C*-Algebras and Quantum Gibbs States
MAP5001 - C*-Algebras and Quantum Gibbs States (At USP catalog - In Portuguese)
MAP5001 - C*-Algebras and Quantum Gibbs States (At USP catalog - In Portuguese)
Tuesdays 16:00 - 18:00 - Room 243
Thursdays 16:00 - 18:00 - Room 243
Papers proposed to the students
Diana Cruz Pestana - Section 4. Topological Entropy (Completely Positive Approximation the C*.Case) Dynamical approximation entropies and topological entropy in operator algebras. Dan Voiculescu. CMP, 1995.
Yuri Gouvea Wagner - Section 7. The KMS Condition and Equilibrium in O_A. Noncommutative Pressure and the Variational Principle in Cuntz–Krieger-type C*-Algebras. David Kerr and Claudia Pinzari. JFA, 2002.
Wilson de Freitas Junior and Gael Leis Barros. On the equivalence of KMS and Gibbs conditions for states of quantum lattice systems. H Araki and P.D.F. Ion. CMP, 1974.
Adriano Alfredo Schneider. Entropy of Local Homeomorphisms With Applications to Infinite Alphabet Shift Spaces. Daniel Gonçalves, Danilo Royer, and Felipe Augusto Tasca, IRMN, 2024.
Gabriel Moniz Arantes. Entropy of shifts on topological graph C∗-algebras. Valentin Deaconu, New York J. Math, 2009. Survey article written by the student.
Gabriel Lube. KMS states for generalized gauge actions on C*-algebras associated with self-similar sets. Gilles de Castro, ETDS, 2023. Survey article written by the student.
Felippe Motibeller. Localization in the random XXZ quantum spin chain Alexander Elgart and Abel Klein, Forum of Mathematics, Sigma 2024. Survey article written by the student.
Bibliography
1. H. Araki, P. D. F. Ion. On the equivalence of KMS and Gibbs conditions for states of quantum lattice systems. Comm. Math. Phys. 35(1): 1-12 (1974).
2. M. Aizenman and B. Nachtergaele. Geometric aspects of quantum spin states. Commun. Math. Phys. 164, 17–63 (1994).
3. J. E. Björnberg and D. Ueltschi. Reflection positivity and infrared bounds for quantum spin systems. The Physics and Mathematics of Elliott Lieb The 90th Anniversary Volume I. PP. 77–108, (2022).
4. H. J. Brascamp. Equilibrium states for a classical lattice gas. Comm. Math. Phys. 18(1): 82-96 (1970).
5. O. Bratteli and D. W. Robinson. Operator Algebras and Quantum Statistical Mechanics 2: Equilibrium States. Models in Quantum Statistical Mechanics. Springer, (2011).
6. O. Bratteli and D. W. Robinson. Operator Algebras and Quantum Statistical Mechanics 1: C*- and W*-Algebras. Symmetry Groups. Decomposition of States. Springer, (2010).
9. R. Exel. Uma Introdução às C*-Álgebras. Mini-curso ministrado na Primeira Bienal da SBM, UFMG, (2002).
10. S. Friedli and Y. Velenik. Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction. Cambridge University Press, (2017).
13. R. B. Israel. Convexity in the Theory of Lattice Gases. Princeton Series in Physics, (2015).
14. G. J. Murphy. C*-Algebras and Operator Theory, (1990).
15. P. Naaijkens. Spin Systems on Infinite Lattices. A Concise Introduction. Lecture Notes in Physics vol. 933, (2017).
16. S. Neshveyev. KMS states on the C*-algebras of non-principal groupoids, J. Operator Theory 70(2), 513-530, (2013).
17. Ian Putnam. Lecture Notes on C*-algebras, (2019).
18. J. Renault. A Groupoid Approach to C*-Algebras. Lecture Notes in Mathematics vol 793, (1980).
19. G. L. Sewell. Quantum Theory of Collective Phenomena (Monographs on the Physics and Chemistry of Materials), Clarendon Press, Oxford, (1986).
20. B. Simon. The Statistical Mechanics of Lattice Gases, Volume I, (2014).
21. A. Sims. Hausdorff étale groupoids and their C*-algebras, in “Operator algebras and dynamics: groupoids, crossed products and Rokhlin dimension” (F. Perera, Ed.) in Advanced Courses in Mathematics. CRM Barcelona, Birkhäuser, (2020).
22. D. Ueltschi. Introduction to Quantum Spin Systems, (2020).