Functional density matrix formulation of quantum statistics
Autor(a) principal: | |
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Data de Publicação: | 2010 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRN |
Texto Completo: | https://repositorio.ufrn.br/jspui/handle/123456789/29788 |
Resumo: | We present a unified formulation for quantum statistical physics based on the representation of the density matrix as a functional integral. For quantum statistical (thermal) field theory, the stochastic variable of the statistical theory is a boundary field configuration. We explore the properties of an effective theory for such boundary configurations and apply it to the computation of the partition function of an interacting one-dimensional quantum-mechanical system at finite temperature. Plots of free energy and specific heat show excellent agreement with more involved semiclassical results. The method of calculation provides an alternative to the usual sum over periodic trajectories: it sums over paths with coincident end points and includes nonvanishing boundary terms. An appropriately modified expansion into modified Matsubara modes is presented |
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Moreira, André BessaCarvalho Filho, Carlos Alberto Aragão deFraga, Eduardo Souza2020-08-06T14:59:10Z2020-08-06T14:59:10Z2010-01-05BESSA, A.; CARVALHO FILHO, C. A. A.; FRAGA, E.S.. Functional density matrix formulation of quantum statistics. Physical Review E, [S.L.], v. 81, n. 1, p. 11, 5 jan. 2010. Disponível em: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.81.011103. Acesso em: 04 ago. 2020. http://dx.doi.org/10.1103/physreve.81.011103.2470-0045https://repositorio.ufrn.br/jspui/handle/123456789/2978810.1103/PhysRevE.81.011103American Physical SocietyAttribution 3.0 Brazilhttp://creativecommons.org/licenses/by/3.0/br/info:eu-repo/semantics/openAccessQuantum statisticsFunctional density matrixFunctional density matrix formulation of quantum statisticsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleWe present a unified formulation for quantum statistical physics based on the representation of the density matrix as a functional integral. For quantum statistical (thermal) field theory, the stochastic variable of the statistical theory is a boundary field configuration. We explore the properties of an effective theory for such boundary configurations and apply it to the computation of the partition function of an interacting one-dimensional quantum-mechanical system at finite temperature. Plots of free energy and specific heat show excellent agreement with more involved semiclassical results. The method of calculation provides an alternative to the usual sum over periodic trajectories: it sums over paths with coincident end points and includes nonvanishing boundary terms. An appropriately modified expansion into modified Matsubara modes is presentedengreponame:Repositório Institucional da UFRNinstname:Universidade Federal do Rio Grande do Norte (UFRN)instacron:UFRNORIGINALFunctionalDensityMatrix_bessa_2010.pdfFunctionalDensityMatrix_bessa_2010.pdfapplication/pdf181072https://repositorio.ufrn.br/bitstream/123456789/29788/1/FunctionalDensityMatrix_bessa_2010.pdf3fdfd1c92d4627cf2adae29b5b0be2cdMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8914https://repositorio.ufrn.br/bitstream/123456789/29788/2/license_rdf4d2950bda3d176f570a9f8b328dfbbefMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81484https://repositorio.ufrn.br/bitstream/123456789/29788/3/license.txte9597aa2854d128fd968be5edc8a28d9MD53TEXTFunctionalDensityMatrix_bessa_2010.pdf.txtFunctionalDensityMatrix_bessa_2010.pdf.txtExtracted texttext/plain37039https://repositorio.ufrn.br/bitstream/123456789/29788/4/FunctionalDensityMatrix_bessa_2010.pdf.txtf12f129b96c9a05a7ea2a21a15fac82bMD54THUMBNAILFunctionalDensityMatrix_bessa_2010.pdf.jpgFunctionalDensityMatrix_bessa_2010.pdf.jpgGenerated Thumbnailimage/jpeg1703https://repositorio.ufrn.br/bitstream/123456789/29788/5/FunctionalDensityMatrix_bessa_2010.pdf.jpg1141be69e661c75b0d6c1c108a7afd10MD55123456789/297882020-08-09 04:51:46.31oai:https://repositorio.ufrn.br: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Repositório de PublicaçõesPUBhttp://repositorio.ufrn.br/oai/opendoar:2020-08-09T07:51:46Repositório Institucional da UFRN - Universidade Federal do Rio Grande do Norte (UFRN)false |
dc.title.pt_BR.fl_str_mv |
Functional density matrix formulation of quantum statistics |
title |
Functional density matrix formulation of quantum statistics |
spellingShingle |
Functional density matrix formulation of quantum statistics Moreira, André Bessa Quantum statistics Functional density matrix |
title_short |
Functional density matrix formulation of quantum statistics |
title_full |
Functional density matrix formulation of quantum statistics |
title_fullStr |
Functional density matrix formulation of quantum statistics |
title_full_unstemmed |
Functional density matrix formulation of quantum statistics |
title_sort |
Functional density matrix formulation of quantum statistics |
author |
Moreira, André Bessa |
author_facet |
Moreira, André Bessa Carvalho Filho, Carlos Alberto Aragão de Fraga, Eduardo Souza |
author_role |
author |
author2 |
Carvalho Filho, Carlos Alberto Aragão de Fraga, Eduardo Souza |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Moreira, André Bessa Carvalho Filho, Carlos Alberto Aragão de Fraga, Eduardo Souza |
dc.subject.por.fl_str_mv |
Quantum statistics Functional density matrix |
topic |
Quantum statistics Functional density matrix |
description |
We present a unified formulation for quantum statistical physics based on the representation of the density matrix as a functional integral. For quantum statistical (thermal) field theory, the stochastic variable of the statistical theory is a boundary field configuration. We explore the properties of an effective theory for such boundary configurations and apply it to the computation of the partition function of an interacting one-dimensional quantum-mechanical system at finite temperature. Plots of free energy and specific heat show excellent agreement with more involved semiclassical results. The method of calculation provides an alternative to the usual sum over periodic trajectories: it sums over paths with coincident end points and includes nonvanishing boundary terms. An appropriately modified expansion into modified Matsubara modes is presented |
publishDate |
2010 |
dc.date.issued.fl_str_mv |
2010-01-05 |
dc.date.accessioned.fl_str_mv |
2020-08-06T14:59:10Z |
dc.date.available.fl_str_mv |
2020-08-06T14:59:10Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
BESSA, A.; CARVALHO FILHO, C. A. A.; FRAGA, E.S.. Functional density matrix formulation of quantum statistics. Physical Review E, [S.L.], v. 81, n. 1, p. 11, 5 jan. 2010. Disponível em: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.81.011103. Acesso em: 04 ago. 2020. http://dx.doi.org/10.1103/physreve.81.011103. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufrn.br/jspui/handle/123456789/29788 |
dc.identifier.issn.none.fl_str_mv |
2470-0045 |
dc.identifier.doi.none.fl_str_mv |
10.1103/PhysRevE.81.011103 |
identifier_str_mv |
BESSA, A.; CARVALHO FILHO, C. A. A.; FRAGA, E.S.. Functional density matrix formulation of quantum statistics. Physical Review E, [S.L.], v. 81, n. 1, p. 11, 5 jan. 2010. Disponível em: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.81.011103. Acesso em: 04 ago. 2020. http://dx.doi.org/10.1103/physreve.81.011103. 2470-0045 10.1103/PhysRevE.81.011103 |
url |
https://repositorio.ufrn.br/jspui/handle/123456789/29788 |
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) instacron:UFRN |
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UFRN |
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UFRN |
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Repositório Institucional da UFRN |
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Repositório Institucional da UFRN |
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