Relevant bibliographies by topics / Quantum trajectories, Quantum mechanics, statistical mechanics

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Quantum trajectories, Quantum mechanics, statistical mechanics'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Quantum trajectories, Quantum mechanics, statistical mechanics"

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Grössing, Gerhard. "Emergence of quantum mechanics from a sub-quantum statistical mechanics." International Journal of Modern Physics B 28, no. 26 (October 20, 2014): 1450179. http://dx.doi.org/10.1142/s0217979214501793.

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A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level. It is further demonstrated both analytically and with the aid of computer simulations that our model provides explanations for various quantum effects such as double-slit or n-slit interference. We show the averaged trajectories emerging from our model to be identical to Bohmian trajectories, albeit without the need to invoke complex wavefunctions or any other quantum mechanical tool. Finally, the model provides new insights into the origins of entanglement, and, in particular, into the phenomenon of a "systemic" non-locality.
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Aragón-Muñoz, L., G. Chacón-Acosta, and H. Hernandez-Hernandez. "Effective quantum tunneling from a semiclassical momentous approach." International Journal of Modern Physics B 34, no. 29 (October 28, 2020): 2050271. http://dx.doi.org/10.1142/s0217979220502719.

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In this work, we study the quantum tunnel effect through a potential barrier within a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution of the system is given in terms of a dynamical system for which we are able to determine numerical effective trajectories for individual particles, similar to the Bohmian description of quantum mechanics. We obtain a complete description of the possible trajectories of the system, finding semiclassical reflected, tunneled and confined paths due to the appearance of an effective time-dependent potential.
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FERRY, D. K., R. AKIS, and J. P. BIRD. "EDGE STATES AND TRAJECTORIES IN QUANTUM DOTS: PROBING THE QUANTUM-CLASSICAL TRANSITION." International Journal of Modern Physics B 21, no. 08n09 (April 10, 2007): 1278–87. http://dx.doi.org/10.1142/s0217979207042744.

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Edge states have been a backbone of our understanding of the experimental basis of the quantum Hall effect for quite some time. Interestingly, this comprises a quantum system with well defined currents and particle trajectories. The role of trajectories in quantum mechanics has been a problematic question of interpretation for quite some time, and the open quantum dot is a natural system in which to probe this question. Contrary to early speculation, a set of well defined quantum states survives in the open quantum dot. These states are the pointer states and provide a transition into the classical states that can be found in these structures. These states provide resonances, which are observable as oscillatory behavior in the magnetoconductance of the dots. But, they have well defined current directions within the dots. Consequently, one expects trajectories to be a property of these states as well. As one crosses from the low to the high field regime, quite steady trajectories and consequent wave functions can easily be identified and examined. In this talk, we review the current understanding and the support for the decoherence theory.
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Yang, Ciann-Dong, and Shiang-Yi Han. "Extending Quantum Probability from Real Axis to Complex Plane." Entropy 23, no. 2 (February 8, 2021): 210. http://dx.doi.org/10.3390/e23020210.

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Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the probability domain extends to the complex space, including the generation of complex trajectory, the definition of the complex probability, and the relation of the complex probability to the quantum probability. The complex treatment proposed in this article applies the optimal quantum guidance law to derive the stochastic differential equation governing a particle’s random motion in the complex plane. The probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy is formed by an ensemble of the complex quantum random trajectories, which are solved from the complex stochastic differential equation. Meanwhile, the probability distribution ρc(t,x,y) is verified by the solution of the complex Fokker–Planck equation. It is shown that quantum probability |Ψ|2 and classical probability can be integrated under the framework of complex probability ρc(t,x,y), such that they can both be derived from ρc(t,x,y) by different statistical ways of collecting spatial points.
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ELLIS, JOHN, N. E. MAVROMATOS, and D. V. NANOPOULOS. "VALLEYS IN NONCRITICAL STRING FOAM SUPPRESS QUANTUM COHERENCE." Modern Physics Letters A 10, no. 05 (February 20, 1995): 425–40. http://dx.doi.org/10.1142/s0217732395000466.

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As an example of our noncritical string approach to microscopic black hole dynamics, we exhibit some string contributions to the [Formula: see text] matrix relating in- and out-state density matrices that do not factorize as a product of S and S† matrices. They are associated with valley trajectories between topological defects on the string worldsheet, that appear as quantum fluctuations in the space-time foam. Through their uv renormalization scale dependences these valleys cause non-Hamiltonian time evolution and suppress off-diagonal entries in the density matrix at large times. Our approach is a realization of previous formulations of nonequilibrium quantum statistical mechanics with an arrow of time.
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Prigogine, Ilya. "From Poincare's Divergences to Quantum Mechanics with Broken Time Symmetry." Zeitschrift für Naturforschung A 52, no. 1-2 (February 1, 1997): 37–45. http://dx.doi.org/10.1515/zna-1997-1-212.

