Correlation Function and Generalized Master Equation of Arbitrary Age

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Article discussing research on correlation function and generalized master equation of arbitrary age.

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12 p.

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Allegrini, Paolo; Aquino, Gerardo; Grigolini, Paolo; Palatella, Luigi; Rosa, Angelo & West, Bruce J. June 10, 2005.

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Article discussing research on correlation function and generalized master equation of arbitrary age.

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12 p.

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Copyright 2005 American Physical Society. The following article appeared in Physical Review E, 71:6; http://pre.aps.org/abstract/PRE/v71/i6/e066109

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.

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  • Physical Review E, 2005, College Park: American Physical Society

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  • Publication Title: Physical Review E
  • Volume: 71
  • Issue: 6
  • Peer Reviewed: Yes

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UNT Scholarly Works

The Scholarly Works Collection is home to materials from the University of North Texas community's research, creative, and scholarly activities and serves as UNT's Open Access Repository. It brings together articles, papers, artwork, music, research data, reports, presentations, and other scholarly and creative products representing the expertise in our university community.** Access to some items in this collection may be restricted.**

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  • June 10, 2005

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  • Sept. 9, 2011, 2:01 p.m.

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  • May 12, 2014, 5:04 p.m.

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Allegrini, Paolo; Aquino, Gerardo; Grigolini, Paolo; Palatella, Luigi; Rosa, Angelo & West, Bruce J. Correlation Function and Generalized Master Equation of Arbitrary Age, article, June 10, 2005; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc40401/: accessed February 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.