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Distribution functions of mesoscopic fluctuations and applicability of the one-parameter scaling

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  • Lerner, I.V.

Abstract

The distribution functions of mesoscopic fluctuations of conductance and current density are discussed in connection with the problem of applicability of the one-parameter scaling. On using the renormalization group analysis of the extended nonlinear σ model which includes the relevant high order gradient operators, it is shown that in a region of weak localization the conductance distribution function is close to Gaussian in its bulk but characterized with the logarithmically normal (LN) asymptotic behavior. In the shape of the distribution function of current density mesoscopic fluctuations, the crossover is shown to exist from the close-to-Gaussian distribution with the LN tails in the weak localization region to the completely LN distribution in the region where the conductance G is still large (G ⪢ e2/h) but quantum corrections to it become essential. Both LN tails and complete LN distribution are not described by the one-parameter scaling and turn out to be nonuniversal. This paper is based on the results of earlier papers.

Suggested Citation

  • Lerner, I.V., 1990. "Distribution functions of mesoscopic fluctuations and applicability of the one-parameter scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 167(1), pages 1-14.
    • Handle: RePEc:eee:phsmap:v:167:y:1990:i:1:p:1-14
    DOI: 10.1016/0378-4371(90)90040-Y
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    References listed on IDEAS

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    1. Coulehan, J.L. & Lerner, G. & Helzlsouer, K. & Welty, T.K. & McLaughlin, J., 1986. "Acute myocardial infarction among Navajo Indians, 1976-83," American Journal of Public Health, American Public Health Association, vol. 76(4), pages 412-414.
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