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Collective Diffusion and a Random Energy Landscape

Michael Schulz·Steffen Trimper
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Abstract

Starting from a master equation in a quantum Hamiltonian form and a coupling to a heat bath we derive an evolution equation for a collective hopping process under the influence of a stochastic energy landscape. There results different equations in case of an arbitrary occupation number per lattice site or in a system under exclusion. Based on scaling arguments it will be demonstrated that both systems belong below the critical dimension $d_c$ to the same universality class leading to anomalous diffusion in the long time limit. The dynamical exponent $z$ can be calculated by an $ε= d_c-d$ expansion. Above the critical dimension we discuss the differences in the diffusion constant for sufficient high temperatures. For a random potential we find a higher mobility for systems with exclusion.

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Michael Schulz, Steffen Trimper. 2000-02-24. Collective Diffusion and a Random Energy Landscape. https://doi.org/10.1103/physreve.62.221

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