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Distribution of local density of states in disordered metallic samples: logarithmically normal asymptotics

A. D. Mirlin
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Abstract

Asymptotical behavior of the distribution function of local density of states (LDOS) in disordered metallic samples is studied with making use of the supersymmetric $σ$--model approach, in combination with the saddle--point method. The LDOS distribution is found to have the logarithmically normal asymptotics for quasi--1D and 2D sample geometry. In the case of a quasi--1D sample, the result is confirmed by the exact solution. In 2D case a perfect agreement with an earlier renormalization group calculation is found. In 3D the found asymptotics is of somewhat different type: $P(ρ)\sim \exp(-\mbox{const}\,|\ln^3ρ|)$.

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A. D. Mirlin. 1995-07-20. Distribution of local density of states in disordered metallic samples: logarithmically normal asymptotics. https://doi.org/10.1103/physrevb.53.1186

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