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Article

The method of functional integration for one-dimensional localization, higher correlators and the average current flowing in a mesoscopic ring in an arbitrary magnetic field

Journal of Experimental and Theoretical Physics. 1993. Vol. 76. No. 6. P. 1099-1109.
Starting from the Abrikosov-Ryzhkin formulation of the 1D random potential problem I find closed functional representations for various physical quantities. These functional integrals are calculated exactly without the use of any perturbative expansions. The expressions for the multipoint densities correlators are obtained. Then I evaluate the mean square dispersion of the size of localized wave functions. As a physical application of the method, I find the expectation value of the persistent current in mesoscopic ring with arbitrary magnetic flux $\Phi$. (For small $\Phi$ this problem has been solved by O.Dorokhov). The case when the random potential has finite correlation length is considered too.