Phys. Rev. E 74, 021108 (2006) [6 pages]
Dynamical origin of memory and renewal
Abstract
References (31)
Citing Articles
R. Cakir, 1 P. Grigolini, 1,2,3 and A. A. Krokhin11Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, Texas 76203, USA
2Dipartimento di Fisica dell'Università di Pisa and INFM, via Buonarroti 2, 56127 Pisa, Italy
3Istituto dei Processi Chimico Fisici del CNR Area della Ricerca di Pisa, Via G. Moruzzi 1, 56124 Pisa, Italy
Received 24 June 2005; revised 5 May 2006; published 8 August 2006
We show that the dynamic approach to fractional Brownian motion (FBM) establishes a link between a non-Poisson renewal process with abrupt jumps resetting to zero the system's memory and correlated dynamic processes, whose individual trajectories keep a nonvanishing memory of their past time evolution. It is well known that the recrossings of the origin by an ordinary one-dimensional diffusion trajectory generates a Lévy (and thus renewal) process of index  =1/2. We prove with theoretical and numerical arguments that this is the special case of a more general condition, insofar as the recrossings produced by the dynamic FBM generates a Lévy process with 0<<1. This result is extended to produce a satisfactory model for the fluorescent signal of blinking quantum dots.
©2006 The American Physical Society
REFERENCES (31)
For access to fully linked references, you need to log in.
For access to fully linked references, you need to Log in.
- M. Kuno, D. P. Fromm, H. F. Hamann, A. Gallagher, and D. J. Nesbitt, J. Chem. Phys. 115, 1028 (2001).
- F. Cichos, J. Martin, and C. von Borczyskowski, Phys. Rev. B 70, 115314 (2004).
- X. Brokmann, J.-P. Hermier, G. Messin, P. Desbiolles, J.-P. Bouchaud, and M. Dahan, Phys. Rev. Lett. 90, 120601 (2003).
- S. Bianco, P. Grigolini, and P. Paradisi, J. Chem. Phys. 123, 174704 (2005).
- G. Margolin and E. Barkai, Phys. Rev. Lett. 94, 080601 (2005).
- G. Aquino, L. Palatella, and P. Grigolini, Phys. Rev. Lett. 93, 050601 (2004).
- J. Tang and R. A. Marcus, Phys. Rev. Lett. 95, 107401 (2005).
- S. C. Lim and S. V. Muniandy, Phys. Rev. E 66, 021114 (2002).
- E. Barkai, Phys. Rev. Lett. 90, 104101 (2003).
- R. Failla, P. Grigolini, M. Ignaccolo, and A. Schwettmann, Phys. Rev. E 70, 010101(R) (2004).
- E. Barkai and Y.-C. Cheng, J. Chem. Phys. 118, 6167 (2003).
- M. Ding and W. Yang, Phys. Rev. E 52, 207 (1995).
- J. Krug, H. Kallabis, S. N. Majumdar, S. J. Cornell, A. J. Bray, and C. Sire, Phys. Rev. E 56, 2702 (1997).
- J. Merikoski, J. Maunuksela, M. Myllys, J. Timonen, and M. J. Alava, Phys. Rev. Lett. 90, 024501 (2003).
- S. N. Majumdar and D. Das, Phys. Rev. E 71, 036129 (2005).
- J. Krug and H. T. Dobbs, Phys. Rev. Lett. 76, 4096 (1996).
- G. Margolin and E. Barkai, J. Chem. Phys. 121, 1566 (2004).
- M. Annunziato, P. Grigolini, and J. Riccardi, Phys. Rev. E 61, 4801 (2000).
- U. Kuhl, F. M. Izrailev, A. A. Krokhin, and H.-J. Stöckmann, Appl. Phys. Lett. 77, 633 (2000);
F. M. Izrailev, A. A. Krokhin, and S. E. Ulloa, Phys. Rev. B 63, 041102(R) (2001).
- G. Aquino, M. Bologna, P. Grigolini, and B. J. West, Phys. Rev. E 70, 036105 (2004).
CITING ARTICLES
For access to citing articles, you need to log in.For access to citing articles, you need to Log in.
|
A new free weekly publication from APS
|
You are not logged in to this journal. Log in
| Subscription Information
View Cart
Download Citation
MyScitation
Print View