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AbstractWe discuss the spectral property of unstable dynamical systems in both classical and quantum mechanics. An important class of unstable dynamical systems corresponds to the Large Poincare Systems (LPS). Conventional perturbation technique leads then to divergences. We introduce methods for the elimination of Poincare divergences to obtain a solution of the spectral problem analytic in the coupling constant. To do so, we have to enlarge the class of permissible transformations, to include non-unitary transformations as well as to extend the Hilbert space. A simple example refers to the Friedrichs model, which was studied independently by George Sudarshan and his co-workers. However, our main interest is the irreducible representations in the Liouville space. In these representations the central quantity is the density matrix, and the eigenfunctions of the Liouville operator cannot be expressed in terms of the wave functions. We suggest that this situation corresponds to quantum chaos. Indeed, classical chaos does not mean that Newton's equation becomes "wrong" but that trajectories loose their operational meaning. Similarly, whenever we have an irreducible representation in the Liouville space this means that the wave function description looses its operational meaning. Additional statistical features appear. A simple example corresponds to persistent interactions in the scattering problem which cannot be treated in the frame of usual S-matrix theory.
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Horton, George, and Chris Dewdney. "A non-local, Lorentz-invariant, hidden-variable interpretation of relativistic quantum mechanics based on particle trajectories." Journal of Physics A: Mathematical and General 34, no. 46 (November 13, 2001): 9871–78. http://dx.doi.org/10.1088/0305-4470/34/46/310.

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Горобей, Н. Н., and А. С. Лукьяненко. "О термодинамических параметрах адиабатически изолированного тела." Физика твердого тела 63, no. 5 (2021): 663. http://dx.doi.org/10.21883/ftt.2021.05.50818.003.

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The definition of the main thermodynamic functions for an adiabatically isolated body with constant internal energy is proposed in the framework of the formalism of the covariant quantum theory with reparametrization invariance of proper time. The modification does not change the dynamic content of the theory at the classical level, but it allows one to define the unitary evolution operator in quantum theory. In this operator, proper time is a measure of the internal movement of the body. The transition to statistical mechanics is carried out by the Wick rotation of proper time in the complex plane. As a result, a representation of the partition function of an isolated body in the form of a Euclidean functional integral on the space of closed trajectories in the configuration space is obtained. For a given internal energy, the average return temperature and free energy are determined, which under lie the thermomechanics of an adiabatically isolated body.
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Krok, Kamila A., Artur P. Durajski, and Radosław Szczȩśniak. "The Abraham–Lorentz force and the time evolution of a chaotic system: The case of charged classical and quantum Duffing oscillators." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 7 (July 2022): 073130. http://dx.doi.org/10.1063/5.0090477.

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This paper proves that the Abraham–Lorentz (AL) force can noticeably modify the trajectories of the charged Duffing oscillators over time. The influence of the reaction force on the oscillator evolution is strongly enhanced if the system is considered at the level of quantum mechanics. For example, the AL force examined within the scope of Newtonian description can change the trajectory of the Duffing oscillator only if it has the mass of an electron. However, we showed that when quantum corrections along with the nondeterministic contributions are taken into account, the reaction force of the electromagnetic field affects noticeably even the oscillator with a mass equal to the mass of the [Formula: see text] ion. The charged Duffing oscillators belong to the class of systems characterized by the chaotic nondeterministic dynamics. In classical terms, the nondeterministic behavior of the discussed systems results from the breaking of the causality principle by the AL force.
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Kovalenko, Andriy. "Multiscale modeling of solvation in chemical and biological nanosystems and in nanoporous materials." Pure and Applied Chemistry 85, no. 1 (January 4, 2013): 159–99. http://dx.doi.org/10.1351/pac-con-12-06-03.

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Statistical–mechanical, 3D-RISM-KH molecular theory of solvation (3D reference interaction site model with the Kovalenko–Hirata closure) is promising as an essential part of multiscale methodology for chemical and biomolecular nanosystems in solution. 3D-RISM-KH explains the molecular mechanisms of self-assembly and conformational stability of synthetic organic rosette nanotubes (RNTs), aggregation of prion proteins and β-sheet amyloid oligomers, protein-ligand binding, and function-related solvation properties of complexes as large as the Gloeobacter violaceus pentameric ligand-gated ion channel (GLIC) and GroEL/ES chaperone. Molecular mechanics/Poisson–Boltzmann (generalized Born) surface area [MM/PB(GB)SA] post-processing of molecular dynamics (MD) trajectories involving SA empirical nonpolar terms is replaced with MM/3D-RISM-KH statistical–mechanical evaluation of the solvation thermodynamics. 3D-RISM-KH has been coupled with multiple time-step (MTS) MD of the solute biomolecule driven by effective solvation forces, which are obtained analytically by converging the 3D-RISM-KH integral equations at outer time-steps and are calculated in between by using solvation force coordinate extrapolation (SFCE) in the subspace of previous solutions to 3D-RISM-KH. The procedure is stabilized by the optimized isokinetic Nosé–Hoover (OIN) chain thermostatting, which enables gigantic outer time-steps up to picoseconds to accurately calculate equilibrium properties. The multiscale OIN/SFCE/3D-RISM-KH algorithm is implemented in the Amber package and illustrated on a fully flexible model of alanine dipeptide in aqueous solution, exhibiting the computational rate of solvent sampling 20 times faster than standard MD with explicit solvent. Further substantial acceleration can be achieved with 3D-RISM-KH efficiently sampling essential events with rare statistics such as exchange and localization of solvent, ions, and ligands at binding sites and pockets of the biomolecule. 3D-RISM-KH was coupled with ab initio complete active space self-consistent field (CASSCF) and orbital-free embedding (OFE) Kohn–Sham (KS) density functional theory (DFT) quantum chemistry methods in an SCF description of electronic structure, optimized geometry, and chemical reactions in solution. The (OFE)KS-DFT/3D-RISM-KH multi-scale method is implemented in the Amsterdam Density Functional (ADF) package and extensively validated against experiment for solvation thermochemistry, photochemistry, conformational equilibria, and activation barriers of various nanosystems in solvents and ionic liquids (ILs). Finally, the replica RISM-KH-VM molecular theory for the solvation structure, thermodynamics, and electrochemistry of electrolyte solutions sorbed in nanoporous materials reveals the molecular mechanisms of sorption and supercapacitance in nanoporous carbon electrodes, which is drastically different from a planar electrical double layer.
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Dissertations / Theses on the topic "Quantum trajectories, Quantum mechanics, statistical mechanics"

