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Generalized Elastic Model: Fractional Langevin Description, Fluctuation Relation and Linear Response

Published online by Cambridge University Press:  24 April 2013

A. Taloni ,
A. Chechkin  and
J. Klafter
A. Taloni
Affiliation:
CNR-IENI, Via R. Cozzi 53, 20125 Milano, Italy
A. Chechkin
Affiliation:
Max-Planck-Institute for Physics of Complex Systems, Noethnitzer Str. 38 D-91187 Dresden, Germany Akhiezer Institute for Theoretical Physics, NSC KIPT, Kharkov 61108, Ukraine
J. Klafter*
Affiliation:
School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
*
⋆ Corresponding author. E-mail: alessandro.taloni@gmail.com
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Abstract

The Generalized Elastic Model is a linear stochastic model which accounts for the behaviour of many physical systems in nature, ranging from polymeric chains to single-file systems. If an external perturbation is exerted only on a single point x⋆ (tagged probe), it propagates throughout the entire system. Within the fractional Langevin equation framework, we study the effect of such a perturbation, in cases of a constant force applied. We report most of the results arising from our previous analysis and, in the present work, we show that the Fox H-functions formalism provides a compact, elegant and useful tool for the study of the scaling properties of any observable. In particular we show how the generalized Kubo fluctuation relations can be expressed in terms of H-functions.

Keywords

fractional Langevin equationsubdiffusionFox H-functionlinear response
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 2: Anomalous diffusion , 2013 , pp. 127 - 143
Copyright
© EDP Sciences, 2013

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