Eigenstate randomization hypothesis: Why does the long-time average equal the microcanonical average?

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 84, Issue 2, 2011, Pages

  Ikeda, Tatsuhiko N ^a   Watanabe, Yu ^a   Ueda, Masahito ^a,b  

^a UNIVERSITY OF TOKYO   (Japan)

^b JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

DIAGONAL ELEMENTS; EIGEN STATE; INTEGRABLE SYSTEMS; MICROCANONICAL ENSEMBLES; QUANTUM SYSTEM; THERMALIZATION; UPPER BOUND;

QUANTUM OPTICS;

QUANTUM ELECTRONICS;

EID: 80052221581     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.021130     Document Type: Article

References (13)

1. H. Tasaki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.1373 80, 1373 (1998).
2. S. Goldstein, J. L. Lebowitz, R. Tumulka, and N. Zanghi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.050403 96, 050403 (2006). (Pubitemid 43270977)
3. S. Popescu, A. J. Short, and A. Winter, Nat. Phys. PRLTAO 1745-2473 10.1038/nphys444 2, 754 (2006). (Pubitemid 44691281)
4. P. Reimann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101. 190403 101, 190403 (2008).
5. J. M. Deutsch, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.43.2046 43, 2046 (1991).
6. M. Srednicki, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.50.888 50, 888 (1994).
7. M. Rigol, V. Dunjko, and M. Olshanii, Nature (London) NATUAS 0028-0836 10.1038/nature06838 452, 854 (2008). (Pubitemid 351550863)
8. B. Fresch and G. J. Moro, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3455998 133, 034509 (2010).
9. ] 2 d t. While he assumed that H has no degeneracy, we can generalize his result to the case in which H has some degeneracies. In this case, the generalized upper bound includes an extra factor 2 K - 1, where K is the maximum number of degeneracies. The detailed discussion of this finding will be reported elsewhere.
10. - 1) correction is added to the right-hand side of Eq.D3. However, this term does not qualitatively change our result.
11. M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.050405 98, 050405 (2007). (Pubitemid 46203541)
12. A. Peres, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.30.504 30, 504 (1984).
13. M. Feingold, N. Moiseyev, and A. Peres, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.30.509 30, 509 (1984).