Finite-time effects and ultraweak ergodicity breaking in superdiffusive dynamics

Physical Review Letters

Volumn 110, Issue 2, 2013, Pages

  Godec, Aljaž ^a,b   Metzler, Ralf ^a,c  

^a UNIVERSITY OF POTSDAM   (Germany)

^b NATIONAL INSTITUTE OF CHEMISTRY   (Slovenia)

^c TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

BALLISTIC MOTIONS; CONSTANT FACTORS; ERGODIC PROPERTY; ERGODICITY; FINITE DURATION; MEAN SQUARED DISPLACEMENT; MEASUREMENT TIME; QUANTITATIVE EVALUATION; SCALING EXPONENT; SECOND MOMENTS; STRONG CONTRAST; SUBDIFFUSION; SUPERDIFFUSIVE DYNAMICS; TIME AVERAGES; TIME-AVERAGED;

ATOMIC PHYSICS;

PHYSICS;

ARTICLE; DIFFUSION; MOVEMENT (PHYSIOLOGY); THEORETICAL MODEL; TIME;

DIFFUSION; MODELS, THEORETICAL; MOVEMENT; TIME FACTORS;

EID: 84872222447     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.110.020603     Document Type: Article

References (41)

1. D. W. Sims, Nature (London) 451, 1098 (2008); NATUAS 0028-0836 10.1038/nature06518 (Pubitemid 351317439)
2. N. E. Humphries, Nature (London) 465, 1066 (2010). NATUAS 0028-0836 10.1038/nature09116
3. T. H. Solomon, E. R. Weeks, and H. L. Swinney, Phys. Rev. Lett. 71, 3975 (1993); PRLTAO 0031-9007 10.1103/PhysRevLett.71.3975
4. G. Zumofen and J. Klafter, Phys. Rev. E 51, 1818 (1995). PLEEE8 1063-651X 10.1103/PhysRevE.51.1818
5. R. Nathan, W. M. Getz, E. Revilla, M. Holyoak, R. Kadmon, D. Saltz, and P. E. Smouse, Proc. Natl. Acad. Sci. U.S.A. 105, 19 052 (2008). PNASA6 0027-8424 10.1073/pnas.0800375105
6. M. C. González, C. A. Hidalgo, and A.-L. Barabási, Nature (London) 453, 779 (2008); NATUAS 0028-0836 10.1038/nature06958 (Pubitemid 351793783)
7. D. Brockmann, Phys. World 23, No. 2, 31 (2010). PHWOEW 0953-8585
8. G. Ramos-Fernández, J. L. Mateos, O. Miramontes, G. Cocho, H. Larralde, and B. Ayala-Orozco, Behav. Ecol. Sociobiol. 55, 223 (2004). BESOD6 0340-5443 10.1007/s00265-003-0700-6 (Pubitemid 38162060)
9. G. Zumofen and J. Klafter, Phys. Rev. E 47, 851 (1993). PLEEE8 1063-651X 10.1103/PhysRevE.47.851
10. G. Zumofen and J. Klafter, Physica (Amsterdam) 69, 436 (1993). PDNPDT 0167-2789 10.1016/0167-2789(93)90105-A
11. T. Geisel and S. Thomae, Phys. Rev. Lett. 52, 1936 (1984). PRLTAO 0031-9007 10.1103/PhysRevLett.52.1936
12. T. Geisel, J. Nierwetberg, and A. Zacherl, Phys. Rev. Lett. 54, 616 (1985). PRLTAO 0031-9007 10.1103/PhysRevLett.54.616
13. R. Fleischmann, T. Geisel, and R. Ketzmerick, Europhys. Lett. 25, 219 (1994). EULEEJ 0295-5075 10.1209/0295-5075/25/3/011
14. S. Marksteiner, K. Ellinger, and P. Zoller, Phys. Rev. A 53, 3409 (1996). PLRAAN 1050-2947 10.1103/PhysRevA.53.3409
15. P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature (London) 453, 495 (2008). NATUAS 0028-0836 10.1038/nature06948 (Pubitemid 351733320)
16. Y.-J. Jung, E. Barkai, and R. J. Silbey, Chem. Phys. 284, 181 (2002). CMPHC2 0301-0104 10.1016/S0301-0104(02)00547-5
17. M. de Jager, F. J. Weissing, P. M. J. Herman, B. A. Nolet, and J. van de Koppel, Science 332, 1551 (2011). SCIEAS 0036-8075 10.1126/science.1201187
