity, the model of 1D quantum harmonic oscillator (QHO) with the stochastic environment is considered. On the basis of orthogonal CPP, the method of stochastic density matrix (SDM) is developed. By S DM method, the thermodynamical potentials, such as the nonequilibrium entropy and the energy of the 'ground state' are constructed in a closed form. The expressions for uncertain relations and Wigner function depending on interaction's constant between 1D QHO and the environment are obtained.

  12. Quantum-mechanical treatment of an electron undergoing synchrotron radiation.

    NASA Technical Reports Server (NTRS)

    White, D.

    1972-01-01

    The problem of an electron moving perpendicular to an intense magnetic field is approached from the framework of quantum mechanics. A numerical solution to the related rate equations describing the probabilities of occupation of the electron's energy states is put forth along with the expected errors involved. The quantum-mechanical approach is found to predict a significant amount of energy broadening with time for an initially monoenergetic electron beam entering a region of an intense magnetic field as long as the product of initial energy and magnetic field is of order 50 MG BeV or larger.

  13. A new teaching approach to quantum mechanical tunneling

    NASA Astrophysics Data System (ADS)

    Gilfoyle, G. P.

    1999-09-01

    The transfer matrix method has been used to investigate quantum mechanical tunneling in introductory quantum mechanics. The method is applied first to calculate the transmission coefficient for tunneling through a rectangular barrier and is then extended to the problem of potential barriers of arbitrary shape, in particular, to radioactive decay. This approach uses matrix methods that are accessible to a broader range of undergraduates than other numerical techniques, the connection between the rectangular barrier problem and potential barriers of arbitrary shape is transparent, and it can be readily executed by undergraduates. The classroom experience with this approach is discussed.

  14. Study on a Possible Darwinian Origin of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Baladrón, C.

    2011-03-01

    A sketchy subquantum theory deeply influenced by Wheeler's ideas (Am. J. Phys. 51:398-404, 1983) and by the de Broglie-Bohm interpretation (Goldstein in Stanford Encyclopedia of Philosophy, 2006) of quantum mechanics is further analyzed. In this theory a fundamental system is defined as a dual entity formed by bare matter and a methodological probabilistic classical Turing machine. The evolution of the system would be determined by three Darwinian informational regulating principles. Some progress in the derivation of the postulates of quantum mechanics from these regulating principles is reported. The entanglement in a bipartite system is preliminarily considered.

  15. Unstable particles in non-relativistic quantum mechanics?

    SciTech Connect

    Hernandez-Coronado, H.

    2011-10-14

    The Schroedinger equation is up-to-a-phase invariant under the Galilei group. This phase leads to the Bargmann's superselection rule, which forbids the existence of the superposition of states with different mass and implies that unstable particles cannot be described consistently in non-relativistic quantum mechanics (NRQM). In this paper we claim that Bargmann's rule neglects physical effects and that a proper description of non-relativistic quantum mechanics requires to take into account this phase through the Extended Galilei group and the definition of its action on spacetime coordinates.

  16. The uncertainty principle determines the nonlocality of quantum mechanics.

    PubMed

    Oppenheim, Jonathan; Wehner, Stephanie

    2010-11-19

    Two central concepts of quantum mechanics are Heisenberg's uncertainty principle and a subtle form of nonlocality that Einstein famously called "spooky action at a distance." These two fundamental features have thus far been distinct concepts. We show that they are inextricably and quantitatively linked: Quantum mechanics cannot be more nonlocal with measurements that respect the uncertainty principle. In fact, the link between uncertainty and nonlocality holds for all physical theories. More specifically, the degree of nonlocality of any theory is determined by two factors: the strength of the uncertainty principle and the strength of a property called "steering," which determines which states can be prepared at one location given a measurement at another.

  17. Spacetime alternatives in the quantum mechanics of a relativistic particle

    SciTech Connect

    Whelan, J.T. Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge, CB3 0EH )

    1994-11-15

    Hartle's generalized quantum mechanics formalism is used to examine spacetime coarse grainings, i.e., sets of alternatives defined with respect to a region extended in time as well as space, in the quantum mechanics of a free relativistic particle. For a simple coarse graining and suitable initial conditions, tractable formulas are found for branch wave functions. Despite the nonlocality of the positive-definite version of the Klein-Gordon inner product, which means that nonoverlapping branches are not sufficient to imply decoherence, some initial conditions are found to give decoherence and allow the consistent assignment of probabilities.

  18. PREFACE: Progress in supersymmetric quantum mechanics

    NASA Astrophysics Data System (ADS)

    Aref'eva, I.; Fernández, D. J.; Hussin, V.; Negro, J.; Nieto, L. M.; Samsonov, B. F.

