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Regular version of the site

Article

New functional integration method for the 1D random potential problem. The statistics of localized wave functions

Physica D: Nonlinear Phenomena. 1995. Vol. 86. No. 1-2. P. 134-148.

 start from the derivation of the Abrikosov-Ryzhkin model for the 1D random potential problem. In its framework I find closed functional representations for various physical quantities. The representation uses number-valued fields only. These functional integrals are calculated exactly without the use of any perturbative expansions. Expressions for the multipoint densities correlators are obtained. These correlators allow to compute the distribution function of inverse sizes of localized wave functions valid both for an infinite sample and for a sample with a finite length.