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CILLUFFO, Dario. "(Un)conditioned open dynamics in quantum optics." Doctoral thesis, Università degli Studi di Palermo, 2021. http://hdl.handle.net/10447/500775.

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The study of the dynamics of open quantum systems sheds light on dissipative processes in quantum mechanics. Any system under continuous measurement is open and the act of measuring induces abrupt changes of the system’s state (collapses). The evolution conditioned to measurement records generates the so-called quantum trajectories. A continuous (unconditioned) evolution of the system is recovered by averaging over a large number of trajectories. Historically this kind of evolution has been the main focus of theoretical investigations. In this dissertation we consider both conditional and unconditional dynamics of quantum optical systems. Unconditioned dynamics is studied through the collision model paradigm. The formalism is described in detail and used for describing generic systems featuring many quantum emitters coupled to a usually one-dimensional field. The negligible-delay regime is widely explored. Collision models are used to unveil the mechanisms underlying the decoherence-free evolution regime typical of these systems, which has received considerable attention in the last years. Then we investigate conditioned dynamics by broadening the study of statistics of quantum trajectories. Specifically, we exploit the information about the emission’s full-counting statistics from large deviations to define a nonclassicality witness. Finally we come back to collision models in order to extend the theory of biased quantum trajectories from Lindblad-like dynamics to sequences of arbitrary dynamical maps, providing at once a transparent physical interpretation.
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Ha, Eugene. "Quantum statistical mechanics of Shimura varieties." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980749964.

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Koch, Werner. "Non-Markovian Dissipative Quantum Mechanics with Stochastic Trajectories." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-63671.

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All fields of physics - be it nuclear, atomic and molecular, solid state, or optical - offer examples of systems which are strongly influenced by the environment of the actual system under investigation. The scope of what is called "the environment" may vary, i.e., how far from the system of interest an interaction between the two does persist. Typically, however, it is much larger than the open system itself. Hence, a fully quantum mechanical treatment of the combined system without approximations and without limitations of the type of system is currently out of reach. With the single assumption of the environment to consist of an internally thermalized set of infinitely many harmonic oscillators, the seminal work of Stockburger and Grabert [Chem. Phys., 268:249-256, 2001] introduced an open system description that captures the environmental influence by means of a stochastic driving of the reduced system. The resulting stochastic Liouville-von Neumann equation describes the full non-Markovian dynamics without explicit memory but instead accounts for it implicitly through the correlations of the complex-valued noise forces. The present thesis provides a first application of the Stockburger-Grabert stochastic Liouville-von Neumann equation to the computation of the dynamics of anharmonic, continuous open systems. In particular, it is demonstrated that trajectory based propagators allow for the construction of a numerically stable propagation scheme. With this approach it becomes possible to achieve the tremendous increase of the noise sample count necessary to stochastically converge the results when investigating such systems with continuous variables. After a test against available analytic results for the dissipative harmonic oscillator, the approach is subsequently applied to the analysis of two different realistic, physical systems. As a first example, the dynamics of a dissipative molecular oscillator is investigated. Long time propagation - until thermalization is reached - is shown to be possible with the presented approach. The properties of the thermalized density are determined and they are ascertained to be independent of the system's initial state. Furthermore, the dependence on the bath's temperature and coupling strength is analyzed and it is demonstrated how a change of the bath parameters can be used to tune the system from the dissociative to the bound regime. A second investigation is conducted for a dissipative tunneling scenario in which a wave packet impinges on a barrier. The dependence of the transmission probability on the initial state's kinetic energy as well as the bath's temperature and coupling strength is computed. For both systems, a comparison with the high-temperature Markovian quantum Brownian limit is performed. The importance of a full non-Markovian treatment is demonstrated as deviations are shown to exist between the two descriptions both in the low temperature cases where they are expected and in some of the high temperature cases where their appearance might not be anticipated as easily.
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Fresch, Barbara. "Typicality, Fluctuations and Quantum Dynamics: Statistical Mechanics of Quantum Systems." Doctoral thesis, Università degli studi di Padova, 2009. http://hdl.handle.net/11577/3426626.

