Semiclassical partition function for the double-well potential

Detalhes bibliográficos
Autor(a) principal: Fogaça, Daniel Kroff
Data de Publicação: 2014
Outros Autores: Moreira, André Bessa, Carvalho Filho, Carlos Alberto Aragão de, Fraga, Eduardo Souza, Jorás, Sergio Eduardo de Carvalho Eyer
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRN
Texto Completo: https://repositorio.ufrn.br/jspui/handle/123456789/29781
Resumo: We compute the partition function and specific heat for a quantum-mechanical particle under the influence of a quartic double-well potential nonperturbatively, using the semiclassical method. Near the region of bounded motion in the inverted potential, the usual quadratic approximation fails due to the existence of multiple classical solutions and caustics. Using the tools of catastrophe theory, we identify the relevant classical solutions, showing that at most two have to be considered. This corresponds to the first step towards the study of spontaneous symmetry breaking and thermal phase transitions in the nonperturbative framework of the boundary effective theory
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spelling Fogaça, Daniel KroffMoreira, André BessaCarvalho Filho, Carlos Alberto Aragão deFraga, Eduardo SouzaJorás, Sergio Eduardo de Carvalho Eyer2020-08-05T17:09:08Z2020-08-05T17:09:08Z2014-07-15KROFF, D.; BESSA, A.; CARVALHO, C. A. A. de; FRAGA, E. S.; JORÁS, S. E.. Semiclassical partition function for the double-well potential. Physical Review D, [s.l.], v. 90, n. 2, p. 1-8, 15 jul. 2014. Disponível em: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.90.025019. Acesso em: 04 ago. 2020. http://dx.doi.org/10.1103/physrevd.90.025019.2470-0029https://repositorio.ufrn.br/jspui/handle/123456789/2978110.1103/PhysRevD.90.025019American Physical SocietyAttribution 3.0 Brazilhttp://creativecommons.org/licenses/by/3.0/br/info:eu-repo/semantics/openAccessSemiclassical partition functionSemiclassical partition function for the double-well potentialinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleWe compute the partition function and specific heat for a quantum-mechanical particle under the influence of a quartic double-well potential nonperturbatively, using the semiclassical method. Near the region of bounded motion in the inverted potential, the usual quadratic approximation fails due to the existence of multiple classical solutions and caustics. Using the tools of catastrophe theory, we identify the relevant classical solutions, showing that at most two have to be considered. This corresponds to the first step towards the study of spontaneous symmetry breaking and thermal phase transitions in the nonperturbative framework of the boundary effective theoryengreponame:Repositório Institucional da UFRNinstname:Universidade Federal do Rio Grande do Norte (UFRN)instacron:UFRNCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8914https://repositorio.ufrn.br/bitstream/123456789/29781/2/license_rdf4d2950bda3d176f570a9f8b328dfbbefMD52TEXTSemiclassicalPartitionFunction_bessa_2014.pdf.txtSemiclassicalPartitionFunction_bessa_2014.pdf.txtExtracted texttext/plain45169https://repositorio.ufrn.br/bitstream/123456789/29781/4/SemiclassicalPartitionFunction_bessa_2014.pdf.txtd8cf4ad8d856b56ab1238f598f8152f0MD54THUMBNAILSemiclassicalPartitionFunction_bessa_2014.pdf.jpgSemiclassicalPartitionFunction_bessa_2014.pdf.jpgGenerated Thumbnailimage/jpeg1702https://repositorio.ufrn.br/bitstream/123456789/29781/5/SemiclassicalPartitionFunction_bessa_2014.pdf.jpg7b4c83969243249b0a18455d760e62f9MD55ORIGINALSemiclassicalPartitionFunction_bessa_2014.pdfSemiclassicalPartitionFunction_bessa_2014.pdfapplication/pdf1187081https://repositorio.ufrn.br/bitstream/123456789/29781/1/SemiclassicalPartitionFunction_bessa_2014.pdf28e4e9bd1b4eb40a33fc1814e035e02aMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81484https://repositorio.ufrn.br/bitstream/123456789/29781/3/license.txte9597aa2854d128fd968be5edc8a28d9MD53123456789/297812020-08-09 04:51:44.679oai:https://repositorio.ufrn.br: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Repositório de PublicaçõesPUBhttp://repositorio.ufrn.br/oai/opendoar:2020-08-09T07:51:44Repositório Institucional da UFRN - Universidade Federal do Rio Grande do Norte (UFRN)false
