General properties of response functions of nonequilibrium steady states

Journal of the Physical Society of Japan

Volumn 79, Issue 1, 2010, Pages

  Shimizu, Akira ^a   Yuge, Tatsuro ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b TOHOKU UNIVERSITY   (Japan)

Author keywords

Asymptotic behavior; Fluctuation dissipation relation; Reciprocal relation; Sum rule

Indexed keywords

EID: 77049127106     PISSN: 00319015     EISSN: 13474073     Source Type: Journal    
DOI: 10.1143/JPSJ.79.013002     Document Type: Article

References (20)

1. R. Kubo, M. Toda, and N. Hashitsume: Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer, Berlin, 1985).
2. D. N. Zubarev: Nonequilibrium Statistical Thermodynamics (Plenum, New York, 1974).
3. L. V. Keldysh: Sov. Phys. JETP 20 (1965) 1018.
4. Y. R. Shen: The Principles of Nonlinear Optics (Willey, New York, 1984), and references cited therein.
5. Optical Nonlinearities and Instabilities in Semiconductors, ed. H. Haug (Academic Press, San Diego, CA, 1988).
6. D. Andrieux and P. Gaspard: J. Stat. Mech. (2007) P02006.
7. M. Baiesi, C. Maes, and B. Wynants: Phys. Rev. Lett. 103 (2009) 010602.
8. A. Shimizu and M. Ueda: Phys. Rev. Lett. 69 (1992) 1403.
9. A. Shimizu and M. Ueda: Phys. Rev. Lett. 86 (2001) 3694, [Errata. 86
10. T. Yuge and A. Shimizu: J. Phys. Soc. Jpn. 78 (2009) 083001.
11. T. Harada and S.-i. Sasa: Phys. Rev. E 73 (2006) 026131.
12. T. Yuge, N. Ito, and A. Shimizu: J. Phys. Soc. Jpn. 74 (2005) 1895.
13. T. Yuge and A. Shimizu: J. Phys. Soc. Jpn. 76 (2007) 093001.
14. T. Yuge and A. Shimizu: Prog. Theor. Phys. Suppl. 178 (2009) 64.
15. The expectation value of a known function of canonical variables, such as the rhs's of eqs. (13)-(15), can be measured experimentally, although the density operator of the NESS is unknown. In contrast, the expectation value of an unknown function, which often appeared in the literature, cannot be measured in general.
16. bT≲hω, the symmetrized time correlation is not necessarily the correct quantum-mechanical expression of time correlation, which means correlation of outcomes of subsequent measurements.
17. See, e.g., §4.8.1 of K. Koshino and A. Shimizu: Phys. Rep. 412 (2005) 191.
18. in, one can make it arbitrarily large by increasing the size of the source of F.
19. H. Hasegawa and T. Nakagomi: J. Stat. Phys. 21 (1979) 191.
20. K. Sekimoto: Stochastic Energetics (Springer, Paris, 2009).