SPATIAL STRUCTURE OF ANOMALOUSLY LOCALIZED STATES IN DISORDERED CONDUCTORS

The spatial structure of wave functions of anomalously localized state s (ALS) in disordered conductors is studied in the framework of the a- model approach. These states are responsible for slowly decaying tails of various distribution functions. In the quasi-one-dimensional case, properties of ALS governing the asymptotic form of the distribution o f eigenfunction amplitudes are investigated with the use of the transf er matrix method, which yields an exact solution to the problem. Compa rison of the results with those obtained in the saddle-point approxima tion to the problem shows that the saddle-point configuration correctl y describes the smoothed intensity of an ALS. On this basis, the prope rties of ALS in higher spatial dimensions are considered. We also stud y the ALS responsible for the asymptotic behavior of distribution func tions of other quantities, such as relaxation time, local and global d ensity of state. It is found that the structure of an ALS may be diffe rent, depending on the specific quantity, for which it constitutes an optimal fluctuation. Relations between various procedures of selection of ALS, and between asymptotics of corresponding distribution functio ns, are discussed. (C) 1997 American Institute of Physics.