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Fokker-Planck equations for eignstate distributions

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Abstract

A simple model of relaxation phenomena is defined with a variable strength of interaction, where the interaction term is given by a Gaussian unitary ensemble. A set of Fokker-Planck equations are derived which describe the gradual delocalization of the eigenstates with respect to the unperturbed energy with increasing strength of interaction. The effect of localization on the time evolution in the model is a nonergodic property: the system has a memory of the initial state.

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Lindblad, G. Fokker-Planck equations for eignstate distributions. Lett Math Phys 25, 161–174 (1992). https://doi.org/10.1007/BF00398313

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  • DOI: https://doi.org/10.1007/BF00398313

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