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Title: Quantum Ohm’s law: Resistance fluctuation in disordered conductors
Authors: Kumar, N.
Issue Date: 1987
Publisher: World Scientific
Citation: Proceedings of the second Asia Pacific physics conference, Bangalore, 1987, Vol.2, p713-728
Abstract: The residual resistance of a microscopically disordered conductor is a non-additive and non-self averaging quantity. This non-classical behavior results, from- the quantum-mechanical interference of scattered wave-amplitudes that dominates resistance at low temperatures. This is a nonperturbative effect, and is pronounced in law dimensions (D). Thus, for D = 1,' this quantum ohmic resistance on the average grows exponentially (non-additively) with the sample length reflecting exponential localization of eigenstates. Moreover, the resistance fluctuates over the ensemble of macro-~ Scopically identical samples with a log-norha1 distribution that broadens with increasing sample length (nonselfaveraging). It is becoming increasingly evident that in higher dimensions these resistance fluctuations – the 'Sinai' fluctuations - dominate the physics at the mobility edge. In this work we develop an "invariant imbedding" approach to treating these fluctuations exactly far D:1. The results are then generalized to D > 1 by means of a Migdal-Kadanoff approximate procedure. For D z 3 , our analysis shows that a one-parameter 0-function depending on the mean conductance alone does not exist. Also, we have a line of fixed points in the parameter space of the first two cumulants of conductance. We also present some exact results on the influence of a finite electric field on the resistance for D=l, where the mean resistance crosses-over from the exponential-to a power-law, while the distribution tends asymptotically to a Poissonian form. Finally, we reformulate the problem of resistance fluctuation in. terms of a maximum entropy principle that seeks out the most unbiased distribution of the transfer matrix subject to certain known constraints. This is a novel method to treat the problem of the random resistance of a strictly onedimensiona1; conductor with static disorder. For the probability distribution of the transfer matrix R of the conductor,. we propose a distribution af maximum information entr'opy, constrainkd by the following physical requirements: (1) flux conservation, ( 2 ) time-reversal invariance, and (3) scaling with the length of the conductor of the two lowest cumulants of a, where A = explu . . The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.
Description: Restricted Access.
Copyright: 1987 World Scientific
Appears in Collections:Research Papers (TP)

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