Kumar, N. (1986) Quantumohmic resistance fluctuation in disordered conductorsa  an invariant imbedding approach Pramana  Journal of Physics, 27 (12). pp. 3342. ISSN 03044289

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Official URL: http://www.ias.ac.in/j_archive/pramana/27/12/334...
Related URL: http://dx.doi.org/10.1007/BF02846326
Abstract
It is now well known that in the extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zerotemperature d.c. resistance of a strictly onedimensional disordered system is nonadditive and nonselfaveraging. 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 reexamined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a FokkerPlanck equation for the full probability distribution of resistance for a onedimensional continuum with a gaussian whitenoise random potential. We then employ the MigdalKadanoff type bond moving procedure and derive theddimensional generalization of the above probability distribution, or rather the associated cumulant function'the free energy'. Ford=3, our analysis shows that the dispersion dominates the mobility edge phenomena in that (i) a oneparameter βfunction depending on the mean conductance only does not exist, (ii) one has a line of fixedpoints in the space of the first two cumulants of conductance, (iii) an approximate treatment gives a diffusioncorrection involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge 'firstorder'. We also report some analytical results for the case of the onedimensional system in the presence of a finite electric field. We find a crossover from the exponential to the powerlaw 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.
Item Type:  Article 

Source:  Copyright of this article belongs to Indian Academy of Sciences. 
Keywords:  Quantumohmic Resistance; Disordered Conductors; Invariant Imbedding; Finite Electric Field; Mobility Edge 
ID Code:  85110 
Deposited On:  29 Feb 2012 13:38 
Last Modified:  19 May 2016 01:17 
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