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Master's Dissertation
DOI
Document
Author
Full name
Rodrigo Souza Frausino
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2018
Supervisor
Committee
Proença, Rodrigo Bissacot (President)
Cerri, Cristina
Exel Filho, Ruy
Title in English
Groupoid C*-algebras, conformal measures and phase transitions
Keywords in English
C*-algebras
Conformal measures
Groupoid
KMS states.
Phase transition
Abstract in English
The objective of this work is the study of phase transitions on the context of Groupoids and their C*-Algebras. The main result of this dissertation is due to Klaus Thomsen in [Tho17], which investigates the connection between conformal measures in the classical formalism and KMS-states in the quantum formalism. The phase transition in the quantum setting is a consequence of this connection between both formalisms and the fact that on the classical setting it was known examples of continuous potentials that show the phenomena of phase transition. The potential used was introduced by Hofbauer [Hof77], an example that shows, dierently from potential of summable variations, potentials only continuous can exhibit phase transition.
Title in Portuguese
C*-álgebras de grupóides, medidas conformes e transições de fase
Keywords in Portuguese
C*-álgebra
Estados KMS
Grupóide
Medidas conformes
Transição de fase
Abstract in Portuguese
O objetivo deste trabalho é o estudo do fenômeno de transição de fase no contexto de Grupóides e suas C*-álgebras. O resultado principal é devido a Klaus Thomsen em [Tho17], que explora a conexão entre medidas conformes no formalismo clássico e estados KMS do contexto quântico. A transição de fase no caso quântico é consequência desta ligação entre os dois formalismos e do fato de que no setting clássico eram conhecidos exemplos de potenciais contínuos que apresentam o fenômeno de transição de fase. O potencial utilizado é aquele introduzido por Hofbauer [Hof77], um exemplo que mostra que, diferentemente de potenciais de variação somável, potenciais apenas contínuos podem apresentar transição de fase.
 
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Publishing Date
2019-04-24
 
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