    2004-10-01

    The theory of integrable systems is grounded in the very beginning of theoretical physics: Kepler's system is an integrable system. This field of dynamical systems, where one looks for exact solutions of the equations of motion, has attracted most of the great figures in mathematical physics: Euler, Lagrange, Jacobi, etc. Liouville was the first to formulate the precise mathematical conditions ensuring solvability `by quadrature' of the dynamical equations, and his theorem still lies at the heart of the recent developments. The modern era started about thirty years ago with the systematic formulation of soliton solutions to nonlinear wave equations. Since then, impressive developments arose both for the classical and the quantum theory. Subtle mathematical techniques were devised for the resolution of these theories, relying on algebra (group theory), analysis and algebraic geometry (Riemann theory of surfaces). We therefore clearly see that the theory of integrable systems lies ab initio at a crossing of physics and mathematics, and that the developments of these last thirty years have strengthened this dual character, which makes it into an archetypal domain of mathematical physics. As regards the classical theory, beyond the direct connections to the various domains of classical soliton physics (hydrodynamics, condensed matter physics, laser optics, particle physics, plasma, biology or information coding), one has witnessed in these recent years more unexpected (and for some of them not yet well understood) connections to a priori farther fields of theoretical physics: string theory (through matrix models), topological field theories (two dimensional Yang--Mills, three dimensional Chern--Simons--Witten), or supersymmetric field theories (for instance the correspondence discovered by Seiberg and Witten between classical integrable models and quantum potentials). Quantum integrable theories provide examples of exactly (non perturbatively) solvable physical models

  19. First-principles study of thermodynamical and mechanical stabilities of thin copper film on tantalum

    NASA Astrophysics Data System (ADS)

    Hashibon, Adham; Elsässer, Christian; Mishin, Yuri; Gumbsch, Peter

    2007-12-01

    The adhesion, stability, and wetting behavior at interfaces between thin Cu films and clean Ta (110) substrates are investigated by first-principles calculations using density functional theory (DFT) in the local-density approximation. Interfaces between pseudomorphic body-centered-tetragonal thin films of Cu, strained face-centered-cubic thin films of Cu, and a single pseudomorphic monolayer of Cu on body-centered-cubic Ta (110) surfaces are studied. Various high-symmetry interface configurations are considered for each case. The mechanical stability of the interfaces is studied by the ideal work of separation, while the thermodynamic stability is investigated by Gibbs’ excess interface energy. All three interfaces are found to be thermodynamically unstable. An energy-weighting scheme extends the use of the DFT calculations to the case of an incoherent misfitting interface. The incoherent monolayer of Cu on Ta is thereby found to be thermodynamically stable. For coverages by more than a monolayer, the Cu atoms are expected to form three-dimensional islands on top of the Cu monolayer. With respect to interface separation, the monolayer is found to be bound more strongly to the Ta substrate than the thin film. Hence, failure is expected to occur not at the Cu/Ta interface but inside the Cu.

  20. Structural, mechanical, and thermodynamic properties of a coarse-grained DNA model

    NASA Astrophysics Data System (ADS)

    Ouldridge, Thomas E.; Louis, Ard A.; Doye, Jonathan P. K.

    2011-02-01

    We explore in detail the structural, mechanical, and thermodynamic properties of a coarse-grained model of DNA similar to that recently introduced in a study of DNA nanotweezers [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, Phys. Rev. Lett. 134, 178101 (2010)]. Effective interactions are used to represent chain connectivity, excluded volume, base stacking, and hydrogen bonding, naturally reproducing a range of DNA behavior. The model incorporates the specificity of Watson-Crick base pairing, but otherwise neglects sequence dependence of interaction strengths, resulting in an "average base" description of DNA. We quantify the relation to experiment of the thermodynamics of single-stranded stacking, duplex hybridization, and hairpin formation, as well as structural properties such as the persistence length of single strands and duplexes, and the elastic torsional and stretching moduli of double helices. We also explore the model's representation of more complex motifs involving dangling ends, bulged bases and internal loops, and the effect of stacking and fraying on the thermodynamics of the duplex formation transition.

  1. Differential Effects of Hydrophobic Core Packing Residues for Thermodynamic and Mechanical Stability of a Hyperthermophilic Protein.

    PubMed

    Tych, Katarzyna M; Batchelor, Matthew; Hoffmann, Toni; Wilson, Michael C; Hughes, Megan L; Paci, Emanuele; Brockwell, David J; Dougan, Lorna

    2016-07-26

    Proteins from organisms that have adapted to environmental extremes provide attractive systems to explore and determine the origins of protein stability. Improved hydrophobic core packing and decreased loop-length flexibility can increase the thermodynamic stability of proteins from hyperthermophilic organisms. However, their impact on protein mechanical stability is not known. Here, we use protein engineering, biophysical characterization, single-molecule force spectroscopy (SMFS), and molecular dynamics (MD) simulations to measure the effect of altering hydrophobic core packing on the stability of the cold shock protein TmCSP from the hyperthermophilic bacterium Thermotoga maritima. We make two variants of TmCSP in which a mutation is made to reduce the size of aliphatic groups from buried hydrophobic side chains. In the first, a mutation is introduced in a long loop (TmCSP L40A); in the other, the mutation is introduced on the C-terminal β-strand (TmCSP V62A). We use MD simulations to confirm that the mutant TmCSP L40A shows the most significant increase in loop flexibility, and mutant TmCSP V62A shows greater disruption to the core packing. We measure the thermodynamic stability (ΔGD-N) of the mutated proteins and show that there is a more significant reduction for TmCSP L40A (ΔΔG = 63%) than TmCSP V62A (ΔΔG = 47%), as might be expected on the basis of the relative reduction in the size of the side chain. By contrast, SMFS measures the mechanical stability (ΔG*) and shows a greater reduction for TmCSP V62A (ΔΔG* = 8.4%) than TmCSP L40A (ΔΔG* = 2.5%). While the impact on the mechanical stability is subtle, the results demonstrate the power of tuning noncovalent interactions to modulate both the thermodynamic and mechanical stability of a protein. Such understanding and control provide the opportunity to design proteins with optimized thermodynamic and mechanical properties.

