C*-Algebras and Quantum Gibbs States
MAP5001 - C*-Algebras and Quantum Gibbs States (At USP catalog - In Portuguese)
Teaching Assistant: Lucas Affonso
Papers used by the students
- On the equivalence between KMS-states and equilibrium states for classical systems. CMP 1977. Aizenman, Goldstein, Gruber, Lebowitz, Martin. (Thiago Brevidelli Garcia and Guilherme de Sousa Sobreira)
- On quantum statistical mechanics of non-Hamiltonian systems. RMP 1972. Kossakowski (Pingao Sun)
- Variational principles for spectral radius of weighted endomorphisms of C(X,D). Trans. Amer. Math. 2020. B. Kwaśniewski and A. Lebedev. (Ivan Granados)
- The Complete Set of Infinite Volume Ground States for Kitaev’s Abelian Quantum Double Models. CMP 2018. Matthew Cha, Pieter Naaijkens & Bruno Nachtergaele. (Henrique Corsini e João Rodrigues).
- Equilibria when the temperature goes to zero. 2023. Klaus Thomsen (Gabriel Guimarães)
- Low Temperature Phase Diagrams of Fermionic Lattice Systems. CMP 2000. C. Borgs & R. Kotecký. (Kelvyn Welsch)
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).
7. N. Datta, R. Fernández and J. Fröhlich. Low-temperature phase diagrams of quantum lattice systems. I. Stability for quantum perturbations of classical systems with finitely-many ground states. Journal of Statistical Physics 84, 455–534, (1996).
8. N. Datta, R. Fernández and J. Fröhlich. Effective Hamiltonians and Phase Diagrams for Tight-Binding Models. Journal of Statistical Physics 96, 545–611, (1999).
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).
11. The Complete Set of Infinite Volume Ground States for Kitaev’s Abelian Quantum Double Models Matthew Cha, Pieter Naaijkens & Bruno Nachtergaele
12. D. Ioffe. Stochastic Geometry of Classical and Quantum Ising Models. In: Kotecký, R. (eds) Methods of Contemporary Mathematical Statistical Physics. Lecture Notes in Mathematics, vol 1970. Springer, Berlin, Heidelberg, (2009).
13. R. B. Israel. Convexity in the Theory of Lattice Gases. Princeton Series in Physics, (2015).
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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).