We consider a random walk on the support of an ergodic simple point process on R-d, d >= 2, furnished with independent energy marks. The jump rates of the random walk decay exponentially in the jump length and depend on the energy marks via a Boltzmann-type factor. This is an effective model for the phonon-induced hopping of electrons in disordered solids in the regime of strong Anderson localization. Under some technical assumption on the point process we prove an upper bound for the diffusion matrix of the random walk in agreement with Mott law. A lower bound for d >= 2 in agreement with Mott law was proved in [8].
Mott law as upper bound for a random walk in a random environment / Faggionato, Alessandra; P., Mathieu. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 281:1(2008), pp. 263-286. [10.1007/s00220-008-0491-8]
Mott law as upper bound for a random walk in a random environment
FAGGIONATO, ALESSANDRA;
2008
Abstract
We consider a random walk on the support of an ergodic simple point process on R-d, d >= 2, furnished with independent energy marks. The jump rates of the random walk decay exponentially in the jump length and depend on the energy marks via a Boltzmann-type factor. This is an effective model for the phonon-induced hopping of electrons in disordered solids in the regime of strong Anderson localization. Under some technical assumption on the point process we prove an upper bound for the diffusion matrix of the random walk in agreement with Mott law. A lower bound for d >= 2 in agreement with Mott law was proved in [8].I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.