C*-algebras, approximately proper equivalence relations and thermodynamic formalism

Detalhes bibliográficos
Autor(a) principal: Exel, Ruy
Data de Publicação: 2004
Outros Autores: Lopes, Artur Oscar
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRGS
Texto Completo: http://hdl.handle.net/10183/27433
Resumo: We introduce a non-commutative generalization of the notion of (approximately proper) equivalence relations and propose the construction of a ‘quotient space’. We then consider certain one-parameter groups of automorphisms of the resulting C*-algebra and prove the existence of KMS states at every temperature. In a model originating from thermodynamicswe prove that these states are unique as well. We also show a relationship between maximizing measures (the analogue of the Aubry–Mathermeasures for expanding maps) and ground states. In the last section we explore an interesting example of phase transitions.
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spelling Exel, RuyLopes, Artur Oscar2011-01-15T05:58:59Z20040143-3857http://hdl.handle.net/10183/27433000426412We introduce a non-commutative generalization of the notion of (approximately proper) equivalence relations and propose the construction of a ‘quotient space’. We then consider certain one-parameter groups of automorphisms of the resulting C*-algebra and prove the existence of KMS states at every temperature. In a model originating from thermodynamicswe prove that these states are unique as well. We also show a relationship between maximizing measures (the analogue of the Aubry–Mathermeasures for expanding maps) and ground states. In the last section we explore an interesting example of phase transitions.application/pdfengErgodic theory and dynamical systems. Cambridge. Vol. 24, no. 4 (2004), p. 1051-1082.C* AlgebrasTermodinâmicaAnálise matemática : Espaço de Hausdorff : Estado KMSC*-algebras, approximately proper equivalence relations and thermodynamic formalismEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSORIGINAL000426412.pdf000426412.pdfTexto completo (inglês)application/pdf319535http://www.lume.ufrgs.br/bitstream/10183/27433/1/000426412.pdfe44a6e07210ae07f2e3564697e672a7bMD51TEXT000426412.pdf.txt000426412.pdf.txtExtracted Texttext/plain80959http://www.lume.ufrgs.br/bitstream/10183/27433/2/000426412.pdf.txt239a52d742d1f9870e636384c2f0da64MD52THUMBNAIL000426412.pdf.jpg000426412.pdf.jpgGenerated Thumbnailimage/jpeg1531http://www.lume.ufrgs.br/bitstream/10183/27433/3/000426412.pdf.jpg6b10fefc5524ae3e2d329f840c8fd242MD5310183/274332021-06-13 04:35:01.186289oai:www.lume.ufrgs.br:10183/27433Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2021-06-13T07:35:01Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false
dc.title.pt_BR.fl_str_mv C*-algebras, approximately proper equivalence relations and thermodynamic formalism
title C*-algebras, approximately proper equivalence relations and thermodynamic formalism
spellingShingle C*-algebras, approximately proper equivalence relations and thermodynamic formalism
Exel, Ruy
C* Algebras
Termodinâmica
Análise matemática : Espaço de Hausdorff : Estado KMS
title_short C*-algebras, approximately proper equivalence relations and thermodynamic formalism
title_full C*-algebras, approximately proper equivalence relations and thermodynamic formalism
title_fullStr C*-algebras, approximately proper equivalence relations and thermodynamic formalism
title_full_unstemmed C*-algebras, approximately proper equivalence relations and thermodynamic formalism
title_sort C*-algebras, approximately proper equivalence relations and thermodynamic formalism
author Exel, Ruy
author_facet Exel, Ruy
Lopes, Artur Oscar
author_role author
author2 Lopes, Artur Oscar
author2_role author
dc.contributor.author.fl_str_mv Exel, Ruy
Lopes, Artur Oscar
dc.subject.por.fl_str_mv C* Algebras
Termodinâmica
Análise matemática : Espaço de Hausdorff : Estado KMS
topic C* Algebras
Termodinâmica
Análise matemática : Espaço de Hausdorff : Estado KMS
description We introduce a non-commutative generalization of the notion of (approximately proper) equivalence relations and propose the construction of a ‘quotient space’. We then consider certain one-parameter groups of automorphisms of the resulting C*-algebra and prove the existence of KMS states at every temperature. In a model originating from thermodynamicswe prove that these states are unique as well. We also show a relationship between maximizing measures (the analogue of the Aubry–Mathermeasures for expanding maps) and ground states. In the last section we explore an interesting example of phase transitions.
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dc.date.accessioned.fl_str_mv 2011-01-15T05:58:59Z
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dc.relation.ispartof.pt_BR.fl_str_mv Ergodic theory and dynamical systems. Cambridge. Vol. 24, no. 4 (2004), p. 1051-1082.
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