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dc.contributor.authorAlonso, J. L.
dc.contributor.authorCastro, Alberto
dc.contributor.authorClemente-Gallardo, Jesús
dc.contributor.authorCuchí Oterino, J. C.
dc.contributor.authorEchenique, Pablo
dc.contributor.authorFalceto, Fernando
dc.date.accessioned2016-09-13T09:24:02Z
dc.date.available2016-09-13T09:24:02Z
dc.date.issued2011
dc.identifier.issn1751-8113
dc.identifier.urihttp://hdl.handle.net/10459.1/57789
dc.description.abstractQuantum dynamics (e.g., the Schrödinger equation) and classical dynamics (e.g., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. The difference between both worlds is due to the presence of extra structure in the quantum case, that leads to the appearance of the probabilistic nature of the measurements and the indetermination and superposition principles. In this paper we first show that the quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann's distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. This work provides the basis for extending stochastic methods to Ehrenfest dynamics.ca_ES
dc.description.sponsorshipThis work has been supported by the research projects E24/1 and E24/3 (DGA, Spain), FIS2009-13364-C02-01 (MICINN, Spain), 200980I064 (CSIC, Spain) and ARAID and Ibercaja grant for young researchers (Spain).ca_ES
dc.language.isoengca_ES
dc.publisherIOP Publishingca_ES
dc.relationMICINN/PN2008-2011/ FIS2009-13364-C02-01ca_ES
dc.relation.isformatofVersió preprint del document publicat a https://doi.org/10.1088/1751-8113/44/39/395004ca_ES
dc.relation.ispartofJournal of Physics A: Mathematical and Theoretical, 2011, vol. 44:395004ca_ES
dc.relation.urihttps://arxiv.org/abs/1010.1494v1
dc.rights(c) IOP Publishing, 2011ca_ES
dc.subjectGeometric quantum mechanicsca_ES
dc.subjectNoséca_ES
dc.subjectEhrenfestca_ES
dc.subjectStatistical mechanicsca_ES
dc.subjectEquilibriumca_ES
dc.titleStatistics and Nosé formalism for Ehrenfest dynamicsca_ES
dc.typearticleca_ES
dc.identifier.idgrec016993
dc.type.versionsubmittedVersionca_ES
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessca_ES
dc.identifier.doihttps://doi.org/10.1088/1751-8113/44/39/395004


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