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Title: Quantum-ohmic resistance fluctuation in disordered conductors an invariant imbedding approach
Authors: Kumar, N.
Issue Date: 1986
Publisher: Indian Academy of Sciences
Citation: Pramana, 1986, Vol.27, p33
Abstract: It is now well known that in the extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c.resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have 1% examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one dimensional continuum with a gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function-'the free energy'. For d = 3, our analysis shows that the dispersion dominate the mobility edge phenomena in that (i) a one-parameter β-function depending on the mean conductance only does not exist, (ii) one has a tine of fixed-points in the space of the first two cumulants of conductance, (iii) an approximate treatment gives a diffusion-correction involving the second cumnlant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge 'first-order'. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric field. We had a cross-over from the exponential to the power-law length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a Poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.
Description: Restricted Access.
ISSN: 0304-4289
Copyright: 1986 Indian Academy of Sciences
Appears in Collections:Research Papers (TP)

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