Correction: Large Deviations in Quantum Lattice Systems: One-Phase Region (Journal of Statistical Physics, (2005), 119, 3-4, (715-746), 10.1007/s10955-005-3015-3);Large deviations in quantum lattice systems: One-phase region

Journal of Statistical Physics

Volumn 119, Issue 3-4, 2005, Pages 715-746

  Lenci, Marco ^a   Rey Bellet, Luc ^b  

^a Stevens Institute of Technology   (United States)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

Fermi gas; Gibbs KMS states; High temperature; One dimension; Quantum large deviations; Quantum spins

Indexed keywords

EID: 21644479421     PISSN: 00224715     EISSN: 15729613     Source Type: Journal    
DOI: 10.1007/s10955-023-03193-5     Document Type: Erratum

References (36)

1. H. Araki, Gibbs states of a one dimensional quantum lattice, Commun. Math. Phys. 14:120-157 (1969).
2. H. Araki, On the equivalence of the KMS condition and the variational principal for quantum lattice systems, Commun. Math. Phys. 38:1-10 (1974).
3. H. Araki and H. Moriya, Equilibrium statistical mechanics of fermion lattice systems, Preprint, 2003.
4. M. van den Berg, J. T. Lewis and J. V. Pulé Large deviations and the boson gas, in Stochastic Mechanics and Stochastic Processes, Lecture Notes in Mathematics 1325 (Springer, Berlin, 1988) pp. 24-39.
5. M. van den Berg, J. T. Lewis and J. V. Pulé, The large deviation principle and some models of an interacting boson gas, Commun. Math. Phys. 118:61-85 (1988).
6. I. Bjelakovic, T. Kröger, R. Siegmund-Schultze and A. Szkola, The Shannon-McMillan theorem for ergodic quantum lattice systems, Preprint, 2003.
7. I. Bjelakovic, T. Kröger, R. Siegmund-Schultze and A. Szkola, Chained typical subspaces: a quantum version of Breiman's Theorem, Preprint, 2003.
8. O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics. Vols. 1 and 2. Texts and Monographs in Physics, (Springer Berlin, Berlin, 1981).
9. dd, C. R. Acad. Sci. Paris Sér. I Math. 303:511-513 (1986).
10. N. Datta, R. Fernández, J. Fröhlich and L. Rey-Bellet, Low-temperature phase diagrams of quantum lattice systems. II. Convergent perturbation expansions and stability in systems with infinite degeneracy, Helv. Phys. Acta 69:752-820 (1996).
11. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Applications of Mathematics 38 (Springer, New York, 1998). 2nd ed.
12. J.-D. Deuschel, D. W. Stroock and H. Zessin, Microcanonical distributions for lattice gases, Commun. Math. Phys. 139:83-101 (1991).
13. R. S. Ellis, Entropy, Large Deviations and Statistical Mechanics. Grundlehren der mathematischen Wissenschaften 271. (Springer, Berlin Heidelberg New York, 1985).
14. H. Föllmer and S. Orey, Large deviations for the empirical field of a Gibbs measure, Ann. Probab. 16:961-977 (1988).
15. G. Gallavotti, J. L. Lebowitz and V. Mastropietro, Large deviations in rarefied quantum gases, J. Statist. Phys. 108:831-861 (2002).
16. d, Ann. Probab. 21:1845-1875 (1993).
17. D. Goderis, A. Verbeure and P. Vets, Noncommutative central limits, Prob. Th. Rel. Fields 82:527-544 (1989).
18. D. Goderis, A. Verbeure and P. Vets, Dynamics of fluctuations for quantum lattice systems, Comm. Math. Phys. 128:533-549 (1990).
19. R. B. Israel, Convexity in the Theory of Lattice Gases. Princeton series in physics (Princeton University Press, Princeton, 1979).
20. O. E. Lanford III, Entropy and equilibrium states in classical statistical mechanics, in Statistical Mechanics and Mathematical Problems. Lecture Notes in Physics 20 (Springer, Berlin Heidelberg New York, 1973), pp. 1-113.
21. J. L. Lebowitz, M. Lenci and H. Spohn, Large deviations for ideal quantum systems, J. Math. Phys. 41:1224-1243 (2000).
22. J. T. Lewis, C.-E. Pfister and W. G. Sullivan, The equivalence of ensembles for lattice systems: some examples and a counterexample, J. Stat. Phys. 77:397-419 (1994).
23. J. T. Lewis, C.-E. Pfister and W. G. Sullivan, Entropy, concentration of probability and conditional limit theorems, Markov Process. Related Fields 1:319-386 (1995).
24. T. Matsui, Bosonic central limit theorem for the one-dimensional XY model, Rev. Math. Phys. 14:675-700 (2002).
25. T. Matsui, On the algebra of fluctuation in quantum spin chains, Preprint (2002).
26. K. Netocny and F. Redig, Large deviations for quantum spin systems, Preprint (2004).
27. P. Ohya and D. Petz, Quantum Entropy and its Use Texts and Monographs in Physics (Springer, Berlin, 1993).
28. S. Olla, Large deviations for Gibbs random fields, Probab. Th. Rel. Fields 77:343-357 (1988).
29. D. Petz, G. A. Raggio and A. Verbeure, Asymptotics of Varadhan-type and the Gibbs variational principle, Commun. Math. Phys. 121:271-282 (1989).
30. D. Petz, First steps towards a Donsker and Varadhan theory in operator algebras, in Quantum Probability and Applications, V, Lecture Notes in Mathematics 1442 (Springer, Berlin, 1990), pp. 311-319.
31. C.-E. Pfister, Thermodynamical aspects of classical lattice systems, in In and Out of Equilibrium (Mambucaba, 2000), Progr. Probab., 51 (Birkhäuser Boston, Boston, MA, 2002), pp. 393-472.
32. G. A. Raggio and R. F. Werner, Quantum statistical mechanics of general mean field systems, Helv. Phys. Acta 62:980-1003 (1989).
33. G. A. Raggio and R. F. Werner The Gibbs variational principle for inhomogeneous mean-field systems, Helv. Phys. Acta 64:633-667 (1991).
34. D. Ruelle, Correlation functional, J. Math. Phys. 6:201-220 (1965).
35. D. Ruelle, Statistical Mechanics: Rigorous Results (World Scientific, River Edge, NJ, 1999).
36. B. Simon, The Statistical Mechanics of Lattice Gases Vol. I. Princeton series in physics (Princeton University Press, Princeton, 1993).