Inhomogeneous diffusion and ergodicity breaking induced by global memory effects

Autores
Budini, Adrian Adolfo
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previoushistory of the walker, being defined by an urn-like memory mechanism. The characteristic function is calculated in an exact way, which allows us todemonstrate that the ensemble of realizations is ballistic. Asymptoticallyeach realization is equivalent to that of a biased Markovian diffusion process with transition rates that strongly differs from one trajectory to another. Using this "inhomogeneous diffusion" feature the ergodic properties of the dynamics are analytically studied through the time-averaged moments. Even in the long time regime they remain random objects. While their average over realizations recover the corresponding ensemble averages, departure between time and ensemble averages is explicitly shown through their probability densities. For the density of the second time-averaged moment an ergodic limit and the limit of infinite lag times do not commutate. All these effects are induced by the memory effects. A generalized Einstein fluctuation-dissipation relation is also obtained for the time-averaged moments.
Fil: Budini, Adrian Adolfo. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigaciones y Aplicaciones no Nucleares. Gerencia de Física (Centro Atómico Constituyentes); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
Materia
Sistemas No-Ergodicos
Super-Difusion
Relation de Einstein
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/74374
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/74374
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network_name_str CONICET Digital (CONICET)
spelling Inhomogeneous diffusion and ergodicity breaking induced by global memory effectsBudini, Adrian AdolfoSistemas No-ErgodicosSuper-DifusionRelation de Einsteinhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previoushistory of the walker, being defined by an urn-like memory mechanism. The characteristic function is calculated in an exact way, which allows us todemonstrate that the ensemble of realizations is ballistic. Asymptoticallyeach realization is equivalent to that of a biased Markovian diffusion process with transition rates that strongly differs from one trajectory to another. Using this "inhomogeneous diffusion" feature the ergodic properties of the dynamics are analytically studied through the time-averaged moments. Even in the long time regime they remain random objects. While their average over realizations recover the corresponding ensemble averages, departure between time and ensemble averages is explicitly shown through their probability densities. For the density of the second time-averaged moment an ergodic limit and the limit of infinite lag times do not commutate. All these effects are induced by the memory effects. A generalized Einstein fluctuation-dissipation relation is also obtained for the time-averaged moments.Fil: Budini, Adrian Adolfo. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigaciones y Aplicaciones no Nucleares. Gerencia de Física (Centro Atómico Constituyentes); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaAmerican Physical Society2016-11-28info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/74374Budini, Adrian Adolfo; Inhomogeneous diffusion and ergodicity breaking induced by global memory effects; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 94; 28-11-2016; 52142-1/101539-3755CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.94.052142info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.052142info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:46:07Zoai:ri.conicet.gov.ar:11336/74374instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:46:07.319CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Inhomogeneous diffusion and ergodicity breaking induced by global memory effects
title Inhomogeneous diffusion and ergodicity breaking induced by global memory effects
spellingShingle Inhomogeneous diffusion and ergodicity breaking induced by global memory effects
Budini, Adrian Adolfo
Sistemas No-Ergodicos
Super-Difusion
Relation de Einstein
title_short Inhomogeneous diffusion and ergodicity breaking induced by global memory effects
title_full Inhomogeneous diffusion and ergodicity breaking induced by global memory effects
title_fullStr Inhomogeneous diffusion and ergodicity breaking induced by global memory effects
title_full_unstemmed Inhomogeneous diffusion and ergodicity breaking induced by global memory effects
title_sort Inhomogeneous diffusion and ergodicity breaking induced by global memory effects
dc.creator.none.fl_str_mv Budini, Adrian Adolfo
author Budini, Adrian Adolfo
author_facet Budini, Adrian Adolfo
author_role author
dc.subject.none.fl_str_mv Sistemas No-Ergodicos
Super-Difusion
Relation de Einstein
topic Sistemas No-Ergodicos
Super-Difusion
Relation de Einstein
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previoushistory of the walker, being defined by an urn-like memory mechanism. The characteristic function is calculated in an exact way, which allows us todemonstrate that the ensemble of realizations is ballistic. Asymptoticallyeach realization is equivalent to that of a biased Markovian diffusion process with transition rates that strongly differs from one trajectory to another. Using this "inhomogeneous diffusion" feature the ergodic properties of the dynamics are analytically studied through the time-averaged moments. Even in the long time regime they remain random objects. While their average over realizations recover the corresponding ensemble averages, departure between time and ensemble averages is explicitly shown through their probability densities. For the density of the second time-averaged moment an ergodic limit and the limit of infinite lag times do not commutate. All these effects are induced by the memory effects. A generalized Einstein fluctuation-dissipation relation is also obtained for the time-averaged moments.
Fil: Budini, Adrian Adolfo. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigaciones y Aplicaciones no Nucleares. Gerencia de Física (Centro Atómico Constituyentes); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
description We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previoushistory of the walker, being defined by an urn-like memory mechanism. The characteristic function is calculated in an exact way, which allows us todemonstrate that the ensemble of realizations is ballistic. Asymptoticallyeach realization is equivalent to that of a biased Markovian diffusion process with transition rates that strongly differs from one trajectory to another. Using this "inhomogeneous diffusion" feature the ergodic properties of the dynamics are analytically studied through the time-averaged moments. Even in the long time regime they remain random objects. While their average over realizations recover the corresponding ensemble averages, departure between time and ensemble averages is explicitly shown through their probability densities. For the density of the second time-averaged moment an ergodic limit and the limit of infinite lag times do not commutate. All these effects are induced by the memory effects. A generalized Einstein fluctuation-dissipation relation is also obtained for the time-averaged moments.
publishDate 2016
dc.date.none.fl_str_mv 2016-11-28
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/74374
Budini, Adrian Adolfo; Inhomogeneous diffusion and ergodicity breaking induced by global memory effects; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 94; 28-11-2016; 52142-1/10
1539-3755
CONICET Digital
CONICET
url http://hdl.handle.net/11336/74374
identifier_str_mv Budini, Adrian Adolfo; Inhomogeneous diffusion and ergodicity breaking induced by global memory effects; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 94; 28-11-2016; 52142-1/10
1539-3755
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.94.052142
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.052142
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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