  2. Quantum mechanics concept assessment: Development and validation study

    NASA Astrophysics Data System (ADS)

    Sadaghiani, Homeyra R.; Pollock, Steven J.

    2015-06-01

    As part of an ongoing investigation of students' learning in first semester upper-division quantum mechanics, we needed a high-quality conceptual assessment instrument for comparing outcomes of different curricular approaches. The process of developing such a tool started with converting a preliminary version of a 14-item open-ended quantum mechanics assessment tool (QMAT) to a multiple-choice (MC) format. Further question refinement, development of effective distractors, adding new questions, and robust statistical analysis has led to a 31-item quantum mechanics concept assessment (QMCA) test. The QMCA is used as post-test only to assess students' knowledge about five main topics of quantum measurement: the time-independent Schrödinger equation, wave functions and boundary conditions, time evolution, and probability density. During two years of testing and refinement, the QMCA has been given in alpha (N =61 ) and beta versions (N =263 ) to students in upper division quantum mechanics courses at 11 different institutions with an average post-test score of 54%. By allowing for comparisons of student learning across different populations and institutions, the QMCA provides instructors and researchers a more standard measure of effectiveness of different curricula or teaching strategies on student conceptual understanding of quantum mechanics. In this paper, we discuss the construction of effective distractors and the use of student interviews and expert feedback to revise and validate both questions and distractors. We include the results of common statistical tests of reliability and validity, which suggest the instrument is presently in a stable, usable, and promising form.

  3. Geometric control of quantum mechanical and nonlinear classical systems

    NASA Astrophysics Data System (ADS)

    Nelson, Richard Joseph

    1999-10-01

    Geometric control refers to the judicious use of the non- commuting nature of inputs and natural dynamics as the basis for control. The last few decades in control system theory have seen the application of differential geometry in proving several important properties of systems, including controllability and observability. Until recently, however, the results of this mathematical geometry have rarely been used as the basis for designing and implementing an actual controller. This thesis demonstrates the application of a judicious selection of inputs, so that if the system is proven to be controllable using geometric methods, one can design input sequences using the same geometry. A demonstration of this method is shown in simulating the attitude control of a satellite: a highly non-linear, non- holonomic control problem. Although not a practical method for large re-orientations of a typical satellite, the approach can be applied to other nonlinear systems. The method is also applied to the closed-loop performance of a quantum mechanical system to demonstrate the feasibility of coherent quantum feedback-something impossible using a conventional controller. Finally, the method is applied in the open-loop control of a quantum mechanical system: in this case, the creation of Greenberger-Horne-Zeilinger correlations among the nuclei of an ensemble of alanine molecules in a nuclear magnetic resonance spectrometer. In each case, the data demonstrate the usefulness of a geometric approach to control. In addition to demonstrations of geometric control in practice, the quantum mechanical experiments also demonstrate for the first time peculiar quantum correlations, including GHZ correlations, that have no classical analog. The quantum experiments further establish nuclear magnetic resonance as a viable and accessible testbed of quantum predictions and processes. (Copies available exclusively from MIT Libraries, Rm. 14- 0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax

  4. How Does Quantum Uncertainty Emerge from Deterministic Bohmian Mechanics?

    NASA Astrophysics Data System (ADS)

    Solé, A.; Oriols, X.; Marian, D.; Zanghì, N.

    2016-10-01

    Bohmian mechanics is a theory that provides a consistent explanation of quantum phenomena in terms of point particles whose motion is guided by the wave function. In this theory, the state of a system of particles is defined by the actual positions of the particles and the wave function of the system; and the state of the system evolves deterministically. Thus, the Bohmian state can be compared with the state in classical mechanics, which is given by the positions and momenta of all the particles, and which also evolves deterministically. However, while in classical mechanics it is usually taken for granted and considered unproblematic that the state is, at least in principle, measurable, this is not the case in Bohmian mechanics. Due to the linearity of the quantum dynamical laws, one essential component of the Bohmian state, the wave function, is not directly measurable. Moreover, it turns out that the measurement of the other component of the state — the positions of the particles — must be mediated by the wave function; a fact that in turn implies that the positions of the particles, though measurable, are constrained by absolute uncertainty. This is the key to understanding how Bohmian mechanics, despite being deterministic, can account for all quantum predictions, including quantum randomness and uncertainty.