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Recently, the possibility of investigating single molecule, or single spin observables, as well as the necessity of a better understanding of the mechanisms underlying quantum dynamics in order to obtain nanoscale devices and nanostructered materials suitable for quantum computing tasks, have revived the interest in foundational aspects of quantum statistical mechanics. This thesis aims to give a contribution to this field by re-considering the statistical characterization of a quantum system at the light of some paradigmatic changes in our understanding of quantum theory which have taken place in the last two decades. In particular the impressive development of quantum information theory has changed the perceptions of quantum entanglement: for a long time it has been considered a somewhat paradoxical property of the matter at the atomic scale, but now it is regarded as an essential and ubiquitous phenomenon whose consequences are affecting the very macroscopic world that we experience. Still the decoherence program has brought out the importance of considering a quantum system together with its environment in order to clarify some key aspects of quantum dynamics. Thus, we start from the idea that quantum correlations are ubiquitous and somewhat uncontrollable in systems with many degrees of freedom which are typically considered in statistical mechanics. As a consequence we assume the standpoint that quantum statistical mechanics has not to be based on the underlying idea of a collection of many, independent quantum systems but rather it has to emerge at the level of a global wavefunction (pure state) which describes the system as well as its environment as a whole. In order to investigate the consequences of these assumptions we study the equilibrium distribution of an isolated quantum system. This is defined, in analogy with the ergodic foundations of classical statistical mechanics, on the basis of the time evolution of the quantum state. Then, we study the emergence of thermodynamic properties in a quantum system by studying the probability distribution of some function of interests, as the entropy and the equilibrium state of a subsystem, on Ensembles of Pure States. Such a probability distribution is derived from the geometry of the Hilbert space, and the theoretical tools suitable for its characterization are developed. On the one hand we perform a numerical sampling of the ensemble distributions by employing Monte Carlo techniques, on the other hand simpler analytical approximation of the geometrical distributions are derived by means of a maximum entropy principle. Model systems composed of an ensemble of spins are chosen to illustrate the salient features which emerge from the developed theoretical framework: the main point is that the Ensemble Distributions of “thermodynamic observables” (entropy or equilibrium state of a subsystem) are sharply peaked around a typical value. From the analysis it emerges that each of the overwhelming majority of the wavefunctions which has appreciable weight in the considered ensemble, is characterized by the same value of the “macroscopic” functions. This is a striking evidence of the “typicality” of these properties. In the essence, our impossibility to know the state of the system in detail does not matter, just for the remarkable fact that almost all quantum states behave essentially in the same way. By virtue of this typicality the study of the behaviour of the typical values of the thermodynamic function become meaningful. Notably, under certain conditions, one recovers the results of standard statistical mechanics, that is, the equilibrium average of the state of a subsystem can be cast in the Boltzmann canonical form at the temperature given by the usual thermodynamical relation . In the second part of the thesis we consider the dynamical aspects of the equilibrium state of a subsystem interacting with its environment. The fluctuations around the equilibrium average critically depends on the entanglement between the system and the environment and on the form of the interaction Hamiltonian. The connection between the dynamics of the fluctuations of an observable at the equilibrium and the relaxation toward the equilibrium from a “non typical” initial value is also investigated with the aid of simple model systems. The study presented in this thesis was partly motivated by a critical analysis of the statistical methods available for the theoretical modelling of magnetic resonance experiments. One of these, the Stochastic Liouville Equation, has been employed in a work completed during the first year of my Ph.D. program in order to interpret some feature of a two dimensional electron spin resonance experiment, [Fresch B., Frezzato D., Moro G. J., Kothe G., Freed J. H.; J. Phys. Chem. B., 110, 24238, (2006)].
Nuove tecnologie hanno reso possibile lo studio spettroscopico di proprietà di singola molecola e di singolo spin, inoltre, gli avanzamenti nel campo delle nanotecnologie, mettono costantemente alla prova la nostra comprensione dei meccanismi che governano la dinamica a livello quantistico. Questi recenti sviluppi stanno rinnovando l’interesse intorno a questioni fondamentali non pienamente comprese e risolte; una di queste questioni riguarda i fondamenti della meccanica statistica quantistica. Lo scopo della presente tesi è quello di dare un contributo in questo affascinante campo, alla luce degli importanti cambiamenti avvenuti negli ultimi vent’ anni nella nostra comprensione della meccanica quantistica. In particolare gli studi condotti nell’ambito della teoria dell’informazione hanno profondamente modificato la nostra percezione dell’ entanglement quantistico. Questo è stato per lungo tempo considerato una proprietà quasi paradossale della materia su scala atomica mentre oggi è ritenuto un fenomeno essenziale e onnipresente importante per comprendere l’emergere del mondo macroscopico così come lo conosciamo. Inoltre, la formulazione e lo sviluppo del cosiddetto “decoherence program” ha introdotto un nuovo paradigma nella descrizione dell’evoluzione temporale dei sistemi quantistici riconoscendo il ruolo fondamentale dell’interazione con l’ambiente nel determinare aspetti essenziali della dinamica. Assumendo una prospettiva in linea con questi progressi, in questa tesi si parte dall’idea che la correlazione quantistica, l’entanglement, non possa essere ignorata nel derivare una descrizione statistica coerente dei sistemi complessi tradizionalmente considerati in meccanica statistica. La logica conseguenza di questo punto di vista è che la meccanica statistica quantistica non possa essere basata sull’idea dell’esistenza di insiemi di sistemi quantistici fra loro indipendenti, ma al contrario debba emergere dalla descrizione in termini di una singola funzione d’onda (stato puro) che descrive il sistema nella sua globalità, i.e. il sottosistema di interesse insieme con il suo ambiente (“environment”). Allo scopo di costruire tale descrizione, in questa tesi si considera in primo luogo la distribuzione di probabilità che descrive lo stato di equilibrio di un sistema quantistico isolato. Essa è definita, in analogia con la teoria ergodica classica, sulla base dell’evoluzione temporale del sistema. Per studiare l’emergere delle proprietà termodinamiche si introducono poi distribuzioni di probabilità su insiemi di stati puri (“Ensemble Distributions”). Tali distribuzioni sono derivate sulla base della geometria dello spazio di Hilbert che descrive il sistema nella sua interezza. Inoltre si sono sviluppati gli strumenti teorici che permettono la caratterizzazione di tali distribuzioni di probabilità: essi consistono da un lato nell’implementazione di metodi numerici di tipo Monte Carlo che permettono il campionamento statistico diretto delle distribuzioni, d’altro canto sono state sviluppate approssimazioni analitiche delle distribuzioni sulla base del principio di massima entropia. I risultati fondamentali che emergono dal quadro teorico sviluppato sono illustrati mediante lo studio della statistica in sistemi di spin: il messaggio fondamentale è che le funzioni termodinamiche, come l’entropia del sistema globale e lo stato di equilibrio di un sottosistema, sono caratterizzate da distribuzioni sull’ ensemble che risultano molto concentrate intorno ad un valore tipico. Dall’analisi condotta si deduce quindi che ognuno dei singoli stati puri considerati nell’insieme è caratterizzato dallo stesso valore delle funzioni termodinamiche studiate. Questa è una chiara evidenza della proprietà di tipicalità, (“typicality”), di queste funzioni. L’essenza di questo risultato è che la nostra incapacità di conoscere i dettagli dello stato quantistico del sistema non è così importante dal momento che la grande maggioranza dei possibili stati che appartengono all’insieme considerato sono caratterizzati dallo stesso valore delle proprietà termodinamiche alle quali siamo interessati. In virtù di tale proprietà risulta sensato studiare gli andamenti dei valori tipici delle proprietà termodinamiche. Sotto certe condizioni si ritrovano i risultati della meccanica statistica standard: in particolare lo stato di equilibrio di un sottosistema risulta essere in media lo stato canonico di Boltzmann alla temperatura definita dall’usuale relazione termodinamica . Nella seconda parte della tesi, invece, si illustra la dinamica associata allo stato di equilibrio di un sistema in interazione con il suo ambiente. Le caratteristiche delle fluttuazioni intorno ai valori medi di equilibrio dipendono sia dall’entanglement tra il sistema e l’ambiente che dal tipo di interazione considerato. Per finire si considera la connessione fra la dinamica delle fluttuazioni all’equilibrio e i processi di rilassamento da uno stato iniziale di non equilibrio. Il lavoro presentato in questa tesi è stato in parte motivato da un analisi critica dei metodi stocastici utilizzati nella modellizzazione teorica delle spettroscopie magnetiche. Durante il primo anno di dottorato tali metodologie sono state impiegate per l’interpretazione di alcune osservabili in esperimenti di risonanza magnetica elettronica bidimensionale. [Fresch B., Frezzato D., Moro G. J., Kothe G., Freed J. H.; J. Phys. Chem. B., 110, 24238, (2006)].
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Wustmann, Waltraut. "Statistical mechanics of time-periodic quantum systems." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-38126.

