Generalized master equation via aging continuous-time random walks

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

Volumn 68, Issue 5 2, 2003, Pages 561231-5612311

  Allegrini, Paolo ^a   Aquino, Gerardo ^b   Grigolini, Paolo ^a,b,c   Palatella, Luigi ^c   Rosa, Angelo ^d  

^a CNR   (Italy)

^b UNIVERSITY OF NORTH TEXAS   (United States)

^c UNIVERSITY OF PISA   (Italy)

^d INFM   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); HAMILTONIANS; MATRIX ALGEBRA; POISSON EQUATION; QUANTUM THEORY; RANDOM PROCESSES; REGRESSION ANALYSIS;

CONTINUOUS-TIME RANDOM WALK (CTRW); GENERALIZED MASTER EQUATION (GME);

STATISTICAL MECHANICS;

EID: 0942267634     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.68.056123     Document Type: Article

References (32)

1. L. Onsager, Phys. Rev. 38, 2265 (1931); 37, 405 (1931).
2. L. Onsager, Phys. Rev. 38, 2265 (1931); 37, 405 (1931).
3. R. Zwanzig, in Lectures in Theoretical Physics, edited by W. E. Brittin et al. (Interscience, New York, 1961), Vol. 3; Quantum Statistical Mechanics, edited by P.H.E. Meijer (Gordon and Breach, London, 1966), p. 139.
4. R. Zwanzig, in Lectures in Theoretical Physics, edited by W. E. Brittin et al. (Interscience, New York, 1961), Vol. 3; Quantum Statistical Mechanics, edited by P.H.E. Meijer (Gordon and Breach, London, 1966), p. 139.
5. P. Grigolini, Adv. Chem. Phys. 62, 1 (1985).
6. E.W. Montroll and G.H. Weiss, J. Math. Phys. 6, 167 (1965).
7. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000); B.J. West, M. Bologna, and P. Grigolini, Physics of Fractal Operators (Springer, New York, 2003).
8. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000); B.J. West, M. Bologna, and P. Grigolini, Physics of Fractal Operators (Springer, New York, 2003).
9. D. Bedeaux, K. Lakatos, and K. Shuler, J. Math. Phys. 12, 22 116 (1971).
10. V.M. Kenkre, E.W. Montroll, and M.F. Shlesinger, J. Stat. Phys. 9, 45 (1973).
11. R. Metzler, Phys. Rev. E 62, 6233 (2000).
12. A. Mazza and P. Grigolini, Phys. Lett. A 238, 169 (1998).
13. V.M. Kenkre, in Excitation Dynamics in Molecular Crystal and Aggregates, Springer Tracts in Modern Physics Vol. 94 (Springer, Berlin, 1982).
14. J. Gambetta and H.M. Wiseman, Phys. Rev. A 66, 012108 (2002).
15. U. Kleinekathöfer, I. Kondov, and M. Schreiber, Phys. Rev. E 66, 037701 (2002).
16. I.M. Sokolov and R. Metzler, Phys. Rev. E 67, 010101(R) (2003).
17. R. Fox, J. Math. Phys. 18, 2331 (1977).
18. T. Geisel, J. Nierwetberg, and A. Zacherl, Phys. Rev. Lett. 54, 616 (1985).
19. D.R. Cox, Renewal Theory (Chapmann and Hall, London, 1967).
20. G. Zumofen and J. Klafter, Phys. Rev. E 47, 851 (1993).
21. E. Barkai, Phys. Rev. Lett. 90, 104101 (2003).
22. L. Fronzoni, P. Grigolini, R. Mannella, and B. Zambon, Phys. Rev. A 34, 3293 (1986).
23. E. Çinlar, Introduction to Stochastic Processes (Prentice-Hall, Englewood Cliffs, NJ, 1975).
24. We have to point out that the use of a judicious choice of the delay distribution to deal with the nonstationary properties of non-Poisson processes is an old topic of stochastic processes (see, for instance, Ref. [20]). We are more physically than mathematically oriented, and for this reason we refer explicitly to the more recent work of Ref. [18].
25. M. Ignaccolo, P. Grigolini, and A. Rosa, Phys. Rev. E 64, 026210 (2001).
26. R. Bettin, R. Mannella, B.J. West, and P. Grigolini, Phys. Rev. E 51, 212 (1995).
27. M. Buiatti and M. Buiatti, Biol. Forum 94, 59 (2001).
28. G. Zumofen and J. Klafter, Physica A 196, 102 (1993).
29. G. Zumofen and J. Klafter, Physica D 69, 436 (1993).
30. Y.-J. Jung, E. Barkai, and R.J. Silbey, Chem. Phys. 284, 181 (2002).
31. A. Crisanti and F. Ritort, J. Phys. A 36, R181 (2003).
32. E. Floriani, R. Mannella, and P. Grigolini, Phys. Rev. E 52, 5910 (1995).