Mott law as lower bound for a random walk in a random environment

Faggionato A, Schulz-Baldes H, Spehner D (2006)

Publication Type: Journal article

Publication year: 2006

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 263

Pages Range: 21-64

Journal Issue: 1

URI: http://de.arxiv.org/abs/math-ph/0407058

DOI: 10.1007/s00220-005-1492-5

Abstract

We consider a random walk on the support of an ergodic stationary simple point process on ℝ d, 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.

Authors with CRIS profile

Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

Involved external institutions

Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) - Leibniz-Institut im Forschungsverbund Berlin e. V. DE Germany (DE) Universität Duisburg-Essen (UDE) DE Germany (DE)

How to cite

APA:

Faggionato, A., Schulz-Baldes, H., & Spehner, D. (2006). Mott law as lower bound for a random walk in a random environment. Communications in Mathematical Physics, 263(1), 21-64. https://doi.org/10.1007/s00220-005-1492-5

MLA:

Faggionato, Alessandra, Hermann Schulz-Baldes, and D. Spehner. "Mott law as lower bound for a random walk in a random environment." Communications in Mathematical Physics 263.1 (2006): 21-64.

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