The velocity of 1D MOTT variable-range hopping with external field
Faggionato, Alessandra; Gantert, Nina; Salvi, Michele (2018), The velocity of 1D MOTT variable-range hopping with external field, Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 54, 3, p. 1165-1203. 10.1214/17-AIHP836
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01523557
Journal nameAnnales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
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Abstract (EN)Mott variable-range hopping is a fundamental mechanism for low–temperature electron conduction in disordered solids in the regime of Anderson localization. In a mean field approximation, it reduces to a random walk (shortly, Mott random walk) on a random marked point process with possible long-range jumps. We consider here the one-dimensional Mott random walk and we add an external field (or a bias to the right). We show that the bias makes the walk transient, and investigate its linear speed. Our main results are conditions for ballisticity (positive linear speed) and for sub-ballisticity (zero linear speed), and the existence in the ballistic regime of an invariant distribution for the environment viewed from the walker, which is mutually absolutely continuous with respect to the original law of the environment. If the point process is a renewal process, the aforementioned conditions result in a sharp criterion for ballisticity. Interestingly, the speed is not always continuous as a function of the bias. Keywords: random walk in random environment, disordered media, ballisticity, environment viewed from the walker, electron transport in disordered solids.
Subjects / Keywordsrandom walk in random environment; disordered media; ballisticity; environ-ment viewed from the walker; electron transport in disordered solids
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