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arXiv · 0802.0478

Localization Theory in Zero Dimension and the Structure of Diffusion Poles

I. M. Suslov
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Abstract

The 1/[-iω+ D(ω, q)q^2] diffusion pole in the localized phase transfers to the 1/ωBerezinskii-Gorkov singularity, which can be analyzed by the instanton method (M V. Sadovskii, 1982; J. L. Cardy, 1978). Straightforward use of this approach leads to contradictions, which do not disappear even if the problem is extremely simplied by taking zero-dimensional limit. On the contrary, they are extremely sharpened in this case and become paradoxes. The main paradox is specified by the following statements: (i) the 1/ωsingularity is determined by high orders of perturbation theory, (ii) the high-order behaviors for two quantities Φ^{RA} and U^{RA} are the same, and (iii) Φ^{RA} has the 1/ωsingularity, whereas U^{RA} does not have it. Solution to the paradox indicates that the instanton method makes it possible to obtain only the 1/(ω+ iγ) singularity, where the parameter γremains indefinite and must be determined from additional conditions. This conceptually confirms the necessity of the self-consistent treatment for the diffusion coefficient that is used in the Vollhardt-Wolfle type theories.

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I. M. Suslov. 2008-02-04. Localization Theory in Zero Dimension and the Structure of Diffusion Poles. https://arxiv.org/abs/0802.0478

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