Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effects

We revisit the problem of Brownian diffusion with drift in order to study finite-size effects in the geometric Galton-Watson branching process. This is possible because of an exact mapping between one-dimensional random walks and geometric branching processes, known as the Harris walk. In this way,...

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Autores: Corral, Á., Garcia-Millan, R., Moloney, N.R., Font-Clos, F.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/446117
Acceso en línea:http://hdl.handle.net/2072/446117
Access Level:acceso abierto
Palabra clave:51
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spelling Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effectsCorral, Á.Garcia-Millan, R.Moloney, N.R.Font-Clos, F.51We revisit the problem of Brownian diffusion with drift in order to study finite-size effects in the geometric Galton-Watson branching process. This is possible because of an exact mapping between one-dimensional random walks and geometric branching processes, known as the Harris walk. In this way, first-passage times of Brownian particles are equivalent to sizes of trees in the branching process (up to a factor of proportionality). Brownian particles that reach a distant reflecting boundary correspond to percolating trees, and those that do not correspond to nonpercolating trees. In fact, both systems display a second-order phase transition between conducting and insulating phases, controlled by the drift velocity in the Brownian system. In the limit of large system size, we obtain exact expressions for the Laplace transforms of the probability distributions and their first and second moments. These quantities are also shown to obey finite-size scaling laws. © 2018 American Physical Society.American Physical Society2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion11 p.application/pdfhttp://hdl.handle.net/2072/446117RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)Inglésinfo:eu-repo/semantics/openAccessoai:recercat.cat:2072/4461172026-05-29T05:05:01Z
dc.title.none.fl_str_mv Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effects
title Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effects
spellingShingle Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effects
Corral, Á.
51
title_short Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effects
title_full Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effects
title_fullStr Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effects
title_full_unstemmed Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effects
title_sort Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effects
dc.creator.none.fl_str_mv Corral, Á.
Garcia-Millan, R.
Moloney, N.R.
Font-Clos, F.
author Corral, Á.
author_facet Corral, Á.
Garcia-Millan, R.
Moloney, N.R.
Font-Clos, F.
author_role author
author2 Garcia-Millan, R.
Moloney, N.R.
Font-Clos, F.
author2_role author
author
author
dc.subject.none.fl_str_mv 51
topic 51
description We revisit the problem of Brownian diffusion with drift in order to study finite-size effects in the geometric Galton-Watson branching process. This is possible because of an exact mapping between one-dimensional random walks and geometric branching processes, known as the Harris walk. In this way, first-passage times of Brownian particles are equivalent to sizes of trees in the branching process (up to a factor of proportionality). Brownian particles that reach a distant reflecting boundary correspond to percolating trees, and those that do not correspond to nonpercolating trees. In fact, both systems display a second-order phase transition between conducting and insulating phases, controlled by the drift velocity in the Brownian system. In the limit of large system size, we obtain exact expressions for the Laplace transforms of the probability distributions and their first and second moments. These quantities are also shown to obey finite-size scaling laws. © 2018 American Physical Society.
publishDate 2018
dc.date.none.fl_str_mv 2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/2072/446117
url http://hdl.handle.net/2072/446117
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 11 p.
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 RECERCAT (Dipòsit de la Recerca de Catalunya)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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