Time-averaged Einstein relation and fluctuating diffusivities for the Lévy walk

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

Volumn 87, Issue 3, 2013, Pages

  Froemberg, D ^a   Barkai, E ^a  

^a BAR ILAN UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL EXPRESSIONS; BALLISTIC PHASE; EINSTEIN RELATIONS; ENHANCED DIFFUSION; ENSEMBLE AVERAGES; MEAN SQUARED DISPLACEMENT; SINGLE PARTICLE TRACKING; STOCHASTIC FRAMEWORK;

CONDENSED MATTER PHYSICS; PHYSICS;

STOCHASTIC MODELS;

EID: 84875988673     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.87.030104     Document Type: Article

References (48)

1. J. P. Bouchaud, J. Phys. I JPGCE8 1155-4304 10.1051/jp1:1992238 2, 1705 (1992).
2. J. P. Bouchaud and A. Georges, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(90)90099-N 195, 127 (1990).
3. A rigorous mathematical theory related to weak ergodicity breaking can be found in J. Aaronson, An Introduction to Infinite Ergodic Theory (American Mathematical Society, Providence, RI, 1997).
4. R. Klages, G. Radons, and I. M. Sokolov, Anomalous Transport (Wiley-VCH, Weinheim, 2008), Chap. 7.
5. G. Bel and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.240602 94, 240602 (2005). (Pubitemid 41636460)
6. A. Rebenshtok and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.210601 99, 210601 (2007); (Pubitemid 350137198)
7. A. Rebenshtok and E. Barkai, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-008-9610-3 133, 565 (2008).
8. Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.058101 101, 058101 (2008).
9. A. Lubelski, I. M. Sokolov, and J. Klafter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.250602 100, 250602 (2008).
10. X. Brokmann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90. 120601 90, 120601 (2003).
11. F. D. Stefani, J. P. Hoogenboom, and E. Barkai, Phys. Today PHTOAD 0031-9228 10.1063/1.3086100 62 (2), 34 (2009).
12. A. V. Weigel, B. Simon, M. M. Tamkun, and D. Krapf, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.1016325108 108, 6438 (2011).
13. J.-H. Jeon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106. 048103 106, 048103 (2011).
14. E. Barkai, Y. Garini, and R. Metzler, Phys. Today PHTOAD 0031-9228 10.1063/PT.3.1677 65 (8), 29 (2012).
15. E. Barkai and V. N. Fleurov, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.58.1296 58, 1296 (1998).
16. T. Akimoto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.108. 164101 108, 164101 (2012).
17. G. Margolin and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.080601 94, 080601 (2005). (Pubitemid 40620642)
18. J. Klafter, M. F. Shlesinger, and G. Zumofen, Phys. Today PHTOAD 0031-9228 10.1063/1.881487 49 (2), 33 (1996).
19. M. F. Shlesinger, B. J. West, and J. Klafter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.58.1100 58, 1100 (1987).
20. M. Magdziarz, W. Szczotka, and P. Åebrowski, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-012-0465-2 147, 74 (2012).
21. N. E. Humphries, Nature (London) NATUAS 0028-0836 10.1038/nature09116 465, 1066 (2010).
22. G. Zumofen and J. Klafter, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.47.851 47, 851 (1993).
23. T. Geisel, A. Zacherl, and G. Radons, Z. Phys. B ZPCMDN 0722-3277 10.1007/BF01310851 71, 117 (1988).
24. T. Geisel, J. Nierwetberg, and A. Zacherl, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.54.616 54, 616 (1985).
25. T. H. Solomon, E. R. Weeks, and H. L. Swinney, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.3975 71, 3975 (1993).
26. G. Margolin and E. Barkai, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1763136 121, 1566 (2004).
27. N. Gal and D. Weihs, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81. 020903 81, 020903 (2010).
28. V. Zaburdaev, S. Denisov, and P. Hänggi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.180601 106, 180601 (2011).
29. Y. Sagi, M. Brook, I. Almog, and N. Davidson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.108.093002 108, 093002 (2012).
30. D. A. Kessler and E. Barkai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.108.230602 108, 230602 (2012).
31. A. Dhar, K. Saito, and B. Derrida, Phys. Rev. E 1539-3755 10.1103/PhysRevE.87.010103 87, 010103 (R) (2013).
32. G. Zumofen, J. Klafter, and A. Blumen, Chem. Phys. CMPHC2 0301-0104 10.1016/0301-0104(90)80062-3 146, 433 (1990).
33. J. Masoliver, K. Lindenberg, and G. H. Weiss, Physica A PHYADX 0378-4371 10.1016/0378-4371(89)90071-X 157, 891 (1989).
34. C. Godrèche and J. M. Luck, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1010364003250 104, 489 (2001).
35. ) 2 Δ 3 / T for T ≠Δ.
36. Provided the two transitions do not fall within a time interval Δ.
37. W. Feller, An Introduction to Probability Theory and its Applications (Wiley, New York, 1966), Vol. 2.
38. ) for τ > 1. In the opposite limit Δ â‰ 1 ≠T we have χ 2 = 2 v 0 2 Δ 3 / (3 T).
39. g (ξ) is the density of the so-called Mittag-Leffler distribution.
40. 1 + Δ) âŒ, Eqs. and.
41. G. Zumofen and J. Klafter, Physica D PDNPDT 0167-2789 10.1016/0167-2789(93)90105-A 69, 436 (1993).
42. E. Barkai and V. N. Fleurov, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.56.6355 56, 6355 (1997).
43. A. Caspi, R. Granek, and M. Elbaum, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.66.011916 66, 011916 (2002). (Pubitemid 40599009)
44. L. Bruno, V. Levi, M. Brunstein, and M. A. Desposito, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.011912 80, 011912 (2009).
45. D. Boyer, D. S. Dean, C. Mejía-Monasterio, and G. Oshanin, Phys. Rev E PLEEE8 1539-3755 10.1103/PhysRevE.86.060101 86, 060101 (R) (2012).
46. A. W. C. Lau, B. D. Hoffmann, A. Davies, J. C. Crocker, and T. C. Lubensky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.198101 91, 198101 (2003).
47. This work reports the PDF of δ 2 ̄ in the case of Lévy flights: K. Burnecki and A. Weron, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.021130 82, 021130 (2010).
48. A. Godec and R. Metzler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.110.020603 110, 020603 (2013).