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The asymptotic state of a quantum system, which is in contact with a heat bath, is strongly disturbed by a time-periodic driving in comparison to a time-independent system. In this thesis an extensive picture of the asymptotic state of time-periodic quantum systems is drawn by relating it to the structure of the corresponding classical phase space. To this end the occupation probabilities of the Floquet states are analyzed with respect to their semiclassical property of being either regular or chaotic. The regular Floquet states are occupied with exponential weights e^{-betaeff Ereg} similar to the canonical weights e^{-beta E} of time-independent systems. The regular energies Ereg are defined by the quantization of the time-periodic system, whose classical properties also determine the effective temperature 1/betaeff. In contrast, the chaotic Floquet states acquire almost equal probabilities, irrespective of their time-averaged energy. Beyond these semiclassical properties the existence of avoided crossings in the spectrum is an intrinsic quantum property of time-periodic systems. Avoided crossings can strongly influence the entire occupation distribution. As an impressive application a novel switching mechanism is proposed in a periodically driven double well potential coupled to a heat bath. By a weak variation of the driving amplitude its asymptotic state is switched from the ground state in one well to a state with higher average energy in the other well
Der asymptotische Zustand eines Quantensystems, das in Kontakt mit einem Wärmebad steht, wird durch einen zeitlich periodischen Antrieb gegenüber einem zeitunabhängigen System nachhaltig verändert. In dieser Arbeit wird ein umfassendes Bild über den asymptotischen Zustand zeitlich periodischer Quantensysteme entworfen, indem es diesen zur Struktur des zugehörigen klassischen Phasenraums in Beziehung setzt. Dazu werden die Besetzungswahrscheinlichkeiten der Floquet-Zustände hinsichtlich ihrer semiklassischen Eigenschaft analysiert, nach welcher sie entweder regulär oder chaotisch sind. Die regulären Floquet-Zustände sind mit exponentiellen Gewichten e^{-betaeff Ereg} ähnlich der kanonischen Verteilung e^{-beta E} zeitunabhängiger Systeme besetzt. Dabei sind die reguläre Energien Ereg durch die Quantisierung des Systems vorgegeben, dessen klassische Eigenschaften auch die effektive Temperatur 1/betaeff bestimmen. Die chaotischen Zustände dagegen haben fast einheitliche Besetzungswahrscheinlichkeiten, welche unabhängig von ihrer mittleren Energie sind. Über diese semiklassischen Eigenschaften hinaus ist das Auftreten von vermiedenen Kreuzungen im Spektrum eine intrinsisch quantenmechanische Eigenschaft zeitlich periodischer Systeme. Diese können die gesamte Besetzungsverteilung nachhaltig beeinflussen und finden eine eindrucksvolle Anwendung in Form eines neuartigen Schaltmechanismus in einem harmonisch modulierten Doppelmuldenpotential in Kontakt mit einem Wärmebad. Der asymptotische Zustand kann unter geringer Variation der Antriebsamplitude vom Grundzustand der einen Mulde in einen Zustand höherer mittlerer Energie in der anderen Mulde geschaltet werden
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Nielsen, Steven Ole. "Mixed quantum-classical dynamics and statistical mechanics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ63602.pdf.

