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We demonstrate that the Einstein relation for the diffusion of a particle inthe random energy landscape with the Gaussian density of states is an exclusive1D property and does not hold in higher dimensions. We also consider theanalytical properties of the particle velocity and diffusivity for the limit ofweak driving force and establish connection between these properties anddimensionality and spatial correlation of the random energy landscape.

physical review. e

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