First-passage statistics for aging diffusion in systems with annealed and quenched disorder

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

Volumn 89, Issue 4, 2014, Pages

  Krüsemann, Henning ^a   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

AMORPHOUS SEMICONDUCTORS; RANDOM PROCESSES;

BIOLOGICAL CELLS; CONTINUOUS TIME RANDOM WALKS; FIRST-PASSAGE TIME; FUNDAMENTAL PROPERTIES; PHYSICAL PROCESS; QUENCHED DISORDER; SCALING EXPONENT; TRACER DISPERSION;

DYNAMICS;

EID: 84899733765     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.89.040101     Document Type: Article

References (73)

1. H. Scher and E. W. Montroll, Phys. Rev. B 12, 2455 (1975). 10.1103/PhysRevB.12.2455
2. R. Steyrleuthner, Adv. Mater. 22, 2799 (2010). ADVMEW 0935-9648 10.1002/adma.201000232
3. J.-P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990); 10.1016/0370-1573(90)90099-N
4. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000) PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3;
5. R. Metzler and J. Klafter, J. Phys. A 37, R161 (2004). JPHAC5 0305-4470 10.1088/0305-4470/37/31/R01 (Pubitemid 39063557)
6. B. Berkowitz, A. Cortis, M. Dentz, and H. Scher, Rev. Geophys. 44, RG2003 (2006) REGEEP 8755-1209 10.1029/2005RG000178;
7. H. Scher, G. Margolin, R. Metzler, J. Klafter, and B. Berkowitz, Geophys. Res. Lett. 29, 1061 (2002). GPRLAJ 0094-8276 10.1029/2001GL014123
8. S. M. A. Tabei, Proc. Natl. Acad. Sci. USA 110, 4911 (2013) PNASA6 0027-8424 10.1073/pnas.1221962110;
9. A. V. Weigel, B. Simon, M. M. Tamkun, and D. Krapf, Proc. Natl. Acad. Sci. USA 108, 6438 (2011). PNASA6 0027-8424 10.1073/pnas.1016325108
10. J.-H. Jeon, Phys. Rev. Lett. 106, 048103 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.048103
11. I. Y. Wong, Phys. Rev. Lett. 92, 178101 (2004) PRLTAO 0031-9007 10.1103/PhysRevLett.92.178101;
12. Q. Xu, L. Feng, R. Sha, N. C. Seeman, and P. M. Chaikin, Phys. Rev. Lett. 106, 228102 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.228102
13. X. Brokmann, Phys. Rev. Lett. 90, 120601 (2003) PRLTAO 0031-9007 10.1103/PhysRevLett.90.120601;
14. G. Margolin and E. Barkai, J. Chem. Phys. 121, 1566 (2004) JCPSA6 0021-9606 10.1063/1.1763136;
15. F. D. Stephani, J. P. Hoogenboom, and E. Barkai, Phys. Today 62, 34 (2009). PHTOAD 0031-9228 10.1063/1.3086100
16. F. Bardou, J.-P. Bouchaud, A. Aspect, and C. Cohen-Tannoudji, Lévy Statistics and Laser Cooling (Cambridge University Press, Cambridge, UK, 2002).
17. J.-P. Bouchaud, J. Phys. I (France) 2, 1705 (1992); 10.1051/jp1:1992238
18. G. Bel and E. Barkai, Phys. Rev. Lett. 94, 240602 (2005) PRLTAO 0031-9007 10.1103/PhysRevLett.94.240602;
19. A. Rebenshtok and E. Barkai, Phys. Rev. Lett. 99, 210601 (2007) PRLTAO 0031-9007 10.1103/PhysRevLett.99.210601;
20. M. A. Lomholt, I. M. Zaid, and R. Metzler, Phys. Rev. Lett. 98, 200603 (2007); PRLTAO 0031-9007 10.1103/PhysRevLett.98.200603 (Pubitemid 47139586)
21. M. Khoury, A. M. Lacasta, J. M. Sancho, and K. Lindenberg, Phys. Rev. Lett. 106, 090602 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.090602
