• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

Einstein relation and linear response in one-dimensional Mott variable-range hopping

Thumbnail
Date
2017
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01646209
Dewey
Probabilités et mathématiques appliquées
Sujet
Mott variable-range hopping; random walk in random environment; randomconductance model; environment seen from the particle; steady states; linear response; Einstein relation
URI
https://basepub.dauphine.fr/handle/123456789/17526
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Faggionato, Alessandra
status unknown
Gantert, Nina
495022 Lehrstuhl fur Warscheinlichkeitstheorie
Salvi, Michele
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
35
Abstract (EN)
We consider one-dimensional Mott variable-range hopping with a bias, and prove the linear response as well as the Einstein relation, under an assumption on the exponential moments of the distances between neighboring points. In a previous paper \cite{FGS} we gave conditions on ballisticity, and proved that in the ballistic case the environment viewed from the particle approaches, for almost any initial environment, a given steady state which is absolutely continuous with respect to the original law of the environment. Here, we show that this bias--dependent steady state has a derivative at zero in terms of the bias (linear response), and use this result to get the Einstein relation. Our approach is new: instead of using e.g. perturbation theory or regeneration times, we show that the Radon-Nikodym derivative of the bias--dependent steady state with respect to the equilibrium state in the unbiased case satisfies an Lp-bound, p>2, uniformly for small bias. This Lp-bound yields, by a general argument not involving our specific model, the statement about the linear response.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.