Localization theory in zero dimension and the structure of the diffusion poles
- Russian Academy of Sciences, Kapitza Institute for Physical Problems (Russian Federation), E-mail: suslov@kapitza.ras.ru
The 1/[-i{omega} + D({omega}, q)q{sup 2}] diffusion pole in the localized phase transfers to the 1/{omega} Berezinskii-Gorkov singularity, which can be analyzed by the instanton method {l_brace}M. V. Sadovskii, Zh. Eksp. Teor. Fiz. 83, 1418 (1982) [Sov. Phys. JETP 56, 816 (1982)] and J. L. Cardy, J. Phys. C 11, L321 (1978){r_brace}. When this approach is used directly, contradictions arise and do not disappear even if the problem is extremely simplified by taking the 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/{omega} singularity is determined by high orders of perturbation theory, (ii) the high-order behaviors for {phi}{sup RA} and U{sup RA} are the same, and (iii) {phi}{sup RA} has the 1/{omega} singularity, whereas U{sup RA} does not have it. Solution to the paradox indicates that the instanton method makes it possible to obtain only the 1/({omega} + 2i{gamma}) singularity, where the parameter {gamma} remains indefinite and must be determined from additional conditions. This conceptually confirms the necessity of the self-consistent treatment of the diffusion coefficient used in the Vollhardt-Woelfle-type theories.
- OSTI ID:
- 21075643
- Journal Information:
- Journal of Experimental and Theoretical Physics, Vol. 105, Issue 6; Other Information: DOI: 10.1134/S1063776107120114; Copyright (c) 2007 Nauka/Interperiodica; Article Copyright (c) 2007 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7761
- Country of Publication:
- United States
- Language:
- English
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