The Weyl law for contractive maps

Autores
Spina, Maria Elena; Rivas, Alejandro Mariano Fidel; Carlo, Gabriel Gustavo
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We find an empirical Weyl law followed by the eigenvalues of contractive maps. An important property is that it is mainly insensitive to the dimension of the corresponding invariant classical set, the strange attractor. The usual explanation for the fractal Weyl law emergence in scattering systems (i.e., having a projective opening) is based on the classical phase space distributions evolved up to the quantum to classical correspondence (Ehrenfest) time. In the contractive case this reasoning fails to describe it. Instead, we conjecture that the support for this behavior is essentially given by the strong non-orthogonality of the eigenvectors of the contractive superoperator. We test the validity of the Weyl law and this conjecture on two paradigmatic systems, the dissipative baker and kicked top maps.
Fil: Spina, Maria Elena. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes. Departamento de Física; Argentina
Fil: Rivas, Alejandro Mariano Fidel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes. Departamento de Física; Argentina
Fil: Carlo, Gabriel Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes. Departamento de Física; Argentina
Materia
Quantum Maps
Quantum Dissipation
Weyl Law
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:11336/26597
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The Weyl law for contractive mapsSpina, Maria ElenaRivas, Alejandro Mariano FidelCarlo, Gabriel GustavoQuantum MapsQuantum DissipationWeyl Lawhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We find an empirical Weyl law followed by the eigenvalues of contractive maps. An important property is that it is mainly insensitive to the dimension of the corresponding invariant classical set, the strange attractor. The usual explanation for the fractal Weyl law emergence in scattering systems (i.e., having a projective opening) is based on the classical phase space distributions evolved up to the quantum to classical correspondence (Ehrenfest) time. In the contractive case this reasoning fails to describe it. Instead, we conjecture that the support for this behavior is essentially given by the strong non-orthogonality of the eigenvectors of the contractive superoperator. We test the validity of the Weyl law and this conjecture on two paradigmatic systems, the dissipative baker and kicked top maps.Fil: Spina, Maria Elena. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes. Departamento de Física; ArgentinaFil: Rivas, Alejandro Mariano Fidel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes. Departamento de Física; ArgentinaFil: Carlo, Gabriel Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes. Departamento de Física; ArgentinaIOP Publishing2013-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/26597Spina, Maria Elena; Rivas, Alejandro Mariano Fidel; Carlo, Gabriel Gustavo; The Weyl law for contractive maps; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 46; 11-2013; 475101-4751131751-81131751-8121CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/1751-8113/46/47/475101info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/46/47/475101info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1303.3462info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:05:44Zoai:ri.conicet.gov.ar:11336/26597instacron: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:34982025-09-10 13:05:45.045CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Weyl law for contractive maps
title The Weyl law for contractive maps
spellingShingle The Weyl law for contractive maps
Spina, Maria Elena
Quantum Maps
Quantum Dissipation
Weyl Law
title_short The Weyl law for contractive maps
title_full The Weyl law for contractive maps
title_fullStr The Weyl law for contractive maps
title_full_unstemmed The Weyl law for contractive maps
title_sort The Weyl law for contractive maps
dc.creator.none.fl_str_mv Spina, Maria Elena
Rivas, Alejandro Mariano Fidel
Carlo, Gabriel Gustavo
author Spina, Maria Elena
author_facet Spina, Maria Elena
Rivas, Alejandro Mariano Fidel
Carlo, Gabriel Gustavo
author_role author
author2 Rivas, Alejandro Mariano Fidel
Carlo, Gabriel Gustavo
author2_role author
author
dc.subject.none.fl_str_mv Quantum Maps
Quantum Dissipation
Weyl Law
topic Quantum Maps
Quantum Dissipation
Weyl Law
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 find an empirical Weyl law followed by the eigenvalues of contractive maps. An important property is that it is mainly insensitive to the dimension of the corresponding invariant classical set, the strange attractor. The usual explanation for the fractal Weyl law emergence in scattering systems (i.e., having a projective opening) is based on the classical phase space distributions evolved up to the quantum to classical correspondence (Ehrenfest) time. In the contractive case this reasoning fails to describe it. Instead, we conjecture that the support for this behavior is essentially given by the strong non-orthogonality of the eigenvectors of the contractive superoperator. We test the validity of the Weyl law and this conjecture on two paradigmatic systems, the dissipative baker and kicked top maps.
Fil: Spina, Maria Elena. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes. Departamento de Física; Argentina
Fil: Rivas, Alejandro Mariano Fidel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes. Departamento de Física; Argentina
Fil: Carlo, Gabriel Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes. Departamento de Física; Argentina
description We find an empirical Weyl law followed by the eigenvalues of contractive maps. An important property is that it is mainly insensitive to the dimension of the corresponding invariant classical set, the strange attractor. The usual explanation for the fractal Weyl law emergence in scattering systems (i.e., having a projective opening) is based on the classical phase space distributions evolved up to the quantum to classical correspondence (Ehrenfest) time. In the contractive case this reasoning fails to describe it. Instead, we conjecture that the support for this behavior is essentially given by the strong non-orthogonality of the eigenvectors of the contractive superoperator. We test the validity of the Weyl law and this conjecture on two paradigmatic systems, the dissipative baker and kicked top maps.
publishDate 2013
dc.date.none.fl_str_mv 2013-11
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/11336/26597
Spina, Maria Elena; Rivas, Alejandro Mariano Fidel; Carlo, Gabriel Gustavo; The Weyl law for contractive maps; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 46; 11-2013; 475101-475113
1751-8113
1751-8121
CONICET Digital
CONICET
url http://hdl.handle.net/11336/26597
identifier_str_mv Spina, Maria Elena; Rivas, Alejandro Mariano Fidel; Carlo, Gabriel Gustavo; The Weyl law for contractive maps; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 46; 11-2013; 475101-475113
1751-8113
1751-8121
CONICET Digital
CONICET
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/10.1088/1751-8113/46/47/475101
info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/46/47/475101
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1303.3462
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
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
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score 12.993085

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