Understanding the Lévy Ratchets in Terms of Lévy Jumps

Autores
Ibáñez, Santiago Agustín; Risau Gusman, Sebastian Luis; Bouzat, Sebastian
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We investigate the overdamped dynamics of a particle in a spatially periodic potential with broken reflection symmetry and subject to the action of a symmetric white Lévy noise. The system (referred to as the Lévy ratchet) has been previously studied using both Langevin and fractional Fokker–Planck formalisms, with the main find being the existence of a preferred direction of motion toward the steepest slope of the potential, producing a non-vanishing current. In this contribution we develop a semi-analytical study combining the Fokker–Planck and Langevin formalisms to explore the role of Lévy flights on the system dynamics. We analyze the departure positions of Lévy jumps that take the particle out of a potential well as well as the rates and lengths of such jumps, and we study the way in which long jumps determine the non-vanishing current. We also discuss the essential difference from the Gaussian-noise case (producing no current). Finally we study the current for different potential shapes as a function of the amplitude of the potential barrier. In particular, we show that standard Lévy ratchets produce a non-vanishing current in the infinite-barrier limit. This latter counterintuitive result can be easily understood in terms of the long Lévy jumps and analytically demonstrated.
Fil: Ibáñez, Santiago Agustín. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Risau Gusman, Sebastian Luis. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Bouzat, Sebastian. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Diffusion
Transport Processes
Stochastic Particle Dynamics
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:11336/9061
Acceder
id CONICETDig_da530d6b69f9e56960132e42f77b66d1
oai_identifier_str oai:ri.conicet.gov.ar:11336/9061
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Understanding the Lévy Ratchets in Terms of Lévy JumpsIbáñez, Santiago AgustínRisau Gusman, Sebastian LuisBouzat, SebastianDiffusionTransport ProcessesStochastic Particle Dynamicshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We investigate the overdamped dynamics of a particle in a spatially periodic potential with broken reflection symmetry and subject to the action of a symmetric white Lévy noise. The system (referred to as the Lévy ratchet) has been previously studied using both Langevin and fractional Fokker–Planck formalisms, with the main find being the existence of a preferred direction of motion toward the steepest slope of the potential, producing a non-vanishing current. In this contribution we develop a semi-analytical study combining the Fokker–Planck and Langevin formalisms to explore the role of Lévy flights on the system dynamics. We analyze the departure positions of Lévy jumps that take the particle out of a potential well as well as the rates and lengths of such jumps, and we study the way in which long jumps determine the non-vanishing current. We also discuss the essential difference from the Gaussian-noise case (producing no current). Finally we study the current for different potential shapes as a function of the amplitude of the potential barrier. In particular, we show that standard Lévy ratchets produce a non-vanishing current in the infinite-barrier limit. This latter counterintuitive result can be easily understood in terms of the long Lévy jumps and analytically demonstrated.Fil: Ibáñez, Santiago Agustín. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Risau Gusman, Sebastian Luis. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Bouzat, Sebastian. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaIop Publishing2013-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/9061Ibáñez, Santiago Agustín; Risau Gusman, Sebastian Luis; Bouzat, Sebastian; Understanding the Lévy Ratchets in Terms of Lévy Jumps; Iop Publishing; Journal Of Statistical Mechanics: Theory And Experiment; 2013; 2007; 2-2013; 1-191742-54681742-5468enginfo:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/1742-5468/2013/02/P02007/metainfo:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2013/02/P02007info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:08:44Zoai:ri.conicet.gov.ar:11336/9061instacron: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:34982025-10-15 15:08:45.206CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Understanding the Lévy Ratchets in Terms of Lévy Jumps
title Understanding the Lévy Ratchets in Terms of Lévy Jumps
spellingShingle Understanding the Lévy Ratchets in Terms of Lévy Jumps
Ibáñez, Santiago Agustín
Diffusion
Transport Processes
Stochastic Particle Dynamics
title_short Understanding the Lévy Ratchets in Terms of Lévy Jumps