  5. Quantum mechanical force field for water with explicit electronic polarization

    PubMed Central

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

    2013-01-01

    A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 106 self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across

  6. Quantum mechanical force field for water with explicit electronic polarization.

    PubMed

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

    2013-08-07

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

  7. Solvable time-dependent models in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Cordero-Soto, Ricardo J.

    In the traditional setting of quantum mechanics, the Hamiltonian operator does not depend on time. While some Schrodinger equations with time-dependent Hamiltonians have been solved, explicitly solvable cases are typically scarce. This thesis is a collection of papers in which this first author along with Suslov, Suazo, and Lopez, has worked on solving a series of Schrodinger equations with a time-dependent quadratic Hamiltonian that has applications in problems of quantum electrodynamics, lasers, quantum devices such as quantum dots, and external varying fields. In particular the author discusses a new completely integrable case of the time-dependent Schrodinger equation in Rn with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator considered by Meiler, Cordero-Soto, and Suslov. A second pair of dual Hamiltonians is found in the momentum representation. Our examples show that in mathematical physics and quantum mechanics a change in the direction of time may require a total change of the system dynamics in order to return the system back to its original quantum state. The author also considers several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schrodinger 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. Finally, the author constructs integrals of motion for several models

  8. Quantum Mechanics, Pattern Recognition, and the Mammalian Brain

    NASA Astrophysics Data System (ADS)

    Chapline, George

    2008-10-01

    Although the usual way of representing Markov processes is time asymmetric, there is a way of describing Markov processes, due to Schrodinger, which is time symmetric. This observation provides a link between quantum mechanics and the layered Bayesian networks that are often used in automated pattern recognition systems. In particular, there is a striking formal similarity between quantum mechanics and a particular type of Bayesian network, the Helmholtz machine, which provides a plausible model for how the mammalian brain recognizes important environmental situations. One interesting aspect of this relationship is that the "wake-sleep" algorithm for training a Helmholtz machine is very similar to the problem of finding the potential for the multi-channel Schrodinger equation. As a practical application of this insight it may be possible to use inverse scattering techniques to study the relationship between human brain wave patterns, pattern recognition, and learning. We also comment on whether there is a relationship between quantum measurements and consciousness.

  9. General formalism of local thermodynamics with an example: Quantum Otto engine with a spin-1 /2 coupled to an arbitrary spin

    NASA Astrophysics Data System (ADS)

    Altintas, Ferdi; Müstecaplıoǧlu, Ã.-zgür E.

    2015-08-01

    We investigate a quantum heat engine with a working substance of two particles, one with a spin-1 /2 and the other with an arbitrary spin (spin s ), coupled by Heisenberg exchange interaction, and subject to an external magnetic field. The engine operates in a quantum Otto cycle. Work harvested in the cycle and its efficiency are calculated using quantum thermodynamical definitions. It is found that the engine has higher efficiencies at higher spins and can harvest work at higher exchange interaction strengths. The role of exchange coupling and spin s on the work output and the thermal efficiency is studied in detail. In addition, the engine operation is analyzed from the perspective of local work and efficiency. We develop a general formalism to explore local thermodynamics applicable to any coupled bipartite system. Our general framework allows for examination of local thermodynamics even when global parameters of the system are varied in thermodynamic cycles. The generalized definitions of local and cooperative work are introduced by using mean field Hamiltonians. The general conditions for which the global work is not equal to the sum of the local works are given in terms of the covariance of the subsystems. Our coupled spin quantum Otto engine is used as an example of the general formalism.

  10. General formalism of local thermodynamics with an example: Quantum Otto engine with a spin-1/2 coupled to an arbitrary spin.

    PubMed

    Altintas, Ferdi; Müstecaplıoğlu, Özgür E

    2015-08-01

    We investigate a quantum heat engine with a working substance of two particles, one with a spin-1/2 and the other with an arbitrary spin (spin s), coupled by Heisenberg exchange interaction, and subject to an external magnetic field. The engine operates in a quantum Otto cycle. Work harvested in the cycle and its efficiency are calculated using quantum thermodynamical definitions. It is found that the engine has higher efficiencies at higher spins and can harvest work at higher exchange interaction strengths. The role of exchange coupling and spin s on the work output and the thermal efficiency is studied in detail. In addition, the engine operation is analyzed from the perspective of local work and efficiency. We develop a general formalism to explore local thermodynamics applicable to any coupled bipartite system. Our general framework allows for examination of local thermodynamics even when global parameters of the system are varied in thermodynamic cycles. The generalized definitions of local and cooperative work are introduced by using mean field Hamiltonians. The general conditions for which the global work is not equal to the sum of the local works are given in terms of the covariance of the subsystems. Our coupled spin quantum Otto engine is used as an example of the general formalism.

  11. Thermodynamic evidence for a dual transport mechanism in a POT peptide transporter.

    PubMed

    Parker, Joanne L; Mindell, Joseph A; Newstead, Simon

    2014-12-02

    Peptide transport plays an important role in cellular homeostasis as a key route for nitrogen acquisition in mammalian cells. PepT1 and PepT2, the mammalian proton coupled peptide transporters (POTs), function to assimilate and retain diet-derived peptides and play important roles in drug pharmacokinetics. A key characteristic of the POT family is the mechanism of peptide selectivity, with members able to recognise and transport >8000 different peptides. In this study, we present thermodynamic evidence that in the bacterial POT family transporter PepTSt, from Streptococcus thermophilus, at least two alternative transport mechanisms operate to move peptides into the cell. Whilst tri-peptides are transported with a proton:peptide stoichiometry of 3:1, di-peptides are co-transported with either 4 or 5 protons. This is the first thermodynamic study of proton:peptide stoichiometry in the POT family and reveals that secondary active transporters can evolve different coupling mechanisms to accommodate and transport chemically and physically diverse ligands across the membrane.

