Diffusion of a particle in the Gaussian random-energy landscape: Einstein relation and analytical properties of average velocity and diffusivity as functions of driving force
Abstract
We demonstrate that the Einstein relation for the diffusion of a particle in the random-energy landscape with the Gaussian density of states is an exclusive one-dimensional property and does not hold in higher dimensions. We also consider the analytical properties of the particle velocity and diffusivity for the limit of weak driving force and establish a connection between these properties and dimensionality and spatial correlation of the random-energy landscape.
- Publication:
-
Physical Review E
- Pub Date:
- July 2018
- DOI:
- 10.1103/PhysRevE.98.012128
- arXiv:
- arXiv:2002.08618
- Bibcode:
- 2018PhRvE..98a2128N
- Keywords:
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- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Materials Science;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 19 pages, 5 figures