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Faggionato, Alessandra; Gantert, Nina; Salvi, Michele

The velocity of 1d Mott variable-range hopping with external field. (English. French summary) Zbl 1401.60182

Ann. Inst. Henri Poincaré, Probab. Stat. 54, No. 3, 1165-1203 (2018).
Summary: 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.

Cited in 2 Reviews
Cited in 7 Documents

MSC:

60K37 Processes in random environments
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
60G50 Sums of independent random variables; random walks
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
82C44 Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics

Keywords:

random walk in random environment; disordered media; ballisticity; environment viewed from the walker; electron transport in disordered solids
PDFBibTeX XMLCite
\textit{A. Faggionato} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 54, No. 3, 1165--1203 (2018; Zbl 1401.60182)
Full Text: DOI arXiv Euclid

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