22. E. Barkai, Y. Garini, and R. Metzler, Phys. Today 65, 29 (2012). PHTOAD 0031-9228 10.1063/PT.3.1677
23. C. Monthus and J.-P. Bouchaud, J. Phys. A 29, 3847 (1996) JPHAC5 0305-4470 10.1088/0305-4470/29/14/012;
24. B. Rinn, P. Maass, and J.-P. Bouchaud, Phys. Rev. Lett. 84, 5403 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.84.5403
25. C. Godrèche and J. M. Luck, J. Stat. Phys. 104, 489 (2001). 10.1023/A:1010364003250
26. Compare also N. H. Bingham, Adv. Appl. Prob. 7, 705 (1975); 10.2307/1426397
27. N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation (Cambridge University Press, Cambridge, UK, 1987).
28. E. Barkai and Y.-C. Cheng, J. Chem. Phys. 118, 6167 (2003). JCPSA6 0021-9606 10.1063/1.1559676
29. Certain aging effects persist for (Equation presented) when (Equation presented) is finite but (Equation presented) has diverging fluctuations: P. Allegrini, Phys. Rev. E 66, 015101 (2002) 1063-651X 10.1103/PhysRevE.66.015101;
30. P. Allegrini, G. Aquino, P. Grigolini, L. Palatella, and A. Rosa, Phys. Rev. E 68, 056123 (2003). 1063-651X 10.1103/PhysRevE.68.056123
31. E. M. Bertin and J.-P. Bouchaud, Phys. Rev. E 67, 026128 (2003) PRLTAO 1063-651X 10.1103/PhysRevE.67.026128;
32. S. Burov and E. Barkai, Phys. Rev. Lett. 98, 250601 (2007). 0031-9007 10.1103/PhysRevLett.98.250601 (Pubitemid 47139918)
33. E. Barkai, Phys. Rev. Lett. 90, 104101 (2003) PRLTAO 0031-9007 10.1103/PhysRevLett.90.104101;
34. T. Geisel and S. Thomae, Phys. Rev. Lett. 52, 1936 (1984) PRLTAO 0031-9007 10.1103/PhysRevLett.52.1936;
35. G. Radons, Adv. Solid State Phys. 38, 439 (1999). 9783-5404 10.1007/BFb0107635
36. M. Schubert, Phys. Rev. B 87, 024203 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87.024203
37. J. H. P. Schulz, E. Barkai, and R. Metzler, Phys. Rev. Lett. 110, 020602 (2013) PRLTAO 0031-9007 10.1103/PhysRevLett.110.020602;
38. J. H. P. Schulz, E. Barkai, and R. Metzler, Phys. Rev. X 4, 011028 (2014). 2160-3308 10.1103/PhysRevX.4.011028
39. B. D. Hughes, Random Walks and Random Environments (Oxford University Press, Oxford, UK, 1995), Vol. 1.
40. The Laplace transform of a function (Equation presented) is defined as (Equation presented).
41. R. Metzler and J. Klafter, Physica A 278, 107 (2000) PHYADX 0378-4371 10.1016/S0378-4371(99)00503-8.
42. S. Redner, A Guide to First-passage Processes (Cambridge University Press, Cambridge, UK, 2001).
43. This transform is defined in terms of (Equation presented).
44. H. Krüsemann, A. Godec, and R. Metzler (unpublished).
45. This method breaks down for long-range correlated Gaussian processes [29] and Lévy flights. See, e.g., A. Zoia, A. Rosso, and M. Kardar, Phys. Rev. E 76, 021116 (2007) PLEEE8 1539-3755 10.1103/PhysRevE.76.021116;
46. A. V. Chechkin, J. Phys. A 36, L537 (2003). JPHAC5 0305-4470 10.1088/0305-4470/36/41/L01 (Pubitemid 37331371)
47. J. Klafter and I. M. Sokolov, First Steps in Random Walks: From Tools to Applications (Cambridge University Press, Cambridge, UK, 2011).
48. S. N. Majumdar, A. Rosso, and A. Zoia, Phys. Rev. Lett. 104, 020602 (2010); PRLTAO 0031-9007 10.1103/PhysRevLett.104.020602
