Classical and quantum models in non-equilibrium statistical mechanics: moment methods and long-time approximations

We consider non-equilibrium open statistical systems, subject to potentials and to external "heat baths" (hb) at thermal equilibrium at temperature T (either with ab initio dissipation or without it). Boltzmann's classical equilibrium distributions generate, as Gaussian weight functio...

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Detalles Bibliográficos
Autor: Fernández Álvarez-Estrada, Ramón
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/44817
Acceso en línea:https://hdl.handle.net/20.500.14352/44817
Access Level:acceso abierto
Palabra clave:53
Brownian-motion
Dynamical semigroups
Irreversibility
Lionville
Particle
Equation
Systems
Field
Física (Física)
22 Física
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spelling Classical and quantum models in non-equilibrium statistical mechanics: moment methods and long-time approximationsFernández Álvarez-Estrada, Ramón53Brownian-motionDynamical semigroupsIrreversibilityLionvilleParticleEquationSystemsFieldFísica (Física)22 FísicaWe consider non-equilibrium open statistical systems, subject to potentials and to external "heat baths" (hb) at thermal equilibrium at temperature T (either with ab initio dissipation or without it). Boltzmann's classical equilibrium distributions generate, as Gaussian weight functions in momenta, orthogonal polynomials in momenta (the position-independent Hermite polynomials H_n's). The moments of non-equilibrium classical distributions, implied by the H_n's, fulfill a hierarchy: for long times, the lowest moment dominates the evolution towards thermal equilibrium, either with dissipation or without it (but under certain approximation). We revisit that hierarchy, whose solution depends on operator continued fractions. We review our generalization of that moment method to classical closed many-particle interacting systems with neither a hb nor ab initio dissipation: with initial states describing thermal equilibrium at T at large distances but non-equilibrium at finite distances, the moment method yields, approximately, irreversible thermalization of the whole system at T, for long times. Generalizations to non-equilibrium quantum interacting systems meet additional difficulties. Three of them are: (i) equilibrium distributions (represented through Wigner functions) are neither Gaussian in momenta nor known in closed form; (ii) they may depend on dissipation; and (iii) the orthogonal polynomials in momenta generated by them depend also on positions. We generalize the moment method, dealing with (i), (ii) and (iii), to some non-equilibrium one-particle quantum interacting systems. Open problems are discussed briefly.Multidisciplinary Digital Publishing InstituteUniversidad Complutense de Madrid20122012-02-0120122012-02-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/44817reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/448172026-06-02T12:44:21Z
dc.title.none.fl_str_mv Classical and quantum models in non-equilibrium statistical mechanics: moment methods and long-time approximations
title Classical and quantum models in non-equilibrium statistical mechanics: moment methods and long-time approximations
spellingShingle Classical and quantum models in non-equilibrium statistical mechanics: moment methods and long-time approximations
Fernández Álvarez-Estrada, Ramón
53
Brownian-motion
Dynamical semigroups
Irreversibility
Lionville
Particle
Equation
Systems
Field
Física (Física)
22 Física
title_short Classical and quantum models in non-equilibrium statistical mechanics: moment methods and long-time approximations
title_full Classical and quantum models in non-equilibrium statistical mechanics: moment methods and long-time approximations
title_fullStr Classical and quantum models in non-equilibrium statistical mechanics: moment methods and long-time approximations
title_full_unstemmed Classical and quantum models in non-equilibrium statistical mechanics: moment methods and long-time approximations
title_sort Classical and quantum models in non-equilibrium statistical mechanics: moment methods and long-time approximations
dc.creator.none.fl_str_mv Fernández Álvarez-Estrada, Ramón
author Fernández Álvarez-Estrada, Ramón
author_facet Fernández Álvarez-Estrada, Ramón
author_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 53
Brownian-motion
Dynamical semigroups
Irreversibility
Lionville
Particle
Equation
Systems
Field
Física (Física)
22 Física
topic 53
Brownian-motion
Dynamical semigroups
Irreversibility
Lionville
Particle
Equation
Systems
Field
Física (Física)
22 Física
description We consider non-equilibrium open statistical systems, subject to potentials and to external "heat baths" (hb) at thermal equilibrium at temperature T (either with ab initio dissipation or without it). Boltzmann's classical equilibrium distributions generate, as Gaussian weight functions in momenta, orthogonal polynomials in momenta (the position-independent Hermite polynomials H_n's). The moments of non-equilibrium classical distributions, implied by the H_n's, fulfill a hierarchy: for long times, the lowest moment dominates the evolution towards thermal equilibrium, either with dissipation or without it (but under certain approximation). We revisit that hierarchy, whose solution depends on operator continued fractions. We review our generalization of that moment method to classical closed many-particle interacting systems with neither a hb nor ab initio dissipation: with initial states describing thermal equilibrium at T at large distances but non-equilibrium at finite distances, the moment method yields, approximately, irreversible thermalization of the whole system at T, for long times. Generalizations to non-equilibrium quantum interacting systems meet additional difficulties. Three of them are: (i) equilibrium distributions (represented through Wigner functions) are neither Gaussian in momenta nor known in closed form; (ii) they may depend on dissipation; and (iii) the orthogonal polynomials in momenta generated by them depend also on positions. We generalize the moment method, dealing with (i), (ii) and (iii), to some non-equilibrium one-particle quantum interacting systems. Open problems are discussed briefly.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-02-01
2012
2012-02-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/44817
url https://hdl.handle.net/20.500.14352/44817
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute
publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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