Relaxation Mode Theory of Hopping Conduction

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Abstract
The one-body master equation is studied. The equation is reduced to the Schrödinger type equation under the detailed balance condition. The method of normal mode is applied to this reduced equation to obtain conductivity and dynamical structure factor. The relaxation modes,coined for eigenvalues of this equation, are classified into two kinds of branches: branch of “diffusion modes” and branches of “non-diffusion modes”. The characteristic roles played by these two branch modes in conductivity and structure factor are clarified by the analytical and numerical investigation of a doubly periodic lattice, which constitutes a model of some superionic conductors.

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