Collective diffusion and a random energy landscape
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. Different equations result for 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 epsilon=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.
Schulz
M
Fachbereich Physik, Martin-Luther-Universitat, Halle D-06099, Germany.
Trimper
S