title_full Understanding the Lévy Ratchets in Terms of Lévy Jumps
title_fullStr Understanding the Lévy Ratchets in Terms of Lévy Jumps
title_full_unstemmed Understanding the Lévy Ratchets in Terms of Lévy Jumps
title_sort Understanding the Lévy Ratchets in Terms of Lévy Jumps
dc.creator.none.fl_str_mv Ibáñez, Santiago Agustín
Risau Gusman, Sebastian Luis
Bouzat, Sebastian
author Ibáñez, Santiago Agustín
author_facet Ibáñez, Santiago Agustín
Risau Gusman, Sebastian Luis
Bouzat, Sebastian
author_role author
author2 Risau Gusman, Sebastian Luis
Bouzat, Sebastian
author2_role author
author
dc.subject.none.fl_str_mv Diffusion
Transport Processes
Stochastic Particle Dynamics
topic Diffusion
Transport Processes
Stochastic Particle Dynamics
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 investigate the overdamped dynamics of a particle in a spatially periodic potential with broken reflection symmetry and subject to the action of a symmetric white Lévy noise. The system (referred to as the Lévy ratchet) has been previously studied using both Langevin and fractional Fokker–Planck formalisms, with the main find being the existence of a preferred direction of motion toward the steepest slope of the potential, producing a non-vanishing current. In this contribution we develop a semi-analytical study combining the Fokker–Planck and Langevin formalisms to explore the role of Lévy flights on the system dynamics. We analyze the departure positions of Lévy jumps that take the particle out of a potential well as well as the rates and lengths of such jumps, and we study the way in which long jumps determine the non-vanishing current. We also discuss the essential difference from the Gaussian-noise case (producing no current). Finally we study the current for different potential shapes as a function of the amplitude of the potential barrier. In particular, we show that standard Lévy ratchets produce a non-vanishing current in the infinite-barrier limit. This latter counterintuitive result can be easily understood in terms of the long Lévy jumps and analytically demonstrated.
Fil: Ibáñez, Santiago Agustín. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Risau Gusman, Sebastian Luis. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Bouzat, Sebastian. Comision Nacional de Energia Atomica. Gerencia del Area de Investigaciones y Aplicaciones no Nucleares. Gerencia de Fisica (CAB); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We investigate the overdamped dynamics of a particle in a spatially periodic potential with broken reflection symmetry and subject to the action of a symmetric white Lévy noise. The system (referred to as the Lévy ratchet) has been previously studied using both Langevin and fractional Fokker–Planck formalisms, with the main find being the existence of a preferred direction of motion toward the steepest slope of the potential, producing a non-vanishing current. In this contribution we develop a semi-analytical study combining the Fokker–Planck and Langevin formalisms to explore the role of Lévy flights on the system dynamics. We analyze the departure positions of Lévy jumps that take the particle out of a potential well as well as the rates and lengths of such jumps, and we study the way in which long jumps determine the non-vanishing current. We also discuss the essential difference from the Gaussian-noise case (producing no current). Finally we study the current for different potential shapes as a function of the amplitude of the potential barrier. In particular, we show that standard Lévy ratchets produce a non-vanishing current in the infinite-barrier limit. This latter counterintuitive result can be easily understood in terms of the long Lévy jumps and analytically demonstrated.
publishDate 2013
dc.date.none.fl_str_mv 2013-02
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/11336/9061
Ibáñez, Santiago Agustín; Risau Gusman, Sebastian Luis; Bouzat, Sebastian; Understanding the Lévy Ratchets in Terms of Lévy Jumps; Iop Publishing; Journal Of Statistical Mechanics: Theory And Experiment; 2013; 2007; 2-2013; 1-19
1742-5468
1742-5468
url http://hdl.handle.net/11336/9061
identifier_str_mv Ibáñez, Santiago Agustín; Risau Gusman, Sebastian Luis; Bouzat, Sebastian; Understanding the Lévy Ratchets in Terms of Lévy Jumps; Iop Publishing; Journal Of Statistical Mechanics: Theory And Experiment; 2013; 2007; 2-2013; 1-19
1742-5468
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/1742-5468/2013/02/P02007/meta
info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2013/02/P02007
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 Iop Publishing
publisher.none.fl_str_mv Iop Publishing
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
_version_ 1846083234383790080
score 13.22299

Publicaciones similares