dc.title.pt_BR.fl_str_mv Semiclassical partition function for the double-well potential
title Semiclassical partition function for the double-well potential
spellingShingle Semiclassical partition function for the double-well potential
Fogaça, Daniel Kroff
Semiclassical partition function
title_short Semiclassical partition function for the double-well potential
title_full Semiclassical partition function for the double-well potential
title_fullStr Semiclassical partition function for the double-well potential
title_full_unstemmed Semiclassical partition function for the double-well potential
title_sort Semiclassical partition function for the double-well potential
author Fogaça, Daniel Kroff
author_facet Fogaça, Daniel Kroff
Moreira, André Bessa
Carvalho Filho, Carlos Alberto Aragão de
Fraga, Eduardo Souza
Jorás, Sergio Eduardo de Carvalho Eyer
author_role author
author2 Moreira, André Bessa
Carvalho Filho, Carlos Alberto Aragão de
Fraga, Eduardo Souza
Jorás, Sergio Eduardo de Carvalho Eyer
author2_role author
author
author
author
dc.contributor.author.fl_str_mv Fogaça, Daniel Kroff
Moreira, André Bessa
Carvalho Filho, Carlos Alberto Aragão de
Fraga, Eduardo Souza
Jorás, Sergio Eduardo de Carvalho Eyer
dc.subject.por.fl_str_mv Semiclassical partition function
topic Semiclassical partition function
description We compute the partition function and specific heat for a quantum-mechanical particle under the influence of a quartic double-well potential nonperturbatively, using the semiclassical method. Near the region of bounded motion in the inverted potential, the usual quadratic approximation fails due to the existence of multiple classical solutions and caustics. Using the tools of catastrophe theory, we identify the relevant classical solutions, showing that at most two have to be considered. This corresponds to the first step towards the study of spontaneous symmetry breaking and thermal phase transitions in the nonperturbative framework of the boundary effective theory
publishDate 2014
dc.date.issued.fl_str_mv 2014-07-15
dc.date.accessioned.fl_str_mv 2020-08-05T17:09:08Z
dc.date.available.fl_str_mv 2020-08-05T17:09:08Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.citation.fl_str_mv KROFF, D.; BESSA, A.; CARVALHO, C. A. A. de; FRAGA, E. S.; JORÁS, S. E.. Semiclassical partition function for the double-well potential. Physical Review D, [s.l.], v. 90, n. 2, p. 1-8, 15 jul. 2014. Disponível em: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.90.025019. Acesso em: 04 ago. 2020. http://dx.doi.org/10.1103/physrevd.90.025019.
dc.identifier.uri.fl_str_mv https://repositorio.ufrn.br/jspui/handle/123456789/29781
dc.identifier.issn.none.fl_str_mv 2470-0029
dc.identifier.doi.none.fl_str_mv 10.1103/PhysRevD.90.025019
identifier_str_mv KROFF, D.; BESSA, A.; CARVALHO, C. A. A. de; FRAGA, E. S.; JORÁS, S. E.. Semiclassical partition function for the double-well potential. Physical Review D, [s.l.], v. 90, n. 2, p. 1-8, 15 jul. 2014. Disponível em: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.90.025019. Acesso em: 04 ago. 2020. http://dx.doi.org/10.1103/physrevd.90.025019.
2470-0029
10.1103/PhysRevD.90.025019
url https://repositorio.ufrn.br/jspui/handle/123456789/29781
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv Attribution 3.0 Brazil
http://creativecommons.org/licenses/by/3.0/br/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution 3.0 Brazil
http://creativecommons.org/licenses/by/3.0/br/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFRN
instname:Universidade Federal do Rio Grande do Norte (UFRN)
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reponame_str Repositório Institucional da UFRN
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