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

Asymptotical behavior of the distribution function of local density of states (LDOS) in disordered metallic samples is studied by 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-one-dimensional (1D) and 2D sample geometries. In the case of a quasi-one-dimensional sample, the result is confirmed by the exact solution. In the 2D case perfect agreement with an earlier renormalization group calculation is found. In 3D the found asymptotic behavior is of a somewhat different type: P(ρ)∼exp(-const×‖${\ln }^3$ρ‖). © 1996 The American Physical Society.