Dynamical Origin of Memory and Renewal

Description:

This article discusses a dynamical origin of memory and renewal.

Creator(s):
Creation Date: August 8, 2006
Partner(s):
UNT College of Arts and Sciences
Collection(s):
UNT Scholarly Works
Usage:
Total Uses: 69
Past 30 days: 3
Yesterday: 2
Creator (Author):
Cakir, Rasit

University of North Texas

Creator (Author):
Grigolini, Paolo

University of North Texas; Universitá di Pisa; Area della Ricerca di Pisa

Creator (Author):
Krokhin, Arkadii A.

University of North Texas

Publisher Info:
Publisher Name: American Physical Society
Place of Publication: [College Park, Maryland]
Date(s):
  • Creation: August 8, 2006
Description:

This article discusses a dynamical origin of memory and renewal.

Degree:
Department: Physics
Note:

Copyright 2006 American Physical Society. The following article appeared in Physical Review Letters E, 74:2; http://pre.aps.org/abstract/PRE/v74/i2/e021108

Note:

Abstract: 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 θ=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<θ<1. This result is extended to produce a satisfactory model for the fluorescent signal of blinking quantum dots.

Physical Description:

6 p.

Language(s):
Subject(s):
Keyword(s): fractional Brownian motion | non-Poisson | Lévy
Source: Physical Review E, 2006, College Park: American Physical Society
Partner:
UNT College of Arts and Sciences
Collection:
UNT Scholarly Works
Identifier:
  • DOI: 10.1103/PhysRevE.74.021108
  • ARK: ark:/67531/metadc40399
Resource Type: Article
Format: Text
Rights:
Access: Public
Citation:
Publication Title: Physical Review E
Volume: 74
Issue: 2
Peer Reviewed: Yes