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

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 $\sigma$--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: $P(ρ)\sim \exp(-\mbox{const}\,|\ln^3ρ|)$.

REVTEX, 14 pages, no figures

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• Nearly Localized States in Weakly Disordered Conductor
• Experimental studies of Chaos and Localization in Quantum Wavefunctions
• Mesoscopic Fluctuations of Eigenfunctions and "Level Velocity" Distribution in Disordered Metals

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