Abstract
A model of diffusion $\ensuremath{\psi}(\mathrm{x},t)=\ensuremath{\Delta}\ensuremath{\psi}(\mathrm{x},t)+V(\mathrm{x})\ensuremath{\psi}(\mathrm{x},t)$ is studied, where $V(\mathrm{x})$ is the Gaussian random potential. It is found that the probability distribution function is concentrated (localized) at some metastable potential attractor, while the localization center hops discontinuously in search of a better metastable attractor. The sample-averaged localization-center displacement is found as ${\ensuremath{\chi}}_{c}\ensuremath{\sim}\frac{t}{2\mathrm{ln}t}$, i.e., it is sub-ballistic.
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