On the distribution of the wave function for systems in thermal equilibrium

Journal of Statistical Physics

Volumn 125, Issue 5-6, 2006, Pages 1193-1221

  Goldstein, Sheldon ^a   Lebowitz, Joel L ^a   Tumulka, Roderich ^b   Zanghì, Nino ^c  

^a RUTGERS UNIVERSITY   (United States)

^b UNIVERSITY OF TÜBINGEN   (Germany)

^c UNIVERSITY OF GENOA   (Italy)

Author keywords

Canonical ensemble in quantum theory; Density matrices; Gaussian measures; Probability measures on Hilbert space

Indexed keywords

EID: 33845890805     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-006-9210-z     Document Type: Article

References (29)

1. M. Aizenman, S. Goldstein, and J. L. Lebowitz, On the stability of equilibrium states of finite classical systems. J. Math. Phys. 16, 1284-1287 (1975).
2. V. I. Arnol'd and A. Avez, Ergodic Problems of Classical Mechanics (Benjamin, New York, 1968).
3. M. Berry, Regular and irregular eigenfunctions. J. Phys. A: Math. Gen. 10, 2083-2091 (1977).
4. H.-P. Breuer and F. Petruccione, Open Quantum Systems (Oxford University Press, 2002).
5. D. C. Brody and L. P. Hughston, The quantum canonical ensemble. J. Math. Phys. 39, 6502-6508 (1998).
6. D. Dürr, S. Goldstein and N. Zanghì, Quantum equilibrium and the origin of absolute uncertainty. J. Statist. Phys. 67, 843-907 (1992).
7. S. Goldstein, Stochastic mechanics and quantum theory. . Statist. Phys. 47, 645-667 (1987).
8. S. Goldstein, J. L. Lebowitz, R. Tumulka, and N. Zanghì, Canonical typicality. Phys. Rev. Lett. 96, 050403 (2006).
9. S. Goldstein, J. L. Lebowitz, R. Tumulka, and N. Zanghì, Typicality of the GAP measure. In preparation.
10. F. Guerra and M. I. Loffredo, Thermal mixtures in stochastic mechanics. Lett. Nuovo Cimento (2) 30, 81-87 (1981).
11. R. Haag, D. Kastler, and E. B. Trych-Pohlmeyer, Stability and equilibrium states. Commun. Math. Phys. 38, 173-193 (1974).
12. S. Hortikar and M. Srednicki, Correlations in chaotic eigenfunctions at large separation. Phys. Rev. Lett. 80(8), 1646-1649 (1998).
13. L. D. Landau and E. M. Lifshitz, Statistical Physics. Volume 5 of Course of Theoretical Physics. Translated from the Russian by E. Peierls and R. F. Peierls (Pergamon, London and Paris, 1959).
14. J. L. Lebowitz, Boltzmann's entropy and time's arrow. Phys. Today 46, 32-38 (1993).
15. J. L. Lebowitz, Microscopic reversibility and macroscopic behavior: physical explanations and mathematical derivations. In 25 Years of Non-Equilibrium Statistical Mechanics, Proceedings, Sitges Conference, Barcelona, Spain, 1994, in Lecture Notes in Physics, J.J. Brey, J. Marro, J.M. Rubã, and M. San Miguel (eds.) (Springer-Verlag, Berlin, 1995).
16. J. L. Lebowitz, Microscopic origins of irreversible macroscopic behavior. Physica (Amsterdam) 263A, 516-527 (1999).
17. A. Martin-Löf, Statistical Mechanics and the Foundations of Thermodynamics. Lecture Notes in Physics 101 (Springer, Berlin, 1979).
18. E. Nelson, Quantum Fluctuations (Princeton University Press, 1985).
19. S. Popescu, A. J. Short, and A. Winter, The foundations of statistical mechanics from entanglement: Individual states vs. averages. Preprint quant-ph/0511225 (2005).
20. S. Popescu, A. J. Short, and A. Winter, Entanglement and the foundations of statistical mechanics. Nature Physics 21(11), 754-758 (2006).
21. D. N. Page, Average entropy of a subsystem. Phys. Rev. Lett. 71(9), 1291-1294 (1993).
22. E. Schrödinger, The exchange of energy according to wave mechanics. Annalen der Physik (4) 83, 956-968 (1927).
23. E. Schrödinger, Statistical Thermodynamics., 2nd edn. (Cambridge University Press, 1952).
24. H. Tasaki, From Quantum dynamics to the canonical distribution: general picture and a rigorous example. Phys. Rev. Lett. 80, 1373-1376 (1998).
25. J. D. Urbina and K. Richter, Random wave models. Preprint (2005). To appear.
26. J. von Neumann, Beweis des Ergodensatzes und des H-Theorems in der neuen Mechanik. Z. Physik 57, 30-70 (1929).
27. J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, 1955).
28. Translation of Mathematische Grundlagen der Quantenmechanik (Springer-Verlag, Berlin, 1932).
29. J. D. Walecka, Fundamentals of Statistical Mechanics. Manuscript and Notes of Felix Bloch (Stanford University Press, Stanford, CA, 1989).