49. see also J.-H. Jeon, A. V. Checkin, and R. Metzler, Europhys. Lett. 94, 20008 (2011). EULEEJ 0295-5075 10.1209/0295-5075/94/20008
50. J. Kursawe, J. H. P. Schulz, and R. Metzler, Phys. Rev. E 88, 062124 (2013). PLEEE8 1539-3755 10.1103/PhysRevE.88.062124
51. A. G. Cherstvy, A. V. Chechkin, and R. Metzler, New J. Phys. 15, 083039 (2013); NJOPFM 1367-2630 10.1088/1367-2630/15/8/083039
52. A. G. Cherstvy and R. Metzler, Phys. Chem. Chem. Phys. 15, 20220 (2013); 10.1039/c3cp53056f
53. P. Massignan, C. Manzo, J. A. Torreno-Pina, M. F. García-Parajo, M. Lewenstein, and G. J. Lapeyre, Jr., Phys. Rev. Lett. 112, 150603 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.112.150603
54. S. C. Lim and S. V. Muniandy, Phys. Rev. E 66, 021114 (2002) PLEEE8 1063-651X 10.1103/PhysRevE.66.021114;
55. F. Thiel and I. M. Sokolov, Phys. Rev. E 89, 012115 (2014). 1539-3755 10.1103/PhysRevE.89.012115
56. Here (Equation presented) denotes a function that is formally defined in terms of its Laplace image as (Equation presented). For (Equation presented), this is no longer a one-sided stable law.
57. R. Metzler, E. Barkai, and J. Klafter, Phys. Rev. Lett. 82, 3563 (1999). PRLTAO 0031-9007 10.1103/PhysRevLett.82.3563
58. S. Burov and E. Barkai, Phys. Rev. E 86, 041137 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.86.041137
59. J. W. Kirchner, X. Feng, and C. Neal, Nature (London) 403, 524 (2000). NATUAS 0028-0836 10.1038/35000537 (Pubitemid 30082193)
60. S. Burov, R. Metzler, and E. Barkai, Proc. Natl. Acad. Sci. USA 107, 13228 (2010). PNASA6 0027-8424 10.1073/pnas.1003693107
61. M. Magdziarz, A. Weron, K. Burnecki, and J. Klafter, Phys. Rev. Lett. 103, 180602 (2009) PRLTAO 0031-9007 10.1103/PhysRevLett.103.180602;
62. K. Burnecki, Biophys. J. 103, 1839 (2012). BIOJAU 0006-3495 10.1016/j.bpj.2012.09.040
63. S. Condamin, V. Tejedor, R. Voituriez, O. Bénichou, and J. Klafter, Proc. Natl. Acad. Sci. USA 105, 5675 (2008). PNASA6 0027-8424 10.1073/pnas.0712158105 (Pubitemid 351758430)
64. I. M. Sokolov, Soft Matter 8, 9043 (2012) PRLTAO 1744-683X 10.1039/c2sm25701g;
65. F. Thiel, F. Flegel, and I. M. Sokolov, Phys. Rev. Lett. 111, 010601 (2013). 0031-9007 10.1103/PhysRevLett.111.010601
66. V. Tejedor, Biophys. J. 98, 1364 (2010) BIOJAU 0006-3495 10.1016/j.bpj.2009.12.4282;
67. J.-H. Jeon, E. Barkai, and R. Metzler, J. Chem. Phys. 139, 121916 (2013) JCPSA6 0021-9606 10.1063/1.4816635;
68. A. Cherstvy, A. V. Chechkin, and R. Metzler, Soft Matter 10, 1591 (2014). 1744-683X 10.1039/c3sm52846d
69. T. Albers and G. Radons, Europhys. Lett. 102, 40006 (2013) EULEEJ 0295-5075 10.1209/0295-5075/102/40006;
70. M. Heidernaetsch, M. Bauer, and G. Radons, J. Chem. Phys. 139, 184105 (2013). JCPSA6 0021-9606 10.1063/1.4828860
71. A. M. Berezhkovskii, L. Dagdug, and S. M. Bezrukov, Biophys. J. 106, L09 (2014) BIOJAU 0006-3495 10.1016/j.bpj.2013.12.013;
72. M. Saxton, Biophys. J. 103, 2411 (2012) BIOJAU 0006-3495 10.1016/j.bpj.2012.10.038;
73. M. Saxton, Biophys. J. 72, 1744 (1997). BIOJAU 0006-3495 10.1016/S0006-3495(97)78820-9