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Lo, Joseph Quin Wai. "Pseudospectral methods in quantum and statistical mechanics." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/1298.

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The pseudospectral method is a family of numerical methods for the solution of differential equations based on the expansion of basis functions defined on a set of grid points. In this thesis, the relationship between the distribution of grid points and the accuracy and convergence of the solution is emphasized. The polynomial and sinc pseudospectral methods are extensively studied along with many applications to quantum and statistical mechanics involving the Fokker-Planck and Schroedinger equations. The grid points used in the polynomial methods coincide with the points of quadrature, which are defined by a set of polynomials orthogonal with respect to a weight function. The choice of the weight function plays an important role in the convergence of the solution. It is observed that rapid convergence is usually achieved when the weight function is chosen to be the square of the ground-state eigenfunction of the problem. The sinc method usually provides a slow convergence as the grid points are uniformly distributed regardless of the behaviour of the solution. For both polynomial and sinc methods, the convergence rate can be improved by redistributing the grid points to more appropriate positions through a transformation of coordinates. The transformation method discussed in this thesis preserves the orthogonality of the basis functions and provides simple expressions for the construction of discretized matrix operators. The convergence rate can be improved by several times in the evaluation of loosely bound eigenstates with an exponential or hyperbolic sine transformation. The transformation can be defined explicitly or implicitly. An explicit transformation is based on a predefined mapping function, while an implicit transformation is constructed by an appropriate set of grid points determined by the behaviour of the solution. The methodologies of these transformations are discussed with some applications to 1D and 2D problems. The implicit transformation is also used as a moving mesh method for the time-dependent Smoluchowski equation when a function with localized behaviour is used as the initial condition.
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Coughtrie, David James. "Gaussian wave packets for quantum statistical mechanics." Thesis, University of Bristol, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.682558.