18. T. H. Harris, Nature (London) 486, 545 (2012). NATUAS 0028-0836 10.1038/nature11098
19. E. Barkai, Y. Garini, and R. Metzler, Phys. Today 65, No. 8, 29 (2012). PHTOAD 0031-9228 10.1063/PT.3.1677
20. Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. 101, 058101 (2008); PRLTAO 0031-9007 10.1103/PhysRevLett.101.058101
21. S. Burov, J.-H. Jeon, R. Metzler, and E. Barkai, Phys. Chem. Chem. Phys. 13, 1800 (2011). PPCPFQ 1463-9076 10.1039/c0cp01879a
22. A. Lubelski, I. M. Sokolov, and J. Klafter, Phys. Rev. Lett. 100, 250602 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.100.250602
23. W. Deng and E. Barkai, Phys. Rev. E 79, 011112 (2009); PLEEE8 1539-3755 10.1103/PhysRevE.79.011112
24. I. Goychuk, Phys. Rev. E 80, 046125 (2009); PLEEE8 1539-3755 10.1103/PhysRevE.80.046125
25. J.-H. Jeon and R. Metzler, Phys. Rev. E 81, 021103 (2010). PLEEE8 1539-3755 10.1103/PhysRevE.81.021103
26. Note that even ergodic anomalous diffusion processes may show nonergodic features under confinement, see J.-H. Jeon and R. Metzler, Phys. Rev. E 85, 021147 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.85.021147
27. A. V. Weigel, B. Simon, M. M. Tamkun, and D. Krapf, Proc. Natl. Acad. Sci. U.S.A. 108, 6438 (2011). PNASA6 0027-8424 10.1073/pnas.1016325108
28. J.-H. Jeon, V. Tejedor, S. Burov, E. Barkai, C. Selhuber-Unkel, K. Berg-Sørensen, L. Oddershede, and R. Metzler, Phys. Rev. Lett. 106, 048103 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.048103
29. M. F. Shlesinger, J. Klafter, and Y. M. Wong, J. Stat. Phys. 27, 499 (1982). JSTPBS 0022-4715 10.1007/BF01011089
30. E. W. Montroll and G. H. Weiss, J. Math. Phys. (N.Y.) 10, 753 (1969); JMAPAQ 0022-2488 10.1063/1.1664902
31. H. Scher and E. W. Montroll, Phys. Rev. B 12, 2455 (1975). PLRBAQ 0556-2805 10.1103/PhysRevB.12.2455
32. J. Klafter, A. Blumen, and M. F. Shlesinger, Phys. Rev. A 35, 3081 (1987). PLRAAN 0556-2791 10.1103/PhysRevA.35.3081
33. J. Klafter, M. F. Shlesinger, and G. Zumofen, Phys. Today 49, No. 2, 33 (1996). PHTOAD 0031-9228 10.1063/1.881487
34. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000); PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3
35. R. Metzler J. Klafter J. Phys. A 37, R161 (2004). JPHAC5 0305-4470 10.1088/0305-4470/37/31/R01 (Pubitemid 39063557)
36. G. Trefán, E. Floriani, B. J. West, and P. Grigolini, Phys. Rev. E 50, 2564 (1994). PLEEE8 1063-651X 10.1103/PhysRevE.50.2564
37. I. M. Sokolov and R. Metzler, Phys. Rev. E 67, 010101 (2003). PLEEE8 1063-651X 10.1103/PhysRevE.67.010101
38. M. Magdziarz, W. Szczotka, and P. Zebrowski, J. Stat. Phys. 147, 74 (2012). JSTPBS 0022-4715 10.1007/s10955-012-0465-2
39. R. Kubo, Rep. Prog. Phys. 29, 255 (1966); RPPHAG 0034-4885 10.1088/0034-4885/29/1/306
40. J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic Press, Amsterdam, 2006), 3rd ed.
41. D. Froemberg and E. Barkai, arXiv:1211.1539.