Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation

This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker-Planck effects, and how it is drastically reduced to a s...

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Autores: Guerrero, Pilar|||0000-0002-5522-7339, López Fernández, José Luis, Montejo-Gámez, Jesús|||0000-0001-9461-6348, Nieto, Juanjo|||0000-0002-4303-1574
Tipo de recurso: artículo
Fecha de publicación:2011
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:181520
Acceso en línea:https://ddd.uab.cat/record/181520
Access Level:acceso abierto
Palabra clave:Equacions no lineals
Quàntums, Teoria dels
Logaritmes
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spelling Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipationGuerrero, Pilar|||0000-0002-5522-7339López Fernández, José LuisMontejo-Gámez, Jesús|||0000-0001-9461-6348Nieto, Juanjo|||0000-0002-4303-1574Equacions no linealsQuàntums, Teoria delsLogaritmesThis paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker-Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial-boundary value problem. This simplification requires the performance of the polar (modulus-argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.Centre de Recerca MatemàticaCentre de Recerca Matemàtica 22011-01-0120112011-01-01Articlehttp://purl.org/coar/resource_type/c_6501AOhttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/181520reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/3.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1815202026-06-06T12:50:31Z
dc.title.none.fl_str_mv Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation
title Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation
spellingShingle Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation
Guerrero, Pilar|||0000-0002-5522-7339
Equacions no lineals
Quàntums, Teoria dels
Logaritmes
title_short Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation
title_full Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation
title_fullStr Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation
title_full_unstemmed Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation
title_sort Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation
dc.creator.none.fl_str_mv Guerrero, Pilar|||0000-0002-5522-7339
López Fernández, José Luis
Montejo-Gámez, Jesús|||0000-0001-9461-6348
Nieto, Juanjo|||0000-0002-4303-1574
author Guerrero, Pilar|||0000-0002-5522-7339
author_facet Guerrero, Pilar|||0000-0002-5522-7339
López Fernández, José Luis
Montejo-Gámez, Jesús|||0000-0001-9461-6348
Nieto, Juanjo|||0000-0002-4303-1574
author_role author
author2 López Fernández, José Luis
Montejo-Gámez, Jesús|||0000-0001-9461-6348
Nieto, Juanjo|||0000-0002-4303-1574
author2_role author
author
author
dc.contributor.none.fl_str_mv Centre de Recerca Matemàtica
dc.subject.none.fl_str_mv Equacions no lineals
Quàntums, Teoria dels
Logaritmes
topic Equacions no lineals
Quàntums, Teoria dels
Logaritmes
description This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker-Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial-boundary value problem. This simplification requires the performance of the polar (modulus-argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.
publishDate 2011
dc.date.none.fl_str_mv 2
2011-01-01
2011
2011-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AO
http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/181520
url https://ddd.uab.cat/record/181520
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
https://creativecommons.org/licenses/by-nc-nd/3.0/
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
https://creativecommons.org/licenses/by-nc-nd/3.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Centre de Recerca Matemàtica
publisher.none.fl_str_mv Centre de Recerca Matemàtica
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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