  12. Thermodynamic mechanism for inhibition of lactose permease by the phosphotransferase protein IIAGlc

    PubMed Central

    Hariharan, Parameswaran; Balasubramaniam, Dhandayuthapani; Peterkofsky, Alan; Kaback, H. Ronald

    2015-01-01

    In a variety of bacteria, the phosphotransferase protein IIAGlc plays a key regulatory role in catabolite repression in addition to its role in the vectorial phosphorylation of glucose catalyzed by the phosphoenolpyruvate:carbohydrate phosphotransferase system (PTS). The lactose permease (LacY) of Escherichia coli catalyzes stoichiometric symport of a galactoside with an H+, using a mechanism in which sugar- and H+-binding sites become alternatively accessible to either side of the membrane. Both the expression (via regulation of cAMP levels) and the activity of LacY are subject to regulation by IIAGlc (inducer exclusion). Here we report the thermodynamic features of the IIAGlc–LacY interaction as measured by isothermal titration calorimetry (ITC). The studies show that IIAGlc binds to LacY with a Kd of about 5 μM and a stoichiometry of unity and that binding is driven by solvation entropy and opposed by enthalpy. Upon IIAGlc binding, the conformational entropy of LacY is restrained, which leads to a significant decrease in sugar affinity. By suppressing conformational dynamics, IIAGlc blocks inducer entry into cells and favors constitutive glucose uptake and utilization. Furthermore, the studies support the notion that sugar binding involves an induced-fit mechanism that is inhibited by IIAGlc binding. The precise mechanism of the inhibition of LacY by IIAGlc elucidated by ITC differs from the inhibition of melibiose permease (MelB), supporting the idea that permeases can differ in their thermodynamic response to binding IIAGlc. PMID:25675534

  13. EDITORIAL: Focus on Mechanical Systems at the Quantum Limit FOCUS ON MECHANICAL SYSTEMS AT THE QUANTUM LIMIT

    NASA Astrophysics Data System (ADS)

    Aspelmeyer, Markus; Schwab, Keith

    2008-09-01

    The last five years have witnessed an amazing development in the field of nano- and micromechanics. What was widely considered fantasy ten years ago is about to become an experimental reality: the quantum regime of mechanical systems is within reach of current experiments. Two factors (among many) have contributed significantly to this situation. As part of the widespread effort into nanoscience and nanofabrication, it is now possible to produce high-quality nanomechanical and micromechanical resonators, spanning length scales of millimetres to nanometres, and frequencies from kilohertz to gigahertz. Researchers coupled these mechanical elements to high-sensitivity actuation and readout systems such as single-electron transistors, quantum dots, atomic point contacts, SQUID loops, high-finesse optical or microwave-cavities etc. Some of these ultra-sensitive readout schemes are in principle capable of detection at the quantum limit and a large part of the experimental effort is at present devoted to achieving this. On the other hand, the fact that the groups working in the field come from various different physics backgrounds—the authors of this editorial are a representative sample—has been a constant source of inspiration for helpful theoretical and experimental tools that have been adapted from other fields to the mechanical realm. To name just one example: ideas from quantum optics have led to the recent demonstration (both in theory and experiment) that coupling a mechanical resonator to a high-finesse optical cavity can be fully analogous to the well-known sideband-resolved laser cooling of ions and hence is capable in principle of cooling a mechanical mode into its quantum ground state. There is no doubt that such interdisciplinarity has been a crucial element for the development of the field. It is interesting to note that a very similar sociological phenomenon occurred earlier in the quantum information community, an area which is deeply enriched by the

  14. Physics on the boundary between classical and quantum mechanics

    NASA Astrophysics Data System (ADS)

    't Hooft, Gerard

    2014-04-01

    Nature's laws in the domain where relativistic effects, gravitational effects and quantum effects are all comparatively strong are far from understood. This domain is called the Planck scale. Conceivably, a theory can be constructed where the quantum nature of phenomena at such scales can be attributed to something fundamentally simpler. However, arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there can't be physical laws that require "conspiracy". It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In the lecture we will show several such counterexamples. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. This theory is often portrayed as to underly the quantum field theory of the subatomic particles, including the "Standard Model". So now the question is asked: how can this model feature "conspiracy", and how bad is that? Is there conspiracy in the vacuum fluctuations?

  15. Ab Initio Quantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

    DOE PAGES

    Dornheim, Tobias; Groth, Simon; Sjostrom, Travis; ...

