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 1D 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 connection between these properties and dimensionality and spatial correlation of the random energy landscape.