Correlation Function and Generalized Master Equation of Arbitrary Age Metadata
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- Main Title Correlation Function and Generalized Master Equation of Arbitrary Age
Author: Allegrini, PaoloCreator Type: PersonalCreator Info: Unitá di Como
Author: Aquino, GerardoCreator Type: PersonalCreator Info: University of North Texas
Author: Grigolini, PaoloCreator Type: PersonalCreator Info: University of North Texas; Universitá di Pisa and INFM; Area della Ricerca di Pisa
Author: Palatella, LuigiCreator Type: PersonalCreator Info: Universitá di Roma
Author: Rosa, AngeloCreator Type: PersonalCreator Info: École Polytechique Fédérale de Lausanne
Author: West, Bruce J.Creator Type: PersonalCreator Info: United States. Army Research Office
Name: American Physical SocietyPlace of Publication: [College Park, Maryland]
- Creation: 2005-06-10
- Content Description: Article discussing research on correlation function and generalized master equation of arbitrary age.
- Physical Description: 12 p.
- Keyword: non-Poisson
- Keyword: arbitrary ages
- Journal: Physical Review E, 2005, College Park: American Physical Society
- Publication Title: Physical Review E
- Volume: 71
- Issue: 6
- Peer Reviewed: True
Name: UNT Scholarly WorksCode: UNTSW
Name: UNT College of Arts and SciencesCode: UNTCAS
- Rights Access: public
- DOI: 10.1103/PhysRevE.71.066109
- Archival Resource Key: ark:/67531/metadc40401
- Academic Department: Physics
- Academic Department: Center for Nonlinear Science
- Display Note: Copyright 2005 American Physical Society. The following article appeared in Physical Review E, 71:6; http://pre.aps.org/abstract/PRE/v71/i6/e066109
- Display Note: 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.