Abstract
Eigenvalue problem for an effective Hamiltonian to describe the dynamics of the center coordinates of the cyclotron motion, derived by Tsukada, is explicitly solved in the case of a single Gaussian type potential. The eigen function does not depend on the range of the potential while the eigenergy does. Assuming random distributions of the strength and range of the potentials and of the positions of potential centers, the frequency dependence of the dynamical conductivity due to the tail states is expected to be given by D(E F ) 2 ω 2 ℓnω in the low frequency and low temperature limit where D(E F ) is the density of states at the Fermi energy E F .
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