Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials

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

Volumn 85, Issue 5, 2012, Pages

  Dechant, A ^a,b   Lutz, E ^a,b   Kessler, D A ^c   Barkai, E ^c  

^a UNIVERSITY OF AUGSBURG   (Germany)

^b FREIE UNIVERSITÄT BERLIN   (Germany)

^c BAR ILAN UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL EXPRESSIONS; BOLTZMANN; BOLTZMANN EQUILIBRIUM; BROWNIAN PARTICLES; CORRELATION FUNCTION; COVARIANT; ERGODICITY; LANGEVIN SIMULATIONS; LOGARITHMIC POTENTIALS; STATIONARY CORRELATION; TIME-AVERAGED; TWO-TIME CORRELATION FUNCTION;

CONDENSED MATTER PHYSICS; PHYSICS;

BROWNIAN MOVEMENT;

EID: 84861935403     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.051124     Document Type: Article

References (46)

1. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1991).
2. A.I. Khinchin, Mathematical Foundations of Statistical Mechanics (Dover, New York, 1949).
3. S. Burov, R. Metzler, and E. Barkai, Proc. Natl. Acad. Sci. (USA) PNASA6 0027-8424 10.1073/pnas.1003693107 107, 13228 (2010).
4. A. Weron and M. Magdziarz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.260603 105, 260603 (2010).
5. A. Rebenshtok and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.210601 99, 210601 (2007). (Pubitemid 350137198)
6. A. Dechant, E. Lutz, D.A. Kessler, and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.107.240603 107, 240603 (2011).
7. G. S. Manning, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1672157 51, 924 (1969).
8. Y. Castin, J. Dalibard, and C. Cohen-Tannoudji, in The Limits of Sisyphus Cooling, edited by, L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, and, F. Strumia, Light Induced Kinetic Effects on Atoms, Ions and Molecules (ETS Editrice, Pisa, 1991).
9. S. Marksteiner, K. Ellinger, and P. Zoller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.53.3409 53, 3409 (1996).
10. H. Katori, S. Schlipf, and H. Walther, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.2221 79, 2221 (1997).
11. E. Lutz, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.051402 67, 051402 (R) (2003).
12. P. Douglas, S. Bergamini, and F. Renzoni, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.110601 96, 110601 (2006).
13. Y. Sagi, M. Brook, I. Almog, and N. Davidson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.108.093002 108, 093002 (2012).
14. D. A. Kessler and E. Barkai, Phys. Rev. Lett. (accepted, 2012).
15. A. Dechant and E. Lutz, Phys. Rev. Lett. (accepted, 2012).
16. E. Levine, D. Mukamel, and G.M. Schütz, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2005-10026-2 70, 565 (2005). (Pubitemid 40758640)
17. P. H. Chavanis and R. Manella, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2010-90839-3 78, 139 (2010).
18. F. Bouchet and T. Dauxois, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.72.045103 72, 045103 (R) (2005). (Pubitemid 43273115)
19. F. Bouchet and T. Dauxois, J. Phys.: Conf. Ser. 1742-6588 10.1088/1742-6596/7/1/003 7, 34 (2005).
20. P. H. Chavanis and M. Lemou, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2007-00276-2 59, 217 (2007). (Pubitemid 47599028)
21. M. O. Vlad, Chaos Solitons Fractals CSFOEH 0960-0779 10.1016/0960- 0779(94)90143-0 4, 191 (1994).
22. H. C. Fogedby and R. Metzler, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.76.061915 76, 061915 (2007).
23. H. C. Fogedby and R. Metzler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.070601 98, 070601 (2007).
24. A. Bar, Y. Kafri, and D. Mukamel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.038103 98, 038103 (2007). (Pubitemid 46137820)
25. L. A. Wu, S. S. Wu, and D. Segal, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.061901 79, 061901 (2009).
26. A. J. Bray, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.62.103 62, 103 (2000).
27. A. E. Cohen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94. 118102 94, 118102 (2005). (Pubitemid 40607142)
28. E. Lutz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.190602 93, 190602 (2004).
29. D. A. Kessler and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.120602 105, 120602 (2010).
30. E. Arvedson, M. Wilkinson, B. Mehlig, and K. Nakamura, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.030601 96, 030601 (2006). (Pubitemid 43248085)
31. V. Bezuglyy, B. Mehlig, M. Wilkinson, K. Nakamura, and E. Arvedson, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.2206878 47, 073301 (2006). (Pubitemid 44179657)
32. F. Mota-Furtado and P. F. O'Mahony, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75.041102 75, 041102 (2007). (Pubitemid 46526895)
33. A. T. Silva, E. K. Lenzi, L. R. Evangelista, M. K. Lenzi, H. V. Ribeiro, and A. A. Tateishi, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.3621823 52, 083301 (2011).
34. H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1986).
35. O. Hirschberg, D. Mukamel, and G. M. Schütz, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.84.041111 84, 041111 (2011).
36. O. Hirschberg, D. Mukamel, and G. M. Schütz, J. Stat. Mech. 1742-5468 10.1088/1742-5468/2012/02/P02001 (2012) P02001.
37. R. Shankar, Principles of Quantum Mechanics (Plenum, New York, 1994).
38. A. Dechant, E. Lutz, D. A. Kessler, and E. Barkai, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-011-0363-z 145, 1524 (2011).
39. J. Farago, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2000-00449-1 52, 379 (2000).
40. G. Doetsch, Introduction of the Theory and Application of the Laplace Transformation (Springer, Berlin, 1974).
41. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
42. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, Amsterdam, 2007).
43. E. Martin, U. Behn, and G. Germano, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.051115 83, 051115 (2011).
44. J. P. Bouchaud, J. Phys. I France JPGCE8 1155-4304 10.1051/jp1:1992238 2, 1705 (1992).
45. G. Margolin and E. Barkai, J. Chem. Phys. 121, 1556 (2004).
46. P. Le Doussal, C. Monthus, and D. S. Fisher, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.59.4795 59, 4795 (1999).