Spatial structure of anomalously localized states in disordered conductors

Abstract

The spatial structure of wave functions of anomalously localized states (ALS) in disordered conductors is studied in the framework of the $\sigma$--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 of eigenfunction amplitudes are investigated with the use of the transfer matrix method, which yields an exact solution to the problem. Comparison of the results with those obtained in the saddle-point approximation to the problem shows that the saddle-point configuration correctly describes the smoothed intensity of an ALS. On this basis, the properties of ALS in higher spatial dimensions are considered. We study also the ALS responsible for the asymptotic behavior of distribution functions of other quantities, such as relaxation time, local and global density of state. It is found that the structure of an ALS may be different, 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 functions, are discussed.

REVTEX, 34 pages

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• Experimental studies of Chaos and Localization in Quantum Wavefunctions
• Mesoscopic Fluctuations of Eigenfunctions and "Level Velocity" Distribution in Disordered Metals
• Statistics of pre-localized states in disordered conductors
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• Signatures of Classical Diffusion in Quantum Fluctuations of 2D Chaotic Systems
• On the spatial structure of anomalously localised states in disordered conductors
• Dielectric response of Anderson and pseudogapped insulators
• Correlations of the local density of states in quasi-one-dimensional wires
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• Field Theory for the Global Density of States Distribution Function in Disordered Conductors
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