State-dependent diffusion in a bistable potential: Conditional probabilities and escape rates

Detalhes bibliográficos
Autor(a) principal: Moreno, Miguel V. [UNESP]
Data de Publicação: 2020
Outros Autores: Barci, Daniel G., Arenas, Zochil González
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1103/PhysRevE.101.062110
http://hdl.handle.net/11449/228823
Resumo: We consider a simple model of a bistable system under the influence of multiplicative noise. We provide a path integral representation of the overdamped Langevin dynamics and compute conditional probabilities and escape rates in the weak noise approximation. The saddle-point solution of the functional integral is given by a diluted gas of instantons and anti-instantons, similar to the additive noise problem. However, in this case, the integration over fluctuations is more involved. We introduce a local time reparametrization that allows its computation in the form of usual Gaussian integrals. We found corrections to the Kramers escape rate produced by the diffusion function which governs the state-dependent diffusion for arbitrary values of the stochastic prescription parameter. Theoretical results are confirmed through numerical simulations.
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spelling State-dependent diffusion in a bistable potential: Conditional probabilities and escape ratesWe consider a simple model of a bistable system under the influence of multiplicative noise. We provide a path integral representation of the overdamped Langevin dynamics and compute conditional probabilities and escape rates in the weak noise approximation. The saddle-point solution of the functional integral is given by a diluted gas of instantons and anti-instantons, similar to the additive noise problem. However, in this case, the integration over fluctuations is more involved. We introduce a local time reparametrization that allows its computation in the form of usual Gaussian integrals. We found corrections to the Kramers escape rate produced by the diffusion function which governs the state-dependent diffusion for arbitrary values of the stochastic prescription parameter. Theoretical results are confirmed through numerical simulations.Instituto de de Física Teórica Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271Departamento de Física Teórica Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524Departamento de Matemática Aplicada IME Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524Instituto de de Física Teórica Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271Universidade Estadual Paulista (UNESP)Universidade do Estado do Rio de Janeiro (UERJ)Moreno, Miguel V. [UNESP]Barci, Daniel G.Arenas, Zochil González2022-04-29T08:28:54Z2022-04-29T08:28:54Z2020-06-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevE.101.062110Physical Review E, v. 101, n. 6, 2020.2470-00532470-0045http://hdl.handle.net/11449/22882310.1103/PhysRevE.101.0621102-s2.0-85088351752Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review Einfo:eu-repo/semantics/openAccess2022-04-29T08:28:54Zoai:repositorio.unesp.br:11449/228823Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462022-04-29T08:28:54Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv State-dependent diffusion in a bistable potential: Conditional probabilities and escape rates
title State-dependent diffusion in a bistable potential: Conditional probabilities and escape rates
spellingShingle State-dependent diffusion in a bistable potential: Conditional probabilities and escape rates
Moreno, Miguel V. [UNESP]
title_short State-dependent diffusion in a bistable potential: Conditional probabilities and escape rates
title_full State-dependent diffusion in a bistable potential: Conditional probabilities and escape rates
title_fullStr State-dependent diffusion in a bistable potential: Conditional probabilities and escape rates
title_full_unstemmed State-dependent diffusion in a bistable potential: Conditional probabilities and escape rates
title_sort State-dependent diffusion in a bistable potential: Conditional probabilities and escape rates
author Moreno, Miguel V. [UNESP]
author_facet Moreno, Miguel V. [UNESP]
Barci, Daniel G.
Arenas, Zochil González
author_role author
author2 Barci, Daniel G.
Arenas, Zochil González
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
Universidade do Estado do Rio de Janeiro (UERJ)
dc.contributor.author.fl_str_mv Moreno, Miguel V. [UNESP]
Barci, Daniel G.
Arenas, Zochil González
description We consider a simple model of a bistable system under the influence of multiplicative noise. We provide a path integral representation of the overdamped Langevin dynamics and compute conditional probabilities and escape rates in the weak noise approximation. The saddle-point solution of the functional integral is given by a diluted gas of instantons and anti-instantons, similar to the additive noise problem. However, in this case, the integration over fluctuations is more involved. We introduce a local time reparametrization that allows its computation in the form of usual Gaussian integrals. We found corrections to the Kramers escape rate produced by the diffusion function which governs the state-dependent diffusion for arbitrary values of the stochastic prescription parameter. Theoretical results are confirmed through numerical simulations.
publishDate 2020
dc.date.none.fl_str_mv 2020-06-01
2022-04-29T08:28:54Z
2022-04-29T08:28:54Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1103/PhysRevE.101.062110
Physical Review E, v. 101, n. 6, 2020.
2470-0053
2470-0045
http://hdl.handle.net/11449/228823
10.1103/PhysRevE.101.062110
2-s2.0-85088351752
url http://dx.doi.org/10.1103/PhysRevE.101.062110
http://hdl.handle.net/11449/228823
identifier_str_mv Physical Review E, v. 101, n. 6, 2020.
2470-0053
2470-0045
10.1103/PhysRevE.101.062110
2-s2.0-85088351752
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Physical Review E
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
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