Math. Model. Nat. Phenom.
Volume 8, Number 2, 2013Anomalous diffusion
|Page(s)||127 - 143|
|Published online||24 April 2013|
Generalized Elastic Model: Fractional Langevin Description, Fluctuation Relation and Linear Response
1 CNR-IENI, Via R. Cozzi
2 Max-Planck-Institute for Physics of Complex Systems, Noethnitzer Str. 38 D-91187 Dresden, Germany
3 Akhiezer Institute for Theoretical Physics, NSC KIPT, Kharkov 61108, Ukraine
4 School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
⋆ Corresponding author. E-mail: firstname.lastname@example.org
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.
Mathematics Subject Classification: 82C31 / 82C70 / 60G22 / 33E20
Key words: fractional Langevin equation / subdiffusion / Fox H-function / linear response
© EDP Sciences, 2013
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