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Thermal (canonical) condensed-phase systems are of considerable interest in computational science, and include for example reactions in solution. Time-independent properties of these systems include free energies and thermally averaged geometries - time-dependent properties include correlation functions and thermal reaction rates. Accounting for quantum effects in such simulations remains a considerable challenge, especially for large systems, due to the quantum nature and high dimensionality of the phase space. Additionally time-dependent properties require treatment of quantum dynamics. Most current methods rely on semi-classical trajectories, path integrals or imaginary-time propagation of wave packets. Trajectory based approaches use continuous phase-space trajectories, similar to classical molecular dynamics, but lack a direct link to a wave packet and so the time-dependent schrodinger equation. Imaginary time propagation methods retain the wave packet, however the imaginary-time trajectory cannot be used as an approximation for real-time dynamics. We present a new approach that combines aspects of both. Using a generalisation of the coherent-state basis allows for mapping of the quantum canonical statistical average onto a phase-space average of the centre and width of thawed Gaussian wave packets. An approximate phase-space density that is exact in the low-temperature harmonic limit, and is a direct function of the phase space is proposed, defining the Gaussian statistical average. A novel Nose-Hoover looped chain thermostat is developed to generate the Gaussian statistical average via the ergodic principle, in conjunction with variational thawed Gaussian wave-packet dynamics. Numerical tests are performed on simple model systems, including quartic bond stretching modes and a double well potential. The Gaussian statistical average is found to be accurate to around 10% for geometric properties at room temperature, but gives energies two to three times too large. An approach to correct the Gaussian statistical average and ensure classical statistics is retrieved at high temperature is then derived, called the switched statistical average. This involves transitioning the potential surface upon which the Gaussian wave packet propagates, and the system property being averaged. Switching functions designed to perform these tasks are derived and tested on model systems. Bond lengths and their uncertainties calculated using the switched statistical average were found to be accurate to within 1% relative to exact results, and similarly for energies. The switched statistical average, calculated with Nose- Hoover looped chain thermostatted Gaussian dynamics, forms a new platform for evaluating statistical properties of quantum condensed-phase systems using an explicit real-time wave packet, whilst retaining appealing features of trajectory based approaches.
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Catarino, Nuno Ricardo. "Quantum statistical mechanics of generalised Frenkel-Kontorova models." Thesis, University of Warwick, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.412848.

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鄒鳳嬌 and Fung-kiu Chow. "Quantum statistical mechanics: a Monte Carlo study of clusters." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31224258.

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Books on the topic "Quantum trajectories, Quantum mechanics, statistical mechanics"

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A, Ranfagni, ed. Trajectories and rays: The path-summation in quantum mechanics and optics. Singapore: World Scientific, 1990.

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Schieve, W. C. Quantum statistical mechanics: Perspectives. Cambridge, N.Y: Cambridge University Press, 2009.

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Schieve, W. C. Quantum statistical mechanics: Perspectives. Cambridge, N.Y: Cambridge University Press, 2009.

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Quantum trajectories. Boca Raton: CRC Press, 2010.

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Bogoli︠u︡bov, N. N. (Nikolaĭ Nikolaevich), ed. Introduction to quantum statistical mechanics. 2nd ed. Hackensack, NJ: World Scientific, 2010.

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Schwabl, Franz. Statistical Mechanics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002.

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Bratteli, Ola. Operator algebras and quantum statistical mechanics 2: Equilibrium states. Models in quantum statistical mechanics. 2nd ed. Berlin: Springer-Verlag, 1997.

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Bratteli, Ola. Operator algebras and quantum statistical mechanics 2: Equilibrium states : models in quantum statistical mechanics. 2nd ed. Berlin: Springer, 1997.

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Irreversibilities in quantum mechanics. Dordrecht: Kluwer Academic, 2000.

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Kon, Mark A. Probability Distributions in Quantum Statistical Mechanics. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0077154.

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Book chapters on the topic "Quantum trajectories, Quantum mechanics, statistical mechanics"

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Dorlas, Teunis C. "Quantum Mechanics." In Statistical Mechanics, 107–18. 2nd ed. Second edition. | Boca Raton : CRC Press, 2021.: CRC Press, 2021. http://dx.doi.org/10.1201/9781003037170-22.

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Berlinsky, A. J., and A. B. Harris. "Quantum Fluids." In Statistical Mechanics, 263–94. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28187-8_11.

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Dorlas, Teunis C. "Quantum Gases." In Statistical Mechanics, 145–52. 2nd ed. Second edition. | Boca Raton : CRC Press, 2021.: CRC Press, 2021. http://dx.doi.org/10.1201/9781003037170-27.

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Schwabl, Franz. "Ideal Quantum Gases." In Statistical Mechanics, 165–220. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04702-6_4.

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Phillies, George D. J. "Quantum Mechanics." In Elementary Lectures in Statistical Mechanics, 169–79. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1264-5_15.

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Glimm, James, and Arthur Jaffe. "Classical Statistical Mechanics." In Quantum Physics, 28–42. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4612-4728-9_2.

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Dürr, Detlef, and Dustin Lazarovici. "Weak Measurements of Trajectories." In Understanding Quantum Mechanics, 149–60. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-40068-2_8.

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Grandy, Walter T. "Quantum Statistical Mechanics." In Foundations of Statistical Mechanics, 84–123. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-3867-0_4.

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Cini, Michele. "Quantum Statistical Mechanics." In UNITEXT for Physics, 351–72. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-71330-4_25.

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Banks, Thomas. "Quantum Statistical Mechanics." In Quantum Mechanics: An Introduction, 261–79. Boca Raton: CRC Press, Taylor & Francis Group, 2018.: CRC Press, 2018. http://dx.doi.org/10.1201/9780429438424-12.

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Conference papers on the topic "Quantum trajectories, Quantum mechanics, statistical mechanics"

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REBOLLEDO, ROLANDO. "OPEN QUANTUM SYSTEMS AND CLASSICAL TRAJECTORIES." In Proceedings of the Mathematical Legacy of R P Feynman & Proceedings of the Open Systems and Quantum Statistical Mechanics. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702364_0007.

