| Description: | This article discusses correlation function and generalized master equation of arbitrary age. 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 fo the conventional Liouville treatment. |
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| Creator(s): | |
| Creation Date: | June 10, 2005 |
| Partner(s): |
UNT College of Arts and Sciences
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| Collection(s): |
UNT Scholarly Works
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| Usage: |
Total Uses: 70
Past 30 days: 5
Yesterday: 0
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| Creator (Author): |
Allegrini, Paolo
Unitá di Como |
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| Creator (Author): |
Aquino, Gerardo
University of North Texas |
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| Creator (Author): |
Grigolini, Paolo
University of North Texas; Universitá di Pisa and INFM; Area della Ricerca di Pisa |
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| Creator (Author): |
Palatella, Luigi
Universitá di Roma |
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| Creator (Author): |
Rosa, Angelo
École Polytechique Fédérale de Lausanne |
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| Creator (Author): |
West, Bruce J.
United States. Army Research Office |
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| Publisher Info: |
Publisher Name: American Physical Society
Place of Publication: [College Park, Maryland]
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| Original Creation Date: | June 10, 2005 | |
| Description: | This article discusses correlation function and generalized master equation of arbitrary age. 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 fo the conventional Liouville treatment. |
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| Degree: |
Department:
Physics
Department:
Center for Nonlinear Science
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| 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 |
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| Physical Description: |
12 p. |
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| Keyword(s): | non-Poisson | arbitrary ages | |
| Source: | Physical Review E, 2005, College Park: American Physical Society | |
| Partner: |
UNT College of Arts and Sciences
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| Collection: |
UNT Scholarly Works
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| Identifier: |
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| Resource Type: | Article | |
| Format: | Text | |
| Rights: |
Access:
Public
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| Citation: |
Publication Title: Physical Review E
Volume: 71
Issue: 6
Peer Reviewed: Yes
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