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

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

1995-07-20

arxiv.org/abs/cond-mat/9507082v1

Phys. Rev. B 53, 1186 (1996)

Physics

Condensed Matter

REVTEX, 14 pages, no figures

Scientific paper

10.1103/PhysRevB.53.1186

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

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