Mott Law as Lower Bound for a Random Walk in a Random Environment

被引:0
作者
A. Faggionato
H. Schulz-Baldes
D. Spehner
机构
[1] Weierstrass Institut für Angewandte Analysis und Stochastic,Institut für Mathematik
[2] Technische Universität Berlin,Fachbereich Physik
[3] Universität Duisburg-Essen,undefined
来源
Communications in Mathematical Physics | 2006年 / 263卷
关键词
Brownian Motion; Random Walk; Transition Rate; Point Process; Random Environment;
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摘要
We consider a random walk on the support of an ergodic stationary simple point process on ℝd, d≥2, which satisfies a mixing condition w.r.t. the translations or has a strictly positive density uniformly on large enough cubes. Furthermore the point process is furnished with independent random bounded energy marks. The transition rates of the random walk decay exponentially in the jump distances and depend on the energies through a factor of the Boltzmann-type. This is an effective model for the phonon-induced hopping of electrons in disordered solids within the regime of strong Anderson localization. We show that the rescaled random walk converges to a Brownian motion whose diffusion coefficient is bounded below by Mott's law for the variable range hopping conductivity at zero frequency. The proof of the lower bound involves estimates for the supercritical regime of an associated site percolation problem.
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页码:21 / 64
页数:43
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