On Mobility and Einstein Relation for Tracers in Time-Mixing Random Environments
Komorowski, Tomasz; Olla, Stefano (2005), On Mobility and Einstein Relation for Tracers in Time-Mixing Random Environments, Journal of Statistical Physics, 118, 3-4, p. 407-435. http://dx.doi.org/10.1007/s10955-004-8815-3
TypeArticle accepté pour publication ou publié
Journal nameJournal of Statistical Physics
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Abstract (EN)In this paper we rigorously establish the existence of the mobility coefficient for a tagged particle in a simple symmetric exclusion process with adsorption/desorption of particles, in a presence of an external force field interacting with the particle. The proof is obtained using a perturbative argument. In addition, we show that, for a constant external field, the mobility of a particle equals to the self-diffusivity coefficient, the so-called Einstein relation. The method can be applied to any system where the environment has a Markovian evolution with a fast convergence to equilibrium (spectral gap property). In this context we find a necessary relation between forward and backward velocity for the validity of the Einstein relation. This relation is always satisfied by reversible systems. We provide an example of a non-reversible system, where the Einstein relation is valid.
Subjects / KeywordsDiffusion; mobility; Einstein relation
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