    2016-10-07

    Here we perform ab initio quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with the linear response theory, we are able to remove finite-size errors from the potential energy over the substantial parts of the warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)]. Extensive new QMC results for up to N = 1000 electrons enable us to compute the potential energy V and the exchange-correlation free energy F xc of the macroscopic electron gas withmore » an unprecedented accuracy of | Δ V | / | V | , | Δ Fxc | / | F | xc ~ 10 $-$3. Finally, a comparison of our new data to the recent parametrization of F xc by Karasiev et al. [Phys. Rev. Lett. 112, 076403 (2014)] reveals significant deviations to the latter.« less

  16. Ab Initio Quantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

    SciTech Connect

    Dornheim, Tobias; Groth, Simon; Sjostrom, Travis; Malone, Fionn D.; Foulkes, W. M. C.; Bonitz, Michael

    2016-10-07

    Here we perform ab initio quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with the linear response theory, we are able to remove finite-size errors from the potential energy over the substantial parts of the warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)]. Extensive new QMC results for up to N = 1000 electrons enable us to compute the potential energy V and the exchange-correlation free energy F xc of the macroscopic electron gas with an unprecedented accuracy of | Δ V | / | V | , | Δ Fxc | / | F | xc ~ 10 $-$3. Finally, a comparison of our new data to the recent parametrization of F xc by Karasiev et al. [Phys. Rev. Lett. 112, 076403 (2014)] reveals significant deviations to the latter.

  17. Ab Initio Quantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit.

    PubMed

    Dornheim, Tobias; Groth, Simon; Sjostrom, Travis; Malone, Fionn D; Foulkes, W M C; Bonitz, Michael

    2016-10-07

    We perform ab initio quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with the linear response theory, we are able to remove finite-size errors from the potential energy over the substantial parts of the warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)]. Extensive new QMC results for up to N=1000 electrons enable us to compute the potential energy V and the exchange-correlation free energy F_{xc} of the macroscopic electron gas with an unprecedented accuracy of |ΔV|/|V|,|ΔF_{xc}|/|F|_{xc}∼10^{-3}. A comparison of our new data to the recent parametrization of F_{xc} by Karasiev et al. [Phys. Rev. Lett. 112, 076403 (2014)] reveals significant deviations to the latter.

  18. METHODOLOGICAL NOTES: Irreversibility in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Kadomtsev, Boris B.

    2003-11-01

    From the Editorial Board. November 9, 2003 would have marked the seventy-fifth birthday of Boris Borisovich Kadomtsev, were he alive. An outstanding theoretical physicist, teacher, and enlightener, a prominent scientist in plasma physics and controlled nuclear fusion, Kadomtsev was also actively involved in science organization activities. In particular, from 1976 until his untimely death on August 19, 1998, Kadomtsev was the Editor-in-Chief of Physics-Uspekhi, and it is owing to his efforts that the journal improved notably during his tenure. Now, the Editorial Board, with gratitude and sorrow, would like to celebrate his birthday and to honor his blessed memory in these pages. There is, however, a rule — indeed an immutable tradition — in the journal that, except for the Personalia section, no anniversary can be marked in any way other than in a scientific publication. This rule was strictly observed under Kadomtsev, and certainly should not be violated now, even when honoring his memory. Fortunately, there is a video which remained of a lecture on modern problems of quantum physics that Kadomtsev delivered on May 12, 1997. Prepared for publication by M B Kadomtsev, the lecture allows the reader to revisit the heritage of B B Kadomtsev, to appreciate his logic in treating this very difficult area of physics, to hear his voice as it were, to recall Boris Borisovich Kadomtsev and to honor his memory.

  19. Virial Coefficients from Unified Statistical Thermodynamics of Quantum Gases Trapped under Generic Power Law Potential in d Dimension and Equivalence of Quantum Gases

    NASA Astrophysics Data System (ADS)

    Bahauddin, Shah Mohammad; Mehedi Faruk, Mir

    2016-09-01

    From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in d = 3 and d = 2. But more importantly we found that, the virial coefficients of Bose and Fermi gases become identical (except the second virial coefficient, where the sign is different) when the gases are trapped under harmonic potential in d = 1. This result suggests the equivalence between Bose and Fermi gases established in d = 1 (J. Stat. Phys. DOI 10.1007/s10955-015-1344-4). Also, it is found that the virial coefficients of two-dimensional free Bose (Fermi) gas are equal to the virial coefficients of one-dimensional harmonically trapped Bose (Fermi) gas.

  20. Parity-dependent non-commutative quantum mechanics

    NASA Astrophysics Data System (ADS)

    Chung, Won Sang

    2017-01-01

    In this paper, we consider the non-commutative quantum mechanics (NCQM) with parity (or space reflection) in two dimensions. Using the parity operators Ri, we construct the deformed Heisenberg algebra with parity in the non-commutative plane. We use this algebra to discuss the isotropic harmonic Hamiltonian with parity.

  1. Efficient Integration of Quantum Mechanical Wave Equations by Unitary Transforms

    SciTech Connect

    Bauke, Heiko; Keitel, Christoph H.

    2009-08-13

    The integration of time dependent quantum mechanical wave equations is a fundamental problem in computational physics and computational chemistry. The energy and momentum spectrum of a wave function imposes fundamental limits on the performance of numerical algorithms for this problem. We demonstrate how unitary transforms can help to surmount these limitations.

  2. Time Symmetric Quantum Mechanics and Causal Classical Physics ?

    NASA Astrophysics Data System (ADS)

    Bopp, Fritz W.

    2017-02-01

    A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual "near future" macroscopic phenomena is attributed to a cosmological asymmetry and to rules governing the transition between microscopic to macroscopic observations. Our interest is a heuristic understanding of the resulting macroscopic physics.

