Münster 1997 – scientific programme
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TT: Tiefe Temperaturen
TT 1: Mesoskopische Systeme
TT 1.7: Fachvortrag
Monday, March 17, 1997, 11:45–12:15, F1
Statistics of eigenfunctions in disordered systems. — •A. Mirlin — Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, 76128 Karlsruhe
Statistics of eigenfunction amplitudes in diffusive systems is studied. Distribution function of local amplitude can be expressed in terms of the supersymmetric σ-model (Fyodorov and Mirlin). This allows to find the exact solution in the quasi-1D case for arbitrary length of the sample, and calculate deviations from the random matrix theory for d>1.
Asymptotics of the distribution function are determined by anomalously localized states, shape of which is calculated in the quasi-1D case. It is shown that shape of such states is different depending on the quantity (local amplitude, local DOS, inverse participation ratio, …), distribution function of which is considered (Mirlin).
Correlations of the amplitude of eigenfunction in remote spatial points, and of the amplitudes of two different eigenfunctions with given energy difference are also studied. These correlations are important for the study of interacting mesoscopic systems. The correlations are week in the metallic regime (of order of 1/g for the same eigenfunction in remote points, or two different eigenfunctions in the same point, and of order of 1/g2 for different eigenfunctions in remote points, where g is dimensionless conductance) (Blanter and Mirlin). They get large, however, near the Anderson transition, explaining the existence of level repulsion in spite of multifractality of eigenfunctions (Mirlin and Fyodorov).