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He, Qin, Rubin Wang, and Xiaochuan Pan. "This paper presents a two-dimensional histogram shifting technique for reversible data hiding algorithm. In order to avoid the distortion drift caused by hiding data into stereo H.264 video, we choose arbitrary embeddable blocks from 4×4 quantized discrete cosine transform luminance blocks which will not affect their adjacent blocks. Two coefficients in each embeddable block are chosen as a hiding coefficient pair. The selected coefficient pairs are classified into different sets on the basis of their values. Data could be hidden according to the set which the value of the coefficient pair belongs to. When the value of one coefficient may be changed by adding or subtracting 1, two data bits could be hidden by using the proposed method, whereas only one data bit could be embedded by employing the conventional histogram shifting. Experiments show that this two-dimensional histogram shifting method can be used to improve the hiding performance." In 10th International Conference on Software Engineering and Applications (SEAS 2021). AIRCC Publishing Corporation, 2021. http://dx.doi.org/10.5121/csit.2021.110205.

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Arc, one virus-like gene, crucial for learning and memory, was dis-covered by researchers in neurological disorders fields, Arc mRNA’s single directed path and allowing protein binding regional restric-tively is a potential investigation on helping shuttle toxic proteins responsible for some diseases related to memory deficiency. Mean time to switching (MTS) is calculated explicitly quantifying the switching process in statistical methods combining Hamiltonian Markov Chain(HMC). The model derived from predator and prey with typeII functional response studies the mechanism of normals with intrin-sic rate of increase and the persisters with the instantaneous discovery rate and converting coefficients. During solving the results, since the numeric method is applied for the 2D approximation of Hamiltonion with intrinsic noise induced switching combining geometric minimum action method. In the application of Hamiltonian Markov Chain, the behavior of the convertion (between mRNA and proteins through 6 states from off to on ) is described with probabilistic conditional logic formula and the final concentration is computed with both Continuous and Discret Time Markov Chain(CTMC/DTMC) through Embedding and Switching Diffusion. The MTS, trajectories and Hamiltonian dynamics demonstrate the practical and robust advantages of our model on interpreting the switching process of genes (IGFs, Hax Arcs and etc.) with respects to memory deficiency in aging process which can be useful in further drug efficiency test and disease curing. Coincidentally, the Hamiltonian is also well used in describing quantum mechanics and convenient for computation with time and position information using quantum bits while in the second model we construct, switching between excitatory and inhibitory neurons, similarity of qubit and neuron is an interesting object as well. Especially with the interactions operated with phase gates, the excitation from the ground state to excitation state is a well analogue to the neuron excitation. Not only on theoretical aspect, the experimental methods in neuron switching model is also inspiring to quantum computing. Most basic one is as stimulate hippocampus can be identical to spontaneous neural excitation(|g>|e>), pi-pulse is utilized to drive the ground state to the higher state. There thus exists prosperous potential to study the transfer between states with our switch models both classical and quantum computationally.
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McHarris, Wm C. "Quantum Mechanics, Nonlinear Dynamics, and Correlated Statistical Mechanics." In FOUNDATIONS OF PROBABILITY AND PHYSICS - 4. AIP, 2007. http://dx.doi.org/10.1063/1.2713481.

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Martynov, Georgy A. "The Statistical Mechanics and Entropy." In QUANTUM LIMITS TO THE SECOND LAW: First International Conference on Quantum Limits to the Second Law. AIP, 2002. http://dx.doi.org/10.1063/1.1523794.

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Curtright, Thomas, Luca Mezincescu, and Rafael Nepomechie. "Quantum Field Theory, Statistical Mechanics,Quantum Groups, and Topology." In NATO Advanced Research Workshop. WORLD SCIENTIFIC, 1992. http://dx.doi.org/10.1142/9789814537605.

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Man’Ko, V. I. "Tomography approach in quantum mechanics and in classical statistical mechanics." In The twentieth international workshop on bayesian inference and maximum entropy methods in science and engineering. AIP, 2001. http://dx.doi.org/10.1063/1.1381906.

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Khrennikov, Andrei. "Quantum Mechanics as an Asymptotic Projection of Statistical Mechanics of Classical Fields." In QUANTUM THEORY: Reconsideration of Foundations - 3. AIP, 2006. http://dx.doi.org/10.1063/1.2158721.

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SULAIMAN, A., F. P. ZEN, H. ALATAS, and L. T. HANDOKO. "STATISTICAL MECHANICS OF DAVYDOV-SCOTT'S PROTEIN MODEL IN THERMAL BATH." In Quantum Mechanics, Elementary Particles, Quantum Cosmology and Complexity. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814335614_0072.

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CATARINO, NUNO R., and ROBERT S. MACKAY. "QUANTUM STATISTICAL MECHANICS OF FRENKEL-KONTOROVA MODELS." In Proceedings of the Third Conference. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704627_0034.

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KHRENNIKOV, ANDREI. "TO QUANTUM MECHANICS THROUGH PROJECTION OF CLASSICAL STATISTICAL MECHANICS ON PRESPACE." In Proceedings of the ZiF Interdisciplinary Research Workshop. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701596_0021.

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