  3. Quantum-mechanical theory of optomechanical Brillouin cooling

    SciTech Connect

    Tomes, Matthew; Bahl, Gaurav; Carmon, Tal; Marquardt, Florian

    2011-12-15

    We analyze how to exploit Brillouin scattering of light from sound for the purpose of cooling optomechanical devices and present a quantum-mechanical theory for Brillouin cooling. Our analysis shows that significant cooling ratios can be obtained with standard experimental parameters. A further improvement of cooling efficiency is possible by increasing the dissipation of the optical anti-Stokes resonance.

  4. A note on misunderstandings of Piron's axioms for quantum mechanics

    NASA Astrophysics Data System (ADS)

    Foulis, D. J.; Randall, C. H.

    1984-01-01

    Piron's axioms for a realistically interpreted quantum mechanics are analyzed in detail within the context of a formal mathematical structure expressed in the conventional set-theoretic idiom of mathematics. As a result, some of the serious misconceptions that have encouraged recent criticisms of Piron's axioms are exposed.

  5. Equivalent emergence of time dependence in classical and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Briggs, John S.

    2015-05-01

    Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes another part. Translating this scenario into both classical and quantum mechanics allows a transition to be made from a time-independent mechanics for the closed composite to a time-dependent description of the observed part alone. The use of Hamilton-Jacobi theory yields a very close parallel between the derivations in classical and quantum mechanics. The time-dependent equations, Hamilton-Jacobi or Schrödinger, appear as approximations since no observed system is truly closed. The quantum case has an additional feature in the condition that the observing environment must become classical in order to define a real classical time variable. This condition leads to a removal of entanglement engendered by the interaction between the observed system and the observing environment. Comparison is made to the similar emergence of time in quantum gravity theory.

  6. Completeness of the Coulomb Wave Functions in Quantum Mechanics

    ERIC Educational Resources Information Center

    Mukunda, N.

    1978-01-01

    Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)

  7. The History of Teaching Quantum Mechanics in Greece

    ERIC Educational Resources Information Center

    Tampakis, Constantin; Skordoulis, Constantin

    2007-01-01

    In this work, our goal is to examine the attitude of the Greek scientific community towards Quantum Mechanics and establish the history of teaching of this theory in Greece. We have examined Physics textbooks written by professors of the University of Athens, as well as records of public speeches, university yearbooks from 1923 to 1970, articles…

  8. Overcoming Misconceptions in Quantum Mechanics with the Time Evolution Operator

    ERIC Educational Resources Information Center

    Quijas, P. C. Garcia; Aguilar, L. M. Arevalo

    2007-01-01

    Recently, there have been many efforts to use the research techniques developed in the field of physics education research to improve the teaching and learning of quantum mechanics. In particular, part of this research is focusing on misconceptions held by students. For instance, a set of misconceptions is associated with the concept of stationary…

  9. Exactly Solvable Quantum Mechanical Potentials: An Alternative Approach.

    ERIC Educational Resources Information Center

    Pronchik, Jeremy N.; Williams, Brian W.

    2003-01-01

    Describes an alternative approach to finding exactly solvable, one-dimensional quantum mechanical potentials. Differs from the usual approach in that instead of starting with a particular potential and seeking solutions to the related Schrodinger equations, it begins with known solutions to second-order ordinary differential equations and seeks to…

  10. Spin and Uncertainty in the Interpretation of Quantum Mechanics.

    ERIC Educational Resources Information Center

    Hestenes, David

    1979-01-01

    Points out that quantum mechanics interpretations, using Heisenberg's Uncertainty Relations for the position and momentum of an electron, have their drawbacks. The interpretations are limited to the Schrodinger theory and fail to take into account either spin or relativity. Shows why spin cannot be ignored. (Author/GA)

  11. Recursive representation of Wronskians in confluent supersymmetric quantum mechanics

    NASA Astrophysics Data System (ADS)

    Contreras-Astorga, Alonso; Schulze-Halberg, Axel

    2017-03-01

    A recursive form of arbitrary-order Wronskian associated with transformation functions in the confluent algorithm of supersymmetric quantum mechanics (SUSY) is constructed. With this recursive form regularity conditions for the generated potentials can be analyzed. Moreover, as byproducts we obtain new representations of solutions to Schrödinger equations that underwent a confluent SUSY-transformation.

  12. Quantum Mechanics Concept Assessment: Development and Validation Study

    ERIC Educational Resources Information Center

    Sadaghiani, Homeyra R.; Pollock, Steven J.

    2015-01-01

    As part of an ongoing investigation of students' learning in first semester upper-division quantum mechanics, we needed a high-quality conceptual assessment instrument for comparing outcomes of different curricular approaches. The process of developing such a tool started with converting a preliminary version of a 14-item open-ended quantum…

  13. Review of Student Difficulties in Upper-Level Quantum Mechanics

    ERIC Educational Resources Information Center

    Singh, Chandralekha; Marshman, Emily

    2015-01-01

    Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical…

  14. Hidden algebra method (quasi-exact-solvability in quantum mechanics)

    SciTech Connect

    Turbiner, Alexander

    1996-02-20

    A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.

