Correlation function and generalized master equation of arbitrary age

Paolo Allegrini, Gerardo Aquino, Paolo Grigolini, Luigi Palatella, Angelo Rosa, and Bruce J. West
Phys. Rev. E 71, 066109 – Published 10 June 2005

Abstract

We study a two-state statistical process with a non-Poisson distribution of sojourn times. In accordance with earlier work, we find that this process is characterized by aging and we study three different ways to define the correlation function of arbitrary age of the corresponding dichotomous fluctuation. These three methods yield exact expressions, thus coinciding with the recent result by Godrèche and Luck [J. Stat. Phys. 104, 489 (2001)]. Actually, non-Poisson statistics yields infinite memory at the probability level, thereby breaking any form of Markovian approximation, including the one adopted herein, to find an approximated analytical formula. For this reason, we check the accuracy of this approximated formula by comparing it with the numerical treatment of the second of the three exact expressions. We find that, although not exact, a simple analytical expression for the correlation function of arbitrary age is very accurate. We establish a connection between the correlation function and a generalized master equation of the same age. Thus this formalism, related to models used in glassy materials, allows us to illustrate an approach to the statistical treatment of blinking quantum dots, bypassing the limitations of the conventional Liouville treatment.

  • Figure
  • Received 17 September 2004

DOI:https://doi.org/10.1103/PhysRevE.71.066109

©2005 American Physical Society

Authors & Affiliations

Paolo Allegrini1, Gerardo Aquino2,*, Paolo Grigolini2,3,4, Luigi Palatella5, Angelo Rosa6, and Bruce J. West7

  • 1INFM, unità di Como, Via Valleggio 11, 22100 Como, Italy
  • 2Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, Texas 76203-1427, USA
  • 3Dipartimento di Fisica dell’Università di Pisa and INFM, Via Buonarroti 2, 56127 Pisa, Italy
  • 4Istituto dei Processi Chimico Fisici del CNR Area della Ricerca di Pisa, Via G. Moruzzi 1, 56124 Pisa, Italy
  • 5Dipartimento di Fisica and Istituto dei Sistemi Complessi del CNR, Università di Roma “La Sapienza,” P.le A. Moro 2, 00185 Rome, Italy
  • 6Institut de Mathématiques B, Faculté des Sciences de Base, École Polytechique Fédérale de Lausanne, 1015 Lausanne, Switzerland
  • 7Mathematics Division, Army Research Office, Research Triangle Park, North Carolina 27709, USA

  • *Corresponding author. Present address: Institute for Theoretical Physics, University of Amsterdam, Valckeniarstraat 65, 1018XE Amsterdam, the Netherlands. Email address: gaquino@science.uva.nl

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Issue

Vol. 71, Iss. 6 — June 2005

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