  15. A multiscale quantum mechanics/electromagnetics method for device simulations.

    PubMed

    Yam, ChiYung; Meng, Lingyi; Zhang, Yu; Chen, GuanHua

    2015-04-07

    Multiscale modeling has become a popular tool for research applying to different areas including materials science, microelectronics, biology, chemistry, etc. In this tutorial review, we describe a newly developed multiscale computational method, incorporating quantum mechanics into electronic device modeling with the electromagnetic environment included through classical electrodynamics. In the quantum mechanics/electromagnetics (QM/EM) method, the regions of the system where active electron scattering processes take place are treated quantum mechanically, while the surroundings are described by Maxwell's equations and a semiclassical drift-diffusion model. The QM model and the EM model are solved, respectively, in different regions of the system in a self-consistent manner. Potential distributions and current densities at the interface between QM and EM regions are employed as the boundary conditions for the quantum mechanical and electromagnetic simulations, respectively. The method is illustrated in the simulation of several realistic systems. In the case of junctionless field-effect transistors, transfer characteristics are obtained and a good agreement between experiments and simulations is achieved. Optical properties of a tandem photovoltaic cell are studied and the simulations demonstrate that multiple QM regions are coupled through the classical EM model. Finally, the study of a carbon nanotube-based molecular device shows the accuracy and efficiency of the QM/EM method.

  16. Econophysics: from Game Theory and Information Theory to Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Jimenez, Edward; Moya, Douglas

    2005-03-01

    Rationality is the universal invariant among human behavior, universe physical laws and ordered and complex biological systems. Econophysics isboth the use of physical concepts in Finance and Economics, and the use of Information Economics in Physics. In special, we will show that it is possible to obtain the Quantum Mechanics principles using Information and Game Theory.

  17. Elementary Quantum Mechanics in a High-Energy Process

    ERIC Educational Resources Information Center

    Denville, A.; And Others

    1978-01-01

    Compares two approaches to strong absorption in elementary quantum mechanics; the black sphere and a model based on the continuum theory of nuclear reactions. Examines the application to proton-antiproton interactions at low momenta and concludes that the second model is the appropriate and simplest to use. (Author/GA)

  18. Quantum mechanical force field for hydrogen fluoride with explicit electronic polarization

    SciTech Connect

    Mazack, Michael J. M.; Gao, Jiali

    2014-05-28

    The explicit polarization (X-Pol) theory is a fragment-based quantum chemical method that explicitly models the internal electronic polarization and intermolecular interactions of a chemical system. X-Pol theory provides a framework to construct a quantum mechanical force field, which we have extended to liquid hydrogen fluoride (HF) in this work. The parameterization, called XPHF, is built upon the same formalism introduced for the XP3P model of liquid water, which is based on the polarized molecular orbital (PMO) semiempirical quantum chemistry method and the dipole-preserving polarization consistent point charge model. We introduce a fluorine parameter set for PMO, and find good agreement for various gas-phase results of small HF clusters compared to experiments and ab initio calculations at the M06-2X/MG3S level of theory. In addition, the XPHF model shows reasonable agreement with experiments for a variety of structural and thermodynamic properties in the liquid state, including radial distribution functions, interaction energies, diffusion coefficients, and densities at various state points.

  19. Quantum mechanical force field for hydrogen fluoride with explicit electronic polarization.

    PubMed

    Mazack, Michael J M; Gao, Jiali

    2014-05-28

    The explicit polarization (X-Pol) theory is a fragment-based quantum chemical method that explicitly models the internal electronic polarization and intermolecular interactions of a chemical system. X-Pol theory provides a framework to construct a quantum mechanical force field, which we have extended to liquid hydrogen fluoride (HF) in this work. The parameterization, called XPHF, is built upon the same formalism introduced for the XP3P model of liquid water, which is based on the polarized molecular orbital (PMO) semiempirical quantum chemistry method and the dipole-preserving polarization consistent point charge model. We introduce a fluorine parameter set for PMO, and find good agreement for various gas-phase results of small HF clusters compared to experiments and ab initio calculations at the M06-2X/MG3S level of theory. In addition, the XPHF model shows reasonable agreement with experiments for a variety of structural and thermodynamic properties in the liquid state, including radial distribution functions, interaction energies, diffusion coefficients, and densities at various state points.

  20. Deterministic quantum evolution through modification of the hypotheses of statistical mechanics

    SciTech Connect

    Schulman, L.S.

    1986-02-01

    It is claimed that for all apparatus capable of performing macroscopic measurements of microscopic systems there exist special internal states for which deterministic quantum evolution alone yields a particular macroscopic outcome rather than a superposition of macroscopically distinct outcomes. Schulman maintains that these special states are distributed uniformly (in a certain sense) among the set of all states. He postulates that in the absence of precise information on apparatus initial conditions one should give equal weight to those microstates that are consistent with the macroscopic state and are special in the sense used above. Evidence is presented for this postulate's recovering the usual quantum probabilities. This theory is fully deterministic, has no collapsing wave functions, and offers a resolution of the quantum measurement problem through a revision of the usual statistical mechanical handling of initial conditions. It requires a single wave function for the entire universe and an all-encompassing conspiracy to arrange the right sort of special wave function for each experiment. As an example Schulman considers a Stern-Gerlach apparatus that measures the z component of the spin of silver atoms that pass through it. Although Schulman does not provide physical or philosophical justification for his central hypothesis, some perspective is given by examining the notions implicit in the usual principles of thermodynamics.